author | wenzelm |
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\begin{isabellebody}% |
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\def\isabellecontext{HOL{\isaliteral{5F}{\isacharunderscore}}Specific}% |
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\isadelimtheory |
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\endisadelimtheory |
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\isatagtheory |
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\isacommand{theory}\isamarkupfalse% |
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\ HOL{\isaliteral{5F}{\isacharunderscore}}Specific\isanewline |
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\isakeyword{imports}\ Base\ Main\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}HOL{\isaliteral{2F}{\isacharslash}}Library{\isaliteral{2F}{\isacharslash}}Old{\isaliteral{5F}{\isacharunderscore}}Recdef{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\isakeyword{begin}% |
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\endisatagtheory |
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{\isafoldtheory}% |
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\isadelimtheory |
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\endisadelimtheory |
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\isamarkupchapter{Isabelle/HOL \label{ch:hol}% |
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} |
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\isamarkuptrue% |
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\isamarkupsection{Higher-Order Logic% |
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} |
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\isamarkuptrue% |
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\begin{isamarkuptext}% |
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Isabelle/HOL is based on Higher-Order Logic, a polymorphic |
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version of Church's Simple Theory of Types. HOL can be best |
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understood as a simply-typed version of classical set theory. The |
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logic was first implemented in Gordon's HOL system |
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\cite{mgordon-hol}. It extends Church's original logic |
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\cite{church40} by explicit type variables (naive polymorphism) and |
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a sound axiomatization scheme for new types based on subsets of |
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existing types. |
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Andrews's book \cite{andrews86} is a full description of the |
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original Church-style higher-order logic, with proofs of correctness |
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and completeness wrt.\ certain set-theoretic interpretations. The |
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particular extensions of Gordon-style HOL are explained semantically |
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in two chapters of the 1993 HOL book \cite{pitts93}. |
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Experience with HOL over decades has demonstrated that higher-order |
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logic is widely applicable in many areas of mathematics and computer |
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science. In a sense, Higher-Order Logic is simpler than First-Order |
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Logic, because there are fewer restrictions and special cases. Note |
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that HOL is \emph{weaker} than FOL with axioms for ZF set theory, |
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which is traditionally considered the standard foundation of regular |
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mathematics, but for most applications this does not matter. If you |
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prefer ML to Lisp, you will probably prefer HOL to ZF. |
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\medskip The syntax of HOL follows \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-calculus and |
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functional programming. Function application is curried. To apply |
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the function \isa{f} of type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}} to the |
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arguments \isa{a} and \isa{b} in HOL, you simply write \isa{{\isaliteral{22}{\isachardoublequote}}f\ a\ b{\isaliteral{22}{\isachardoublequote}}} (as in ML or Haskell). There is no ``apply'' operator; the |
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existing application of the Pure \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-calculus is re-used. |
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Note that in HOL \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} means ``\isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{22}{\isachardoublequote}}} applied to |
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the pair \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} (which is notation for \isa{{\isaliteral{22}{\isachardoublequote}}Pair\ a\ b{\isaliteral{22}{\isachardoublequote}}}). The latter typically introduces extra formal efforts that can |
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be avoided by currying functions by default. Explicit tuples are as |
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infrequent in HOL formalizations as in good ML or Haskell programs. |
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\medskip Isabelle/HOL has a distinct feel, compared to other |
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object-logics like Isabelle/ZF. It identifies object-level types |
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with meta-level types, taking advantage of the default |
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type-inference mechanism of Isabelle/Pure. HOL fully identifies |
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object-level functions with meta-level functions, with native |
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abstraction and application. |
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These identifications allow Isabelle to support HOL particularly |
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nicely, but they also mean that HOL requires some sophistication |
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from the user. In particular, an understanding of Hindley-Milner |
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type-inference with type-classes, which are both used extensively in |
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the standard libraries and applications. Beginners can set |
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\hyperlink{attribute.show-types}{\mbox{\isa{show{\isaliteral{5F}{\isacharunderscore}}types}}} or even \hyperlink{attribute.show-sorts}{\mbox{\isa{show{\isaliteral{5F}{\isacharunderscore}}sorts}}} to get more |
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explicit information about the result of type-inference.% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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\isamarkupsection{Inductive and coinductive definitions \label{sec:hol-inductive}% |
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} |
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\isamarkuptrue% |
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\begin{isamarkuptext}% |
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An \emph{inductive definition} specifies the least predicate |
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or set \isa{R} closed under given rules: applying a rule to |
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elements of \isa{R} yields a result within \isa{R}. For |
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example, a structural operational semantics is an inductive |
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definition of an evaluation relation. |
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Dually, a \emph{coinductive definition} specifies the greatest |
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predicate or set \isa{R} that is consistent with given rules: |
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every element of \isa{R} can be seen as arising by applying a rule |
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to elements of \isa{R}. An important example is using |
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bisimulation relations to formalise equivalence of processes and |
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infinite data structures. |
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Both inductive and coinductive definitions are based on the |
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Knaster-Tarski fixed-point theorem for complete lattices. The |
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collection of introduction rules given by the user determines a |
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functor on subsets of set-theoretic relations. The required |
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monotonicity of the recursion scheme is proven as a prerequisite to |
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the fixed-point definition and the resulting consequences. This |
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works by pushing inclusion through logical connectives and any other |
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operator that might be wrapped around recursive occurrences of the |
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defined relation: there must be a monotonicity theorem of the form |
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\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C4D3E}{\isasymM}}\ A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{5C3C4D3E}{\isasymM}}\ B{\isaliteral{22}{\isachardoublequote}}}, for each premise \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4D3E}{\isasymM}}\ R\ t{\isaliteral{22}{\isachardoublequote}}} in an |
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introduction rule. The default rule declarations of Isabelle/HOL |
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already take care of most common situations. |
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\begin{matharray}{rcl} |
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\indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\indexdef{HOL}{command}{inductive\_set}\hypertarget{command.HOL.inductive-set}{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\indexdef{HOL}{command}{coinductive\_set}\hypertarget{command.HOL.coinductive-set}{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isa{attribute} \\ |
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\end{matharray} |
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\begin{railoutput} |
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\rail@begin{10}{} |
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\rail@bar |
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\rail@term{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}}}[] |
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\rail@nextbar{2} |
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\rail@term{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}}[] |
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\rail@nextbar{3} |
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\rail@term{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
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\rail@endbar |
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\rail@cr{5} |
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\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
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\rail@bar |
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\rail@nextbar{6} |
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\rail@term{\isa{\isakeyword{for}}}[] |
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\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{6} |
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\rail@term{\isa{\isakeyword{where}}}[] |
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\rail@nont{\isa{clauses}}[] |
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\rail@endbar |
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\rail@cr{8} |
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\rail@bar |
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\rail@nextbar{9} |
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\rail@term{\isa{\isakeyword{monos}}}[] |
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\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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\rail@endbar |
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\rail@end |
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\rail@begin{3}{\isa{clauses}} |
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\rail@plus |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
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\rail@nextplus{2} |
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\rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[] |
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\rail@endplus |
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\rail@end |
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\rail@begin{3}{} |
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\rail@term{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{add}}[] |
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\rail@nextbar{2} |
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\rail@term{\isa{del}}[] |
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\rail@endbar |
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\rail@end |
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\end{railoutput} |
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\begin{description} |
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\item \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}} and \hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}} define (co)inductive predicates from the introduction |
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rules. |
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The propositions given as \isa{{\isaliteral{22}{\isachardoublequote}}clauses{\isaliteral{22}{\isachardoublequote}}} in the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} part are either rules of the usual \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} format |
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(with arbitrary nesting), or equalities using \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}}. The |
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latter specifies extra-logical abbreviations in the sense of |
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\indexref{}{command}{abbreviation}\hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}. Introducing abstract syntax |
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simultaneously with the actual introduction rules is occasionally |
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useful for complex specifications. |
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The optional \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} part contains a list of parameters of |
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the (co)inductive predicates that remain fixed throughout the |
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definition, in contrast to arguments of the relation that may vary |
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in each occurrence within the given \isa{{\isaliteral{22}{\isachardoublequote}}clauses{\isaliteral{22}{\isachardoublequote}}}. |
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The optional \hyperlink{keyword.monos}{\mbox{\isa{\isakeyword{monos}}}} declaration contains additional |
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\emph{monotonicity theorems}, which are required for each operator |
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applied to a recursive set in the introduction rules. |
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\item \hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}} and \hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}} are wrappers for to the previous commands for |
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native HOL predicates. This allows to define (co)inductive sets, |
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where multiple arguments are simulated via tuples. |
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\item \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} declares monotonicity rules in the |
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context. These rule are involved in the automated monotonicity |
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proof of the above inductive and coinductive definitions. |
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\end{description}% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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% |
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\isamarkupsubsection{Derived rules% |
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} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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A (co)inductive definition of \isa{R} provides the following |
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main theorems: |
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\begin{description} |
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\item \isa{R{\isaliteral{2E}{\isachardot}}intros} is the list of introduction rules as proven |
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theorems, for the recursive predicates (or sets). The rules are |
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also available individually, using the names given them in the |
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theory file; |
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\item \isa{R{\isaliteral{2E}{\isachardot}}cases} is the case analysis (or elimination) rule; |
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\item \isa{R{\isaliteral{2E}{\isachardot}}induct} or \isa{R{\isaliteral{2E}{\isachardot}}coinduct} is the (co)induction |
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rule. |
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\end{description} |
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When several predicates \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are |
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defined simultaneously, the list of introduction rules is called |
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\isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5F}{\isacharunderscore}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}intros{\isaliteral{22}{\isachardoublequote}}}, the case analysis rules are |
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called \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2E}{\isachardot}}cases{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}cases{\isaliteral{22}{\isachardoublequote}}}, and the list |
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of mutual induction rules is called \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5F}{\isacharunderscore}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}inducts{\isaliteral{22}{\isachardoublequote}}}.% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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% |
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\isamarkupsubsection{Monotonicity theorems% |
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} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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The context maintains a default set of theorems that are used |
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in monotonicity proofs. New rules can be declared via the |
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\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} attribute. See the main Isabelle/HOL |
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sources for some examples. The general format of such monotonicity |
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theorems is as follows: |
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\begin{itemize} |
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\item Theorems of the form \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C4D3E}{\isasymM}}\ A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{5C3C4D3E}{\isasymM}}\ B{\isaliteral{22}{\isachardoublequote}}}, for proving |
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monotonicity of inductive definitions whose introduction rules have |
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premises involving terms such as \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4D3E}{\isasymM}}\ R\ t{\isaliteral{22}{\isachardoublequote}}}. |
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\item Monotonicity theorems for logical operators, which are of the |
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general form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}. For example, in |
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the case of the operator \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequote}}}, the corresponding theorem is |
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\[ |
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\infer{\isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}} |
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\] |
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\item De Morgan style equations for reasoning about the ``polarity'' |
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of expressions, e.g. |
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\[ |
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\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ P{\isaliteral{22}{\isachardoublequote}}} \qquad\qquad |
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\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ Q{\isaliteral{22}{\isachardoublequote}}} |
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\] |
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\item Equations for reducing complex operators to more primitive |
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ones whose monotonicity can easily be proved, e.g. |
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\[ |
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\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q{\isaliteral{22}{\isachardoublequote}}} \qquad\qquad |
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\isa{{\isaliteral{22}{\isachardoublequote}}Ball\ A\ P\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ x{\isaliteral{22}{\isachardoublequote}}} |
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\] |
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\end{itemize}% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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% |
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\isamarkupsubsubsection{Examples% |
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} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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The finite powerset operator can be defined inductively like this:% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse% |
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\ Fin\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{for}\ A\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\isakeyword{where}\isanewline |
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\ \ empty{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Fin\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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{\isaliteral{7C}{\isacharbar}}\ insert{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Fin\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ insert\ a\ B\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Fin\ A{\isaliteral{22}{\isachardoublequoteclose}}% |
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\begin{isamarkuptext}% |
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The accessible part of a relation is defined as follows:% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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\isacommand{inductive}\isamarkupfalse% |
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\ acc\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\ \ \isakeyword{for}\ r\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infix}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C707265633E}{\isasymprec}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline |
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\isakeyword{where}\ acc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}y{\isaliteral{2E}{\isachardot}}\ y\ {\isaliteral{5C3C707265633E}{\isasymprec}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ acc\ r\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ acc\ r\ x{\isaliteral{22}{\isachardoublequoteclose}}% |
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\begin{isamarkuptext}% |
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Common logical connectives can be easily characterized as |
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non-recursive inductive definitions with parameters, but without |
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arguments.% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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\isacommand{inductive}\isamarkupfalse% |
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\ AND\ \isakeyword{for}\ A\ B\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ bool\isanewline |
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\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ AND\ A\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\isanewline |
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\isacommand{inductive}\isamarkupfalse% |
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\ OR\ \isakeyword{for}\ A\ B\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ bool\isanewline |
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\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ OR\ A\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ OR\ A\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\isanewline |
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\isacommand{inductive}\isamarkupfalse% |
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\ EXISTS\ \isakeyword{for}\ B\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ a\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ EXISTS\ B{\isaliteral{22}{\isachardoublequoteclose}}% |
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\begin{isamarkuptext}% |
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Here the \isa{{\isaliteral{22}{\isachardoublequote}}cases{\isaliteral{22}{\isachardoublequote}}} or \isa{{\isaliteral{22}{\isachardoublequote}}induct{\isaliteral{22}{\isachardoublequote}}} rules produced by |
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the \hyperlink{command.inductive}{\mbox{\isa{\isacommand{inductive}}}} package coincide with the expected |
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elimination rules for Natural Deduction. Already in the original |
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article by Gerhard Gentzen \cite{Gentzen:1935} there is a hint that |
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each connective can be characterized by its introductions, and the |
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elimination can be constructed systematically.% |
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\end{isamarkuptext}% |
329 |
\isamarkuptrue% |
|
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% |
|
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\isamarkupsection{Recursive functions \label{sec:recursion}% |
332 |
} |
|
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\isamarkuptrue% |
|
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% |
|
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\begin{isamarkuptext}% |
|
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\begin{matharray}{rcl} |
|
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\indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
338 |
\indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
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\indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
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\indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
26849 | 341 |
\end{matharray} |
342 |
||
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\begin{railoutput} |
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\rail@begin{2}{} |
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\rail@term{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
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\rail@term{\isa{\isakeyword{where}}}[] |
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\rail@nont{\isa{equations}}[] |
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\rail@end |
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\rail@begin{4}{} |
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\rail@bar |
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\rail@term{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\isa{functionopts}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
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\rail@cr{3} |
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\rail@term{\isa{\isakeyword{where}}}[] |
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\rail@nont{\isa{equations}}[] |
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\rail@end |
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\rail@begin{3}{\isa{equations}} |
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\rail@plus |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
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\rail@nextplus{2} |
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\rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[] |
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\rail@endplus |
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\rail@end |
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\rail@begin{3}{\isa{functionopts}} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@plus |
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\rail@bar |
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\rail@term{\isa{sequential}}[] |
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\rail@nextbar{1} |
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\rail@term{\isa{domintros}}[] |
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\rail@endbar |
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\rail@nextplus{2} |
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\rail@cterm{\isa{{\isaliteral{2C}{\isacharcomma}}}}[] |
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\rail@endplus |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@end |
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\rail@begin{2}{} |
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\rail@term{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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\rail@endbar |
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\rail@end |
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\end{railoutput} |
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|
26849 | 406 |
|
28788 | 407 |
\begin{description} |
26849 | 408 |
|
28788 | 409 |
\item \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} defines primitive recursive |
42912 | 410 |
functions over datatypes (see also \indexref{HOL}{command}{datatype}\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} and |
411 |
\indexref{HOL}{command}{rep\_datatype}\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}}). The given \isa{equations} |
|
412 |
specify reduction rules that are produced by instantiating the |
|
413 |
generic combinator for primitive recursion that is available for |
|
414 |
each datatype. |
|
415 |
||
416 |
Each equation needs to be of the form: |
|
417 |
||
418 |
\begin{isabelle}% |
|
419 |
{\isaliteral{22}{\isachardoublequote}}f\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{28}{\isacharparenleft}}C\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{29}{\isacharparenright}}\ z\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ z\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3D}{\isacharequal}}\ rhs{\isaliteral{22}{\isachardoublequote}}% |
|
420 |
\end{isabelle} |
|
421 |
||
422 |
