author | wenzelm |
Sun, 15 Apr 2012 13:21:13 +0200 | |
changeset 47483 | 3f704717a67f |
parent 47482 | a83b25e5bad3 |
child 47484 | e94cc23d434a |
permissions | -rw-r--r-- |
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\begin{isabellebody}% |
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\def\isabellecontext{Spec}% |
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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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\ Spec\isanewline |
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\isakeyword{imports}\ Base\ Main\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{Specifications% |
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} |
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\isamarkuptrue% |
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\begin{isamarkuptext}% |
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The Isabelle/Isar theory format integrates specifications and |
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proofs, supporting interactive development with unlimited undo |
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operation. There is an integrated document preparation system (see |
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\chref{ch:document-prep}), for typesetting formal developments |
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together with informal text. The resulting hyper-linked PDF |
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documents can be used both for WWW presentation and printed copies. |
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The Isar proof language (see \chref{ch:proofs}) is embedded into the |
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theory language as a proper sub-language. Proof mode is entered by |
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stating some \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}} or \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}} at the theory |
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level, and left again with the final conclusion (e.g.\ via \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}). Some theory specification mechanisms also require a proof, |
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such as \hyperlink{command.typedef}{\mbox{\isa{\isacommand{typedef}}}} in HOL, which demands non-emptiness of |
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the representing sets.% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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\isamarkupsection{Defining theories \label{sec:begin-thy}% |
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} |
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\isamarkuptrue% |
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\begin{isamarkuptext}% |
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\begin{matharray}{rcl} |
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\indexdef{}{command}{theory}\hypertarget{command.theory}{\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}toplevel\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\indexdef{global}{command}{end}\hypertarget{command.global.end}{\hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ toplevel{\isaliteral{22}{\isachardoublequote}}} \\ |
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\end{matharray} |
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Isabelle/Isar theories are defined via theory files, which may |
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contain both specifications and proofs; occasionally definitional |
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mechanisms also require some explicit proof. The theory body may be |
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sub-structured by means of \emph{local theory targets}, such as |
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\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}} and \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}. |
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The first proper command of a theory is \hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}, which |
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indicates imports of previous theories and optional dependencies on |
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other source files (usually in ML). Just preceding the initial |
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\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}} command there may be an optional \hyperlink{command.header}{\mbox{\isa{\isacommand{header}}}} declaration, which is only relevant to document |
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preparation: see also the other section markup commands in |
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\secref{sec:markup}. |
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A theory is concluded by a final \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} command, |
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one that does not belong to a local theory target. No further |
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commands may follow such a global \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}}, |
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although some user-interfaces might pretend that trailing input is |
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admissible. |
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\begin{railoutput} |
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\rail@begin{4}{} |
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\rail@term{\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}}[] |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@nont{\isa{imports}}[] |
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\rail@cr{2} |
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\rail@bar |
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\rail@nextbar{3} |
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\rail@nont{\isa{keywords}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{3} |
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\rail@nont{\isa{uses}}[] |
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\rail@endbar |
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\rail@term{\isa{\isakeyword{begin}}}[] |
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\rail@end |
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\rail@begin{2}{\isa{imports}} |
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\rail@term{\isa{\isakeyword{imports}}}[] |
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\rail@plus |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@nextplus{1} |
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\rail@endplus |
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\rail@end |
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\rail@begin{3}{\isa{keywords}} |
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\rail@term{\isa{\isakeyword{keywords}}}[] |
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\rail@plus |
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\rail@plus |
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\rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[] |
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\rail@nextplus{1} |
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\rail@endplus |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@nont{\hyperlink{syntax.tags}{\mbox{\isa{tags}}}}[] |
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\rail@endbar |
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\rail@nextplus{2} |
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\rail@cterm{\isa{\isakeyword{and}}}[] |
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\rail@endplus |
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\rail@end |
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\rail@begin{3}{\isa{uses}} |
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\rail@term{\isa{\isakeyword{uses}}}[] |
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\rail@plus |
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\rail@bar |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.parname}{\mbox{\isa{parname}}}}[] |
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\rail@endbar |
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\rail@nextplus{2} |
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\rail@endplus |
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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.theory}{\mbox{\isa{\isacommand{theory}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C494D504F5254533E}{\isasymIMPORTS}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} |
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starts a new theory \isa{A} based on the merge of existing |
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theories \isa{{\isaliteral{22}{\isachardoublequote}}B\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}. Due to the possibility to import more |
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than one ancestor, the resulting theory structure of an Isabelle |
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session forms a directed acyclic graph (DAG). Isabelle takes care |
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that sources contributing to the development graph are always |
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up-to-date: changed files are automatically rechecked whenever a |
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theory header specification is processed. |
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The optional \indexdef{}{keyword}{keywords}\hypertarget{keyword.keywords}{\hyperlink{keyword.keywords}{\mbox{\isa{\isakeyword{keywords}}}}} specification declares outer |
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syntax (\chref{ch:outer-syntax}) that is introduced in this theory |
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later on (rare in end-user applications). Both minor keywords and |
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major keywords of the Isar command language need to be specified, in |
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order to make parsing of proof documents work properly. Command |
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keywords need to be classified according to their structural role in |
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the formal text. Examples may be seen in Isabelle/HOL sources |
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itself, such as \hyperlink{keyword.keywords}{\mbox{\isa{\isakeyword{keywords}}}}~\verb|"typedef"| |
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\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ thy{\isaliteral{5F}{\isacharunderscore}}goal{\isaliteral{22}{\isachardoublequote}}} or \hyperlink{keyword.keywords}{\mbox{\isa{\isakeyword{keywords}}}}~\verb|"datatype"| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ thy{\isaliteral{5F}{\isacharunderscore}}decl{\isaliteral{22}{\isachardoublequote}}} for theory-level declarations |
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with and without proof, respectively. Additional \hyperlink{syntax.tags}{\mbox{\isa{tags}}} |
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provide defaults for document preparation (\secref{sec:tags}). |
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The optional \indexdef{}{keyword}{uses}\hypertarget{keyword.uses}{\hyperlink{keyword.uses}{\mbox{\isa{\isakeyword{uses}}}}} specification declares additional |
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dependencies on external files (notably ML sources). Files will be |
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loaded immediately (as ML), unless the name is parenthesized. The |
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latter case records a dependency that needs to be resolved later in |
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the text, usually via explicit \indexref{}{command}{use}\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}} for ML files; |