such that \isa{C} is a datatype constructor, \isa{rhs} contains |
|
423 |
only the free variables on the left-hand side (or from the context), |
|
424 |
and all recursive occurrences of \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{22}{\isachardoublequote}}} in \isa{{\isaliteral{22}{\isachardoublequote}}rhs{\isaliteral{22}{\isachardoublequote}}} are of |
|
425 |
the form \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} for some \isa{i}. At most one |
|
426 |
reduction rule for each constructor can be given. The order does |
|
427 |
not matter. For missing constructors, the function is defined to |
|
428 |
return a default value, but this equation is made difficult to |
|
429 |
access for users. |
|
430 |
||
431 |
The reduction rules are declared as \hyperlink{attribute.simp}{\mbox{\isa{simp}}} by default, |
|
432 |
which enables standard proof methods like \hyperlink{method.simp}{\mbox{\isa{simp}}} and |
|
433 |
\hyperlink{method.auto}{\mbox{\isa{auto}}} to normalize expressions of \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{22}{\isachardoublequote}}} applied to |
|
434 |
datatype constructions, by simulating symbolic computation via |
|
435 |
rewriting. |
|
26849 | 436 |
|
28788 | 437 |
\item \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} defines functions by general |
26849 | 438 |
wellfounded recursion. A detailed description with examples can be |
439 |
found in \cite{isabelle-function}. The function is specified by a |
|
440 |
set of (possibly conditional) recursive equations with arbitrary |
|
441 |
pattern matching. The command generates proof obligations for the |
|
442 |
completeness and the compatibility of patterns. |
|
443 |
||
444 |
The defined function is considered partial, and the resulting |
|
40406 | 445 |
simplification rules (named \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{22}{\isachardoublequote}}}) and induction rule |
446 |
(named \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}pinduct{\isaliteral{22}{\isachardoublequote}}}) are guarded by a generated domain |
|
447 |
predicate \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5F}{\isacharunderscore}}dom{\isaliteral{22}{\isachardoublequote}}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}} |
|
26849 | 448 |
command can then be used to establish that the function is total. |
449 |
||
40406 | 450 |
\item \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} is a shorthand notation for ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}sequential{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, followed by automated |
28788 | 451 |
proof attempts regarding pattern matching and termination. See |
452 |
\cite{isabelle-function} for further details. |
|
26849 | 453 |
|
28788 | 454 |
\item \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}~\isa{f} commences a |
26849 | 455 |
termination proof for the previously defined function \isa{f}. If |
456 |
this is omitted, the command refers to the most recent function |
|
457 |
definition. After the proof is closed, the recursive equations and |
|
458 |
the induction principle is established. |
|
459 |
||
28788 | 460 |
\end{description} |
26849 | 461 |
|
27452 | 462 |
Recursive definitions introduced by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} |
42912 | 463 |
command accommodate reasoning by induction (cf.\ \hyperlink{method.induct}{\mbox{\isa{induct}}}): |
464 |
rule \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}induct{\isaliteral{22}{\isachardoublequote}}} refers to a specific induction rule, with |
|
465 |
parameters named according to the user-specified equations. Cases |
|
466 |
are numbered starting from 1. For \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}, the |
|
467 |
induction principle coincides with structural recursion on the |
|
468 |
datatype where the recursion is carried out. |
|
26849 | 469 |
|
470 |
The equations provided by these packages may be referred later as |
|
40406 | 471 |
theorem list \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}simps{\isaliteral{22}{\isachardoublequote}}}, where \isa{f} is the (collective) |
26849 | 472 |
name of the functions defined. Individual equations may be named |
473 |
explicitly as well. |
|
474 |
||
26902 | 475 |
The \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accepts the following |
26849 | 476 |
options. |
477 |
||
28788 | 478 |
\begin{description} |
26849 | 479 |
|
28788 | 480 |
\item \isa{sequential} enables a preprocessor which disambiguates |
481 |
overlapping patterns by making them mutually disjoint. Earlier |
|
482 |
equations take precedence over later ones. This allows to give the |
|
483 |
specification in a format very similar to functional programming. |
|
484 |
Note that the resulting simplification and induction rules |
|
485 |
correspond to the transformed specification, not the one given |
|
26849 | 486 |
originally. This usually means that each equation given by the user |
36139 | 487 |
may result in several theorems. Also note that this automatic |
26849 | 488 |
transformation only works for ML-style datatype patterns. |
489 |
||
28788 | 490 |
\item \isa{domintros} enables the automated generation of |
26849 | 491 |
introduction rules for the domain predicate. While mostly not |
492 |
needed, they can be helpful in some proofs about partial functions. |
|
493 |
||
28788 | 494 |
\end{description}% |
26849 | 495 |
\end{isamarkuptext}% |
496 |
\isamarkuptrue% |
|
497 |
% |
|
42912 | 498 |
\isamarkupsubsubsection{Example: evaluation of expressions% |
499 |
} |
|
500 |
\isamarkuptrue% |
|
501 |
% |
|
502 |
\begin{isamarkuptext}% |
|
503 |
Subsequently, we define mutual datatypes for arithmetic and |
|
504 |
boolean expressions, and use \hyperlink{command.primrec}{\mbox{\isa{\isacommand{primrec}}}} for evaluation |
|
505 |
functions that follow the same recursive structure.% |
|
506 |
\end{isamarkuptext}% |
|
507 |
\isamarkuptrue% |
|
508 |
\isacommand{datatype}\isamarkupfalse% |
|
509 |
\ {\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{3D}{\isacharequal}}\isanewline |
|
510 |
\ \ \ \ IF\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
511 |
\ \ {\isaliteral{7C}{\isacharbar}}\ Sum\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
512 |
\ \ {\isaliteral{7C}{\isacharbar}}\ Diff\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
513 |
\ \ {\isaliteral{7C}{\isacharbar}}\ Var\ {\isaliteral{27}{\isacharprime}}a\isanewline |
|
514 |
\ \ {\isaliteral{7C}{\isacharbar}}\ Num\ nat\isanewline |
|
515 |
\isakeyword{and}\ {\isaliteral{27}{\isacharprime}}a\ bexp\ {\isaliteral{3D}{\isacharequal}}\isanewline |
|
516 |
\ \ \ \ Less\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
517 |
\ \ {\isaliteral{7C}{\isacharbar}}\ And\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
518 |
\ \ {\isaliteral{7C}{\isacharbar}}\ Neg\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}% |
|
519 |
\begin{isamarkuptext}% |
|
520 |
\medskip Evaluation of arithmetic and boolean expressions% |
|
521 |
\end{isamarkuptext}% |
|
522 |
\isamarkuptrue% |
|
523 |
\isacommand{primrec}\isamarkupfalse% |
|
524 |
\ evala\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
525 |
\ \ \isakeyword{and}\ evalb\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ bexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
526 |
\isakeyword{where}\isanewline |
|
527 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ evalb\ env\ b\ then\ evala\ env\ a{\isadigit{1}}\ else\ evala\ env\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
528 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}Sum\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ evala\ env\ a{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ evala\ env\ a{\isadigit{2}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
529 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}Diff\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ evala\ env\ a{\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ evala\ env\ a{\isadigit{2}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
530 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}Var\ v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ env\ v{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
531 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}Num\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
532 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evalb\ env\ {\isaliteral{28}{\isacharparenleft}}Less\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}evala\ env\ a{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ evala\ env\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
533 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evalb\ env\ {\isaliteral{28}{\isacharparenleft}}And\ b{\isadigit{1}}\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}evalb\ env\ b{\isadigit{1}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ evalb\ env\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
534 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}evalb\ env\ {\isaliteral{28}{\isacharparenleft}}Neg\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ evalb\ env\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}% |
|
535 |
\begin{isamarkuptext}% |
|
536 |
Since the value of an expression depends on the value of its |
|
537 |
variables, the functions \isa{evala} and \isa{evalb} take an |
|
538 |
additional parameter, an \emph{environment} that maps variables to |
|
539 |
their values. |
|
540 |
||
541 |
\medskip Substitution on expressions can be defined similarly. The |
|
542 |
mapping \isa{f} of type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequote}}} given as a |
|
543 |
parameter is lifted canonically on the types \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequote}}} and |
|
544 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequote}}}, respectively.% |
|
545 |
\end{isamarkuptext}% |
|
546 |
\isamarkuptrue% |
|
547 |
\isacommand{primrec}\isamarkupfalse% |
|
548 |
\ substa\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ aexp{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
549 |
\ \ \isakeyword{and}\ substb\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ aexp{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ bexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
550 |
\isakeyword{where}\isanewline |
|
551 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}substa\ f\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ IF\ {\isaliteral{28}{\isacharparenleft}}substb\ f\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
552 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substa\ f\ {\isaliteral{28}{\isacharparenleft}}Sum\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Sum\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
553 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substa\ f\ {\isaliteral{28}{\isacharparenleft}}Diff\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Diff\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
554 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substa\ f\ {\isaliteral{28}{\isacharparenleft}}Var\ v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ v{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
555 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substa\ f\ {\isaliteral{28}{\isacharparenleft}}Num\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Num\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
556 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substb\ f\ {\isaliteral{28}{\isacharparenleft}}Less\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Less\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ f\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
557 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substb\ f\ {\isaliteral{28}{\isacharparenleft}}And\ b{\isadigit{1}}\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ And\ {\isaliteral{28}{\isacharparenleft}}substb\ f\ b{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substb\ f\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
558 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}substb\ f\ {\isaliteral{28}{\isacharparenleft}}Neg\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Neg\ {\isaliteral{28}{\isacharparenleft}}substb\ f\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}% |
|
559 |
\begin{isamarkuptext}% |
|
560 |
In textbooks about semantics one often finds substitution |
|
561 |
theorems, which express the relationship between substitution and |
|
562 |
evaluation. For \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequote}}}, we can prove |
|
563 |
such a theorem by mutual induction, followed by simplification.% |
|
564 |
\end{isamarkuptext}% |
|
565 |
\isamarkuptrue% |
|
566 |
\isacommand{lemma}\isamarkupfalse% |
|
567 |
\ subst{\isaliteral{5F}{\isacharunderscore}}one{\isaliteral{3A}{\isacharcolon}}\isanewline |
|
568 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}substa\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ evala\ {\isaliteral{28}{\isacharparenleft}}env\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ evala\ env\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
569 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}evalb\ env\ {\isaliteral{28}{\isacharparenleft}}substb\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ evalb\ {\isaliteral{28}{\isacharparenleft}}env\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ evala\ env\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
570 |
% |
|
571 |
\isadelimproof |
|
572 |
\ \ % |
|
573 |
\endisadelimproof |
|
574 |
% |
|
575 |
\isatagproof |
|
576 |
\isacommand{by}\isamarkupfalse% |
|
577 |
\ {\isaliteral{28}{\isacharparenleft}}induct\ a\ \isakeyword{and}\ b{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all% |
|
578 |
\endisatagproof |
|
579 |
{\isafoldproof}% |
|
580 |
% |
|
581 |
\isadelimproof |
|
582 |
\isanewline |
|
583 |
% |
|
584 |
\endisadelimproof |
|
585 |
\isanewline |
|
586 |
\isacommand{lemma}\isamarkupfalse% |
|
587 |
\ subst{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{3A}{\isacharcolon}}\isanewline |
|
588 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}evala\ env\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ evala\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ evala\ env\ {\isaliteral{28}{\isacharparenleft}}s\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
589 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}evalb\ env\ {\isaliteral{28}{\isacharparenleft}}substb\ s\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ evalb\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ evala\ env\ {\isaliteral{28}{\isacharparenleft}}s\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
590 |
% |
|
591 |
\isadelimproof |
|
592 |
\ \ % |
|
593 |
\endisadelimproof |
|
594 |
% |
|
595 |
\isatagproof |
|
596 |
\isacommand{by}\isamarkupfalse% |
|
597 |
\ {\isaliteral{28}{\isacharparenleft}}induct\ a\ \isakeyword{and}\ b{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all% |
|
598 |
\endisatagproof |
|
599 |
{\isafoldproof}% |
|
600 |
% |
|
601 |
\isadelimproof |
|
602 |
% |
|
603 |
\endisadelimproof |
|
604 |
% |
|
605 |
\isamarkupsubsubsection{Example: a substitution function for terms% |
|
606 |
} |
|
607 |
\isamarkuptrue% |
|
608 |
% |
|
609 |
\begin{isamarkuptext}% |
|
610 |
Functions on datatypes with nested recursion are also defined |
|
611 |
by mutual primitive recursion.% |
|
612 |
\end{isamarkuptext}% |
|
613 |
\isamarkuptrue% |
|
614 |
\isacommand{datatype}\isamarkupfalse% |
|
615 |
\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{22}{\isachardoublequoteopen}}term{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{3D}{\isacharequal}}\ Var\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{7C}{\isacharbar}}\ App\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term\ list{\isaliteral{22}{\isachardoublequoteclose}}% |
|
616 |
\begin{isamarkuptext}% |
|
617 |
A substitution function on type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term{\isaliteral{22}{\isachardoublequote}}} can be |
|
618 |
defined as follows, by working simultaneously on \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term\ list{\isaliteral{22}{\isachardoublequote}}}:% |
|
619 |
\end{isamarkuptext}% |
|
620 |
\isamarkuptrue% |
|
621 |
\isacommand{primrec}\isamarkupfalse% |
|
622 |
\ subst{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline |
|
623 |
\ \ subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term\ list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
624 |
\isakeyword{where}\isanewline |
|
625 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}subst{\isaliteral{5F}{\isacharunderscore}}term\ f\ {\isaliteral{28}{\isacharparenleft}}Var\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
626 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}subst{\isaliteral{5F}{\isacharunderscore}}term\ f\ {\isaliteral{28}{\isacharparenleft}}App\ b\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ App\ b\ {\isaliteral{28}{\isacharparenleft}}subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ f\ ts{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
627 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
628 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ f\ {\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{23}{\isacharhash}}\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ subst{\isaliteral{5F}{\isacharunderscore}}term\ f\ t\ {\isaliteral{23}{\isacharhash}}\ subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ f\ ts{\isaliteral{22}{\isachardoublequoteclose}}% |
|
629 |
\begin{isamarkuptext}% |
|
630 |
The recursion scheme follows the structure of the unfolded |
|
631 |
definition of type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ term{\isaliteral{22}{\isachardoublequote}}}. To prove properties of this |
|
632 |
substitution function, mutual induction is needed:% |
|
633 |
\end{isamarkuptext}% |
|
634 |
\isamarkuptrue% |
|
635 |
\isacommand{lemma}\isamarkupfalse% |
|
636 |
\ {\isaliteral{22}{\isachardoublequoteopen}}subst{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{28}{\isacharparenleft}}subst{\isaliteral{5F}{\isacharunderscore}}term\ f{\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ f{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ subst{\isaliteral{5F}{\isacharunderscore}}term\ f{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}subst{\isaliteral{5F}{\isacharunderscore}}term\ f{\isadigit{2}}\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline |
|
637 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ {\isaliteral{28}{\isacharparenleft}}subst{\isaliteral{5F}{\isacharunderscore}}term\ f{\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ f{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ ts\ {\isaliteral{3D}{\isacharequal}}\ subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ f{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}subst{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}list\ f{\isadigit{2}}\ ts{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
638 |
% |
|
639 |
\isadelimproof |
|
640 |
\ \ % |
|
641 |
\endisadelimproof |
|
642 |
% |
|
643 |
\isatagproof |
|
644 |
\isacommand{by}\isamarkupfalse% |
|
645 |
\ {\isaliteral{28}{\isacharparenleft}}induct\ t\ \isakeyword{and}\ ts{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all% |
|
646 |
\endisatagproof |
|
647 |
{\isafoldproof}% |
|
648 |
% |
|
649 |
\isadelimproof |
|
650 |
% |
|
651 |
\endisadelimproof |
|
652 |
% |
|
653 |
\isamarkupsubsubsection{Example: a map function for infinitely branching trees% |
|
654 |
} |
|
655 |
\isamarkuptrue% |
|
656 |
% |
|
657 |
\begin{isamarkuptext}% |
|
658 |
Defining functions on infinitely branching datatypes by |
|
659 |
primitive recursion is just as easy.% |
|
660 |
\end{isamarkuptext}% |
|
661 |
\isamarkuptrue% |
|
662 |
\isacommand{datatype}\isamarkupfalse% |
|
663 |
\ {\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{3D}{\isacharequal}}\ Atom\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{7C}{\isacharbar}}\ Branch\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ tree{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
664 |
\isanewline |
|
665 |
\isacommand{primrec}\isamarkupfalse% |
|
666 |
\ map{\isaliteral{5F}{\isacharunderscore}}tree\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ tree{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
667 |
\isakeyword{where}\isanewline |
|
668 |
\ \ {\isaliteral{22}{\isachardoublequoteopen}}map{\isaliteral{5F}{\isacharunderscore}}tree\ f\ {\isaliteral{28}{\isacharparenleft}}Atom\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Atom\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
669 |
{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}map{\isaliteral{5F}{\isacharunderscore}}tree\ f\ {\isaliteral{28}{\isacharparenleft}}Branch\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Branch\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ map{\isaliteral{5F}{\isacharunderscore}}tree\ f\ {\isaliteral{28}{\isacharparenleft}}ts\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}% |
|
670 |
\begin{isamarkuptext}% |
|
671 |
Note that all occurrences of functions such as \isa{ts} |
|
672 |
above must be applied to an argument. In particular, \isa{{\isaliteral{22}{\isachardoublequote}}map{\isaliteral{5F}{\isacharunderscore}}tree\ f\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ ts{\isaliteral{22}{\isachardoublequote}}} is not allowed here.% |
|
673 |
\end{isamarkuptext}% |
|
674 |
\isamarkuptrue% |
|
675 |
% |
|
676 |
\begin{isamarkuptext}% |
|
677 |
Here is a simple composition lemma for \isa{map{\isaliteral{5F}{\isacharunderscore}}tree}:% |
|
678 |
\end{isamarkuptext}% |
|
679 |
\isamarkuptrue% |
|
680 |
\isacommand{lemma}\isamarkupfalse% |
|
681 |
\ {\isaliteral{22}{\isachardoublequoteopen}}map{\isaliteral{5F}{\isacharunderscore}}tree\ g\ {\isaliteral{28}{\isacharparenleft}}map{\isaliteral{5F}{\isacharunderscore}}tree\ f\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ map{\isaliteral{5F}{\isacharunderscore}}tree\ {\isaliteral{28}{\isacharparenleft}}g\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ f{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
682 |
% |
|
683 |
\isadelimproof |
|
684 |
\ \ % |
|
685 |
\endisadelimproof |
|
686 |
% |
|
687 |
\isatagproof |
|
688 |
\isacommand{by}\isamarkupfalse% |
|
689 |
\ {\isaliteral{28}{\isacharparenleft}}induct\ t{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all% |
|
690 |
\endisatagproof |
|
691 |
{\isafoldproof}% |
|
692 |
% |
|
693 |
\isadelimproof |
|
694 |
% |
|
695 |
\endisadelimproof |
|
696 |
% |
|
26849 | 697 |
\isamarkupsubsection{Proof methods related to recursive definitions% |
698 |
} |
|
699 |
\isamarkuptrue% |
|
700 |
% |
|
701 |
\begin{isamarkuptext}% |
|
702 |
\begin{matharray}{rcl} |
|
40406 | 703 |
\indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat-completeness}{\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}}}} & : & \isa{method} \\ |
28788 | 704 |
\indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isa{method} \\ |
40406 | 705 |
\indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}}} & : & \isa{method} \\ |
706 |
\indexdef{HOL}{method}{size\_change}\hypertarget{method.HOL.size-change}{\hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}}} & : & \isa{method} \\ |
|
26849 | 707 |
\end{matharray} |
708 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
709 |
\begin{railoutput} |
42662 | 710 |
\rail@begin{1}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
711 |
\rail@term{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
712 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
713 |
\rail@end |
42662 | 714 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
715 |
\rail@term{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
716 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
717 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
718 |
\rail@cnont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
719 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
720 |
\rail@end |
42662 | 721 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
722 |
\rail@term{\hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
723 |
\rail@nont{\isa{orders}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
724 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
725 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
726 |
\rail@cnont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
727 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
728 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
729 |
\rail@begin{4}{\isa{orders}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
730 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
731 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
732 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
733 |
\rail@term{\isa{max}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
734 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
735 |
\rail@term{\isa{min}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
736 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
737 |
\rail@term{\isa{ms}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
738 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
739 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
740 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
741 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
742 |
|
26849 | 743 |
|
28788 | 744 |
\begin{description} |
26849 | 745 |
|
40406 | 746 |
\item \hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}}} is a specialized method to |
26849 | 747 |
solve goals regarding the completeness of pattern matching, as |
26902 | 748 |
required by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} package (cf.\ |
26849 | 749 |
\cite{isabelle-function}). |
750 |
||
28788 | 751 |
\item \hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}~\isa{R} introduces a termination |
26849 | 752 |
proof using the relation \isa{R}. The resulting proof state will |
753 |
contain goals expressing that \isa{R} is wellfounded, and that the |
|
754 |
arguments of recursive calls decrease with respect to \isa{R}. |
|
755 |
Usually, this method is used as the initial proof step of manual |
|
756 |
termination proofs. |
|
757 |
||
40406 | 758 |
\item \hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}} attempts a fully |
26849 | 759 |
automated termination proof by searching for a lexicographic |
760 |
combination of size measures on the arguments of the function. The |
|
26902 | 761 |
method accepts the same arguments as the \hyperlink{method.auto}{\mbox{\isa{auto}}} method, |
42930 | 762 |
which it uses internally to prove local descents. The \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}} modifiers are accepted (as for \hyperlink{method.auto}{\mbox{\isa{auto}}}). |
26849 | 763 |
|
764 |
In case of failure, extensive information is printed, which can help |
|
765 |
to analyse the situation (cf.\ \cite{isabelle-function}). |
|
766 |
||
40406 | 767 |
\item \hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}} also works on termination goals, |
33858 | 768 |
using a variation of the size-change principle, together with a |
769 |
graph decomposition technique (see \cite{krauss_phd} for details). |
|
770 |
Three kinds of orders are used internally: \isa{max}, \isa{min}, |
|
771 |
and \isa{ms} (multiset), which is only available when the theory |
|
772 |
\isa{Multiset} is loaded. When no order kinds are given, they are |
|
773 |
tried in order. The search for a termination proof uses SAT solving |
|
774 |
internally. |
|
775 |
||
42930 | 776 |
For local descent proofs, the \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}} modifiers are |
777 |
accepted (as for \hyperlink{method.auto}{\mbox{\isa{auto}}}). |
|
33858 | 778 |
|
28788 | 779 |
\end{description}% |
26849 | 780 |
\end{isamarkuptext}% |
781 |
\isamarkuptrue% |
|
782 |
% |
|
40171 | 783 |
\isamarkupsubsection{Functions with explicit partiality% |
784 |
} |
|
785 |
\isamarkuptrue% |
|
786 |
% |
|
787 |
\begin{isamarkuptext}% |
|
788 |
\begin{matharray}{rcl} |
|
40406 | 789 |
\indexdef{HOL}{command}{partial\_function}\hypertarget{command.HOL.partial-function}{\hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
790 |
\indexdef{HOL}{attribute}{partial\_function\_mono}\hypertarget{attribute.HOL.partial-function-mono}{\hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}}} & : & \isa{attribute} \\ |
|
40171 | 791 |
\end{matharray} |
792 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
793 |
\begin{railoutput} |
42662 | 794 |
\rail@begin{5}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
795 |
\rail@term{\hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
796 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
797 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
798 |
\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
799 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
800 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
42617 | 801 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
802 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
803 |
\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
804 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
805 |
\rail@term{\isa{\isakeyword{where}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
806 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
807 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
808 |
\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
809 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
810 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
811 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
812 |
\end{railoutput} |
42617 | 813 |
|
40171 | 814 |
|
815 |
\begin{description} |
|
816 |
||
42617 | 817 |
\item \hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mode{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} defines |
818 |
recursive functions based on fixpoints in complete partial |
|
819 |
orders. No termination proof is required from the user or |
|
820 |
constructed internally. Instead, the possibility of non-termination |
|
821 |
is modelled explicitly in the result type, which contains an |
|
822 |
explicit bottom element. |
|
40171 | 823 |
|
824 |
Pattern matching and mutual recursion are currently not supported. |
|
825 |
Thus, the specification consists of a single function described by a |
|
826 |
single recursive equation. |
|
827 |
||
828 |
There are no fixed syntactic restrictions on the body of the |
|
829 |
function, but the induced functional must be provably monotonic |
|
830 |
wrt.\ the underlying order. The monotonicitity proof is performed |
|
831 |
internally, and the definition is rejected when it fails. The proof |
|
832 |
can be influenced by declaring hints using the |
|
40406 | 833 |
\hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}} attribute. |
40171 | 834 |
|
835 |
The mandatory \isa{mode} argument specifies the mode of operation |
|
836 |
of the command, which directly corresponds to a complete partial |
|
837 |
order on the result type. By default, the following modes are |
|
42123 | 838 |
defined: |
40171 | 839 |
|
840 |
\begin{description} |
|
841 |
\item \isa{option} defines functions that map into the \isa{option} type. Here, the value \isa{None} is used to model a |
|
842 |
non-terminating computation. Monotonicity requires that if \isa{None} is returned by a recursive call, then the overall result |
|
843 |
must also be \isa{None}. This is best achieved through the use of |
|
40406 | 844 |
the monadic operator \isa{{\isaliteral{22}{\isachardoublequote}}Option{\isaliteral{2E}{\isachardot}}bind{\isaliteral{22}{\isachardoublequote}}}. |
42123 | 845 |
|
40171 | 846 |
\item \isa{tailrec} defines functions with an arbitrary result |
40406 | 847 |
type and uses the slightly degenerated partial order where \isa{{\isaliteral{22}{\isachardoublequote}}undefined{\isaliteral{22}{\isachardoublequote}}} is the bottom element. Now, monotonicity requires that |
40171 | 848 |
if \isa{undefined} is returned by a recursive call, then the |
849 |
overall result must also be \isa{undefined}. In practice, this is |
|
850 |
only satisfied when each recursive call is a tail call, whose result |
|
851 |
is directly returned. Thus, this mode of operation allows the |
|
852 |
definition of arbitrary tail-recursive functions. |
|
853 |
\end{description} |
|
854 |
||
855 |
Experienced users may define new modes by instantiating the locale |
|
40406 | 856 |
\isa{{\isaliteral{22}{\isachardoublequote}}partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}definitions{\isaliteral{22}{\isachardoublequote}}} appropriately. |
40171 | 857 |
|
40406 | 858 |
\item \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}} declares rules for |
40171 | 859 |
use in the internal monononicity proofs of partial function |
860 |
definitions. |
|
861 |
||
862 |
\end{description}% |
|
863 |
\end{isamarkuptext}% |
|
864 |
\isamarkuptrue% |
|
865 |
% |
|
26849 | 866 |
\isamarkupsubsection{Old-style recursive function definitions (TFL)% |
867 |
} |
|
868 |
\isamarkuptrue% |
|
869 |
% |
|
870 |
\begin{isamarkuptext}% |
|
40406 | 871 |
The old TFL commands \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} and \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}} for defining recursive are mostly obsolete; \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} or \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} should be used instead. |
26849 | 872 |
|
873 |
\begin{matharray}{rcl} |
|
40406 | 874 |
\indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
875 |