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other file formats require specific load commands defined by the |
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corresponding tools or packages. |
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\item \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} concludes the current theory |
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definition. Note that some other commands, e.g.\ local theory |
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targets \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}} or \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}} may involve a |
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\hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}} that needs to be matched by \hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}, according to the usual rules for nested blocks. |
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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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\isamarkupsection{Local theory targets \label{sec:target}% |
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} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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\begin{matharray}{rcll} |
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\indexdef{}{command}{context}\hypertarget{command.context}{\hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\indexdef{local}{command}{end}\hypertarget{command.local.end}{\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
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\end{matharray} |
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A local theory target is a context managed separately within the |
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enclosing theory. Contexts may introduce parameters (fixed |
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variables) and assumptions (hypotheses). Definitions and theorems |
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depending on the context may be added incrementally later on. |
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\emph{Named contexts} refer to locales (cf.\ \secref{sec:locale}) or |
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type classes (cf.\ \secref{sec:class}); the name ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' |
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signifies the global theory context. |
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\emph{Unnamed contexts} may introduce additional parameters and |
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assumptions, and results produced in the context are generalized |
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accordingly. Such auxiliary contexts may be nested within other |
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targets, like \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}, \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}, \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}, \hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}. |
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\begin{railoutput} |
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\rail@begin{3}{} |
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\rail@term{\hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}}[] |
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\rail@bar |
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\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
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\rail@nextbar{1} |
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\rail@plus |
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\rail@nont{\hyperlink{syntax.context-elem}{\mbox{\isa{context{\isaliteral{5F}{\isacharunderscore}}elem}}}}[] |
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\rail@nextplus{2} |
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\rail@endplus |
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\rail@endbar |
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\rail@term{\isa{\isakeyword{begin}}}[] |
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\rail@end |
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\rail@begin{1}{\indexdef{}{syntax}{target}\hypertarget{syntax.target}{\hyperlink{syntax.target}{\mbox{\isa{target}}}}} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@term{\isa{\isakeyword{in}}}[] |
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\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@end |
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\end{railoutput} |
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||
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\begin{description} |
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|
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\item \hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} opens a named |
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context, by recommencing an existing locale or class \isa{c}. |
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Note that locale and class definitions allow to include the |
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\hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}} keyword as well, in order to continue the local |
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theory immediately after the initial specification. |
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|
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\item \hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}elements\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} opens an |
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unnamed context, by extending the enclosing global or local theory |
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target by the given context elements (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C46495845533E}{\isasymFIXES}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}{\isaliteral{22}{\isachardoublequote}}} etc.). This means any results stemming from |
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definitions and proofs in the extended context will be exported into |
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the enclosing target by lifting over extra parameters and premises. |
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\item \hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}} concludes the current local theory, |
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according to the nesting of contexts. Note that a global \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} has a different meaning: it concludes the theory |
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itself (\secref{sec:begin-thy}). |
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|
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\item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}}\indexdef{}{keyword}{in}\hypertarget{keyword.in}{\hyperlink{keyword.in}{\mbox{\isa{\isakeyword{in}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} given after any |
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local theory command specifies an immediate target, e.g.\ |
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``\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C494E3E}{\isasymIN}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' or ``\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C494E3E}{\isasymIN}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}''. This works both in a local or |
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global theory context; the current target context will be suspended |
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for this command only. Note that ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C494E3E}{\isasymIN}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' will |
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always produce a global result independently of the current target |
235 |
context. |
|
236 |
||
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\end{description} |
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|
239 |
The exact meaning of results produced within a local theory context |
|
240 |
depends on the underlying target infrastructure (locale, type class |
|
241 |
etc.). The general idea is as follows, considering a context named |
|
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\isa{c} with parameter \isa{x} and assumption \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}. |
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|
244 |
Definitions are exported by introducing a global version with |
|
245 |
additional arguments; a syntactic abbreviation links the long form |
|
246 |
with the abstract version of the target context. For example, |
|
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\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} becomes \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{2E}{\isachardot}}a\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} at the theory |
248 |
level (for arbitrary \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{22}{\isachardoublequote}}}), together with a local |
|
249 |
abbreviation \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c{\isaliteral{2E}{\isachardot}}a\ x{\isaliteral{22}{\isachardoublequote}}} in the target context (for the |
|
27042 | 250 |
fixed parameter \isa{x}). |
251 |
||
252 |
Theorems are exported by discharging the assumptions and |
|
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generalizing the parameters of the context. For example, \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} becomes \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{2E}{\isachardot}}a{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}, again for arbitrary |
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\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{22}{\isachardoublequote}}}. |
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|
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\medskip The Isabelle/HOL library contains numerous applications of |
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locales and classes, e.g.\ see \verb|~~/src/HOL/Algebra|. An |
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example for an unnamed auxiliary contexts is given in \verb|~~/src/HOL/Isar_Examples/Group_Context.thy|.% |
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\end{isamarkuptext}% |
260 |
\isamarkuptrue% |
|
261 |
% |
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262 |
\isamarkupsection{Basic specification elements% |
|
263 |
} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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\begin{matharray}{rcll} |
|
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\indexdef{}{command}{axiomatization}\hypertarget{command.axiomatization}{\hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\ |
269 |
\indexdef{}{command}{definition}\hypertarget{command.definition}{\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}} & : & \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{}{attribute}{defn}\hypertarget{attribute.defn}{\hyperlink{attribute.defn}{\mbox{\isa{defn}}}} & : & \isa{attribute} \\ |
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\indexdef{}{command}{abbreviation}\hypertarget{command.abbreviation}{\hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
272 |
\indexdef{}{command}{print\_abbrevs}\hypertarget{command.print-abbrevs}{\hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}abbrevs}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{22}{\isachardoublequote}}} \\ |
|
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\end{matharray} |
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||
275 |
These specification mechanisms provide a slightly more abstract view |
|
276 |
than the underlying primitives of \hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}, \hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}} (see \secref{sec:consts}), and \hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}} (see |
|
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\secref{sec:axms-thms}). In particular, type-inference is commonly |
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available, and result names need not be given. |
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\begin{railoutput} |
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\rail@begin{2}{} |
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\rail@term{\hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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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{1} |
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\rail@term{\isa{\isakeyword{where}}}[] |
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\rail@nont{\isa{specs}}[] |
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\rail@endbar |
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\rail@end |
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\rail@begin{5}{} |
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\rail@term{\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}}[] |
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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{3} |
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\rail@bar |
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\rail@nextbar{4} |
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\rail@nont{\isa{decl}}[] |
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\rail@term{\isa{\isakeyword{where}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{4} |
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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@end |
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\rail@begin{5}{} |
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\rail@term{\hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}}[] |
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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{\hyperlink{syntax.mode}{\mbox{\isa{mode}}}}[] |
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\rail@endbar |
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\rail@cr{3} |
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\rail@bar |
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\rail@nextbar{4} |
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\rail@nont{\isa{decl}}[] |
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\rail@term{\isa{\isakeyword{where}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
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\rail@end |
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\rail@begin{4}{\indexdef{}{syntax}{fixes}\hypertarget{syntax.fixes}{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}} |
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\rail@plus |
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\rail@bar |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
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\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
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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.mixfix}{\mbox{\isa{mixfix}}}}[] |
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\rail@endbar |
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\rail@nextbar{2} |
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\rail@nont{\hyperlink{syntax.vars}{\mbox{\isa{vars}}}}[] |
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\rail@endbar |
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\rail@nextplus{3} |
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\rail@cterm{\isa{\isakeyword{and}}}[] |
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\rail@endplus |
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\rail@end |
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\rail@begin{3}{\isa{specs}} |
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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.props}{\mbox{\isa{props}}}}[] |
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\rail@nextplus{2} |
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\rail@cterm{\isa{\isakeyword{and}}}[] |
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\rail@endplus |
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\rail@end |
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\rail@begin{2}{\isa{decl}} |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
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\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
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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.mixfix}{\mbox{\isa{mixfix}}}}[] |
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\rail@endbar |
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\rail@end |
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372 |
\end{railoutput} |
27042 | 373 |
|
374 |
||
28788 | 375 |
\begin{description} |
27042 | 376 |
|
40406 | 377 |
\item \hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} |
28788 | 378 |
introduces several constants simultaneously and states axiomatic |
379 |
properties for these. The constants are marked as being specified |
|
380 |
once and for all, which prevents additional specifications being |
|
381 |
issued later on. |
|
27042 | 382 |
|
383 |
Note that axiomatic specifications are only appropriate when |
|
28110 | 384 |
declaring a new logical system; axiomatic specifications are |
385 |
restricted to global theory contexts. Normal applications should |
|
386 |
only use definitional mechanisms! |
|
27042 | 387 |
|
40406 | 388 |
\item \hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eq{\isaliteral{22}{\isachardoublequote}}} produces an |
389 |
internal definition \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} according to the specification |
|
27042 | 390 |
given as \isa{eq}, which is then turned into a proven fact. The |
391 |
given proposition may deviate from internal meta-level equality |
|
392 |
according to the rewrite rules declared as \hyperlink{attribute.defn}{\mbox{\isa{defn}}} by the |
|
40406 | 393 |
object-logic. This usually covers object-level equality \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}} and equivalence \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C65667472696768746172726F773E}{\isasymleftrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}}. End-users normally need not |
27042 | 394 |
change the \hyperlink{attribute.defn}{\mbox{\isa{defn}}} setup. |
395 |
||
396 |
Definitions may be presented with explicit arguments on the LHS, as |
|
40406 | 397 |
well as additional conditions, e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}f\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} instead of |
398 |
\isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}y\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ g\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ u{\isaliteral{22}{\isachardoublequote}}} instead of an |
|
399 |
unrestricted \isa{{\isaliteral{22}{\isachardoublequote}}g\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ u{\isaliteral{22}{\isachardoublequote}}}. |
|
27042 | 400 |
|
40406 | 401 |
\item \hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eq{\isaliteral{22}{\isachardoublequote}}} introduces a |
28788 | 402 |
syntactic constant which is associated with a certain term according |
403 |
to the meta-level equality \isa{eq}. |
|
27042 | 404 |
|
405 |
Abbreviations participate in the usual type-inference process, but |
|
406 |
are expanded before the logic ever sees them. Pretty printing of |
|
407 |
terms involves higher-order rewriting with rules stemming from |
|
408 |
reverted abbreviations. This needs some care to avoid overlapping |
|
409 |
or looping syntactic replacements! |
|
410 |
||
411 |
The optional \isa{mode} specification restricts output to a |
|
412 |
particular print mode; using ``\isa{input}'' here achieves the |
|
413 |
effect of one-way abbreviations. The mode may also include an |
|
414 |
``\hyperlink{keyword.output}{\mbox{\isa{\isakeyword{output}}}}'' qualifier that affects the concrete syntax |
|
415 |
declared for abbreviations, cf.\ \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}} in |
|
416 |
\secref{sec:syn-trans}. |
|
417 |
||
40406 | 418 |
\item \hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}abbrevs}}}} prints all constant abbreviations |
27042 | 419 |
of the current context. |
420 |
||
28788 | 421 |
\end{description}% |
27042 | 422 |
\end{isamarkuptext}% |
423 |
\isamarkuptrue% |
|
424 |
% |
|
425 |
\isamarkupsection{Generic declarations% |
|
426 |
} |
|
427 |
\isamarkuptrue% |
|
428 |
% |
|
429 |
\begin{isamarkuptext}% |
|
47483 | 430 |
\begin{matharray}{rcl} |
431 |
\indexdef{}{command}{declaration}\hypertarget{command.declaration}{\hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
432 |
\indexdef{}{command}{syntax\_declaration}\hypertarget{command.syntax-declaration}{\hyperlink{command.syntax-declaration}{\mbox{\isa{\isacommand{syntax{\isaliteral{5F}{\isacharunderscore}}declaration}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
433 |
\indexdef{}{command}{declare}\hypertarget{command.declare}{\hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
434 |
\end{matharray} |
|
435 |
||
436 |
Arbitrary operations on the background context may be wrapped-up as |
|
27042 | 437 |
generic declaration elements. Since the underlying concept of local |
438 |
theories may be subject to later re-interpretation, there is an |
|
439 |
additional dependency on a morphism that tells the difference of the |
|
440 |
original declaration context wrt.\ the application context |
|
441 |
encountered later on. A fact declaration is an important special |
|
442 |
case: it consists of a theorem which is applied to the context by |
|
443 |
means of an attribute. |
|
444 |
||
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\begin{railoutput} |
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\rail@begin{5}{} |
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447 |
\rail@bar |
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\rail@term{\hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}}[] |
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449 |
\rail@nextbar{1} |
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\rail@term{\hyperlink{command.syntax-declaration}{\mbox{\isa{\isacommand{syntax{\isaliteral{5F}{\isacharunderscore}}declaration}}}}}[] |
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451 |
\rail@endbar |
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452 |
\rail@bar |
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453 |
\rail@nextbar{1} |
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454 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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455 |
\rail@term{\isa{\isakeyword{pervasive}}}[] |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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457 |
\rail@endbar |
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\rail@cr{3} |
42596
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459 |
\rail@bar |
42704 | 460 |
\rail@nextbar{4} |
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461 |
\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
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462 |
\rail@endbar |
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463 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
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464 |
\rail@end |
42662 | 465 |
\rail@begin{2}{} |
42596
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466 |
\rail@term{\hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}}[] |
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|
467 |
\rail@bar |
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parents:
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|
468 |
\rail@nextbar{1} |
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modernized rail diagrams using @{rail} antiquotation;
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parents:
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|
469 |
\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
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modernized rail diagrams using @{rail} antiquotation;
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parents:
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|
470 |
\rail@endbar |
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modernized rail diagrams using @{rail} antiquotation;
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parents:
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|
471 |
\rail@plus |
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modernized rail diagrams using @{rail} antiquotation;
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|
472 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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parents:
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|
473 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
474 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
475 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
476 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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changeset
|
477 |
\end{railoutput} |
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modernized rail diagrams using @{rail} antiquotation;
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changeset
|
478 |
|
27042 | 479 |
|
28788 | 480 |
\begin{description} |
27042 | 481 |
|
28788 | 482 |
\item \hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}~\isa{d} adds the declaration |
27042 | 483 |
function \isa{d} of ML type \verb|declaration|, to the current |
484 |
local theory under construction. In later application contexts, the |
|
485 |
function is transformed according to the morphisms being involved in |
|
486 |
the interpretation hierarchy. |
|
487 |
||
40406 | 488 |
If the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}pervasive{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option is given, the corresponding |
33516 | 489 |
declaration is applied to all possible contexts involved, including |
490 |
the global background theory. |
|
491 |
||
40784 | 492 |
\item \hyperlink{command.syntax-declaration}{\mbox{\isa{\isacommand{syntax{\isaliteral{5F}{\isacharunderscore}}declaration}}}} is similar to \hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}, but is meant to affect only ``syntactic'' tools by |
493 |
convention (such as notation and type-checking information). |
|
494 |
||
28788 | 495 |
\item \hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}~\isa{thms} declares theorems to the |
27042 | 496 |
current local theory context. No theorem binding is involved here, |
497 |
unlike \hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}} or \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}} (cf.\ |
|
498 |
\secref{sec:axms-thms}), so \hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}} only has the effect |
|
499 |
of applying attributes as included in the theorem specification. |
|
500 |
||
28788 | 501 |
\end{description}% |
27042 | 502 |
\end{isamarkuptext}% |
503 |
\isamarkuptrue% |
|
504 |
% |
|
505 |
\isamarkupsection{Locales \label{sec:locale}% |
|
506 |
} |
|
507 |
\isamarkuptrue% |
|
508 |
% |
|
509 |
\begin{isamarkuptext}% |
|
33847 | 510 |
Locales are parametric named local contexts, consisting of a list of |
27042 | 511 |
declaration elements that are modeled after the Isar proof context |
512 |
commands (cf.\ \secref{sec:proof-context}).% |
|
513 |
\end{isamarkuptext}% |
|
514 |
\isamarkuptrue% |
|
515 |
% |
|
33847 | 516 |
\isamarkupsubsection{Locale expressions \label{sec:locale-expr}% |
517 |
} |
|
518 |
\isamarkuptrue% |
|
519 |
% |
|
520 |
\begin{isamarkuptext}% |
|
521 |
A \emph{locale expression} denotes a structured context composed of |
|
522 |
instances of existing locales. The context consists of a list of |
|
523 |
instances of declaration elements from the locales. Two locale |
|
524 |
instances are equal if they are of the same locale and the |
|
525 |
parameters are instantiated with equivalent terms. Declaration |
|
526 |
elements from equal instances are never repeated, thus avoiding |
|
527 |
duplicate declarations. |
|
528 |
||
42596
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parents:
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changeset
|
529 |
\begin{railoutput} |
42617 | 530 |
\rail@begin{3}{\indexdef{}{syntax}{locale\_expr}\hypertarget{syntax.locale-expr}{\hyperlink{syntax.locale-expr}{\mbox{\isa{locale{\isaliteral{5F}{\isacharunderscore}}expr}}}}} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
531 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
532 |
\rail@nont{\isa{instance}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
533 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
534 |
\rail@cterm{\isa{{\isaliteral{2B}{\isacharplus}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
535 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
536 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
537 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
538 |
\rail@term{\isa{\isakeyword{for}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
539 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
540 |
\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
541 |
\rail@nextplus{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
542 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
543 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
544 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
545 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
546 |
\rail@begin{2}{\isa{instance}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
547 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
548 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
549 |
\rail@nont{\isa{qualifier}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
550 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
551 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
552 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
553 |
\rail@bar |
42617 | 554 |
\rail@nont{\isa{pos{\isaliteral{5F}{\isacharunderscore}}insts}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
555 |
\rail@nextbar{1} |
42617 | 556 |
\rail@nont{\isa{named{\isaliteral{5F}{\isacharunderscore}}insts}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
557 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
558 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
559 |
\rail@begin{3}{\isa{qualifier}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
560 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
561 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
562 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
563 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
564 |
\rail@term{\isa{{\isaliteral{3F}{\isacharquery}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
565 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
566 |
\rail@term{\isa{{\isaliteral{21}{\isacharbang}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
567 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
568 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
569 |
\rail@end |
42617 | 570 |
\rail@begin{3}{\isa{pos{\isaliteral{5F}{\isacharunderscore}}insts}} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
571 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
572 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
573 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
574 |
\rail@term{\isa{{\isaliteral{5F}{\isacharunderscore}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
575 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
576 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
577 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
578 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
579 |
\rail@end |
42617 | 580 |
\rail@begin{2}{\isa{named{\isaliteral{5F}{\isacharunderscore}}insts}} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
581 |
\rail@term{\isa{\isakeyword{where}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
582 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
583 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
584 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
585 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
586 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
587 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
588 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
589 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
590 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
591 |
|
33847 | 592 |
|
593 |
A locale instance consists of a reference to a locale and either |
|
594 |
positional or named parameter instantiations. Identical |
|
595 |
instantiations (that is, those that instante a parameter by itself) |
|
40406 | 596 |
may be omitted. The notation `\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}' enables to omit the |
40256 | 597 |
instantiation for a parameter inside a positional instantiation. |
33847 | 598 |
|
599 |
Terms in instantiations are from the context the locale expressions |
|
600 |
is declared in. Local names may be added to this context with the |
|
601 |
optional for clause. In addition, syntax declarations from one |
|
602 |
instance are effective when parsing subsequent instances of the same |
|
603 |
expression. |
|
604 |
||
605 |
Instances have an optional qualifier which applies to names in |
|
606 |
declarations. Names include local definitions and theorem names. |
|
607 |
If present, the qualifier itself is either optional |
|
608 |
(``\texttt{?}''), which means that it may be omitted on input of the |
|
609 |
qualified name, or mandatory (``\texttt{!}''). If neither |
|
610 |
``\texttt{?}'' nor ``\texttt{!}'' are present, the command's default |
|
611 |
is used. For \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}} and \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}} |
|
612 |
the default is ``mandatory'', for \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}} and \hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}} the default is ``optional''.% |
|
613 |
\end{isamarkuptext}% |
|
614 |
\isamarkuptrue% |
|
615 |
% |
|
616 |
\isamarkupsubsection{Locale declarations% |
|
27042 | 617 |
} |
618 |
\isamarkuptrue% |
|
619 |
% |
|
620 |
\begin{isamarkuptext}% |
|
621 |
\begin{matharray}{rcl} |
|
40406 | 622 |
\indexdef{}{command}{locale}\hypertarget{command.locale}{\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
623 |
\indexdef{}{command}{print\_locale}\hypertarget{command.print-locale}{\hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
624 |
\indexdef{}{command}{print\_locales}\hypertarget{command.print-locales}{\hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locales}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
625 |
\indexdef{}{method}{intro\_locales}\hypertarget{method.intro-locales}{\hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}}} & : & \isa{method} \\ |
|
626 |
\indexdef{}{method}{unfold\_locales}\hypertarget{method.unfold-locales}{\hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}}} & : & \isa{method} \\ |
|
27042 | 627 |
\end{matharray} |
628 |
||
629 |
\indexisarelem{fixes}\indexisarelem{constrains}\indexisarelem{assumes} |
|
28788 | 630 |
\indexisarelem{defines}\indexisarelem{notes} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
631 |
\begin{railoutput} |
42662 | 632 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
633 |
\rail@term{\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
634 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
635 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
636 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
637 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
638 |
\rail@nont{\hyperlink{syntax.locale}{\mbox{\isa{locale}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
639 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
640 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
641 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
642 |
\rail@term{\isa{\isakeyword{begin}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
643 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
644 |
\rail@end |
42662 | 645 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
646 |
\rail@term{\hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
647 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
648 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
649 |
\rail@term{\isa{{\isaliteral{21}{\isacharbang}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