\indexdef{HOL}{command}{recdef\_tc}\hypertarget{command.HOL.recdef-tc}{\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
26849 | 876 |
\end{matharray} |
877 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
878 |
\begin{railoutput} |
42662 | 879 |
\rail@begin{5}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
880 |
\rail@term{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
881 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
882 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
883 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
884 |
\rail@term{\isa{\isakeyword{permissive}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
885 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
886 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
887 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
888 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
889 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
890 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
891 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
892 |
\rail@nextplus{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
893 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
894 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
895 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
896 |
\rail@nont{\isa{hints}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
897 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
898 |
\rail@end |
42662 | 899 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
900 |
\rail@nont{\isa{recdeftc}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
901 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
902 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
903 |
\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
904 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
905 |
\rail@nont{\isa{tc}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
906 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
907 |
\rail@begin{2}{\isa{hints}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
908 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
909 |
\rail@term{\isa{\isakeyword{hints}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
910 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
911 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
912 |
\rail@cnont{\isa{recdefmod}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
913 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
914 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
915 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
916 |
\rail@begin{4}{\isa{recdefmod}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
917 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
918 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
919 |
\rail@term{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
920 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
921 |
\rail@term{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
922 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
923 |
\rail@term{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
924 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
925 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
926 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
927 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
928 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
929 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
930 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
931 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
932 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
933 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
934 |
\rail@nont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
935 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
936 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
937 |
\rail@begin{2}{\isa{tc}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
938 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
939 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
940 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
941 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
942 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
943 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
944 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
945 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
946 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
947 |
|
26849 | 948 |
|
28788 | 949 |
\begin{description} |
42123 | 950 |
|
28788 | 951 |
\item \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} defines general well-founded |
26849 | 952 |
recursive functions (using the TFL package), see also |
40406 | 953 |
\cite{isabelle-HOL}. The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}permissive{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' option tells |
26849 | 954 |
TFL to recover from failed proof attempts, returning unfinished |
40406 | 955 |
results. The \isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}, \isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}, and \isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf} hints refer to auxiliary rules to be used in the internal |
26902 | 956 |
automated proof process of TFL. Additional \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}} |
42930 | 957 |
declarations may be given to tune the context of the Simplifier |
958 |
(cf.\ \secref{sec:simplifier}) and Classical reasoner (cf.\ |
|
959 |
\secref{sec:classical}). |
|
42123 | 960 |
|
40406 | 961 |
\item \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} recommences the |
26849 | 962 |
proof for leftover termination condition number \isa{i} (default |
26902 | 963 |
1) as generated by a \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} definition of |
26849 | 964 |
constant \isa{c}. |
42123 | 965 |
|
26902 | 966 |
Note that in most cases, \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} is able to finish |
26849 | 967 |
its internal proofs without manual intervention. |
968 |
||
28788 | 969 |
\end{description} |
26849 | 970 |
|
26902 | 971 |
\medskip Hints for \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} may be also declared |
26849 | 972 |
globally, using the following attributes. |
973 |
||
974 |
\begin{matharray}{rcl} |
|
40406 | 975 |
\indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef-simp}{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}}} & : & \isa{attribute} \\ |
976 |
\indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}}} & : & \isa{attribute} \\ |
|
977 |
\indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}}} & : & \isa{attribute} \\ |
|
26849 | 978 |
\end{matharray} |
979 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
980 |
\begin{railoutput} |
42662 | 981 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
982 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
983 |
\rail@term{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
984 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
985 |
\rail@term{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
986 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
987 |
\rail@term{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
988 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
989 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
990 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
991 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
992 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
993 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
994 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
995 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
996 |
\end{railoutput}% |
26849 | 997 |
\end{isamarkuptext}% |
998 |
\isamarkuptrue% |
|
999 |
% |
|
42908 | 1000 |
\isamarkupsection{Datatypes \label{sec:hol-datatype}% |
26849 | 1001 |
} |
1002 |
\isamarkuptrue% |
|
1003 |
% |
|
1004 |
\begin{isamarkuptext}% |
|
42908 | 1005 |
\begin{matharray}{rcl} |
1006 |
\indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1007 |
\indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep-datatype}{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
26849 | 1008 |
\end{matharray} |
1009 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1010 |
\begin{railoutput} |
42908 | 1011 |
\rail@begin{2}{} |
1012 |
\rail@term{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}}[] |
|
1013 |
\rail@plus |
|
1014 |
\rail@nont{\isa{spec}}[] |
|
1015 |
\rail@nextplus{1} |
|
1016 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
|
1017 |
\rail@endplus |
|
1018 |
\rail@end |
|
1019 |
\rail@begin{3}{} |
|
1020 |
\rail@term{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}}}[] |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1021 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1022 |
\rail@nextbar{1} |
42908 | 1023 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
1024 |
\rail@plus |
|
1025 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1026 |
\rail@nextplus{2} |
|
1027 |
\rail@endplus |
|
1028 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1029 |
\rail@endbar |
42908 | 1030 |
\rail@plus |
1031 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
|
1032 |
\rail@nextplus{1} |
|
1033 |
\rail@endplus |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1034 |
\rail@end |
42908 | 1035 |
\rail@begin{2}{\isa{spec}} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1036 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1037 |
\rail@nextbar{1} |
42908 | 1038 |
\rail@nont{\hyperlink{syntax.parname}{\mbox{\isa{parname}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1039 |
\rail@endbar |
42908 | 1040 |
\rail@nont{\hyperlink{syntax.typespec}{\mbox{\isa{typespec}}}}[] |
1041 |
\rail@bar |
|
1042 |
\rail@nextbar{1} |
|
1043 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
|
1044 |
\rail@endbar |
|
1045 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
|
1046 |
\rail@plus |
|
1047 |
\rail@nont{\isa{cons}}[] |
|
1048 |
\rail@nextplus{1} |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1049 |
\rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1050 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1051 |
\rail@end |
42908 | 1052 |
\rail@begin{2}{\isa{cons}} |
1053 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1054 |
\rail@plus |
|
1055 |
\rail@nextplus{1} |
|
1056 |
\rail@cnont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
|
1057 |
\rail@endplus |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1058 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1059 |
\rail@nextbar{1} |
42908 | 1060 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1061 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1062 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1063 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
1064 |
|
26849 | 1065 |
|
28788 | 1066 |
\begin{description} |
26849 | 1067 |
|
42908 | 1068 |
\item \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} defines inductive datatypes in |
1069 |
HOL. |
|
1070 |
||
1071 |
\item \hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}} represents existing types as |
|
42909 | 1072 |
datatypes. |
1073 |
||
1074 |
For foundational reasons, some basic types such as \isa{nat}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{22}{\isachardoublequote}}}, \isa{bool} and \isa{unit} are |
|
1075 |
introduced by more primitive means using \indexref{}{command}{typedef}\hyperlink{command.typedef}{\mbox{\isa{\isacommand{typedef}}}}. To |
|
1076 |
recover the rich infrastructure of \hyperlink{command.datatype}{\mbox{\isa{\isacommand{datatype}}}} (e.g.\ rules |
|
1077 |
for \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} and the primitive recursion |
|
1078 |
combinators), such types may be represented as actual datatypes |
|
1079 |
later. This is done by specifying the constructors of the desired |
|
1080 |
type, and giving a proof of the induction rule, distinctness and |
|
1081 |
injectivity of constructors. |
|
1082 |
||
1083 |
For example, see \verb|~~/src/HOL/Sum_Type.thy| for the |
|
1084 |
representation of the primitive sum type as fully-featured datatype. |
|
42908 | 1085 |
|
1086 |
\end{description} |
|
1087 |
||
42909 | 1088 |
The generated rules for \hyperlink{method.induct}{\mbox{\isa{induct}}} and \hyperlink{method.cases}{\mbox{\isa{cases}}} provide |
1089 |
case names according to the given constructors, while parameters are |
|
1090 |
named after the types (see also \secref{sec:cases-induct}). |
|
42908 | 1091 |
|
1092 |
See \cite{isabelle-HOL} for more details on datatypes, but beware of |
|
1093 |
the old-style theory syntax being used there! Apart from proper |
|
1094 |
proof methods for case-analysis and induction, there are also |
|
1095 |
emulations of ML tactics \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} available, see \secref{sec:hol-induct-tac}; these admit |
|
1096 |
to refer directly to the internal structure of subgoals (including |
|
1097 |
internally bound parameters).% |
|
1098 |
\end{isamarkuptext}% |
|
1099 |
\isamarkuptrue% |
|
1100 |
% |
|
42910
6834af822a8b
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|
1101 |
\isamarkupsubsubsection{Examples% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
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diff
changeset
|
1102 |
} |
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diff
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|
1103 |
\isamarkuptrue% |
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parents:
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diff
changeset
|
1104 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
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diff
changeset
|
1105 |
\begin{isamarkuptext}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
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parents:
42909
diff
changeset
|
1106 |
We define a type of finite sequences, with slightly different |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1107 |
names than the existing \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequote}}} that is already in \hyperlink{theory.Main}{\mbox{\isa{Main}}}:% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1108 |
\end{isamarkuptext}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1109 |
\isamarkuptrue% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1110 |
\isacommand{datatype}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1111 |
\ {\isaliteral{27}{\isacharprime}}a\ seq\ {\isaliteral{3D}{\isacharequal}}\ Empty\ {\isaliteral{7C}{\isacharbar}}\ Seq\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ seq{\isaliteral{22}{\isachardoublequoteclose}}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1112 |
\begin{isamarkuptext}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1113 |
We can now prove some simple lemma by structural induction:% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1114 |
\end{isamarkuptext}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1115 |
\isamarkuptrue% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1116 |
\isacommand{lemma}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1117 |
\ {\isaliteral{22}{\isachardoublequoteopen}}Seq\ x\ xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1118 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1119 |
\isadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1120 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1121 |
\endisadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1122 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1123 |
\isatagproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1124 |
\isacommand{proof}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1125 |
\ {\isaliteral{28}{\isacharparenleft}}induct\ xs\ arbitrary{\isaliteral{3A}{\isacharcolon}}\ x{\isaliteral{29}{\isacharparenright}}\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
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diff
changeset
|
1126 |
\ \ \isacommand{case}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1127 |
\ Empty% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1128 |
\begin{isamarkuptxt}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1129 |
This case can be proved using the simplifier: the freeness |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1130 |
properties of the datatype are already declared as \hyperlink{attribute.simp}{\mbox{\isa{simp}}} rules.% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1131 |
\end{isamarkuptxt}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1132 |
\isamarkuptrue% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1133 |
\ \ \isacommand{show}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1134 |
\ {\isaliteral{22}{\isachardoublequoteopen}}Seq\ x\ Empty\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ Empty{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1135 |
\ \ \ \ \isacommand{by}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1136 |
\ simp\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1137 |
\isacommand{next}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1138 |
\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1139 |
\ \ \isacommand{case}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1140 |
\ {\isaliteral{28}{\isacharparenleft}}Seq\ y\ ys{\isaliteral{29}{\isacharparenright}}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1141 |
\begin{isamarkuptxt}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1142 |
The step case is proved similarly.% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1143 |
\end{isamarkuptxt}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1144 |
\isamarkuptrue% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1145 |
\ \ \isacommand{show}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1146 |
\ {\isaliteral{22}{\isachardoublequoteopen}}Seq\ x\ {\isaliteral{28}{\isacharparenleft}}Seq\ y\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ Seq\ y\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1147 |
\ \ \ \ \isacommand{using}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1148 |
\ {\isaliteral{60}{\isacharbackquoteopen}}Seq\ y\ ys\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ ys{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{by}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1149 |
\ simp\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1150 |
\isacommand{qed}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1151 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1152 |
\endisatagproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1153 |
{\isafoldproof}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1154 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1155 |
\isadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1156 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1157 |
\endisadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1158 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1159 |
\begin{isamarkuptext}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1160 |
Here is a more succinct version of the same proof:% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1161 |
\end{isamarkuptext}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1162 |
\isamarkuptrue% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1163 |
\isacommand{lemma}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1164 |
\ {\isaliteral{22}{\isachardoublequoteopen}}Seq\ x\ xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1165 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1166 |
\isadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1167 |
\ \ % |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1168 |
\endisadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1169 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1170 |
\isatagproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1171 |
\isacommand{by}\isamarkupfalse% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1172 |
\ {\isaliteral{28}{\isacharparenleft}}induct\ xs\ arbitrary{\isaliteral{3A}{\isacharcolon}}\ x{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1173 |
\endisatagproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1174 |
{\isafoldproof}% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1175 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1176 |
\isadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1177 |
% |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1178 |
\endisadelimproof |
6834af822a8b
updated and simplified HOL datatype examples (NB: special treatment of distinctness has been discontinued in the vicinity of 542b34b178ec);
wenzelm
parents:
42909
diff
changeset
|
1179 |
% |
42908 | 1180 |
\isamarkupsection{Records \label{sec:hol-record}% |
1181 |
} |
|
1182 |
\isamarkuptrue% |
|
1183 |
% |
|
1184 |
\begin{isamarkuptext}% |
|
1185 |
In principle, records merely generalize the concept of tuples, where |
|
1186 |
components may be addressed by labels instead of just position. The |
|
1187 |
logical infrastructure of records in Isabelle/HOL is slightly more |
|
1188 |
advanced, though, supporting truly extensible record schemes. This |
|
1189 |
admits operations that are polymorphic with respect to record |
|
1190 |
extension, yielding ``object-oriented'' effects like (single) |
|
1191 |
inheritance. See also \cite{NaraschewskiW-TPHOLs98} for more |
|
1192 |
details on object-oriented verification and record subtyping in HOL.% |
|
1193 |
\end{isamarkuptext}% |
|
1194 |
\isamarkuptrue% |
|
1195 |
% |
|
1196 |
\isamarkupsubsection{Basic concepts% |
|
1197 |
} |
|
1198 |
\isamarkuptrue% |
|
1199 |
% |
|
1200 |
\begin{isamarkuptext}% |
|
1201 |
Isabelle/HOL supports both \emph{fixed} and \emph{schematic} records |
|
1202 |
at the level of terms and types. The notation is as follows: |
|
1203 |
||
1204 |
\begin{center} |
|
1205 |
\begin{tabular}{l|l|l} |
|
1206 |
& record terms & record types \\ \hline |
|
1207 |
fixed & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1208 |
schematic & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} & |
|
1209 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ M{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1210 |
\end{tabular} |
|
1211 |
\end{center} |
|
1212 |
||
1213 |
\noindent The ASCII representation of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{7C}{\isacharbar}}\ x\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}. |
|
1214 |
||
1215 |
A fixed record \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} has field \isa{x} of value |
|
1216 |
\isa{a} and field \isa{y} of value \isa{b}. The corresponding |
|
1217 |
type is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, assuming that \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{22}{\isachardoublequote}}} |
|
1218 |
and \isa{{\isaliteral{22}{\isachardoublequote}}b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{22}{\isachardoublequote}}}. |
|
1219 |
||
1220 |
A record scheme like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} contains fields |
|
1221 |
\isa{x} and \isa{y} as before, but also possibly further fields |
|
1222 |
as indicated by the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' notation (which is actually part |
|
1223 |
of the syntax). The improper field ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' of a record |
|
1224 |
scheme is called the \emph{more part}. Logically it is just a free |
|
1225 |
variable, which is occasionally referred to as ``row variable'' in |
|
1226 |
the literature. The more part of a record scheme may be |
|
1227 |
instantiated by zero or more further components. For example, the |
|
1228 |
previous scheme may get instantiated to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, where \isa{m{\isaliteral{27}{\isacharprime}}} refers to a different more part. |
|
1229 |
Fixed records are special instances of record schemes, where |
|
1230 |
``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' is properly terminated by the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ unit{\isaliteral{22}{\isachardoublequote}}} |
|
1231 |
element. In fact, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} is just an abbreviation |
|
1232 |
for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}. |
|
26849 | 1233 |
|
42908 | 1234 |
\medskip Two key observations make extensible records in a simply |
1235 |
typed language like HOL work out: |
|
1236 |
||
1237 |
\begin{enumerate} |
|
1238 |
||
1239 |
\item the more part is internalized, as a free term or type |
|
1240 |
variable, |
|
1241 |
||
1242 |
\item field names are externalized, they cannot be accessed within |
|
1243 |
the logic as first-class values. |
|
1244 |
||
1245 |
\end{enumerate} |
|
1246 |
||
1247 |
\medskip In Isabelle/HOL record types have to be defined explicitly, |
|
1248 |
fixing their field names and types, and their (optional) parent |
|
1249 |
record. Afterwards, records may be formed using above syntax, while |
|
1250 |
obeying the canonical order of fields as given by their declaration. |
|
1251 |
The record package provides several standard operations like |
|
1252 |
selectors and updates. The common setup for various generic proof |
|
1253 |
tools enable succinct reasoning patterns. See also the Isabelle/HOL |
|
1254 |
tutorial \cite{isabelle-hol-book} for further instructions on using |
|
1255 |
records in practice.% |
|
1256 |
\end{isamarkuptext}% |
|
1257 |
\isamarkuptrue% |
|
1258 |
% |
|
1259 |
\isamarkupsubsection{Record specifications% |
|
1260 |
} |
|
1261 |
\isamarkuptrue% |
|
1262 |
% |
|
1263 |
\begin{isamarkuptext}% |
|
1264 |
\begin{matharray}{rcl} |
|
1265 |
\indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1266 |
\end{matharray} |
|
26849 | 1267 |
|
42908 | 1268 |
\begin{railoutput} |
1269 |
\rail@begin{4}{} |
|
1270 |
\rail@term{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}}[] |
|
1271 |
\rail@nont{\hyperlink{syntax.typespec-sorts}{\mbox{\isa{typespec{\isaliteral{5F}{\isacharunderscore}}sorts}}}}[] |
|
1272 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
|
1273 |
\rail@cr{2} |
|
1274 |
\rail@bar |
|
1275 |
\rail@nextbar{3} |
|
1276 |
\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
|
1277 |
\rail@term{\isa{{\isaliteral{2B}{\isacharplus}}}}[] |
|
1278 |
\rail@endbar |
|
1279 |
\rail@plus |
|
1280 |
\rail@nont{\hyperlink{syntax.constdecl}{\mbox{\isa{constdecl}}}}[] |
|
1281 |
\rail@nextplus{3} |
|
1282 |
\rail@endplus |
|
1283 |
\rail@end |
|
1284 |
\end{railoutput} |
|
1285 |
||
1286 |
||
1287 |
\begin{description} |
|
1288 |
||
1289 |
\item \hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{2B}{\isacharplus}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} defines extensible record type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}}, |
|
1290 |
derived from the optional parent record \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} by adding new |
|
1291 |
field components \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} etc. |
|
1292 |
||
1293 |
The type variables of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} need to be |
|
1294 |
covered by the (distinct) parameters \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}. Type constructor \isa{t} has to be new, while \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} needs to specify an instance of an existing record type. At |
|
1295 |
least one new field \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} has to be specified. |
|
1296 |
Basically, field names need to belong to a unique record. This is |
|
1297 |
not a real restriction in practice, since fields are qualified by |
|
1298 |
the record name internally. |
|
1299 |
||
1300 |
The parent record specification \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} is optional; if omitted |
|
1301 |
\isa{t} becomes a root record. The hierarchy of all records |
|
1302 |
declared within a theory context forms a forest structure, i.e.\ a |
|
1303 |
set of trees starting with a root record each. There is no way to |
|
1304 |
merge multiple parent records! |
|
1305 |
||
1306 |
For convenience, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} is made a |
|
1307 |
type abbreviation for the fixed record type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, likewise is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequote}}} made an abbreviation for |
|
1308 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}. |
|
26849 | 1309 |
|
28788 | 1310 |
\end{description}% |
26849 | 1311 |
\end{isamarkuptext}% |
1312 |
\isamarkuptrue% |
|
1313 |
% |
|
42908 | 1314 |
\isamarkupsubsection{Record operations% |
1315 |
} |
|
1316 |
\isamarkuptrue% |
|
1317 |
% |
|
1318 |
\begin{isamarkuptext}% |
|
1319 |
Any record definition of the form presented above produces certain |
|
1320 |
standard operations. Selectors and updates are provided for any |
|
1321 |
field, including the improper one ``\isa{more}''. There are also |
|
1322 |
cumulative record constructor functions. To simplify the |
|
1323 |
presentation below, we assume for now that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} is a root record with fields \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}. |
|
1324 |
||
1325 |
\medskip \textbf{Selectors} and \textbf{updates} are available for |
|
1326 |
any field (including ``\isa{more}''): |
|
1327 |
||
1328 |
\begin{matharray}{lll} |
|
1329 |
\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1330 |
\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5F}{\isacharunderscore}}update{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1331 |
\end{matharray} |
|
1332 |
||
1333 |
There is special syntax for application of updates: \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} abbreviates term \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{5F}{\isacharunderscore}}update\ a\ r{\isaliteral{22}{\isachardoublequote}}}. Further notation for |
|
1334 |
repeated updates is also available: \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} may be written \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}. Note that |
|
1335 |
because of postfix notation the order of fields shown here is |
|
1336 |
reverse than in the actual term. Since repeated updates are just |
|
1337 |
function applications, fields may be freely permuted in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, as far as logical equality is concerned. |
|
1338 |
Thus commutativity of independent updates can be proven within the |
|
1339 |
logic for any two fields, but not as a general theorem. |
|
1340 |
||
1341 |
\medskip The \textbf{make} operation provides a cumulative record |
|
1342 |
constructor function: |
|
1343 |
||
1344 |
\begin{matharray}{lll} |
|
1345 |
\isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1346 |
\end{matharray} |
|
1347 |
||
1348 |
\medskip We now reconsider the case of non-root records, which are |
|
1349 |
derived of some parent. In general, the latter may depend on |
|
1350 |
another parent as well, resulting in a list of \emph{ancestor |
|
1351 |
records}. Appending the lists of fields of all ancestors results in |
|
1352 |
a certain field prefix. The record package automatically takes care |
|
1353 |
of this by lifting operations over this context of ancestor fields. |
|
1354 |
Assuming that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} has ancestor |
|
1355 |
fields \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}}, |
|
1356 |
the above record operations will get the following types: |
|
1357 |
||
1358 |
\medskip |
|
1359 |
\begin{tabular}{lll} |
|
1360 |
\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1361 |
\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5F}{\isacharunderscore}}update{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1362 |
\isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1363 |
\end{tabular} |
|
1364 |
\medskip |
|
1365 |
||
1366 |
\noindent Some further operations address the extension aspect of a |
|
1367 |
derived record scheme specifically: \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} produces a |
|
1368 |
record fragment consisting of exactly the new fields introduced here |
|
1369 |
(the result may serve as a more part elsewhere); \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}} |
|
1370 |
takes a fixed record and adds a given more part; \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} restricts a record scheme to a fixed record. |
|
1371 |
||
1372 |
\medskip |
|
1373 |
\begin{tabular}{lll} |
|
1374 |
\isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1375 |
\isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1376 |
\isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1377 |
\end{tabular} |
|
1378 |
\medskip |
|
1379 |
||
1380 |
\noindent Note that \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} coincide |
|
1381 |
for root records.% |
|
1382 |
\end{isamarkuptext}% |
|
1383 |
\isamarkuptrue% |
|
1384 |
% |
|
1385 |
\isamarkupsubsection{Derived rules and proof tools% |
|
26849 | 1386 |
} |
1387 |
\isamarkuptrue% |
|
1388 |
% |
|
1389 |
\begin{isamarkuptext}% |
|
42908 | 1390 |
The record package proves several results internally, declaring |
1391 |
these facts to appropriate proof tools. This enables users to |
|
1392 |
reason about record structures quite conveniently. Assume that |
|
1393 |
\isa{t} is a record type as specified above. |
|
1394 |
||
1395 |
\begin{enumerate} |
|
1396 |
||
1397 |
\item Standard conversions for selectors or updates applied to |
|
1398 |
record constructor terms are made part of the default Simplifier |
|
1399 |
context; thus proofs by reduction of basic operations merely require |
|
1400 |
the \hyperlink{method.simp}{\mbox{\isa{simp}}} method without further arguments. These rules |