650 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
651 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
652 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
653 |
\rail@begin{5}{\indexdef{}{syntax}{locale}\hypertarget{syntax.locale}{\hyperlink{syntax.locale}{\mbox{\isa{locale}}}}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
654 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
655 |
\rail@plus |
42617 | 656 |
\rail@nont{\hyperlink{syntax.context-elem}{\mbox{\isa{context{\isaliteral{5F}{\isacharunderscore}}elem}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
657 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
658 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
659 |
\rail@nextbar{2} |
42617 | 660 |
\rail@nont{\hyperlink{syntax.locale-expr}{\mbox{\isa{locale{\isaliteral{5F}{\isacharunderscore}}expr}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
661 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
662 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
663 |
\rail@term{\isa{{\isaliteral{2B}{\isacharplus}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
664 |
\rail@plus |
42617 | 665 |
\rail@nont{\hyperlink{syntax.context-elem}{\mbox{\isa{context{\isaliteral{5F}{\isacharunderscore}}elem}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
666 |
\rail@nextplus{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
667 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
668 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
669 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
670 |
\rail@end |
42617 | 671 |
\rail@begin{12}{\indexdef{}{syntax}{context\_elem}\hypertarget{syntax.context-elem}{\hyperlink{syntax.context-elem}{\mbox{\isa{context{\isaliteral{5F}{\isacharunderscore}}elem}}}}} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
672 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
673 |
\rail@term{\isa{\isakeyword{fixes}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
674 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
675 |
\rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
676 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
677 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
678 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
679 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
680 |
\rail@term{\isa{\isakeyword{constrains}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
681 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
682 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
683 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
684 |
\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
685 |
\rail@nextplus{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
686 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
687 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
688 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
689 |
\rail@term{\isa{\isakeyword{assumes}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
690 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
691 |
\rail@nont{\hyperlink{syntax.props}{\mbox{\isa{props}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
692 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
693 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
694 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
695 |
\rail@nextbar{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
696 |
\rail@term{\isa{\isakeyword{defines}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
697 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
698 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
699 |
\rail@nextbar{7} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
700 |
\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
701 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
702 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
703 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
704 |
\rail@nextbar{7} |
42705 | 705 |
\rail@nont{\hyperlink{syntax.prop-pat}{\mbox{\isa{prop{\isaliteral{5F}{\isacharunderscore}}pat}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
706 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
707 |
\rail@nextplus{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
708 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
709 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
710 |
\rail@nextbar{9} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
711 |
\rail@term{\isa{\isakeyword{notes}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
712 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
713 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
714 |
\rail@nextbar{10} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
715 |
\rail@nont{\hyperlink{syntax.thmdef}{\mbox{\isa{thmdef}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
716 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
717 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
718 |
\rail@nextplus{11} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
719 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
720 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
721 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
722 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
723 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
724 |
|
27042 | 725 |
|
28788 | 726 |
\begin{description} |
27042 | 727 |
|
40406 | 728 |
\item \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}loc\ {\isaliteral{3D}{\isacharequal}}\ import\ {\isaliteral{2B}{\isacharplus}}\ body{\isaliteral{22}{\isachardoublequote}}} defines a |
27042 | 729 |
new locale \isa{loc} as a context consisting of a certain view of |
730 |
existing locales (\isa{import}) plus some additional elements |
|
731 |
(\isa{body}). Both \isa{import} and \isa{body} are optional; |
|
732 |
the degenerate form \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}~\isa{loc} defines an empty |
|
733 |
locale, which may still be useful to collect declarations of facts |
|
734 |
later on. Type-inference on locale expressions automatically takes |
|
735 |
care of the most general typing that the combined context elements |
|
736 |
may acquire. |
|
737 |
||
33847 | 738 |
The \isa{import} consists of a structured locale expression; see |
739 |
\secref{sec:proof-context} above. Its for clause defines the local |
|
740 |
parameters of the \isa{import}. In addition, locale parameters |
|
741 |
whose instantance is omitted automatically extend the (possibly |
|
742 |
empty) for clause: they are inserted at its beginning. This means |
|
743 |
that these parameters may be referred to from within the expression |
|
744 |
and also in the subsequent context elements and provides a |
|
745 |
notational convenience for the inheritance of parameters in locale |
|
746 |
declarations. |
|
27042 | 747 |
|
33847 | 748 |
The \isa{body} consists of context elements. |
27042 | 749 |
|
28788 | 750 |
\begin{description} |
27042 | 751 |
|
40406 | 752 |
\item \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} declares a local |
753 |
parameter of type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} and mixfix annotation \isa{mx} (both |
|
754 |
are optional). The special syntax declaration ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C5354525543545552453E}{\isasymSTRUCTURE}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means that \isa{x} may be referenced |
|
27042 | 755 |
implicitly in this context. |
756 |
||
40406 | 757 |
\item \hyperlink{element.constrains}{\mbox{\isa{\isakeyword{constrains}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} introduces a type |
758 |
constraint \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} on the local parameter \isa{x}. This |
|
38110 | 759 |
element is deprecated. The type constraint should be introduced in |
33847 | 760 |
the for clause or the relevant \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}} element. |
27042 | 761 |
|
40406 | 762 |
\item \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} |
27042 | 763 |
introduces local premises, similar to \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} within a |
764 |
proof (cf.\ \secref{sec:proof-context}). |
|
765 |
||
40406 | 766 |
\item \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} defines a previously |
27042 | 767 |
declared parameter. This is similar to \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}} within a |
768 |
proof (cf.\ \secref{sec:proof-context}), but \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}} |
|
769 |
takes an equational proposition instead of variable-term pair. The |
|
770 |
left-hand side of the equation may have additional arguments, e.g.\ |
|
40406 | 771 |
``\hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}f\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}''. |
27042 | 772 |
|
40406 | 773 |
\item \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} |
27042 | 774 |
reconsiders facts within a local context. Most notably, this may |
775 |
include arbitrary declarations in any attribute specifications |
|
776 |
included here, e.g.\ a local \hyperlink{attribute.simp}{\mbox{\isa{simp}}} rule. |
|
777 |
||
28788 | 778 |
The initial \isa{import} specification of a locale expression |
779 |
maintains a dynamic relation to the locales being referenced |
|
780 |
(benefiting from any later fact declarations in the obvious manner). |
|
27042 | 781 |
|
28788 | 782 |
\end{description} |
27042 | 783 |
|
40406 | 784 |
Note that ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' patterns given |
27042 | 785 |
in the syntax of \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} and \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}} above |
786 |
are illegal in locale definitions. In the long goal format of |
|
787 |
\secref{sec:goals}, term bindings may be included as expected, |
|
788 |
though. |
|
789 |
||
33847 | 790 |
\medskip Locale specifications are ``closed up'' by |
40406 | 791 |
turning the given text into a predicate definition \isa{loc{\isaliteral{5F}{\isacharunderscore}}axioms} and deriving the original assumptions as local lemmas |
27042 | 792 |
(modulo local definitions). The predicate statement covers only the |
793 |
newly specified assumptions, omitting the content of included locale |
|
794 |
expressions. The full cumulative view is only provided on export, |
|
795 |
involving another predicate \isa{loc} that refers to the complete |
|
796 |
specification text. |
|
797 |
||
798 |
In any case, the predicate arguments are those locale parameters |
|
799 |
that actually occur in the respective piece of text. Also note that |
|
800 |
these predicates operate at the meta-level in theory, but the locale |
|
801 |
packages attempts to internalize statements according to the |
|
40406 | 802 |
object-logic setup (e.g.\ replacing \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} by \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}}, and |
803 |
\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} in HOL; see also |
|
804 |
\secref{sec:object-logic}). Separate introduction rules \isa{loc{\isaliteral{5F}{\isacharunderscore}}axioms{\isaliteral{2E}{\isachardot}}intro} and \isa{loc{\isaliteral{2E}{\isachardot}}intro} are provided as well. |
|
27042 | 805 |
|
40406 | 806 |
\item \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}locale{\isaliteral{22}{\isachardoublequote}}} prints the |
33868 | 807 |
contents of the named locale. The command omits \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}} |
40406 | 808 |
elements by default. Use \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} to |
33868 | 809 |
have them included. |
27042 | 810 |
|
40406 | 811 |
\item \hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locales}}}} prints the names of all locales |
27042 | 812 |
of the current theory. |
813 |
||
40406 | 814 |
\item \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}} and \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}} |
27042 | 815 |
repeatedly expand all introduction rules of locale predicates of the |
40406 | 816 |
theory. While \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}} only applies the \isa{loc{\isaliteral{2E}{\isachardot}}intro} introduction rules and therefore does not decend to |
817 |
assumptions, \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}} is more aggressive and applies |
|
818 |
\isa{loc{\isaliteral{5F}{\isacharunderscore}}axioms{\isaliteral{2E}{\isachardot}}intro} as well. Both methods are aware of locale |
|
28728 | 819 |
specifications entailed by the context, both from target statements, |
820 |
and from interpretations (see below). New goals that are entailed |
|
821 |
by the current context are discharged automatically. |
|
27042 | 822 |
|
28788 | 823 |
\end{description}% |
27042 | 824 |
\end{isamarkuptext}% |
825 |
\isamarkuptrue% |
|
826 |
% |
|
33847 | 827 |
\isamarkupsubsection{Locale interpretations% |
27042 | 828 |
} |
829 |
\isamarkuptrue% |
|
830 |
% |
|
831 |
\begin{isamarkuptext}% |
|
47483 | 832 |
\begin{matharray}{rcl} |
40406 | 833 |
\indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
834 |
\indexdef{}{command}{interpret}\hypertarget{command.interpret}{\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
41434
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
835 |
\indexdef{}{command}{sublocale}\hypertarget{command.sublocale}{\hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
41435 | 836 |
\indexdef{}{command}{print\_dependencies}\hypertarget{command.print-dependencies}{\hyperlink{command.print-dependencies}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}dependencies}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
40406 | 837 |
\indexdef{}{command}{print\_interps}\hypertarget{command.print-interps}{\hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}interps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
27042 | 838 |
\end{matharray} |
839 |
||
47483 | 840 |
Locale expressions may be instantiated, and the instantiated facts |
841 |
added to the current context. This requires a proof of the |
|
842 |
instantiated specification and is called \emph{locale |
|
843 |
interpretation}. Interpretation is possible in locales \hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}, theories (command \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}) and |
|
844 |
also within a proof body (command \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}). |
|
845 |
||
42596
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modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
846 |
\begin{railoutput} |
42662 | 847 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
848 |
\rail@term{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}}[] |
42617 | 849 |
\rail@nont{\hyperlink{syntax.locale-expr}{\mbox{\isa{locale{\isaliteral{5F}{\isacharunderscore}}expr}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
850 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
851 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
852 |
\rail@nont{\isa{equations}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
853 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
854 |
\rail@end |
42662 | 855 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
856 |
\rail@term{\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}}[] |
42617 | 857 |
\rail@nont{\hyperlink{syntax.locale-expr}{\mbox{\isa{locale{\isaliteral{5F}{\isacharunderscore}}expr}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
858 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
859 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
860 |
\rail@nont{\isa{equations}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
861 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
862 |
\rail@end |
42704 | 863 |
\rail@begin{5}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
864 |
\rail@term{\hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
865 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
866 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
867 |
\rail@term{\isa{{\isaliteral{3C}{\isacharless}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
868 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
869 |
\rail@term{\isa{{\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
870 |
\rail@endbar |
42617 | 871 |
\rail@nont{\hyperlink{syntax.locale-expr}{\mbox{\isa{locale{\isaliteral{5F}{\isacharunderscore}}expr}}}}[] |
42704 | 872 |
\rail@cr{3} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
873 |
\rail@bar |
42704 | 874 |
\rail@nextbar{4} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
875 |
\rail@nont{\isa{equations}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
876 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
877 |
\rail@end |
42662 | 878 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
879 |
\rail@term{\hyperlink{command.print-dependencies}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}dependencies}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
880 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
881 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
882 |
\rail@term{\isa{{\isaliteral{21}{\isacharbang}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
883 |
\rail@endbar |
42617 | 884 |
\rail@nont{\hyperlink{syntax.locale-expr}{\mbox{\isa{locale{\isaliteral{5F}{\isacharunderscore}}expr}}}}[] |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
885 |
\rail@end |
42662 | 886 |
\rail@begin{1}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
887 |
\rail@term{\hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}interps}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
888 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
889 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
890 |
\rail@begin{3}{\isa{equations}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
891 |
\rail@term{\isa{\isakeyword{where}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
892 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
893 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
894 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
895 |
\rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
896 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
897 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
898 |
\rail@nextplus{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
899 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
900 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
901 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
902 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
903 |
|
27042 | 904 |
|
28788 | 905 |
\begin{description} |
27042 | 906 |
|
40406 | 907 |
\item \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}expr\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eqns{\isaliteral{22}{\isachardoublequote}}} |
33847 | 908 |
interprets \isa{expr} in the theory. The command generates proof |
909 |
obligations for the instantiated specifications (assumes and defines |
|
910 |
elements). Once these are discharged by the user, instantiated |
|
911 |
facts are added to the theory in a post-processing phase. |
|
912 |
||
913 |
Additional equations, which are unfolded during |
|
27042 | 914 |
post-processing, may be given after the keyword \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}}. |
915 |
This is useful for interpreting concepts introduced through |
|
41434
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
916 |
definitions. The equations must be proved. |
27042 | 917 |
|
918 |
The command is aware of interpretations already active in the |
|
28085
914183e229e9
Interpretation commands no longer accept interpretation attributes.
ballarin
parents:
27834
diff
changeset
|
919 |
theory, but does not simplify the goal automatically. In order to |
40406 | 920 |
simplify the proof obligations use methods \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}} |
921 |
or \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}}. Post-processing is not applied to |
|
28085
914183e229e9
Interpretation commands no longer accept interpretation attributes.
ballarin
parents:
27834
diff
changeset
|
922 |
facts of interpretations that are already active. This avoids |
914183e229e9
Interpretation commands no longer accept interpretation attributes.
ballarin
parents:
27834
diff
changeset
|
923 |
duplication of interpreted facts, in particular. Note that, in the |
914183e229e9
Interpretation commands no longer accept interpretation attributes.
ballarin
parents:
27834
diff
changeset
|
924 |
case of a locale with import, parts of the interpretation may |
914183e229e9
Interpretation commands no longer accept interpretation attributes.
ballarin
parents:
27834
diff
changeset
|
925 |
already be active. The command will only process facts for new |
914183e229e9
Interpretation commands no longer accept interpretation attributes.
ballarin
parents:
27834
diff
changeset
|
926 |
parts. |
27042 | 927 |
|
928 |
Adding facts to locales has the effect of adding interpreted facts |
|
41434
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
929 |
to the theory for all interpretations as well. That is, |
27042 | 930 |
interpretations dynamically participate in any facts added to |
41434
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
931 |
locales. Note that if a theory inherits additional facts for a |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
932 |
locale through one parent and an interpretation of that locale |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
933 |
through another parent, the additional facts will not be |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
934 |
interpreted. |
27042 | 935 |
|
40406 | 936 |
\item \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}expr\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eqns{\isaliteral{22}{\isachardoublequote}}} interprets |
38110 | 937 |
\isa{expr} in the proof context and is otherwise similar to |
938 |
interpretation in theories. Note that rewrite rules given to |
|
41434
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
939 |
\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}} after the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} keyword should be |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
940 |
explicitly universally quantified. |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
941 |
|
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
942 |
\item \hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ expr\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eqns{\isaliteral{22}{\isachardoublequote}}} |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
943 |
interprets \isa{expr} in the locale \isa{name}. A proof that |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
944 |
the specification of \isa{name} implies the specification of |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
945 |
\isa{expr} is required. As in the localized version of the |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
946 |
theorem command, the proof is in the context of \isa{name}. After |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
947 |
the proof obligation has been discharged, the facts of \isa{expr} |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
948 |
become part of locale \isa{name} as \emph{derived} context |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
949 |
elements and are available when the context \isa{name} is |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
950 |
subsequently entered. Note that, like import, this is dynamic: |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
951 |
facts added to a locale part of \isa{expr} after interpretation |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
952 |
become also available in \isa{name}. |
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
changeset
|
953 |
|
710cdb9e0d17
Documentation for 'interpret' and 'sublocale' with mixins.
ballarin
parents:
41249
diff
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|
954 |
Only specification fragments of \isa{expr} that are not already |
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|
955 |
part of \isa{name} (be it imported, derived or a derived fragment |
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|
956 |
of the import) are considered in this process. This enables |
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diff
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|
957 |
circular interpretations provided that no infinite chains are |
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Documentation for 'interpret' and 'sublocale' with mixins.