|
1401 |
are available as \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}simps{\isaliteral{22}{\isachardoublequote}}}, too. |
|
1402 |
||
1403 |
\item Selectors applied to updated records are automatically reduced |
|
1404 |
by an internal simplification procedure, which is also part of the |
|
1405 |
standard Simplifier setup. |
|
1406 |
||
1407 |
\item Inject equations of a form analogous to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} are declared to the Simplifier and Classical |
|
1408 |
Reasoner as \hyperlink{attribute.iff}{\mbox{\isa{iff}}} rules. These rules are available as |
|
1409 |
\isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}iffs{\isaliteral{22}{\isachardoublequote}}}. |
|
1410 |
||
1411 |
\item The introduction rule for record equality analogous to \isa{{\isaliteral{22}{\isachardoublequote}}x\ r\ {\isaliteral{3D}{\isacharequal}}\ x\ r{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ r\ {\isaliteral{3D}{\isacharequal}}\ y\ r{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ r\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} is declared to the Simplifier, |
|
1412 |
and as the basic rule context as ``\hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}''. |
|
1413 |
The rule is called \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}equality{\isaliteral{22}{\isachardoublequote}}}. |
|
1414 |
||
1415 |
\item Representations of arbitrary record expressions as canonical |
|
1416 |
constructor terms are provided both in \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} format (cf.\ the generic proof methods of the same name, |
|
1417 |
\secref{sec:cases-induct}). Several variations are available, for |
|
1418 |
fixed records, record schemes, more parts etc. |
|
1419 |
||
1420 |
The generic proof methods are sufficiently smart to pick the most |
|
1421 |
sensible rule according to the type of the indicated record |
|
1422 |
expression: users just need to apply something like ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' to a certain proof problem. |
|
1423 |
||
1424 |
\item The derived record operations \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} are \emph{not} |
|
1425 |
treated automatically, but usually need to be expanded by hand, |
|
1426 |
using the collective fact \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}defs{\isaliteral{22}{\isachardoublequote}}}. |
|
1427 |
||
1428 |
\end{enumerate}% |
|
1429 |
\end{isamarkuptext}% |
|
1430 |
\isamarkuptrue% |
|
1431 |
% |
|
42911 | 1432 |
\isamarkupsubsubsection{Examples% |
1433 |
} |
|
1434 |
\isamarkuptrue% |
|
1435 |
% |
|
1436 |
\begin{isamarkuptext}% |
|
1437 |
See \verb|~~/src/HOL/ex/Records.thy|, for example.% |
|
1438 |
\end{isamarkuptext}% |
|
1439 |
\isamarkuptrue% |
|
1440 |
% |
|
42908 | 1441 |
\isamarkupsection{Adhoc tuples% |
1442 |
} |
|
1443 |
\isamarkuptrue% |
|
1444 |
% |
|
1445 |
\begin{isamarkuptext}% |
|
1446 |
\begin{matharray}{rcl} |
|
1447 |
\indexdef{HOL}{attribute}{split\_format}\hypertarget{attribute.HOL.split-format}{\hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\ |
|
1448 |
\end{matharray} |
|
1449 |
||
1450 |
\begin{railoutput} |
|
1451 |
\rail@begin{2}{} |
|
1452 |
\rail@term{\hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}}[] |
|
1453 |
\rail@bar |
|
1454 |
\rail@nextbar{1} |
|
1455 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
|
1456 |
\rail@term{\isa{complete}}[] |
|
1457 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
|
1458 |
\rail@endbar |
|
1459 |
\rail@end |
|
1460 |
\end{railoutput} |
|
1461 |
||
26849 | 1462 |
|
1463 |
\begin{description} |
|
1464 |
||
42908 | 1465 |
\item \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}complete{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} causes |
1466 |
arguments in function applications to be represented canonically |
|
1467 |
according to their tuple type structure. |
|
26849 | 1468 |
|
42908 | 1469 |
Note that this operation tends to invent funny names for new local |
1470 |
parameters introduced. |
|
26849 | 1471 |
|
42908 | 1472 |
\end{description}% |
26849 | 1473 |
\end{isamarkuptext}% |
1474 |
\isamarkuptrue% |
|
1475 |
% |
|
42908 | 1476 |
\isamarkupsection{Typedef axiomatization \label{sec:hol-typedef}% |
26849 | 1477 |
} |
1478 |
\isamarkuptrue% |
|
1479 |
% |
|
1480 |
\begin{isamarkuptext}% |
|
42908 | 1481 |
A Gordon/HOL-style type definition is a certain axiom scheme |
1482 |
that identifies a new type with a subset of an existing type. More |
|
1483 |
precisely, the new type is defined by exhibiting an existing type |
|
1484 |
\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}, a set \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ set{\isaliteral{22}{\isachardoublequote}}}, and a theorem that proves |
|
1485 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequote}}}. Thus \isa{A} is a non-empty subset of \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}, and the new type denotes this subset. New functions are |
|
1486 |
postulated that establish an isomorphism between the new type and |
|
1487 |
the subset. In general, the type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} may involve type |
|
1488 |
variables \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} which means that the type definition |
|
1489 |
produces a type constructor \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} depending on |
|
1490 |
those type arguments. |
|
1491 |
||
1492 |
The axiomatization can be considered a ``definition'' in the sense |
|
1493 |
of the particular set-theoretic interpretation of HOL |
|
1494 |
\cite{pitts93}, where the universe of types is required to be |
|
1495 |
downwards-closed wrt.\ arbitrary non-empty subsets. Thus genuinely |
|
1496 |
new types introduced by \hyperlink{command.typedef}{\mbox{\isa{\isacommand{typedef}}}} stay within the range |
|
1497 |
of HOL models by construction. Note that \indexref{}{command}{type\_synonym}\hyperlink{command.type-synonym}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}synonym}}}} from Isabelle/Pure merely introduces syntactic |
|
1498 |
abbreviations, without any logical significance. |
|
1499 |
||
1500 |
\begin{matharray}{rcl} |
|
1501 |
\indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1502 |
\end{matharray} |
|
1503 |
||
1504 |
\begin{railoutput} |
|
1505 |
\rail@begin{2}{} |
|
1506 |
\rail@term{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}}[] |
|
1507 |
\rail@bar |
|
1508 |
\rail@nextbar{1} |
|
1509 |
\rail@nont{\isa{alt{\isaliteral{5F}{\isacharunderscore}}name}}[] |
|
1510 |
\rail@endbar |
|
1511 |
\rail@nont{\isa{abs{\isaliteral{5F}{\isacharunderscore}}type}}[] |
|
1512 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
|
1513 |
\rail@nont{\isa{rep{\isaliteral{5F}{\isacharunderscore}}set}}[] |
|
1514 |
\rail@end |
|
1515 |
\rail@begin{3}{\isa{alt{\isaliteral{5F}{\isacharunderscore}}name}} |
|
1516 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
|
1517 |
\rail@bar |
|
1518 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1519 |
\rail@nextbar{1} |
|
1520 |
\rail@term{\isa{\isakeyword{open}}}[] |
|
1521 |
\rail@nextbar{2} |
|
1522 |
\rail@term{\isa{\isakeyword{open}}}[] |
|
1523 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1524 |
\rail@endbar |
|
1525 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
|
1526 |
\rail@end |
|
1527 |
\rail@begin{2}{\isa{abs{\isaliteral{5F}{\isacharunderscore}}type}} |
|
1528 |
\rail@nont{\hyperlink{syntax.typespec-sorts}{\mbox{\isa{typespec{\isaliteral{5F}{\isacharunderscore}}sorts}}}}[] |
|
1529 |
\rail@bar |
|
1530 |
\rail@nextbar{1} |
|
1531 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
|
1532 |
\rail@endbar |
|
1533 |
\rail@end |
|
1534 |
\rail@begin{2}{\isa{rep{\isaliteral{5F}{\isacharunderscore}}set}} |
|
1535 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
|
1536 |
\rail@bar |
|
1537 |
\rail@nextbar{1} |
|
1538 |
\rail@term{\isa{\isakeyword{morphisms}}}[] |
|
1539 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1540 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1541 |
\rail@endbar |
|
1542 |
\rail@end |
|
1543 |
\end{railoutput} |
|
1544 |
||
1545 |
||
1546 |
\begin{description} |
|
26849 | 1547 |
|
42908 | 1548 |
\item \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{22}{\isachardoublequote}}} |
1549 |
axiomatizes a type definition in the background theory of the |
|
1550 |
current context, depending on a non-emptiness result of the set |
|
1551 |
\isa{A} that needs to be proven here. The set \isa{A} may |
|
1552 |
contain type variables \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} as specified on the LHS, |
|
1553 |
but no term variables. |
|
1554 |
||
1555 |
Even though a local theory specification, the newly introduced type |
|
1556 |
constructor cannot depend on parameters or assumptions of the |
|
1557 |
context: this is structurally impossible in HOL. In contrast, the |
|
1558 |
non-emptiness proof may use local assumptions in unusual situations, |
|
1559 |
which could result in different interpretations in target contexts: |
|
1560 |
the meaning of the bijection between the representing set \isa{A} |
|
1561 |
and the new type \isa{t} may then change in different application |
|
1562 |
contexts. |
|
1563 |
||
1564 |
By default, \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}} defines both a type |
|
1565 |
constructor \isa{t} for the new type, and a term constant \isa{t} for the representing set within the old type. Use the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}open{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' option to suppress a separate constant definition |
|
1566 |
altogether. The injection from type to set is called \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t}, |
|
1567 |
its inverse \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t}, unless explicit \hyperlink{keyword.HOL.morphisms}{\mbox{\isa{\isakeyword{morphisms}}}} specification provides alternative names. |
|
1568 |
||
1569 |
The core axiomatization uses the locale predicate \isa{type{\isaliteral{5F}{\isacharunderscore}}definition} as defined in Isabelle/HOL. Various basic |
|
1570 |
consequences of that are instantiated accordingly, re-using the |
|
1571 |
locale facts with names derived from the new type constructor. Thus |
|
1572 |
the generic \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Rep} is turned into the specific |
|
1573 |
\isa{{\isaliteral{22}{\isachardoublequote}}Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{22}{\isachardoublequote}}}, for example. |
|
26849 | 1574 |
|
42908 | 1575 |
Theorems \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Rep}, \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Rep{\isaliteral{5F}{\isacharunderscore}}inverse}, and \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Abs{\isaliteral{5F}{\isacharunderscore}}inverse} |
1576 |
provide the most basic characterization as a corresponding |
|
1577 |
injection/surjection pair (in both directions). The derived rules |
|
1578 |
\isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Rep{\isaliteral{5F}{\isacharunderscore}}inject} and \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Abs{\isaliteral{5F}{\isacharunderscore}}inject} provide a more convenient version of |
|
1579 |
injectivity, suitable for automated proof tools (e.g.\ in |
|
1580 |
declarations involving \hyperlink{attribute.simp}{\mbox{\isa{simp}}} or \hyperlink{attribute.iff}{\mbox{\isa{iff}}}). |
|
1581 |
Furthermore, the rules \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Rep{\isaliteral{5F}{\isacharunderscore}}cases}~/ \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Rep{\isaliteral{5F}{\isacharunderscore}}induct}, and \isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Abs{\isaliteral{5F}{\isacharunderscore}}cases}~/ |
|
1582 |
\isa{type{\isaliteral{5F}{\isacharunderscore}}definition{\isaliteral{2E}{\isachardot}}Abs{\isaliteral{5F}{\isacharunderscore}}induct} provide alternative views on |
|
1583 |
surjectivity. These rules are already declared as set or type rules |
|
1584 |
for the generic \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} methods, |
|
1585 |
respectively. |
|
1586 |
||
1587 |
An alternative name for the set definition (and other derived |
|
1588 |
entities) may be specified in parentheses; the default is to use |
|
1589 |
\isa{t} directly. |
|
1590 |
||
1591 |
\end{description} |
|
1592 |
||
1593 |
\begin{warn} |
|
1594 |
If you introduce a new type axiomatically, i.e.\ via \indexref{}{command}{typedecl}\hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}} and \indexref{}{command}{axiomatization}\hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}, the minimum requirement |
|
1595 |
is that it has a non-empty model, to avoid immediate collapse of the |
|
1596 |
HOL logic. Moreover, one needs to demonstrate that the |
|
1597 |
interpretation of such free-form axiomatizations can coexist with |
|
1598 |
that of the regular \indexdef{}{command}{typedef}\hypertarget{command.typedef}{\hyperlink{command.typedef}{\mbox{\isa{\isacommand{typedef}}}}} scheme, and any extension |
|
1599 |
that other people might have introduced elsewhere (e.g.\ in HOLCF |
|
1600 |
\cite{MuellerNvOS99}). |
|
1601 |
\end{warn}% |
|
1602 |
\end{isamarkuptext}% |
|
1603 |
\isamarkuptrue% |
|
1604 |
% |
|
1605 |
\isamarkupsubsubsection{Examples% |
|
1606 |
} |
|
1607 |
\isamarkuptrue% |
|
1608 |
% |
|
1609 |
\begin{isamarkuptext}% |
|
1610 |
Type definitions permit the introduction of abstract data |
|
1611 |
types in a safe way, namely by providing models based on already |
|
1612 |
existing types. Given some abstract axiomatic description \isa{P} |
|
1613 |
of a type, this involves two steps: |
|
1614 |
||
1615 |
\begin{enumerate} |
|
26849 | 1616 |
|
42908 | 1617 |
\item Find an appropriate type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} and subset \isa{A} which |
1618 |
has the desired properties \isa{P}, and make a type definition |
|
1619 |
based on this representation. |
|
1620 |
||
1621 |
\item Prove that \isa{P} holds for \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} by lifting \isa{P} |
|
1622 |
from the representation. |
|
1623 |
||
1624 |
\end{enumerate} |
|
1625 |
||
1626 |
You can later forget about the representation and work solely in |
|
1627 |
terms of the abstract properties \isa{P}. |
|
26849 | 1628 |
|
42908 | 1629 |
\medskip The following trivial example pulls a three-element type |
1630 |
into existence within the formal logical environment of HOL.% |
|
1631 |
\end{isamarkuptext}% |
|
1632 |
\isamarkuptrue% |
|
1633 |
\isacommand{typedef}\isamarkupfalse% |
|
1634 |
\ three\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}True{\isaliteral{2C}{\isacharcomma}}\ True{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}True{\isaliteral{2C}{\isacharcomma}}\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}False{\isaliteral{2C}{\isacharcomma}}\ True{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
1635 |
% |
|
1636 |
\isadelimproof |
|
1637 |
\ \ % |
|
1638 |
\endisadelimproof |
|
1639 |
% |
|
1640 |
\isatagproof |
|
1641 |
\isacommand{by}\isamarkupfalse% |
|
1642 |
\ blast% |
|
1643 |
\endisatagproof |
|
1644 |
{\isafoldproof}% |
|
1645 |
% |
|
1646 |
\isadelimproof |
|
1647 |
\isanewline |
|
1648 |
% |
|
1649 |
\endisadelimproof |
|
1650 |
\isanewline |
|
1651 |
\isacommand{definition}\isamarkupfalse% |
|
1652 |
\ {\isaliteral{22}{\isachardoublequoteopen}}One\ {\isaliteral{3D}{\isacharequal}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isaliteral{28}{\isacharparenleft}}True{\isaliteral{2C}{\isacharcomma}}\ True{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
1653 |
\isacommand{definition}\isamarkupfalse% |
|
1654 |
\ {\isaliteral{22}{\isachardoublequoteopen}}Two\ {\isaliteral{3D}{\isacharequal}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isaliteral{28}{\isacharparenleft}}True{\isaliteral{2C}{\isacharcomma}}\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
1655 |
\isacommand{definition}\isamarkupfalse% |
|
1656 |
\ {\isaliteral{22}{\isachardoublequoteopen}}Three\ {\isaliteral{3D}{\isacharequal}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isaliteral{28}{\isacharparenleft}}False{\isaliteral{2C}{\isacharcomma}}\ True{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
1657 |
\isanewline |
|
1658 |
\isacommand{lemma}\isamarkupfalse% |
|
1659 |
\ three{\isaliteral{5F}{\isacharunderscore}}distinct{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}One\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ Two{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}One\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ Three{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}Two\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ Three{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
1660 |
% |
|
1661 |
\isadelimproof |
|
1662 |
\ \ % |
|
1663 |
\endisadelimproof |
|
1664 |
% |
|
1665 |
\isatagproof |
|
1666 |
\isacommand{by}\isamarkupfalse% |
|
1667 |
\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ One{\isaliteral{5F}{\isacharunderscore}}def\ Two{\isaliteral{5F}{\isacharunderscore}}def\ Three{\isaliteral{5F}{\isacharunderscore}}def\ Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inject\ three{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}% |
|
1668 |
\endisatagproof |
|
1669 |
{\isafoldproof}% |
|
1670 |
% |
|
1671 |
\isadelimproof |
|
1672 |
\isanewline |
|
1673 |
% |
|
1674 |
\endisadelimproof |
|
1675 |
\isanewline |
|
1676 |
\isacommand{lemma}\isamarkupfalse% |
|
1677 |
\ three{\isaliteral{5F}{\isacharunderscore}}cases{\isaliteral{3A}{\isacharcolon}}\isanewline |
|
1678 |
\ \ \isakeyword{fixes}\ x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ three\ \isakeyword{obtains}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ One{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ Two{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ Three{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
1679 |
% |
|
1680 |
\isadelimproof |
|
1681 |
\ \ % |
|
1682 |
\endisadelimproof |
|
1683 |
% |
|
1684 |
\isatagproof |
|
1685 |
\isacommand{by}\isamarkupfalse% |
|
1686 |
\ {\isaliteral{28}{\isacharparenleft}}cases\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ One{\isaliteral{5F}{\isacharunderscore}}def\ Two{\isaliteral{5F}{\isacharunderscore}}def\ Three{\isaliteral{5F}{\isacharunderscore}}def\ Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inject\ three{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}% |
|
1687 |
\endisatagproof |
|
1688 |
{\isafoldproof}% |
|
1689 |
% |
|
1690 |
\isadelimproof |
|
1691 |
% |
|
1692 |
\endisadelimproof |
|
1693 |
% |
|
1694 |
\begin{isamarkuptext}% |
|
1695 |
Note that such trivial constructions are better done with |
|
1696 |
derived specification mechanisms such as \hyperlink{command.datatype}{\mbox{\isa{\isacommand{datatype}}}}:% |
|
1697 |
\end{isamarkuptext}% |
|
1698 |
\isamarkuptrue% |
|
1699 |
\isacommand{datatype}\isamarkupfalse% |
|
1700 |
\ three{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ One{\isaliteral{27}{\isacharprime}}\ {\isaliteral{7C}{\isacharbar}}\ Two{\isaliteral{27}{\isacharprime}}\ {\isaliteral{7C}{\isacharbar}}\ Three{\isaliteral{27}{\isacharprime}}% |
|
1701 |
\begin{isamarkuptext}% |
|
1702 |
This avoids re-doing basic definitions and proofs from the |
|
1703 |
primitive \hyperlink{command.typedef}{\mbox{\isa{\isacommand{typedef}}}} above.% |
|
1704 |
\end{isamarkuptext}% |
|
1705 |
\isamarkuptrue% |
|
1706 |
% |
|
1707 |
\isamarkupsection{Functorial structure of types% |
|
1708 |
} |
|
1709 |
\isamarkuptrue% |
|
1710 |
% |
|
1711 |
\begin{isamarkuptext}% |
|
1712 |
\begin{matharray}{rcl} |
|
1713 |
\indexdef{HOL}{command}{enriched\_type}\hypertarget{command.HOL.enriched-type}{\hyperlink{command.HOL.enriched-type}{\mbox{\isa{\isacommand{enriched{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} |
|
1714 |
\end{matharray} |
|
26849 | 1715 |
|
42908 | 1716 |
\begin{railoutput} |
1717 |
\rail@begin{2}{} |
|
1718 |
\rail@term{\hyperlink{command.HOL.enriched-type}{\mbox{\isa{\isacommand{enriched{\isaliteral{5F}{\isacharunderscore}}type}}}}}[] |
|
1719 |
\rail@bar |
|
1720 |
\rail@nextbar{1} |
|
1721 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
|
1722 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
|
1723 |
\rail@endbar |
|
1724 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
|
1725 |
\rail@end |
|
1726 |
\end{railoutput} |
|
1727 |
||
1728 |
||
1729 |
\begin{description} |
|
26849 | 1730 |
|
42908 | 1731 |
\item \hyperlink{command.HOL.enriched-type}{\mbox{\isa{\isacommand{enriched{\isaliteral{5F}{\isacharunderscore}}type}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}prefix{\isaliteral{3A}{\isacharcolon}}\ m{\isaliteral{22}{\isachardoublequote}}} allows to |
1732 |
prove and register properties about the functorial structure of type |
|
1733 |
constructors. These properties then can be used by other packages |
|
1734 |
to deal with those type constructors in certain type constructions. |
|
1735 |
Characteristic theorems are noted in the current local theory. By |
|
1736 |
default, they are prefixed with the base name of the type |
|
1737 |
constructor, an explicit prefix can be given alternatively. |
|
1738 |
||
1739 |
The given term \isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{22}{\isachardoublequote}}} is considered as \emph{mapper} for the |
|
1740 |
corresponding type constructor and must conform to the following |
|
1741 |
type pattern: |
|
26849 | 1742 |
|
42908 | 1743 |
\begin{matharray}{lll} |
1744 |
\isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & |
|
1745 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub k\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1746 |
\end{matharray} |
|
1747 |
||
1748 |
\noindent where \isa{t} is the type constructor, \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} are distinct |
|
1749 |
type variables free in the local theory and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, |
|
1750 |
\ldots, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub k{\isaliteral{22}{\isachardoublequote}}} is a subsequence of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, \ldots, |
|
1751 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}}. |
|
1752 |
||
1753 |
\end{description}% |
|
26849 | 1754 |
\end{isamarkuptext}% |
1755 |
\isamarkuptrue% |
|
1756 |
% |
|
43993
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1757 |
\isamarkupsection{Quotient types% |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1758 |
} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1759 |
\isamarkuptrue% |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1760 |
% |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1761 |
\begin{isamarkuptext}% |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1762 |
The quotient package defines a new quotient type given a raw type |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1763 |
and a partial equivalence relation. |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1764 |
It also includes automation for transporting definitions and theorems. |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1765 |
It can automatically produce definitions and theorems on the quotient type, |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1766 |
given the corresponding constants and facts on the raw type. |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1767 |
|
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1768 |
\begin{matharray}{rcl} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1769 |
\indexdef{HOL}{command}{quotient\_type}\hypertarget{command.HOL.quotient-type}{\hyperlink{command.HOL.quotient-type}{\mbox{\isa{\isacommand{quotient{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\ |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1770 |
\indexdef{HOL}{command}{quotient\_definition}\hypertarget{command.HOL.quotient-definition}{\hyperlink{command.HOL.quotient-definition}{\mbox{\isa{\isacommand{quotient{\isaliteral{5F}{\isacharunderscore}}definition}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\ |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1771 |
\indexdef{HOL}{command}{print\_quotmaps}\hypertarget{command.HOL.print-quotmaps}{\hyperlink{command.HOL.print-quotmaps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}quotmaps}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}}\\ |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1772 |
\indexdef{HOL}{command}{print\_quotients}\hypertarget{command.HOL.print-quotients}{\hyperlink{command.HOL.print-quotients}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}quotients}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}}\\ |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1773 |
\indexdef{HOL}{command}{print\_quotconsts}\hypertarget{command.HOL.print-quotconsts}{\hyperlink{command.HOL.print-quotconsts}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}quotconsts}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}}\\ |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1774 |
\end{matharray} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1775 |
|
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1776 |
\begin{railoutput} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1777 |
\rail@begin{2}{} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1778 |
\rail@term{\hyperlink{command.HOL.quotient-type}{\mbox{\isa{\isacommand{quotient{\isaliteral{5F}{\isacharunderscore}}type}}}}}[] |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1779 |
\rail@plus |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1780 |
\rail@nont{\isa{spec}}[] |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1781 |
\rail@nextplus{1} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1782 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1783 |
\rail@endplus |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1784 |
\rail@end |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1785 |
\rail@begin{5}{\isa{spec}} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
bulwahn
parents:
43914
diff
changeset
|
1786 |
\rail@nont{\hyperlink{syntax.typespec}{\mbox{\isa{typespec}}}}[] |
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|
1787 |
\rail@bar |
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|
1788 |
\rail@nextbar{1} |
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|
1789 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
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|
1790 |
\rail@endbar |
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|
1791 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
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|
1792 |
\rail@cr{3} |
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|
1793 |
\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
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|
1794 |
\rail@term{\isa{{\isaliteral{2F}{\isacharslash}}}}[] |
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|
1795 |
\rail@bar |
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|
1796 |
\rail@nextbar{4} |
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|
1797 |
\rail@term{\isa{partial}}[] |
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|
1798 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
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|
1799 |
\rail@endbar |
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|
1800 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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|
1801 |
\rail@end |
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|
1802 |
\end{railoutput} |
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|
1803 |
|
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|
1804 |
|
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|
1805 |
\begin{railoutput} |
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|
1806 |
\rail@begin{4}{} |
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|
1807 |
\rail@term{\hyperlink{command.HOL.quotient-definition}{\mbox{\isa{\isacommand{quotient{\isaliteral{5F}{\isacharunderscore}}definition}}}}}[] |
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changeset
|
1808 |
\rail@bar |
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|
1809 |
\rail@nextbar{1} |
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|
1810 |
\rail@nont{\isa{constdecl}}[] |
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|
1811 |
\rail@endbar |
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parents:
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changeset
|
1812 |
\rail@bar |
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parents:
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changeset
|
1813 |
\rail@nextbar{1} |
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|
1814 |
\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
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|
1815 |
\rail@endbar |
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|
1816 |
\rail@cr{3} |
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|
1817 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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|
1818 |
\rail@term{\isa{is}}[] |
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|
1819 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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|
1820 |
\rail@end |
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|
1821 |
\rail@begin{2}{\isa{constdecl}} |
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|
1822 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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|
1823 |
\rail@bar |
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parents:
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changeset
|
1824 |
\rail@nextbar{1} |
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|
1825 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
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changeset
|
1826 |
\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
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parents:
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|
1827 |
\rail@endbar |
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rudimentary documentation of the quotient package in the isar reference manual
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parents:
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changeset
|
1828 |
\rail@bar |
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parents:
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changeset
|
1829 |
\rail@nextbar{1} |
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|
1830 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
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parents:
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|
1831 |
\rail@endbar |
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changeset
|
1832 |
\rail@end |
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|
1833 |
\end{railoutput} |
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changeset
|
1834 |
|
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
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changeset
|
1835 |
|
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
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changeset
|
1836 |
\begin{description} |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
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parents:
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diff
changeset
|
1837 |
|
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|
1838 |
\item \hyperlink{command.HOL.quotient-type}{\mbox{\isa{\isacommand{quotient{\isaliteral{5F}{\isacharunderscore}}type}}}} defines quotient types. |
b141d7a3d4e3
rudimentary documentation of the quotient package in the isar reference manual
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|
1839 |
|
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|
1840 |
\item \hyperlink{command.HOL.quotient-definition}{\mbox{\isa{\isacommand{quotient{\isaliteral{5F}{\isacharunderscore}}definition}}}} defines a constant on the quotient type. |
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|
1841 |
|
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|
1842 |
\item \hyperlink{command.HOL.print-quotmaps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}quotmaps}}}} prints quotient map functions. |
b141d7a3d4e3
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changeset
|
1843 |
|
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rudimentary documentation of the quotient package in the isar reference manual
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changeset
|
1844 |
\item \hyperlink{command.HOL.print-quotients}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}quotients}}}} prints quotients. |
b141d7a3d4e3
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|
1845 |
|
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|
1846 |
\item \hyperlink{command.HOL.print-quotconsts}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}quotconsts}}}} prints quotient constants. |
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|
1847 |
|
b141d7a3d4e3
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changeset
|
1848 |
\end{description}% |
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changeset
|
1849 |
\end{isamarkuptext}% |
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|
1850 |
\isamarkuptrue% |
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|
1851 |
% |
43994 | 1852 |
\isamarkupsection{Coercive subtyping% |
1853 |
} |
|
1854 |
\isamarkuptrue% |
|
1855 |
% |
|
1856 |
\begin{isamarkuptext}% |
|
1857 |
\begin{matharray}{rcl} |
|
1858 |
\indexdef{HOL}{attribute}{coercion}\hypertarget{attribute.HOL.coercion}{\hyperlink{attribute.HOL.coercion}{\mbox{\isa{coercion}}}} & : & \isa{attribute} \\ |
|
1859 |
\indexdef{HOL}{attribute}{coercion\_enabled}\hypertarget{attribute.HOL.coercion-enabled}{\hyperlink{attribute.HOL.coercion-enabled}{\mbox{\isa{coercion{\isaliteral{5F}{\isacharunderscore}}enabled}}}} & : & \isa{attribute} \\ |
|
1860 |
\indexdef{HOL}{attribute}{coercion\_map}\hypertarget{attribute.HOL.coercion-map}{\hyperlink{attribute.HOL.coercion-map}{\mbox{\isa{coercion{\isaliteral{5F}{\isacharunderscore}}map}}}} & : & \isa{attribute} \\ |
|
1861 |
\end{matharray} |
|
1862 |
||
1863 |
\begin{railoutput} |
|
1864 |
\rail@begin{2}{} |
|
1865 |
\rail@term{\hyperlink{attribute.HOL.coercion}{\mbox{\isa{coercion}}}}[] |
|
1866 |
\rail@bar |
|
1867 |
\rail@nextbar{1} |
|
1868 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
|
1869 |
\rail@endbar |
|
1870 |
\rail@end |
|
1871 |
\end{railoutput} |
|
1872 |
||
1873 |
\begin{railoutput} |
|
1874 |
\rail@begin{2}{} |
|
1875 |
\rail@term{\hyperlink{attribute.HOL.coercion-map}{\mbox{\isa{coercion{\isaliteral{5F}{\isacharunderscore}}map}}}}[] |
|
1876 |
\rail@bar |
|
1877 |
\rail@nextbar{1} |
|
1878 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
|
1879 |
\rail@endbar |
|
1880 |
\rail@end |
|
1881 |
\end{railoutput} |
|
1882 |
||
1883 |
||
1884 |
Coercive subtyping allows the user to omit explicit type conversions, |
|
1885 |
also called \emph{coercions}. Type inference will add them as |
|
1886 |
necessary when parsing a term. See |
|
1887 |
\cite{traytel-berghofer-nipkow-2011} for details. |
|
1888 |
||
1889 |
\begin{description} |
|
1890 |
||
1891 |
\item \hyperlink{attribute.HOL.coercion}{\mbox{\isa{coercion}}}~\isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{22}{\isachardoublequote}}} registers a new |
|
1892 |
coercion function \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} where \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} are nullary type constructors. Coercions are |
|
1893 |
composed by the inference algorithm if needed. Note that the type |
|
1894 |
inference algorithm is complete only if the registered coercions form |
|
1895 |
a lattice. |
|
1896 |
||
1897 |
||
1898 |
\item \hyperlink{attribute.HOL.coercion-map}{\mbox{\isa{coercion{\isaliteral{5F}{\isacharunderscore}}map}}}~\isa{{\isaliteral{22}{\isachardoublequote}}map{\isaliteral{22}{\isachardoublequote}}} registers a new |
|
1899 |
map function to lift coercions through type constructors. The function |
|
1900 |
\isa{{\isaliteral{22}{\isachardoublequote}}map{\isaliteral{22}{\isachardoublequote}}} must conform to the following type pattern |
|
1901 |
||
1902 |
\begin{matharray}{lll} |
|
1903 |
\isa{{\isaliteral{22}{\isachardoublequote}}map{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & |
|
1904 |
\isa{{\isaliteral{22}{\isachardoublequote}}f\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ f\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1905 |
\end{matharray} |
|
1906 |
||
1907 |
where \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{22}{\isachardoublequote}}} is a type constructor and \isa{{\isaliteral{22}{\isachardoublequote}}f\isaliteral{5C3C5E697375623E}{}\isactrlisub i{\isaliteral{22}{\isachardoublequote}}} is of |
|
1908 |
type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i{\isaliteral{22}{\isachardoublequote}}} or |
|
1909 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i{\isaliteral{22}{\isachardoublequote}}}. |
|
1910 |
Registering a map function overwrites any existing map function for |
|
1911 |
this particular type constructor. |
|
1912 |
||
1913 |
||
1914 |
\item \hyperlink{attribute.HOL.coercion-enabled}{\mbox{\isa{coercion{\isaliteral{5F}{\isacharunderscore}}enabled}}} enables the coercion |
|
1915 |
inference algorithm. |
|
1916 |
||
1917 |
\end{description}% |
|
1918 |
\end{isamarkuptext}% |
|
1919 |
\isamarkuptrue% |
|
1920 |
% |
|
26849 | 1921 |
\isamarkupsection{Arithmetic proof support% |
1922 |
} |
|
1923 |
\isamarkuptrue% |
|
1924 |
% |
|
1925 |
\begin{isamarkuptext}% |
|
1926 |
\begin{matharray}{rcl} |
|
28788 | 1927 |
\indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{method} \\ |
30863 | 1928 |
\indexdef{HOL}{attribute}{arith}\hypertarget{attribute.HOL.arith}{\hyperlink{attribute.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{attribute} \\ |
40406 | 1929 |
\indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isaliteral{5F}{\isacharunderscore}}split}}}} & : & \isa{attribute} \\ |
26849 | 1930 |
\end{matharray} |
1931 |
||
26902 | 1932 |
The \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} method decides linear arithmetic problems |
26849 | 1933 |
(on types \isa{nat}, \isa{int}, \isa{real}). Any current |
1934 |
facts are inserted into the goal before running the procedure. |
|
1935 |
||
30863 | 1936 |
The \hyperlink{attribute.HOL.arith}{\mbox{\isa{arith}}} attribute declares facts that are |
1937 |
always supplied to the arithmetic provers implicitly. |
|
26849 | 1938 |
|
40406 | 1939 |
The \hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isaliteral{5F}{\isacharunderscore}}split}}} attribute declares case split |
30865 | 1940 |
rules to be expanded before \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} is invoked. |
30863 | 1941 |
|
1942 |
Note that a simpler (but faster) arithmetic prover is |
|
1943 |
already invoked by the Simplifier.% |
|
26849 | 1944 |
\end{isamarkuptext}% |
1945 |
\isamarkuptrue% |
|
1946 |
% |
|
30172 | 1947 |
\isamarkupsection{Intuitionistic proof search% |
1948 |
} |
|
1949 |
\isamarkuptrue% |
|
1950 |
% |
|
1951 |
\begin{isamarkuptext}% |
|
1952 |
\begin{matharray}{rcl} |
|
1953 |
\indexdef{HOL}{method}{iprover}\hypertarget{method.HOL.iprover}{\hyperlink{method.HOL.iprover}{\mbox{\isa{iprover}}}} & : & \isa{method} \\ |
|
1954 |
\end{matharray} |
|
1955 |
||
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1956 |
\begin{railoutput} |
42662 | 1957 |
\rail@begin{2}{} |
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1958 |
\rail@term{\hyperlink{method.HOL.iprover}{\mbox{\isa{iprover}}}}[] |
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1959 |
\rail@plus |
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|
1960 |
\rail@nextplus{1} |
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|
1961 |
\rail@cnont{\hyperlink{syntax.rulemod}{\mbox{\isa{rulemod}}}}[] |
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1962 |
\rail@endplus |
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|
1963 |
\rail@end |
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|
1964 |
\end{railoutput} |
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|
1965 |
|
30172 | 1966 |
|
1967 |
The \hyperlink{method.HOL.iprover}{\mbox{\isa{iprover}}} method performs intuitionistic proof |
|
1968 |
search, depending on specifically declared rules from the context, |
|
1969 |
or given as explicit arguments. Chained facts are inserted into the |
|
35613 | 1970 |
goal before commencing proof search. |
1971 |
||
30172 | 1972 |
Rules need to be classified as \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}}, |
1973 |
\hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}}, or \hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}}; here the |
|
40406 | 1974 |
``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' indicator refers to ``safe'' rules, which may be |
30172 | 1975 |
applied aggressively (without considering back-tracking later). |
40406 | 1976 |
Rules declared with ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' are ignored in proof search (the |
42626 | 1977 |
single-step \hyperlink{method.Pure.rule}{\mbox{\isa{rule}}} method still observes these). An |
30172 | 1978 |
explicit weight annotation may be given as well; otherwise the |
1979 |
number of rule premises will be taken into account here.% |
|
1980 |
\end{isamarkuptext}% |
|
1981 |
\isamarkuptrue% |
|
1982 |
% |
|
43578
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|
1983 |
\isamarkupsection{Model Elimination and Resolution% |
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|
1984 |
} |
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|
1985 |
\isamarkuptrue% |
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|
1986 |
% |
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|
1987 |
\begin{isamarkuptext}% |
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|
1988 |
\begin{matharray}{rcl} |
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|
1989 |
\indexdef{HOL}{method}{meson}\hypertarget{method.HOL.meson}{\hyperlink{method.HOL.meson}{\mbox{\isa{meson}}}} & : & \isa{method} \\ |
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|
1990 |
\indexdef{HOL}{method}{metis}\hypertarget{method.HOL.metis}{\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}} & : & \isa{method} \\ |
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|
1991 |
\end{matharray} |
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|
1992 |
|
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|
1993 |
\begin{railoutput} |
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|
1994 |
\rail@begin{2}{} |
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|
1995 |
\rail@term{\hyperlink{method.HOL.meson}{\mbox{\isa{meson}}}}[] |
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|
1996 |
\rail@bar |
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|
1997 |
\rail@nextbar{1} |
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|
1998 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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|
1999 |
\rail@endbar |
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|
2000 |
\rail@end |
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|
2001 |
\rail@begin{5}{} |
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|
2002 |
\rail@term{\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}}[] |
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|
2003 |
\rail@bar |
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|
2004 |
\rail@nextbar{1} |
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|
2005 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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|
2006 |
\rail@bar |
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|
2007 |
\rail@term{\isa{partial{\isaliteral{5F}{\isacharunderscore}}types}}[] |
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|
2008 |
\rail@nextbar{2} |
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|
2009 |
\rail@term{\isa{full{\isaliteral{5F}{\isacharunderscore}}types}}[] |
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|
2010 |
\rail@nextbar{3} |
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|
2011 |
\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}types}}[] |
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|
2012 |
\rail@nextbar{4} |
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|
2013 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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|
2014 |
\rail@endbar |
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|
2015 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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|
2016 |
\rail@endbar |
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|
2017 |
\rail@bar |
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|
2018 |
\rail@nextbar{1} |
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|
2019 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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|
2020 |
\rail@endbar |
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|
2021 |
\rail@end |
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|
2022 |
\end{railoutput} |
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|
2023 |
|
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|
2024 |
|
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|
2025 |
The \hyperlink{method.HOL.meson}{\mbox{\isa{meson}}} method implements Loveland's model elimination |
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|
2026 |
procedure \cite{loveland-78}. See \verb|~~/src/HOL/ex/Meson_Test.thy| for |
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|
2027 |
examples. |
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|
2028 |
|
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|
2029 |
The \hyperlink{method.HOL.metis}{\mbox{\isa{metis}}} method combines ordered resolution and ordered |
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|
2030 |
paramodulation to find first-order (or mildly higher-order) proofs. The first |
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|
2031 |
optional argument specifies a type encoding; see the Sledgehammer manual |
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|
2032 |
\cite{isabelle-sledgehammer} for details. The \verb|~~/src/HOL/Metis_Examples| directory contains several small theories |
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|
2033 |
developed to a large extent using Metis.% |
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|
2034 |
\end{isamarkuptext}% |
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|
2035 |
\isamarkuptrue% |
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|
2036 |
% |
30172 | 2037 |
\isamarkupsection{Coherent Logic% |
2038 |
} |
|
2039 |
\isamarkuptrue% |
|
2040 |
% |
|
2041 |
\begin{isamarkuptext}% |
|
2042 |
\begin{matharray}{rcl} |
|
2043 |
\indexdef{HOL}{method}{coherent}\hypertarget{method.HOL.coherent}{\hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}}} & : & \isa{method} \\ |
|
2044 |
\end{matharray} |
|
2045 |
||
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2046 |
\begin{railoutput} |
42662 | 2047 |
\rail@begin{2}{} |
42596
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|
2048 |
\rail@term{\hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}}}[] |
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|
2049 |
\rail@bar |
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|
2050 |
\rail@nextbar{1} |
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|
2051 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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|
2052 |
\rail@endbar |
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|
2053 |
\rail@end |
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|
2054 |
\end{railoutput} |
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|
2055 |
|
30172 | 2056 |
|
2057 |
The \hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}} method solves problems of |
|
2058 |
\emph{Coherent Logic} \cite{Bezem-Coquand:2005}, which covers |
|
2059 |
applications in confluence theory, lattice theory and projective |
|
40802 | 2060 |
geometry. See \verb|~~/src/HOL/ex/Coherent.thy| for some |
30172 | 2061 |
examples.% |
2062 |
\end{isamarkuptext}% |
|
2063 |
\isamarkuptrue% |
|
2064 |
% |
|
42215
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|
2065 |
\isamarkupsection{Proving propositions% |
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|
2066 |
} |
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|
2067 |
\isamarkuptrue% |
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|
2068 |
% |
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|
2069 |
\begin{isamarkuptext}% |
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|
2070 |
In addition to the standard proof methods, a number of diagnosis |
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|
2071 |
tools search for proofs and provide an Isar proof snippet on success. |
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|
2072 |
These tools are available via the following commands. |
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|
2073 |
|
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|
2074 |
\begin{matharray}{rcl} |
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|
2075 |
\indexdef{HOL}{command}{solve\_direct}\hypertarget{command.HOL.solve-direct}{\hyperlink{command.HOL.solve-direct}{\mbox{\isa{\isacommand{solve{\isaliteral{5F}{\isacharunderscore}}direct}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
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|
2076 |
\indexdef{HOL}{command}{try}\hypertarget{command.HOL.try}{\hyperlink{command.HOL.try}{\mbox{\isa{\isacommand{try}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
43040 | 2077 |
\indexdef{HOL}{command}{try\_methods}\hypertarget{command.HOL.try-methods}{\hyperlink{command.HOL.try-methods}{\mbox{\isa{\isacommand{try{\isaliteral{5F}{\isacharunderscore}}methods}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
42215
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|
2078 |
\indexdef{HOL}{command}{sledgehammer}\hypertarget{command.HOL.sledgehammer}{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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changeset
|
2079 |
\indexdef{HOL}{command}{sledgehammer\_params}\hypertarget{command.HOL.sledgehammer-params}{\hyperlink{command.HOL.sledgehammer-params}{\mbox{\isa{\isacommand{sledgehammer{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2080 |
\end{matharray} |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2081 |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2082 |
\begin{railoutput} |
43040 | 2083 |
\rail@begin{1}{} |
2084 |
\rail@term{\hyperlink{command.HOL.try}{\mbox{\isa{\isacommand{try}}}}}[] |
|
2085 |
\rail@end |
|
42662 | 2086 |
\rail@begin{6}{} |
43040 | 2087 |
\rail@term{\hyperlink{command.HOL.try-methods}{\mbox{\isa{\isacommand{try{\isaliteral{5F}{\isacharunderscore}}methods}}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2088 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2089 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2090 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2091 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2092 |
\rail@term{\isa{simp}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2093 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2094 |
\rail@term{\isa{intro}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2095 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2096 |
\rail@term{\isa{elim}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2097 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2098 |
\rail@term{\isa{dest}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2099 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2100 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2101 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2102 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2103 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2104 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2105 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2106 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2107 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2108 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2109 |
\rail@end |
42662 | 2110 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2111 |
\rail@term{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2112 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2113 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2114 |
\rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2115 |
\rail@nont{\isa{args}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2116 |
\rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2117 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2118 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2119 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2120 |
\rail@nont{\isa{facts}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2121 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2122 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2123 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2124 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2125 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2126 |
\rail@end |
42662 | 2127 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2128 |
\rail@term{\hyperlink{command.HOL.sledgehammer-params}{\mbox{\isa{\isacommand{sledgehammer{\isaliteral{5F}{\isacharunderscore}}params}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2129 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2130 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2131 |
\rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2132 |
\rail@nont{\isa{args}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2133 |
\rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2134 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2135 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2136 |
\rail@begin{2}{\isa{args}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2137 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2138 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2139 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2140 |
\rail@nont{\isa{value}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2141 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2142 |
\rail@cterm{\isa{{\isaliteral{2C}{\isacharcomma}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2143 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2144 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2145 |
\rail@begin{5}{\isa{facts}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2146 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2147 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2148 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2149 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2150 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2151 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2152 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2153 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2154 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2155 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2156 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2157 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2158 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2159 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2160 |
\rail@nextplus{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2161 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2162 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2163 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2164 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2165 |
\end{railoutput} |
43040 | 2166 |
% FIXME check args "value" |
42215
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2167 |
|
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2168 |
\begin{description} |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2169 |
|
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2170 |
\item \hyperlink{command.HOL.solve-direct}{\mbox{\isa{\isacommand{solve{\isaliteral{5F}{\isacharunderscore}}direct}}}} checks whether the current subgoals can |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2171 |
be solved directly by an existing theorem. Duplicate lemmas can be detected |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2172 |
in this way. |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2173 |
|
43040 | 2174 |
\item \hyperlink{command.HOL.try-methods}{\mbox{\isa{\isacommand{try{\isaliteral{5F}{\isacharunderscore}}methods}}}} attempts to prove a subgoal using a combination |
42215
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2175 |
of standard proof methods (\isa{auto}, \isa{simp}, \isa{blast}, etc.). |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2176 |
Additional facts supplied via \isa{{\isaliteral{22}{\isachardoublequote}}simp{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}intro{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}, |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2177 |
\isa{{\isaliteral{22}{\isachardoublequote}}elim{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}, and \isa{{\isaliteral{22}{\isachardoublequote}}dest{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} are passed to the appropriate proof |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2178 |
methods. |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2179 |
|
43914
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
43578
diff
changeset
|
2180 |
\item \hyperlink{command.HOL.try}{\mbox{\isa{\isacommand{try}}}} attempts to prove or disprove a subgoal |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
43578
diff
changeset
|
2181 |
using a combination of provers and disprovers (\isa{{\isaliteral{22}{\isachardoublequote}}solve{\isaliteral{5F}{\isacharunderscore}}direct{\isaliteral{22}{\isachardoublequote}}}, |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
43578
diff
changeset
|
2182 |
\isa{{\isaliteral{22}{\isachardoublequote}}quickcheck{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}try{\isaliteral{5F}{\isacharunderscore}}methods{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}sledgehammer{\isaliteral{22}{\isachardoublequote}}}, |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
43578
diff
changeset
|
2183 |
\isa{{\isaliteral{22}{\isachardoublequote}}nitpick{\isaliteral{22}{\isachardoublequote}}}). |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
43578
diff
changeset
|
2184 |
|
42215
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2185 |
\item \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}} attempts to prove a subgoal using external |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2186 |
automatic provers (resolution provers and SMT solvers). See the Sledgehammer |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2187 |
manual \cite{isabelle-sledgehammer} for details. |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2188 |
|
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
42123
diff
changeset
|
2189 |
\item \hyperlink{command.HOL.sledgehammer-params}{\mbox{\isa{\isacommand{sledgehammer{\isaliteral{5F}{\isacharunderscore}}params}}}} changes |
de9d43c427ae
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diff
changeset
|
2190 |
\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}} configuration options persistently. |
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parents:
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diff
changeset
|
2191 |
|
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2192 |
\end{description}% |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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diff
changeset
|
2193 |
\end{isamarkuptext}% |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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diff
changeset
|
2194 |
\isamarkuptrue% |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2195 |
% |
31913 | 2196 |
\isamarkupsection{Checking and refuting propositions% |
2197 |
} |
|
2198 |
\isamarkuptrue% |
|
2199 |
% |
|
2200 |
\begin{isamarkuptext}% |
|
2201 |
Identifying incorrect propositions usually involves evaluation of |
|
42215
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
42123
diff
changeset
|
2202 |
particular assignments and systematic counterexample search. This |
31913 | 2203 |
is supported by the following commands. |
2204 |
||
2205 |
\begin{matharray}{rcl} |
|
40406 | 2206 |
\indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
2207 |
\indexdef{HOL}{command}{quickcheck}\hypertarget{command.HOL.quickcheck}{\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
42215
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parents:
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diff
changeset
|
2208 |
\indexdef{HOL}{command}{refute}\hypertarget{command.HOL.refute}{\hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
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parents:
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diff
changeset
|
2209 |
\indexdef{HOL}{command}{nitpick}\hypertarget{command.HOL.nitpick}{\hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
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parents:
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diff
changeset
|
2210 |
\indexdef{HOL}{command}{quickcheck\_params}\hypertarget{command.HOL.quickcheck-params}{\hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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parents:
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diff
changeset
|
2211 |
\indexdef{HOL}{command}{refute\_params}\hypertarget{command.HOL.refute-params}{\hyperlink{command.HOL.refute-params}{\mbox{\isa{\isacommand{refute{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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parents:
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diff
changeset
|
2212 |
\indexdef{HOL}{command}{nitpick\_params}\hypertarget{command.HOL.nitpick-params}{\hyperlink{command.HOL.nitpick-params}{\mbox{\isa{\isacommand{nitpick{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} |
31913 | 2213 |
\end{matharray} |
2214 |
||
42596
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|
2215 |
\begin{railoutput} |
42662 | 2216 |
\rail@begin{2}{} |
42596
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|
2217 |
\rail@term{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}[] |
6c621a9d612a
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|
2218 |
\rail@bar |
6c621a9d612a
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parents:
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diff
changeset
|
2219 |
\rail@nextbar{1} |
6c621a9d612a
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parents:
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diff
changeset
|
2220 |
\rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[] |
6c621a9d612a
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parents:
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changeset
|
2221 |
\rail@nont{\isa{name}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2222 |
\rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
2223 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2224 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2225 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2226 |
\rail@nont{\isa{modes}}[] |
6c621a9d612a
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parents:
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diff
changeset
|
2227 |
\rail@endbar |
6c621a9d612a
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parents:
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diff
changeset
|
2228 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
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diff
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|
2229 |
\rail@end |
42662 | 2230 |
\rail@begin{3}{} |
42596
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wenzelm
parents:
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diff
changeset
|
2231 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2232 |
\rail@term{\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}}[] |
6c621a9d612a
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parents:
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diff
changeset
|
2233 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2234 |
\rail@term{\hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2235 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2236 |
\rail@term{\hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}}}[] |
6c621a9d612a
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wenzelm
parents:
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diff
changeset
|
2237 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2238 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2239 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2240 |
\rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2241 |
\rail@nont{\isa{args}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2242 |
\rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2243 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2244 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2245 |
\rail@nextbar{1} |
6c621a9d612a
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parents:
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diff
changeset
|
2246 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
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parents:
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diff
changeset
|
2247 |
\rail@endbar |
6c621a9d612a
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parents:
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diff
changeset
|
2248 |
\rail@end |
42662 | 2249 |
\rail@begin{3}{} |
42596
6c621a9d612a
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parents:
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diff
changeset
|
2250 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2251 |
\rail@term{\hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2252 |
\rail@nextbar{1} |
6c621a9d612a
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parents:
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diff
changeset
|
2253 |
\rail@term{\hyperlink{command.HOL.refute-params}{\mbox{\isa{\isacommand{refute{\isaliteral{5F}{\isacharunderscore}}params}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2254 |
\rail@nextbar{2} |
6c621a9d612a
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parents:
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diff
changeset
|
2255 |
\rail@term{\hyperlink{command.HOL.nitpick-params}{\mbox{\isa{\isacommand{nitpick{\isaliteral{5F}{\isacharunderscore}}params}}}}}[] |
6c621a9d612a
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parents:
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diff