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diff
changeset
|
958 |
generated in the locale hierarchy. |
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Documentation for 'interpret' and 'sublocale' with mixins.
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diff
changeset
|
959 |
|
710cdb9e0d17
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diff
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|
960 |
If interpretations of \isa{name} exist in the current theory, the |
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Documentation for 'interpret' and 'sublocale' with mixins.
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diff
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|
961 |
command adds interpretations for \isa{expr} as well, with the same |
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diff
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|
962 |
qualifier, although only for fragments of \isa{expr} that are not |
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|
963 |
interpreted in the theory already. |
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diff
changeset
|
964 |
|
710cdb9e0d17
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diff
changeset
|
965 |
Equations given after \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} amend the morphism through |
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|
966 |
which \isa{expr} is interpreted. This enables to map definitions |
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|
967 |
from the interpreted locales to entities of \isa{name}. This |
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changeset
|
968 |
feature is experimental. |
27042 | 969 |
|
41435 | 970 |
\item \hyperlink{command.print-dependencies}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}dependencies}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}expr{\isaliteral{22}{\isachardoublequote}}} is useful for |
971 |
understanding the effect of an interpretation of \isa{{\isaliteral{22}{\isachardoublequote}}expr{\isaliteral{22}{\isachardoublequote}}}. It |
|
972 |
lists all locale instances for which interpretations would be added |
|
973 |
to the current context. Variant \hyperlink{command.print-dependencies}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}dependencies}}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} prints all locale instances that |
|
974 |
would be considered for interpretation, and would be interpreted in |
|
975 |
an empty context (that is, without interpretations). |
|
976 |
||
40406 | 977 |
\item \hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}interps}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}locale{\isaliteral{22}{\isachardoublequote}}} lists all |
978 |
interpretations of \isa{{\isaliteral{22}{\isachardoublequote}}locale{\isaliteral{22}{\isachardoublequote}}} in the current theory or proof |
|
38110 | 979 |
context, including those due to a combination of a \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}} or \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}} and one or several |
980 |
\hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}} declarations. |
|
33868 | 981 |
|
28788 | 982 |
\end{description} |
27042 | 983 |
|
984 |
\begin{warn} |
|
985 |
Since attributes are applied to interpreted theorems, |
|
986 |
interpretation may modify the context of common proof tools, e.g.\ |
|
33868 | 987 |
the Simplifier or Classical Reasoner. As the behavior of such |
988 |
tools is \emph{not} stable under interpretation morphisms, manual |
|
989 |
declarations might have to be added to the target context of the |
|
990 |
interpretation to revert such declarations. |
|
27042 | 991 |
\end{warn} |
992 |
||
993 |
\begin{warn} |
|
38110 | 994 |
An interpretation in a theory or proof context may subsume previous |
27042 | 995 |
interpretations. This happens if the same specification fragment |
996 |
is interpreted twice and the instantiation of the second |
|
997 |
interpretation is more general than the interpretation of the |
|
33847 | 998 |
first. The locale package does not attempt to remove subsumed |
999 |
interpretations. |
|
27042 | 1000 |
\end{warn}% |
1001 |
\end{isamarkuptext}% |
|
1002 |
\isamarkuptrue% |
|
1003 |
% |
|
1004 |
\isamarkupsection{Classes \label{sec:class}% |
|
1005 |
} |
|
1006 |
\isamarkuptrue% |
|
1007 |
% |
|
1008 |
\begin{isamarkuptext}% |
|
47483 | 1009 |
\begin{matharray}{rcl} |
40406 | 1010 |
\indexdef{}{command}{class}\hypertarget{command.class}{\hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
1011 |
\indexdef{}{command}{instantiation}\hypertarget{command.instantiation}{\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1012 |
\indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
42626 | 1013 |
\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\ |
40406 | 1014 |
\indexdef{}{command}{subclass}\hypertarget{command.subclass}{\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
1015 |
\indexdef{}{command}{print\_classes}\hypertarget{command.print-classes}{\hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}classes}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1016 |
\indexdef{}{command}{class\_deps}\hypertarget{command.class-deps}{\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\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}}} \\ |
|
1017 |
\indexdef{}{method}{intro\_classes}\hypertarget{method.intro-classes}{\hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}}} & : & \isa{method} \\ |
|
27042 | 1018 |
\end{matharray} |
1019 |
||
47483 | 1020 |
A class is a particular locale with \emph{exactly one} type variable |
1021 |
\isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Beyond the underlying locale, a corresponding type class |
|
1022 |
is established which is interpreted logically as axiomatic type |
|
1023 |
class \cite{Wenzel:1997:TPHOL} whose logical content are the |
|
1024 |
assumptions of the locale. Thus, classes provide the full |
|
1025 |
generality of locales combined with the commodity of type classes |
|
1026 |
(notably type-inference). See \cite{isabelle-classes} for a short |
|
1027 |
tutorial. |
|
1028 |
||
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|
1029 |
\begin{railoutput} |
42704 | 1030 |
\rail@begin{2}{} |
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|
1031 |
\rail@term{\hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}}[] |
42704 | 1032 |
\rail@nont{\isa{class{\isaliteral{5F}{\isacharunderscore}}spec}}[] |
1033 |
\rail@bar |
|
1034 |
\rail@nextbar{1} |
|
1035 |
\rail@term{\isa{\isakeyword{begin}}}[] |
|
1036 |
\rail@endbar |
|
1037 |
\rail@end |
|
1038 |
\rail@begin{5}{\isa{class{\isaliteral{5F}{\isacharunderscore}}spec}} |
|
42596
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|
1039 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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|
1040 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
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changeset
|
1041 |
\rail@bar |
42617 | 1042 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
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changeset
|
1043 |
\rail@term{\isa{{\isaliteral{2B}{\isacharplus}}}}[] |
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|
1044 |
\rail@plus |
42617 | 1045 |
\rail@nont{\hyperlink{syntax.context-elem}{\mbox{\isa{context{\isaliteral{5F}{\isacharunderscore}}elem}}}}[] |
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changeset
|
1046 |
\rail@nextplus{1} |
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diff
changeset
|
1047 |
\rail@endplus |
6c621a9d612a
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changeset
|
1048 |
\rail@nextbar{2} |
42617 | 1049 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
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changeset
|
1050 |
\rail@nextbar{3} |
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changeset
|
1051 |
\rail@plus |
42617 | 1052 |
\rail@nont{\hyperlink{syntax.context-elem}{\mbox{\isa{context{\isaliteral{5F}{\isacharunderscore}}elem}}}}[] |
42596
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changeset
|
1053 |
\rail@nextplus{4} |
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changeset
|
1054 |
\rail@endplus |
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diff
changeset
|
1055 |
\rail@endbar |
6c621a9d612a
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changeset
|
1056 |
\rail@end |
42662 | 1057 |
\rail@begin{2}{} |
42596
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changeset
|
1058 |
\rail@term{\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}}[] |
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|
1059 |
\rail@plus |
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changeset
|
1060 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
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changeset
|
1061 |
\rail@nextplus{1} |
6c621a9d612a
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changeset
|
1062 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
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changeset
|
1063 |
\rail@endplus |
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changeset
|
1064 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
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|
1065 |
\rail@nont{\hyperlink{syntax.arity}{\mbox{\isa{arity}}}}[] |
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|
1066 |
\rail@term{\isa{\isakeyword{begin}}}[] |
6c621a9d612a
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changeset
|
1067 |
\rail@end |
42704 | 1068 |
\rail@begin{5}{} |
42596