changeset
|
2256 |
\rail@endbar |
6c621a9d612a
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parents:
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diff
changeset
|
2257 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2258 |
\rail@nextbar{1} |
6c621a9d612a
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parents:
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diff
changeset
|
2259 |
\rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[] |
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changeset
|
2260 |
\rail@nont{\isa{args}}[] |
6c621a9d612a
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parents:
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changeset
|
2261 |
\rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[] |
6c621a9d612a
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parents:
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changeset
|
2262 |
\rail@endbar |
6c621a9d612a
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parents:
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changeset
|
2263 |
\rail@end |
6c621a9d612a
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parents:
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changeset
|
2264 |
\rail@begin{2}{\isa{modes}} |
6c621a9d612a
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diff
changeset
|
2265 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
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diff
changeset
|
2266 |
\rail@plus |
6c621a9d612a
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parents:
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diff
changeset
|
2267 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
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changeset
|
2268 |
\rail@nextplus{1} |
6c621a9d612a
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parents:
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diff
changeset
|
2269 |
\rail@endplus |
6c621a9d612a
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parents:
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changeset
|
2270 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
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parents:
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diff
changeset
|
2271 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
2272 |
\rail@begin{2}{\isa{args}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2273 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
2274 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
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changeset
|
2275 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
2276 |
\rail@nont{\isa{value}}[] |
6c621a9d612a
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wenzelm
parents:
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diff
changeset
|
2277 |
\rail@nextplus{1} |
6c621a9d612a
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changeset
|
2278 |
\rail@cterm{\isa{{\isaliteral{2C}{\isacharcomma}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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changeset
|
2279 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
2280 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
2281 |
\end{railoutput} |
6c621a9d612a
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|
2282 |
% FIXME check "value" |
31913 | 2283 |
|
2284 |
\begin{description} |
|
2285 |
||
2286 |
\item \hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t} evaluates and prints a |
|
2287 |
term; optionally \isa{modes} can be specified, which are |
|
42926 | 2288 |
appended to the current print mode; see \secref{sec:print-modes}. |
31913 | 2289 |
Internally, the evaluation is performed by registered evaluators, |
2290 |
which are invoked sequentially until a result is returned. |
|
2291 |
Alternatively a specific evaluator can be selected using square |
|
37444 | 2292 |
brackets; typical evaluators use the current set of code equations |
42926 | 2293 |
to normalize and include \isa{simp} for fully symbolic |
2294 |
evaluation using the simplifier, \isa{nbe} for |
|
2295 |
\emph{normalization by evaluation} and \emph{code} for code |
|
2296 |
generation in SML. |
|
31913 | 2297 |
|
2298 |
\item \hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}} tests the current goal for |
|
42215
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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changeset
|
2299 |
counterexamples using a series of assignments for its |
31913 | 2300 |
free variables; by default the first subgoal is tested, an other |
2301 |
can be selected explicitly using an optional goal index. |
|
40937 | 2302 |
Assignments can be chosen exhausting the search space upto a given |
43914
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
43578
diff
changeset
|
2303 |
size, or using a fixed number of random assignments in the search space, |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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changeset
|
2304 |
or exploring the search space symbolically using narrowing. |
40937 | 2305 |
By default, quickcheck uses exhaustive testing. |
31913 | 2306 |
A number of configuration options are supported for |
2307 |
\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}, notably: |
|
2308 |
||
2309 |
\begin{description} |
|
2310 |
||
43914
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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changeset
|
2311 |
\item[\isa{tester}] specifies which testing approach to apply. |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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changeset
|
2312 |
There are three testers, \isa{exhaustive}, |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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diff
changeset
|
2313 |
\isa{random}, and \isa{narrowing}. |
40937 | 2314 |
An unknown configuration option is treated as an argument to tester, |
2315 |
making \isa{{\isaliteral{22}{\isachardoublequote}}tester\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} optional. |
|
43914
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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diff
changeset
|
2316 |
When multiple testers are given, these are applied in parallel. |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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changeset
|
2317 |
If no tester is specified, quickcheck uses the testers that are |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
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diff
changeset
|
2318 |
set active, i.e., configurations |
64819f353c53
updating documentation about quickcheck; adding information about try
bulwahn
parents:
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diff
changeset
|
2319 |
\isa{quickcheck{\isaliteral{5F}{\isacharunderscore}}exhaustive{\isaliteral{5F}{\isacharunderscore}}active}, \isa{quickcheck{\isaliteral{5F}{\isacharunderscore}}random{\isaliteral{5F}{\isacharunderscore}}active}, |
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updating documentation about quickcheck; adding information about try
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|
2320 |
\isa{quickcheck{\isaliteral{5F}{\isacharunderscore}}narrowing{\isaliteral{5F}{\isacharunderscore}}active} are set to true. |
40254 | 2321 |
\item[\isa{size}] specifies the maximum size of the search space |
2322 |
for assignment values. |
|
2323 |
||
42123 | 2324 |
\item[\isa{eval}] takes a term or a list of terms and evaluates |
2325 |
these terms under the variable assignment found by quickcheck. |
|
2326 |
||
40254 | 2327 |
\item[\isa{iterations}] sets how many sets of assignments are |
2328 |
generated for each particular size. |
|
2329 |
||
40406 | 2330 |
\item[\isa{no{\isaliteral{5F}{\isacharunderscore}}assms}] specifies whether assumptions in |
40254 | 2331 |
structured proofs should be ignored. |
2332 |
||
2333 |
\item[\isa{timeout}] sets the time limit in seconds. |
|
31913 | 2334 |
|
40406 | 2335 |
\item[\isa{default{\isaliteral{5F}{\isacharunderscore}}type}] sets the type(s) generally used to |
40254 | 2336 |
instantiate type variables. |
2337 |
||
2338 |
\item[\isa{report}] if set quickcheck reports how many tests |
|
2339 |
fulfilled the preconditions. |
|
31913 | 2340 |
|
40254 | 2341 |
\item[\isa{quiet}] if not set quickcheck informs about the |
2342 |
current size for assignment values. |
|
2343 |
||
2344 |
\item[\isa{expect}] can be used to check if the user's |
|
40406 | 2345 |
expectation was met (\isa{no{\isaliteral{5F}{\isacharunderscore}}expectation}, \isa{no{\isaliteral{5F}{\isacharunderscore}}counterexample}, or \isa{counterexample}). |
35351
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|
2346 |
|
31913 | 2347 |
\end{description} |
2348 |
||
2349 |
These option can be given within square brackets. |
|
2350 |
||
42215
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|
2351 |
\item \hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}} changes |
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changeset
|
2352 |
\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}} configuration options persistently. |
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changeset
|
2353 |
|
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changeset
|
2354 |
\item \hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}} tests the current goal for |
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|
2355 |
counterexamples using a reduction to SAT. The following configuration |
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|
2356 |
options are supported: |
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|
2357 |
|
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|
2358 |
\begin{description} |
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changeset
|
2359 |
|
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|
2360 |
\item[\isa{minsize}] specifies the minimum size (cardinality) of the |
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|
2361 |
models to search for. |
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changeset
|
2362 |
|
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|
2363 |
\item[\isa{maxsize}] specifies the maximum size (cardinality) of the |
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changeset
|
2364 |
models to search for. Nonpositive values mean $\infty$. |
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diff
changeset
|
2365 |
|
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diff
changeset
|
2366 |
\item[\isa{maxvars}] specifies the maximum number of Boolean variables |
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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diff
changeset
|
2367 |
to use when transforming the term into a propositional formula. |
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parents:
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diff
changeset
|
2368 |
Nonpositive values mean $\infty$. |
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parents:
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diff
changeset
|
2369 |
|
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diff
changeset
|
2370 |
\item[\isa{satsolver}] specifies the SAT solver to use. |
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diff
changeset
|
2371 |
|
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diff
changeset
|
2372 |
\item[\isa{no{\isaliteral{5F}{\isacharunderscore}}assms}] specifies whether assumptions in |
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parents:
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diff
changeset
|
2373 |
structured proofs should be ignored. |
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2374 |
|
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diff
changeset
|
2375 |
\item[\isa{maxtime}] sets the time limit in seconds. |
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2376 |
|
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parents:
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diff
changeset
|
2377 |
\item[\isa{expect}] can be used to check if the user's |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2378 |
expectation was met (\isa{genuine}, \isa{potential}, |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2379 |
\isa{none}, or \isa{unknown}). |
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2380 |
|
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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diff
changeset
|
2381 |
\end{description} |
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changeset
|
2382 |
|
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2383 |
These option can be given within square brackets. |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2384 |
|
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diff
changeset
|
2385 |
\item \hyperlink{command.HOL.refute-params}{\mbox{\isa{\isacommand{refute{\isaliteral{5F}{\isacharunderscore}}params}}}} changes |
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diff
changeset
|
2386 |
\hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}} configuration options persistently. |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2387 |
|
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2388 |
\item \hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}} tests the current goal for counterexamples |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2389 |
using a reduction to first-order relational logic. See the Nitpick manual |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2390 |
\cite{isabelle-nitpick} for details. |
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document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
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parents:
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diff
changeset
|
2391 |
|
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parents:
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diff
changeset
|
2392 |
\item \hyperlink{command.HOL.nitpick-params}{\mbox{\isa{\isacommand{nitpick{\isaliteral{5F}{\isacharunderscore}}params}}}} changes |
de9d43c427ae
document "nitpick(_params)", "refute(_params)", "try", "sledgehammer(_params)", and "solve_direct"
blanchet
parents:
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diff
changeset
|
2393 |
\hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}} configuration options persistently. |
31913 | 2394 |
|
2395 |
\end{description}% |
|
2396 |
\end{isamarkuptext}% |
|
2397 |
\isamarkuptrue% |
|
2398 |
% |
|
28788 | 2399 |
\isamarkupsection{Unstructured case analysis and induction \label{sec:hol-induct-tac}% |
26849 | 2400 |
} |
2401 |
\isamarkuptrue% |
|
2402 |
% |
|
2403 |
\begin{isamarkuptext}% |
|
27124 | 2404 |
The following tools of Isabelle/HOL support cases analysis and |
2405 |
induction in unstructured tactic scripts; see also |
|
2406 |
\secref{sec:cases-induct} for proper Isar versions of similar ideas. |
|
26849 | 2407 |
|
2408 |
\begin{matharray}{rcl} |
|
40406 | 2409 |
\indexdef{HOL}{method}{case\_tac}\hypertarget{method.HOL.case-tac}{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
2410 |
\indexdef{HOL}{method}{induct\_tac}\hypertarget{method.HOL.induct-tac}{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
2411 |
\indexdef{HOL}{method}{ind\_cases}\hypertarget{method.HOL.ind-cases}{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
2412 |
\indexdef{HOL}{command}{inductive\_cases}\hypertarget{command.HOL.inductive-cases}{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
26849 | 2413 |
\end{matharray} |
2414 |
||
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changeset
|
2415 |
\begin{railoutput} |
42662 | 2416 |
\rail@begin{2}{} |
42596
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changeset
|
2417 |
\rail@term{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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changeset
|
2418 |
\rail@bar |
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changeset
|
2419 |
\rail@nextbar{1} |
42705 | 2420 |
\rail@nont{\hyperlink{syntax.goal-spec}{\mbox{\isa{goal{\isaliteral{5F}{\isacharunderscore}}spec}}}}[] |
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changeset
|
2421 |
\rail@endbar |
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changeset
|
2422 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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|
2423 |
\rail@bar |
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changeset
|
2424 |
\rail@nextbar{1} |
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changeset
|
2425 |
\rail@nont{\isa{rule}}[] |
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changeset
|
2426 |
\rail@endbar |
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changeset
|
2427 |
\rail@end |
42662 | 2428 |
\rail@begin{3}{} |
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changeset
|
2429 |
\rail@term{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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|
2430 |
\rail@bar |
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changeset
|
2431 |
\rail@nextbar{1} |
42705 | 2432 |
\rail@nont{\hyperlink{syntax.goal-spec}{\mbox{\isa{goal{\isaliteral{5F}{\isacharunderscore}}spec}}}}[] |
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changeset
|
2433 |
\rail@endbar |
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changeset
|
2434 |
\rail@bar |
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changeset
|
2435 |
\rail@nextbar{1} |
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changeset
|
2436 |
\rail@plus |
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changeset
|
2437 |
\rail@nont{\hyperlink{syntax.insts}{\mbox{\isa{insts}}}}[] |
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|
2438 |
\rail@nextplus{2} |
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|
2439 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
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changeset
|
2440 |
\rail@endplus |
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changeset
|
2441 |
\rail@endbar |
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parents:
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changeset
|
2442 |
\rail@bar |
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parents:
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changeset
|
2443 |
\rail@nextbar{1} |
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parents:
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changeset
|
2444 |
\rail@nont{\isa{rule}}[] |
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changeset
|
2445 |
\rail@endbar |
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changeset
|
2446 |
\rail@end |
42662 | 2447 |
\rail@begin{3}{} |
42596
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changeset
|
2448 |
\rail@term{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}}[] |
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|
2449 |
\rail@plus |
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modernized rail diagrams using @{rail} antiquotation;
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changeset
|
2450 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
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changeset
|
2451 |
\rail@nextplus{1} |
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parents:
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changeset
|
2452 |
\rail@endplus |
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parents:
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changeset
|
2453 |
\rail@bar |
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parents:
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changeset
|
2454 |
\rail@nextbar{1} |
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parents:
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changeset
|
2455 |
\rail@term{\isa{\isakeyword{for}}}[] |
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changeset
|
2456 |
\rail@plus |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@nextplus{2} |
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|
2459 |
\rail@endplus |
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|
2460 |
\rail@endbar |
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|
2461 |
\rail@end |
42662 | 2462 |
\rail@begin{3}{} |
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|
2463 |
\rail@term{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}}}[] |
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|
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\rail@plus |
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|
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\rail@bar |
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|
2466 |
\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
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|
2468 |
\rail@endbar |
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|
2469 |
\rail@plus |
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|
2470 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
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2471 |
\rail@nextplus{1} |
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|
2472 |
\rail@endplus |
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2473 |
\rail@nextplus{2} |
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2474 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
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|
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\rail@endplus |
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|
2476 |
\rail@end |
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|
2477 |
\rail@begin{1}{\isa{rule}} |
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\rail@term{\isa{rule}}[] |
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|
2479 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
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\rail@nont{\hyperlink{syntax.thmref}{\mbox{\isa{thmref}}}}[] |
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\rail@end |
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|
2482 |
\end{railoutput} |
26849 | 2483 |
|
2484 |
||
28788 | 2485 |
\begin{description} |
26849 | 2486 |
|
40406 | 2487 |
\item \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} admit |
28788 | 2488 |
to reason about inductive types. Rules are selected according to |
2489 |
the declarations by the \hyperlink{attribute.cases}{\mbox{\isa{cases}}} and \hyperlink{attribute.induct}{\mbox{\isa{induct}}} |
|
2490 |
attributes, cf.\ \secref{sec:cases-induct}. The \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} package already takes care of this. |
|
27124 | 2491 |
|
2492 |
These unstructured tactics feature both goal addressing and dynamic |
|
26849 | 2493 |
instantiation. Note that named rule cases are \emph{not} provided |
27124 | 2494 |
as would be by the proper \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} proof |
40406 | 2495 |
methods (see \secref{sec:cases-induct}). Unlike the \hyperlink{method.induct}{\mbox{\isa{induct}}} method, \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} does not handle structured rule |
27124 | 2496 |
statements, only the compact object-logic conclusion of the subgoal |
2497 |
being addressed. |
|
42123 | 2498 |
|
40406 | 2499 |
\item \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} and \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}} provide an interface to the internal \verb|mk_cases| operation. Rules are simplified in an unrestricted |
26861 | 2500 |
forward manner. |
26849 | 2501 |
|
40406 | 2502 |
While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} is a proof method to apply the |
2503 |
result immediately as elimination rules, \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}} provides case split theorems at the theory level |
|
2504 |
for later use. The \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} argument of the \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} method allows to specify a list of variables that should |
|
26849 | 2505 |
be generalized before applying the resulting rule. |
2506 |
||
28788 | 2507 |
\end{description}% |
26849 | 2508 |
\end{isamarkuptext}% |
2509 |
\isamarkuptrue% |
|
2510 |
% |
|
2511 |
\isamarkupsection{Executable code% |
|
2512 |
} |
|
2513 |
\isamarkuptrue% |
|
2514 |
% |
|
2515 |
\begin{isamarkuptext}% |
|
42627
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2516 |
For validation purposes, it is often useful to \emph{execute} |
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|
2517 |
specifications. In principle, execution could be simulated by |
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|
2518 |
Isabelle's inference kernel, i.e. by a combination of resolution and |
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|
2519 |
simplification. Unfortunately, this approach is rather inefficient. |
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|
2520 |
A more efficient way of executing specifications is to translate |
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|
2521 |
them into a functional programming language such as ML. |
26849 | 2522 |
|
42627
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|
2523 |
Isabelle provides two generic frameworks to support code generation |
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|
2524 |
from executable specifications. Isabelle/HOL instantiates these |
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|
2525 |
mechanisms in a way that is amenable to end-user applications.% |
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|
2526 |
\end{isamarkuptext}% |
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|
2527 |
\isamarkuptrue% |
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|
2528 |
% |
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|
2529 |
\isamarkupsubsection{The new code generator (F. Haftmann)% |
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|
2530 |
} |
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|
2531 |
\isamarkuptrue% |
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|
2532 |
% |
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|
2533 |
\begin{isamarkuptext}% |
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|
2534 |
This framework generates code from functional programs |
37422 | 2535 |
(including overloading using type classes) to SML \cite{SML}, OCaml |
38813 | 2536 |
\cite{OCaml}, Haskell \cite{haskell-revised-report} and Scala |
42627
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|
2537 |
\cite{scala-overview-tech-report}. Conceptually, code generation is |
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|
2538 |
split up in three steps: \emph{selection} of code theorems, |
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|
2539 |
\emph{translation} into an abstract executable view and |
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|
2540 |
\emph{serialization} to a specific \emph{target language}. |
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|
2541 |
Inductive specifications can be executed using the predicate |
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|
2542 |
compiler which operates within HOL. See \cite{isabelle-codegen} for |
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|
2543 |
an introduction. |
37422 | 2544 |
|
2545 |
\begin{matharray}{rcl} |
|
40406 | 2546 |
\indexdef{HOL}{command}{export\_code}\hypertarget{command.HOL.export-code}{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
37422 | 2547 |
\indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\ |
40406 | 2548 |
\indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
2549 |
\indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2550 |
\indexdef{HOL}{command}{print\_codesetup}\hypertarget{command.HOL.print-codesetup}{\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2551 |
\indexdef{HOL}{attribute}{code\_inline}\hypertarget{attribute.HOL.code-inline}{\hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}}} & : & \isa{attribute} \\ |
|
2552 |
\indexdef{HOL}{attribute}{code\_post}\hypertarget{attribute.HOL.code-post}{\hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}}} & : & \isa{attribute} \\ |
|
2553 |
\indexdef{HOL}{command}{print\_codeproc}\hypertarget{command.HOL.print-codeproc}{\hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2554 |
\indexdef{HOL}{command}{code\_thms}\hypertarget{command.HOL.code-thms}{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2555 |
\indexdef{HOL}{command}{code\_deps}\hypertarget{command.HOL.code-deps}{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2556 |
\indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2557 |
\indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2558 |
\indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2559 |
\indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2560 |
\indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2561 |
\indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2562 |
\indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2563 |
\indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
2564 |
\indexdef{HOL}{command}{code\_reflect}\hypertarget{command.HOL.code-reflect}{\hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} |
|
37422 | 2565 |
\end{matharray} |
2566 |
||
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2567 |
\begin{railoutput} |
42662 | 2568 |
\rail@begin{11}{} |
42596
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|
2569 |
\rail@term{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}}}[] |
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|
2570 |
\rail@plus |
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|
2571 |
\rail@nont{\isa{constexpr}}[] |
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2572 |
\rail@nextplus{1} |
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|
2573 |
\rail@endplus |
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|
2574 |
\rail@cr{3} |
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|
2575 |
\rail@bar |
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|
2576 |
\rail@nextbar{4} |
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|
2577 |
\rail@plus |
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2578 |
\rail@term{\isa{\isakeyword{in}}}[] |
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|
2579 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2580 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2581 |
\rail@nextbar{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2582 |
\rail@term{\isa{\isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2583 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2584 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2585 |
\rail@cr{7} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2586 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2587 |
\rail@nextbar{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2588 |
\rail@term{\isa{\isakeyword{file}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2589 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2590 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2591 |
\rail@nextbar{9} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2592 |
\rail@term{\isa{{\isaliteral{2D}{\isacharminus}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2593 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2594 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2595 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2596 |
\rail@nextbar{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2597 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2598 |
\rail@nont{\isa{args}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2599 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2600 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2601 |
\rail@nextplus{10} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2602 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2603 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2604 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2605 |
\rail@begin{1}{\isa{const}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2606 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2607 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2608 |
\rail@begin{3}{\isa{constexpr}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2609 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2610 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2611 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2612 |
\rail@term{\isa{name{\isaliteral{2E}{\isachardot}}{\isaliteral{5F}{\isacharunderscore}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2613 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2614 |
\rail@term{\isa{{\isaliteral{5F}{\isacharunderscore}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2615 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2616 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2617 |
\rail@begin{1}{\isa{typeconstructor}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2618 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2619 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2620 |
\rail@begin{1}{\isa{class}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2621 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2622 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2623 |
\rail@begin{4}{\isa{target}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2624 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2625 |
\rail@term{\isa{SML}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2626 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2627 |
\rail@term{\isa{OCaml}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2628 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2629 |
\rail@term{\isa{Haskell}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2630 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2631 |
\rail@term{\isa{Scala}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2632 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2633 |
\rail@end |
42662 | 2634 |
\rail@begin{4}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2635 |
\rail@term{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2636 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2637 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2638 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2639 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2640 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2641 |
\rail@term{\isa{abstype}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2642 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2643 |
\rail@term{\isa{abstract}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2644 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2645 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2646 |
\rail@end |
42662 | 2647 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2648 |
\rail@term{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2649 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2650 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2651 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2652 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2653 |
\rail@end |
42662 | 2654 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2655 |
\rail@term{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2656 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2657 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2658 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2659 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2660 |
\rail@end |
42662 | 2661 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2662 |
\rail@term{\hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2663 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2664 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2665 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2666 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2667 |
\rail@end |
42662 | 2668 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2669 |
\rail@term{\hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2670 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2671 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2672 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2673 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2674 |
\rail@end |
42662 | 2675 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2676 |
\rail@term{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2677 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2678 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2679 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2680 |
\rail@nont{\isa{constexpr}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2681 |
\rail@nextplus{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2682 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2683 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2684 |
\rail@end |
42662 | 2685 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2686 |
\rail@term{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2687 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2688 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2689 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2690 |
\rail@nont{\isa{constexpr}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2691 |
\rail@nextplus{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2692 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2693 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2694 |
\rail@end |
42662 | 2695 |
\rail@begin{7}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2696 |
\rail@term{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2697 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2698 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2699 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2700 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2701 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2702 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2703 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2704 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2705 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2706 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2707 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2708 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2709 |
\rail@nont{\isa{syntax}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2710 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2711 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2712 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2713 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2714 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2715 |
\rail@nextplus{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2716 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2717 |
\rail@end |
42662 | 2718 |
\rail@begin{7}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2719 |
\rail@term{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2720 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2721 |
\rail@nont{\isa{typeconstructor}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2722 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2723 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2724 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2725 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2726 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2727 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2728 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2729 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2730 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2731 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2732 |
\rail@nont{\isa{syntax}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2733 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2734 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2735 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2736 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2737 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2738 |
\rail@nextplus{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2739 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2740 |
\rail@end |
42662 | 2741 |
\rail@begin{9}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2742 |
\rail@term{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2743 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2744 |
\rail@nont{\isa{class}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2745 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2746 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2747 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2748 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2749 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2750 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2751 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2752 |
\rail@cr{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2753 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2754 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2755 |
\rail@nextbar{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2756 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2757 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2758 |
\rail@nextplus{7} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2759 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2760 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2761 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2762 |
\rail@nextplus{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2763 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2764 |
\rail@end |
42662 | 2765 |
\rail@begin{7}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2766 |
\rail@term{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2767 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2768 |
\rail@nont{\isa{typeconstructor}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2769 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2770 |
\rail@nont{\isa{class}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2771 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2772 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2773 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2774 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2775 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2776 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2777 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2778 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2779 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2780 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2781 |
\rail@term{\isa{{\isaliteral{2D}{\isacharminus}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2782 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2783 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2784 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2785 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2786 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2787 |
\rail@nextplus{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2788 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2789 |
\rail@end |
42662 | 2790 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2791 |
\rail@term{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2792 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2793 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2794 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2795 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2796 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2797 |
\rail@end |
42662 | 2798 |
\rail@begin{1}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2799 |
\rail@term{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2800 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2801 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2802 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2803 |
\rail@end |
42662 | 2804 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2805 |
\rail@term{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2806 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2807 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2808 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2809 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2810 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2811 |
\rail@term{\isa{{\isaliteral{2D}{\isacharminus}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2812 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2813 |
\rail@end |
42662 | 2814 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2815 |
\rail@term{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2816 |
\rail@nont{\isa{target}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2817 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2818 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2819 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2820 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2821 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2822 |
\rail@end |
42662 | 2823 |
\rail@begin{11}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2824 |
\rail@term{\hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2825 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2826 |
\rail@cr{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2827 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2828 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2829 |
\rail@term{\isa{\isakeyword{datatypes}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2830 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2831 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2832 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2833 |
\rail@term{\isa{{\isaliteral{5F}{\isacharunderscore}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2834 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2835 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2836 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2837 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2838 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2839 |
\rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2840 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2841 |
\rail@nextplus{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2842 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2843 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2844 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2845 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2846 |
\rail@cr{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2847 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2848 |
\rail@nextbar{9} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2849 |
\rail@term{\isa{\isakeyword{functions}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2850 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2851 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2852 |
\rail@nextplus{10} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2853 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2854 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2855 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2856 |
\rail@nextbar{9} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2857 |
\rail@term{\isa{\isakeyword{file}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2858 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2859 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2860 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2861 |
\rail@begin{4}{\isa{syntax}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2862 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2863 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2864 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2865 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2866 |
\rail@term{\isa{\isakeyword{infix}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2867 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2868 |
\rail@term{\isa{\isakeyword{infixl}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2869 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2870 |
\rail@term{\isa{\isakeyword{infixr}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2871 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2872 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2873 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2874 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2875 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
2876 |
\end{railoutput} |
37422 | 2877 |
|
2878 |
||
2879 |
\begin{description} |
|
2880 |
||
40406 | 2881 |
\item \hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}} generates code for a given list |
39608 | 2882 |
of constants in the specified target language(s). If no |
2883 |
serialization instruction is given, only abstract code is generated |
|
2884 |
internally. |
|
37422 | 2885 |
|
2886 |
Constants may be specified by giving them literally, referring to |
|
40406 | 2887 |
all executable contants within a certain theory by giving \isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}, or referring to \emph{all} executable constants currently |
2888 |
available by giving \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}. |
|
37422 | 2889 |
|
2890 |
By default, for each involved theory one corresponding name space |
|
2891 |
module is generated. Alternativly, a module name may be specified |
|
40406 | 2892 |
after the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}}}} keyword; then \emph{all} code is |
37422 | 2893 |
placed in this module. |
2894 |
||
39608 | 2895 |
For \emph{SML}, \emph{OCaml} and \emph{Scala} the file specification |
2896 |
refers to a single file; for \emph{Haskell}, it refers to a whole |
|
2897 |
directory, where code is generated in multiple files reflecting the |
|
2898 |
module hierarchy. Omitting the file specification denotes standard |
|
37749 | 2899 |
output. |
37422 | 2900 |
|
2901 |
Serializers take an optional list of arguments in parentheses. For |
|
40406 | 2902 |
\emph{SML} and \emph{OCaml}, ``\isa{no{\isaliteral{5F}{\isacharunderscore}}signatures}`` omits |
37422 | 2903 |
explicit module signatures. |
42123 | 2904 |
|
39608 | 2905 |
For \emph{Haskell} a module name prefix may be given using the |
40406 | 2906 |
``\isa{{\isaliteral{22}{\isachardoublequote}}root{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}'' argument; ``\isa{string{\isaliteral{5F}{\isacharunderscore}}classes}'' adds a |
39608 | 2907 |
``\verb|deriving (Read, Show)|'' clause to each appropriate |
2908 |
datatype declaration. |
|
37422 | 2909 |
|
2910 |
\item \hyperlink{attribute.HOL.code}{\mbox{\isa{code}}} explicitly selects (or with option |
|
40406 | 2911 |
``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' deselects) a code equation for code generation. |
38462
34d3de1254cd
formally document `code abstype` and `code abstract` attributes
haftmann
parents:
37820
diff
changeset
|
2912 |
Usually packages introducing code equations provide a reasonable |
40406 | 2913 |
default setup for selection. Variants \isa{{\isaliteral{22}{\isachardoublequote}}code\ abstype{\isaliteral{22}{\isachardoublequote}}} and |
2914 |
\isa{{\isaliteral{22}{\isachardoublequote}}code\ abstract{\isaliteral{22}{\isachardoublequote}}} declare abstract datatype certificates or |
|
38462
34d3de1254cd
formally document `code abstype` and `code abstract` attributes
haftmann
parents:
37820
diff
changeset
|
2915 |
code equations on abstract datatype representations respectively. |
37422 | 2916 |
|
40406 | 2917 |
\item \hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}} declares constants which are not |
39608 | 2918 |
required to have a definition by means of code equations; if needed |
2919 |
these are implemented by program abort instead. |
|
37422 | 2920 |
|
40406 | 2921 |
\item \hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}} specifies a constructor set |
37422 | 2922 |
for a logical type. |
2923 |
||
40406 | 2924 |
\item \hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}} gives an overview on |
37422 | 2925 |
selected code equations and code generator datatypes. |
2926 |
||
40406 | 2927 |
\item \hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}} declares (or with option |
2928 |
``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' removes) inlining theorems which are applied as |
|
39608 | 2929 |
rewrite rules to any code equation during preprocessing. |
37422 | 2930 |
|
40406 | 2931 |
\item \hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}} declares (or with option ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' removes) theorems which are applied as rewrite rules to any |
39608 | 2932 |
result of an evaluation. |
37422 | 2933 |
|
40406 | 2934 |
\item \hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}} prints the setup of the code |
39608 | 2935 |
generator preprocessor. |
37422 | 2936 |
|
40406 | 2937 |
\item \hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}} prints a list of theorems |
37422 | 2938 |
representing the corresponding program containing all given |
2939 |
constants after preprocessing. |
|
2940 |
||
40406 | 2941 |
\item \hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}} visualizes dependencies of |
37422 | 2942 |
theorems representing the corresponding program containing all given |
2943 |
constants after preprocessing. |
|
2944 |
||
40406 | 2945 |
\item \hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}} associates a list of constants |
37422 | 2946 |
with target-specific serializations; omitting a serialization |
2947 |
deletes an existing serialization. |
|
2948 |
||
40406 | 2949 |
\item \hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}} associates a list of type |
37422 | 2950 |
constructors with target-specific serializations; omitting a |
2951 |
serialization deletes an existing serialization. |
|
2952 |
||
40406 | 2953 |
\item \hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}} associates a list of classes |
37422 | 2954 |
with target-specific class names; omitting a serialization deletes |
2955 |
an existing serialization. This applies only to \emph{Haskell}. |
|
2956 |
||
40406 | 2957 |
\item \hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}} declares a list of type |
37422 | 2958 |
constructor / class instance relations as ``already present'' for a |
40406 | 2959 |
given target. Omitting a ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' deletes an existing |
37422 | 2960 |
``already present'' declaration. This applies only to |
2961 |
\emph{Haskell}. |
|
2962 |
||
40406 | 2963 |
\item \hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}} declares a list of names as |
37422 | 2964 |
reserved for a given target, preventing it to be shadowed by any |
2965 |
generated code. |
|
2966 |
||
40406 | 2967 |
\item \hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}} provides an auxiliary mechanism |
37422 | 2968 |
to generate monadic code for Haskell. |
2969 |
||
40406 | 2970 |
\item \hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}} adds arbitrary named content |
2971 |
(``include'') to generated code. A ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' as last argument |
|
37422 | 2972 |
will remove an already added ``include''. |
2973 |
||
40406 | 2974 |
\item \hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}} declares aliasings from one |
37422 | 2975 |
module name onto another. |
2976 |
||
40406 | 2977 |
\item \hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}} without a ``\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}'' |
39608 | 2978 |
argument compiles code into the system runtime environment and |
2979 |
modifies the code generator setup that future invocations of system |
|
40406 | 2980 |
runtime code generation referring to one of the ``\isa{{\isaliteral{22}{\isachardoublequote}}datatypes{\isaliteral{22}{\isachardoublequote}}}'' or ``\isa{{\isaliteral{22}{\isachardoublequote}}functions{\isaliteral{22}{\isachardoublequote}}}'' entities use these precompiled |
2981 |
entities. With a ``\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}'' argument, the corresponding code |
|
39608 | 2982 |
is generated into that specified file without modifying the code |
2983 |
generator setup. |
|
2984 |
||
42627
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2985 |
\end{description}% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2986 |
\end{isamarkuptext}% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2987 |
\isamarkuptrue% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2988 |
% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2989 |
\isamarkupsubsection{The old code generator (S. Berghofer)% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2990 |
} |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2991 |
\isamarkuptrue% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2992 |
% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2993 |
\begin{isamarkuptext}% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2994 |
This framework generates code from both functional and |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2995 |
relational programs to SML, as explained below. |
26849 | 2996 |
|
2997 |
\begin{matharray}{rcl} |
|
42627
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2998 |
\indexdef{}{command}{code\_module}\hypertarget{command.code-module}{\hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
2999 |
\indexdef{}{command}{code\_library}\hypertarget{command.code-library}{\hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3000 |
\indexdef{}{command}{consts\_code}\hypertarget{command.consts-code}{\hyperlink{command.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3001 |
\indexdef{}{command}{types\_code}\hypertarget{command.types-code}{\hyperlink{command.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
42626 | 3002 |
\indexdef{}{attribute}{code}\hypertarget{attribute.code}{\hyperlink{attribute.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\ |
26849 | 3003 |
\end{matharray} |
3004 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3005 |
\begin{railoutput} |
42662 | 3006 |
\rail@begin{11}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3007 |
\rail@bar |
42627
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3008 |
\rail@term{\hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3009 |
\rail@nextbar{1} |
42627
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3010 |
\rail@term{\hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3011 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3012 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3013 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3014 |
\rail@nont{\isa{modespec}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3015 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3016 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3017 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3018 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3019 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3020 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3021 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3022 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3023 |
\rail@term{\isa{\isakeyword{file}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3024 |
\rail@nont{\isa{name}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3025 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3026 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3027 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3028 |
\rail@term{\isa{\isakeyword{imports}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3029 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3030 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3031 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3032 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3033 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3034 |
\rail@cr{7} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3035 |
\rail@term{\isa{\isakeyword{contains}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3036 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3037 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3038 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3039 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3040 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3041 |
\rail@nextplus{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3042 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3043 |
\rail@nextbar{9} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3044 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3045 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3046 |
\rail@nextplus{10} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3047 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3048 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3049 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3050 |
\rail@begin{2}{\isa{modespec}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3051 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3052 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3053 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3054 |
\rail@cnont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3055 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3056 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3057 |
\rail@end |
42662 | 3058 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3059 |
\rail@term{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3060 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3061 |
\rail@nont{\isa{codespec}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3062 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3063 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3064 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3065 |
\rail@begin{2}{\isa{codespec}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3066 |
\rail@nont{\isa{const}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3067 |
\rail@nont{\isa{template}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3068 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3069 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3070 |
\rail@nont{\isa{attachment}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3071 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3072 |
\rail@end |
42662 | 3073 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3074 |
\rail@term{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3075 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3076 |
\rail@nont{\isa{tycodespec}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3077 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3078 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3079 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3080 |
\rail@begin{2}{\isa{tycodespec}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3081 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3082 |
\rail@nont{\isa{template}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3083 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3084 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3085 |
\rail@nont{\isa{attachment}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3086 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3087 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3088 |
\rail@begin{1}{\isa{const}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3089 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3090 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3091 |
\rail@begin{1}{\isa{template}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3092 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3093 |
\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3094 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3095 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3096 |
\rail@begin{2}{\isa{attachment}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3097 |
\rail@term{\isa{attach}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3098 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3099 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3100 |
\rail@nont{\isa{modespec}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3101 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3102 |
\rail@term{\isa{{\isaliteral{7B}{\isacharbraceleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3103 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3104 |
\rail@term{\isa{{\isaliteral{7D}{\isacharbraceright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3105 |
\rail@end |
42662 | 3106 |
\rail@begin{2}{} |
42626 | 3107 |
\rail@term{\hyperlink{attribute.code}{\mbox{\isa{code}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3108 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3109 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3110 |
\rail@nont{\isa{name}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3111 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3112 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3113 |
\end{railoutput}% |
26849 | 3114 |
\end{isamarkuptext}% |
3115 |
\isamarkuptrue% |
|
3116 |
% |
|
42627
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3117 |
\isamarkupsubsubsection{Invoking the code generator% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3118 |
} |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3119 |
\isamarkuptrue% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3120 |
% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3121 |
\begin{isamarkuptext}% |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3122 |
The code generator is invoked via the \hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}} |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3123 |
and \hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}} commands, which correspond to |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3124 |
\emph{incremental} and \emph{modular} code generation, respectively. |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3125 |
|
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3126 |
\begin{description} |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3127 |
|
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3128 |
\item [Modular] For each theory, an ML structure is generated, |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3129 |
containing the code generated from the constants defined in this |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3130 |
theory. |
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|
3131 |
|
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|
3132 |
\item [Incremental] All the generated code is emitted into the same |
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|
3133 |
structure. This structure may import code from previously generated |
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|
3134 |
structures, which can be specified via \hyperlink{keyword.imports}{\mbox{\isa{\isakeyword{imports}}}}. |
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|
3135 |
Moreover, the generated structure may also be referred to in later |
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|
3136 |
invocations of the code generator. |
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changeset
|
3137 |
|
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|
3138 |
\end{description} |
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changeset
|
3139 |
|
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|
3140 |
After the \hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}} and \hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}} |
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|
3141 |
keywords, the user may specify an optional list of ``modes'' in |
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|
3142 |
parentheses. These can be used to instruct the code generator to |
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|
3143 |
emit additional code for special purposes, e.g.\ functions for |
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|
3144 |
converting elements of generated datatypes to Isabelle terms, or |
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|
3145 |
test data generators. The list of modes is followed by a module |
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|
3146 |
name. The module name is optional for modular code generation, but |
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|
3147 |
must be specified for incremental code generation. |
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changeset
|
3148 |
|
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|
3149 |
The code can either be written to a file, in which case a file name |
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|
3150 |
has to be specified after the \hyperlink{keyword.file}{\mbox{\isa{\isakeyword{file}}}} keyword, or be loaded |
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|
3151 |
directly into Isabelle's ML environment. In the latter case, the |
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|
3152 |
\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}} theory command can be used to inspect the results |
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|
3153 |
interactively, for example. |
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|
3154 |
|
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|
3155 |
The terms from which to generate code can be specified after the |
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|
3156 |
\hyperlink{keyword.contains}{\mbox{\isa{\isakeyword{contains}}}} keyword, either as a list of bindings, or just |
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|
3157 |
as a list of terms. In the latter case, the code generator just |
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|
3158 |
produces code for all constants and types occuring in the term, but |
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|
3159 |
does not bind the compiled terms to ML identifiers. |
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changeset
|
3160 |
|
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|
3161 |
Here is an example:% |
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|
3162 |
\end{isamarkuptext}% |
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|
3163 |
\isamarkuptrue% |
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|
3164 |
\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}\isamarkupfalse% |
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|
3165 |
\ Test\isanewline |
42652 | 3166 |
\isakeyword{contains}\ test\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}foldl\ op\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{4}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}% |
42627
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|
3167 |
\begin{isamarkuptext}% |
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|
3168 |
\noindent This binds the result of compiling the given term to |
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|
3169 |
the ML identifier \verb|Test.test|.% |
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|
3170 |
\end{isamarkuptext}% |
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|
3171 |
\isamarkuptrue% |
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changeset
|
3172 |
% |
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changeset
|
3173 |
\isadelimML |
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changeset
|
3174 |
% |
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changeset
|
3175 |
\endisadelimML |
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changeset
|
3176 |
% |
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changeset
|
3177 |
\isatagML |
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|
3178 |
\isacommand{ML}\isamarkupfalse% |
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|
3179 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ % |
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|
3180 |
\isaantiq |
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|
3181 |
assert{}% |
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changeset
|
3182 |
\endisaantiq |
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|
3183 |
\ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{2E}{\isachardot}}test\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}% |
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|
3184 |
\endisatagML |
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|
3185 |
{\isafoldML}% |
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changeset
|
3186 |
% |
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|
3187 |
\isadelimML |
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|
3188 |
% |
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|
3189 |
\endisadelimML |
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|
3190 |
% |
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|
3191 |
\isamarkupsubsubsection{Configuring the code generator% |
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|
3192 |
} |
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|
3193 |
\isamarkuptrue% |
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|
3194 |
% |
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|
3195 |
\begin{isamarkuptext}% |
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|
3196 |
When generating code for a complex term, the code generator |
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|
3197 |
recursively calls itself for all subterms. When it arrives at a |
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|
3198 |
constant, the default strategy of the code generator is to look up |
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|
3199 |
its definition and try to generate code for it. Constants which |
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|
3200 |
have no definitions that are immediately executable, may be |
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|
3201 |
associated with a piece of ML code manually using the \indexref{}{command}{consts\_code}\hyperlink{command.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}} command. It takes a list whose elements consist of a |
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|
3202 |
constant (given in usual term syntax -- an explicit type constraint |
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|
3203 |
accounts for overloading), and a mixfix template describing the ML |
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|
3204 |
code. The latter is very much the same as the mixfix templates used |
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|
3205 |
when declaring new constants. The most notable difference is that |
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|
3206 |
terms may be included in the ML template using antiquotation |
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|
3207 |
brackets \verb|{|\verb|*|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{22}{\isachardoublequote}}}~\verb|*|\verb|}|. |
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changeset
|
3208 |
|
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|
3209 |
A similar mechanism is available for types: \indexref{}{command}{types\_code}\hyperlink{command.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}} associates type constructors with specific ML code. |
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changeset
|
3210 |
|
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|
3211 |
For example, the following declarations copied from \verb|~~/src/HOL/Product_Type.thy| describe how the product type of |
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|
3212 |
Isabelle/HOL should be compiled to ML.% |
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|
3213 |
\end{isamarkuptext}% |
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|
3214 |
\isamarkuptrue% |
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|
3215 |
\isacommand{typedecl}\isamarkupfalse% |
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changeset
|
3216 |
\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ prod\isanewline |
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changeset
|
3217 |
\isacommand{consts}\isamarkupfalse% |
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|
3218 |
\ Pair\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ prod{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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changeset
|
3219 |
\isanewline |
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|
3220 |
\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse% |
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|
3221 |
\ prod\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline |
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changeset
|
3222 |
\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse% |
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|
3223 |
\ Pair\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}% |
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changeset
|
3224 |
\begin{isamarkuptext}% |
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changeset
|
3225 |
Sometimes, the code associated with a constant or type may |
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|
3226 |
need to refer to auxiliary functions, which have to be emitted when |
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|
3227 |
the constant is used. Code for such auxiliary functions can be |
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|
3228 |
declared using \hyperlink{keyword.attach}{\mbox{\isa{\isakeyword{attach}}}}. For example, the \isa{wfrec} |
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changeset
|
3229 |
function can be implemented as follows:% |
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changeset
|
3230 |
\end{isamarkuptext}% |
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changeset
|
3231 |
\isamarkuptrue% |
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changeset
|
3232 |
\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse% |
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|
3233 |
\ wfrec\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6D6F64756C653E}{\isasymmodule}}wfrec{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ \ \isanewline |
42652 | 3234 |
\isakeyword{attach}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ fun\ wfrec\ f\ x\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{28}{\isacharparenleft}}wfrec\ f{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{2A7D}{\isacharverbatimclose}}% |
42627
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3235 |
\begin{isamarkuptext}% |
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3236 |
If the code containing a call to \isa{wfrec} resides in an |
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|
3237 |
ML structure different from the one containing the function |
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|
3238 |
definition attached to \isa{wfrec}, the name of the ML structure |
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|
3239 |
(followed by a ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2E}{\isachardot}}{\isaliteral{22}{\isachardoublequote}}}'') is inserted in place of ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6D6F64756C653E}{\isasymmodule}}{\isaliteral{22}{\isachardoublequote}}}'' in the above template. The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' means that |
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3240 |
the code generator should ignore the first argument of \isa{wfrec}, i.e.\ the termination relation, which is usually not |
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|
3241 |
executable. |
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|
3242 |
|
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|
3243 |
\medskip Another possibility of configuring the code generator is to |
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|
3244 |
register theorems to be used for code generation. Theorems can be |
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|
3245 |
registered via the \hyperlink{attribute.code}{\mbox{\isa{code}}} attribute. It takes an optional |
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|
3246 |
name as an argument, which indicates the format of the |
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|
3247 |
theorem. Currently supported formats are equations (this is the |
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|
3248 |
default when no name is specified) and horn clauses (this is |
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|
3249 |
indicated by the name \texttt{ind}). The left-hand sides of |
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|
3250 |
equations may only contain constructors and distinct variables, |
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|
3251 |
whereas horn clauses must have the same format as introduction rules |
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|
3252 |
of inductive definitions. |
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3253 |
|
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|
3254 |
The following example specifies three equations from which to |
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3255 |
generate code for \isa{{\isaliteral{22}{\isachardoublequote}}op\ {\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}} on natural numbers (see also |
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|
3256 |
\verb|~~/src/HOL/Nat.thy|).% |
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|
3257 |
\end{isamarkuptext}% |
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|
3258 |
\isamarkuptrue% |
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|
3259 |
\isacommand{lemma}\isamarkupfalse% |
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|
3260 |
\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}Suc\ m\ {\isaliteral{3C}{\isacharless}}\ Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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|
3261 |
\ \ \isakeyword{and}\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
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|
3262 |
\ \ \isakeyword{and}\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}% |
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|
3263 |
\isadelimproof |
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|
3264 |
\ % |
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|
3265 |
\endisadelimproof |
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|
3266 |
% |
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|
3267 |
\isatagproof |
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|
3268 |
\isacommand{by}\isamarkupfalse% |
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|
3269 |
\ simp{\isaliteral{5F}{\isacharunderscore}}all% |
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|
3270 |
\endisatagproof |
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|
3271 |
{\isafoldproof}% |
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|
3272 |
% |
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|
3273 |
\isadelimproof |
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|
3274 |
% |
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|
3275 |
\endisadelimproof |
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|
3276 |
% |
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|
3277 |
\isamarkupsubsubsection{Specific HOL code generators% |
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|
3278 |
} |
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|
3279 |
\isamarkuptrue% |
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|
3280 |
% |
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|
3281 |
\begin{isamarkuptext}% |
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|
3282 |
The basic code generator framework offered by Isabelle/Pure |
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|
3283 |
has already been extended with additional code generators for |
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|
3284 |
specific HOL constructs. These include datatypes, recursive |
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|
3285 |
functions and inductive relations. The code generator for inductive |
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|
3286 |
relations can handle expressions of the form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{22}{\isachardoublequote}}}, where \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{22}{\isachardoublequote}}} is an inductively defined relation. If at |
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|
3287 |
least one of the \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} is a dummy pattern ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}'', |
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|
3288 |
the above expression evaluates to a sequence of possible answers. If |
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|
3289 |
all of the \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} are proper terms, the expression evaluates |
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|
3290 |
to a boolean value. |
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|
3291 |
|
42652 | 3292 |
The following example demonstrates this for beta-reduction on lambda |
3293 |
terms (see also \verb|~~/src/HOL/Proofs/Lambda/Lambda.thy|).% |
|
3294 |
\end{isamarkuptext}% |
|
3295 |
\isamarkuptrue% |
|
3296 |
\isacommand{datatype}\isamarkupfalse% |
|
3297 |
\ dB\ {\isaliteral{3D}{\isacharequal}}\isanewline |
|
3298 |
\ \ \ \ Var\ nat\isanewline |
|
3299 |
\ \ {\isaliteral{7C}{\isacharbar}}\ App\ dB\ dB\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6465677265653E}{\isasymdegree}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{2}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline |
|
3300 |
\ \ {\isaliteral{7C}{\isacharbar}}\ Abs\ dB\isanewline |
|
3301 |
\isanewline |
|
3302 |
\isacommand{primrec}\isamarkupfalse% |
|
3303 |
\ lift\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}dB\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ dB{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3304 |
\isakeyword{where}\isanewline |
|
3305 |
\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}lift\ {\isaliteral{28}{\isacharparenleft}}Var\ i{\isaliteral{29}{\isacharparenright}}\ k\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ i\ {\isaliteral{3C}{\isacharless}}\ k\ then\ Var\ i\ else\ Var\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3306 |
\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}lift\ {\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ t{\isaliteral{29}{\isacharparenright}}\ k\ {\isaliteral{3D}{\isacharequal}}\ lift\ s\ k\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ lift\ t\ k{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3307 |
\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}lift\ {\isaliteral{28}{\isacharparenleft}}Abs\ s{\isaliteral{29}{\isacharparenright}}\ k\ {\isaliteral{3D}{\isacharequal}}\ Abs\ {\isaliteral{28}{\isacharparenleft}}lift\ s\ {\isaliteral{28}{\isacharparenleft}}k\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3308 |
\isanewline |
|
3309 |
\isacommand{primrec}\isamarkupfalse% |
|
3310 |
\ subst\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}dB\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ dB\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ dB{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{3}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline |
|
3311 |
\isakeyword{where}\isanewline |
|
3312 |
\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}Var\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{2F}{\isacharslash}}k{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline |
|
3313 |
\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ k\ {\isaliteral{3C}{\isacharless}}\ i\ then\ Var\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ else\ if\ i\ {\isaliteral{3D}{\isacharequal}}\ k\ then\ s\ else\ Var\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3314 |
\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ u{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{2F}{\isacharslash}}k{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{2F}{\isacharslash}}k{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ u{\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{2F}{\isacharslash}}k{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3315 |
\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}Abs\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{2F}{\isacharslash}}k{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ Abs\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{5B}{\isacharbrackleft}}lift\ s\ {\isadigit{0}}\ {\isaliteral{2F}{\isacharslash}}\ k{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3316 |
\isanewline |
|
3317 |
\isacommand{inductive}\isamarkupfalse% |
|
3318 |
\ beta\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}dB\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ dB\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline |
|
3319 |
\isakeyword{where}\isanewline |
|
3320 |
\ \ \ \ beta{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Abs\ s\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ t\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ s{\isaliteral{5B}{\isacharbrackleft}}t{\isaliteral{2F}{\isacharslash}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3321 |
\ \ {\isaliteral{7C}{\isacharbar}}\ appL{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ t\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ s\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ u\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ t\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ u{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3322 |
\ \ {\isaliteral{7C}{\isacharbar}}\ appR{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ t\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ u\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ s\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ u\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ t{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3323 |
\ \ {\isaliteral{7C}{\isacharbar}}\ abs{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ t\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Abs\ s\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ Abs\ t{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3324 |
\isanewline |
|
3325 |
\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}\isamarkupfalse% |
|
3326 |
\ Test\isanewline |
|
3327 |
\isakeyword{contains}\isanewline |
|
3328 |
\ \ test{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}Abs\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ Var\ {\isadigit{0}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ Var\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
|
3329 |
\ \ test{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}Abs\ {\isaliteral{28}{\isacharparenleft}}Abs\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isadigit{0}}\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ Var\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ {\isaliteral{28}{\isacharparenleft}}Abs\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6465677265653E}{\isasymdegree}}\ Var\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequoteclose}}% |
|
3330 |
\begin{isamarkuptext}% |
|
3331 |
In the above example, \verb|Test.test1| evaluates to a boolean, |
|
3332 |
whereas \verb|Test.test2| is a lazy sequence whose elements can be |
|
3333 |
inspected separately.% |
|
3334 |
\end{isamarkuptext}% |
|
3335 |
\isamarkuptrue% |
|
3336 |
% |
|
3337 |
\isadelimML |
|
3338 |
% |
|
3339 |
\endisadelimML |
|
3340 |
% |
|
3341 |
\isatagML |
|
3342 |
\isacommand{ML}\isamarkupfalse% |
|
3343 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ % |
|
3344 |
\isaantiq |
|
3345 |
assert{}% |
|
3346 |
\endisaantiq |
|
3347 |
\ Test{\isaliteral{2E}{\isachardot}}test{\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline |
|
3348 |
\isacommand{ML}\isamarkupfalse% |
|
3349 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ val\ results\ {\isaliteral{3D}{\isacharequal}}\ DSeq{\isaliteral{2E}{\isachardot}}list{\isaliteral{5F}{\isacharunderscore}}of\ Test{\isaliteral{2E}{\isachardot}}test{\isadigit{2}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline |
|
3350 |
\isacommand{ML}\isamarkupfalse% |
|
3351 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ % |
|
3352 |
\isaantiq |
|
3353 |
assert{}% |
|
3354 |
\endisaantiq |
|
3355 |
\ {\isaliteral{28}{\isacharparenleft}}length\ results\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}% |
|
3356 |
\endisatagML |
|
3357 |
{\isafoldML}% |
|
3358 |
% |
|
3359 |
\isadelimML |
|
3360 |
% |
|
3361 |
\endisadelimML |
|
3362 |
% |
|
3363 |
\begin{isamarkuptext}% |
|
3364 |
\medskip The theory underlying the HOL code generator is described |
|
42627
8749742785b8
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wenzelm
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diff
changeset
|
3365 |
more detailed in \cite{Berghofer-Nipkow:2002}. More examples that |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
42626
diff
changeset
|
3366 |
illustrate the usage of the code generator can be found e.g.\ in |
8749742785b8
moved material about old codegen to isar-ref manual;
wenzelm
parents:
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diff
changeset
|
3367 |
\verb|~~/src/HOL/MicroJava/J/JListExample.thy| and \verb|~~/src/HOL/MicroJava/JVM/JVMListExample.thy|.% |
8749742785b8
moved material about old codegen to isar-ref manual;
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changeset
|
3368 |
\end{isamarkuptext}% |
8749742785b8
moved material about old codegen to isar-ref manual;
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42626
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changeset
|
3369 |
\isamarkuptrue% |
8749742785b8
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changeset
|
3370 |
% |
27047 | 3371 |
\isamarkupsection{Definition by specification \label{sec:hol-specification}% |
3372 |
} |
|
3373 |
\isamarkuptrue% |
|
3374 |
% |
|
3375 |
\begin{isamarkuptext}% |
|
3376 |
\begin{matharray}{rcl} |
|
40406 | 3377 |
\indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
3378 |
\indexdef{HOL}{command}{ax\_specification}\hypertarget{command.HOL.ax-specification}{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
27047 | 3379 |
\end{matharray} |
3380 |
||
42596
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wenzelm
parents:
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changeset
|
3381 |
\begin{railoutput} |
42662 | 3382 |
\rail@begin{6}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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changeset
|
3383 |
\rail@bar |
6c621a9d612a
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changeset
|
3384 |
\rail@term{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}}[] |
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modernized rail diagrams using @{rail} antiquotation;
wenzelm
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changeset
|
3385 |
\rail@nextbar{1} |
6c621a9d612a
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wenzelm
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changeset
|
3386 |
\rail@term{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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diff
changeset
|
3387 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3388 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3389 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3390 |
\rail@nont{\isa{decl}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3391 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3392 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3393 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3394 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3395 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3396 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3397 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3398 |
\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3399 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3400 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3401 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3402 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3403 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3404 |
\rail@begin{2}{\isa{decl}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3405 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3406 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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changeset
|
3407 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
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changeset
|
3408 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3409 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3410 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3411 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3412 |
\rail@term{\isa{\isakeyword{overloaded}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3413 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3414 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3415 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3416 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3417 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
42215
diff
changeset
|
3418 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
3419 |
|
27047 | 3420 |
|
28788 | 3421 |
\begin{description} |
27047 | 3422 |
|
40406 | 3423 |
\item \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}decls\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} sets up a |
27047 | 3424 |
goal stating the existence of terms with the properties specified to |
3425 |
hold for the constants given in \isa{decls}. After finishing the |
|
3426 |
proof, the theory will be augmented with definitions for the given |
|
3427 |
constants, as well as with theorems stating the properties for these |
|
3428 |
constants. |
|
3429 |
||
40406 | 3430 |
\item \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}decls\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} sets up |
28788 | 3431 |
a goal stating the existence of terms with the properties specified |
3432 |
to hold for the constants given in \isa{decls}. After finishing |
|
3433 |
the proof, the theory will be augmented with axioms expressing the |
|
3434 |
properties given in the first place. |
|
27047 | 3435 |
|
28788 | 3436 |
\item \isa{decl} declares a constant to be defined by the |
27047 | 3437 |
specification given. The definition for the constant \isa{c} is |
40406 | 3438 |
bound to the name \isa{c{\isaliteral{5F}{\isacharunderscore}}def} unless a theorem name is given in |
27047 | 3439 |
the declaration. Overloaded constants should be declared as such. |
3440 |
||
28788 | 3441 |
\end{description} |
27047 | 3442 |
|
40406 | 3443 |
Whether to use \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} or \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}} is to some extent a matter of style. \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} introduces no new axioms, and so by |
3444 |
construction cannot introduce inconsistencies, whereas \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}} does introduce axioms, but only after the |
|
27047 | 3445 |
user has explicitly proven it to be safe. A practical issue must be |
3446 |
considered, though: After introducing two constants with the same |
|
3447 |
properties using \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}, one can prove |
|
3448 |
that the two constants are, in fact, equal. If this might be a |
|
40406 | 3449 |
problem, one should use \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}.% |
27047 | 3450 |
\end{isamarkuptext}% |
3451 |
\isamarkuptrue% |
|
3452 |
% |
|
26849 | 3453 |
\isadelimtheory |
3454 |
% |
|
3455 |
\endisadelimtheory |
|
3456 |
% |
|
3457 |
\isatagtheory |
|
26840 | 3458 |
\isacommand{end}\isamarkupfalse% |
3459 |
% |
|
3460 |
\endisatagtheory |
|
3461 |
{\isafoldtheory}% |
|
3462 |
% |
|
3463 |
\isadelimtheory |
|
3464 |
% |
|
3465 |
\endisadelimtheory |
|
26849 | 3466 |
\isanewline |
26840 | 3467 |
\end{isabellebody}% |
3468 |
%%% Local Variables: |
|
3469 |
%%% mode: latex |
|
3470 |
%%% TeX-master: "root" |
|
3471 |
%%% End: |