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changeset
|
1069 |
\rail@term{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}}[] |
42704 | 1070 |
\rail@bar |
1071 |
\rail@nextbar{1} |
|
42596
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modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
1072 |
\rail@plus |
6c621a9d612a
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changeset
|
1073 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
42704 | 1074 |
\rail@nextplus{2} |
42596
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changeset
|
1075 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
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changeset
|
1076 |
\rail@endplus |
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changeset
|
1077 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
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changeset
|
1078 |
\rail@nont{\hyperlink{syntax.arity}{\mbox{\isa{arity}}}}[] |
42704 | 1079 |
\rail@nextbar{3} |
1080 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
|
1081 |
\rail@bar |
|
1082 |
\rail@term{\isa{{\isaliteral{3C}{\isacharless}}}}[] |
|
1083 |
\rail@nextbar{4} |
|
1084 |
\rail@term{\isa{{\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}}}[] |
|
1085 |
\rail@endbar |
|
1086 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
|
1087 |
\rail@endbar |
|
42596
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changeset
|
1088 |
\rail@end |
42662 | 1089 |
\rail@begin{2}{} |
42596
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changeset
|
1090 |
\rail@term{\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}}[] |
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changeset
|
1091 |
\rail@bar |
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changeset
|
1092 |
\rail@nextbar{1} |
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changeset
|
1093 |
\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
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|
1094 |
\rail@endbar |
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|
1095 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
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|
1096 |
\rail@end |
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|
1097 |
\end{railoutput} |
42617 | 1098 |
|
27042 | 1099 |
|
28788 | 1100 |
\begin{description} |
27042 | 1101 |
|
40406 | 1102 |
\item \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3D}{\isacharequal}}\ superclasses\ {\isaliteral{2B}{\isacharplus}}\ body{\isaliteral{22}{\isachardoublequote}}} defines |
27042 | 1103 |
a new class \isa{c}, inheriting from \isa{superclasses}. This |
1104 |
introduces a locale \isa{c} with import of all locales \isa{superclasses}. |
|
1105 |
||
1106 |
Any \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}} in \isa{body} are lifted to the global |
|
40406 | 1107 |
theory level (\emph{class operations} \isa{{\isaliteral{22}{\isachardoublequote}}f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} of class \isa{c}), mapping the local type parameter |
1108 |
\isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} to a schematic type variable \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{22}{\isachardoublequote}}}. |
|
27042 | 1109 |
|
1110 |
Likewise, \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} in \isa{body} are also lifted, |
|
40406 | 1111 |
mapping each local parameter \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} to its |
1112 |
corresponding global constant \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}. The |
|
1113 |
corresponding introduction rule is provided as \isa{c{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{5F}{\isacharunderscore}}axioms{\isaliteral{2E}{\isachardot}}intro}. This rule should be rarely needed directly |
|
1114 |
--- the \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} method takes care of the details of |
|
27042 | 1115 |
class membership proofs. |
1116 |
||
40406 | 1117 |
\item \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}s\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} opens a theory target (cf.\ \secref{sec:target}) which |
1118 |
allows to specify class operations \isa{{\isaliteral{22}{\isachardoublequote}}f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} corresponding |
|
1119 |
to sort \isa{s} at the particular type instance \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}}. A plain \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} command in the |
|
28788 | 1120 |
target body poses a goal stating these type arities. The target is |
1121 |
concluded by an \indexref{local}{command}{end}\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}} command. |
|
27042 | 1122 |
|
1123 |
Note that a list of simultaneous type constructors may be given; |
|
31914 | 1124 |
this corresponds nicely to mutually recursive type definitions, e.g.\ |
27042 | 1125 |
in Isabelle/HOL. |
1126 |
||
28788 | 1127 |
\item \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} in an instantiation target body sets |
40406 | 1128 |
up a goal stating the type arities claimed at the opening \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}. The proof would usually proceed by \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}}, and then establish the characteristic theorems of |
27042 | 1129 |
the type classes involved. After finishing the proof, the |
1130 |
background theory will be augmented by the proven type arities. |
|
1131 |
||
40406 | 1132 |
On the theory level, \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}s{\isaliteral{22}{\isachardoublequote}}} provides a convenient way to instantiate a type class with no |
37115 | 1133 |
need to specify operations: one can continue with the |
31681 | 1134 |
instantiation proof immediately. |
1135 |
||
28788 | 1136 |
\item \hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}~\isa{c} in a class context for class |
27042 | 1137 |
\isa{d} sets up a goal stating that class \isa{c} is logically |
1138 |
contained in class \isa{d}. After finishing the proof, class |
|
1139 |
\isa{d} is proven to be subclass \isa{c} and the locale \isa{c} is interpreted into \isa{d} simultaneously. |
|
1140 |
||
31681 | 1141 |
A weakend form of this is available through a further variant of |
40406 | 1142 |
\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}: \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} opens |
1143 |
a proof that class \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} implies \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} without reference |
|
31681 | 1144 |
to the underlying locales; this is useful if the properties to prove |
1145 |
the logical connection are not sufficent on the locale level but on |
|
1146 |
the theory level. |
|
1147 |
||
40406 | 1148 |
\item \hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}classes}}}} prints all classes in the current |
27042 | 1149 |
theory. |
1150 |
||
40406 | 1151 |
\item \hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isaliteral{5F}{\isacharunderscore}}deps}}}} visualizes all classes and their |
29706 | 1152 |
subclass relations as a Hasse diagram. |
1153 |
||
40406 | 1154 |
\item \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} repeatedly expands all class |
27042 | 1155 |
introduction rules of this theory. Note that this method usually |
1156 |
needs not be named explicitly, as it is already included in the |
|
1157 |
default proof step (e.g.\ of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}). In particular, |
|
1158 |
instantiation of trivial (syntactic) classes may be performed by a |
|
40406 | 1159 |
single ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' proof step. |
26870 | 1160 |
|
28788 | 1161 |
\end{description}% |
26870 | 1162 |
\end{isamarkuptext}% |
1163 |
\isamarkuptrue% |
|
1164 |
% |
|
27042 | 1165 |
\isamarkupsubsection{The class target% |
1166 |
} |
|
1167 |
\isamarkuptrue% |
|
1168 |
% |
|
1169 |
\begin{isamarkuptext}% |
|
1170 |
%FIXME check |
|
1171 |
||
1172 |
A named context may refer to a locale (cf.\ \secref{sec:target}). |
|
1173 |
If this locale is also a class \isa{c}, apart from the common |
|
1174 |
locale target behaviour the following happens. |
|
1175 |
||
1176 |
\begin{itemize} |
|
1177 |
||
40406 | 1178 |
\item Local constant declarations \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} referring to the |
1179 |
local type parameter \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} and local parameters \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} |
|
1180 |
are accompanied by theory-level constants \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} |
|
1181 |
referring to theory-level class operations \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}. |
|
27042 | 1182 |
|
1183 |
\item Local theorem bindings are lifted as are assumptions. |
|
1184 |
||
40406 | 1185 |
\item Local syntax refers to local operations \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} and |
1186 |
global operations \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} uniformly. Type inference |
|
27042 | 1187 |
resolves ambiguities. In rare cases, manual type annotations are |
1188 |
needed. |
|
1189 |
||
1190 |
\end{itemize}% |
|
1191 |
\end{isamarkuptext}% |
|
1192 |
\isamarkuptrue% |
|
1193 |
% |
|
37768
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1194 |
\isamarkupsubsection{Co-regularity of type classes and arities% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1195 |
} |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1196 |
\isamarkuptrue% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1197 |
% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1198 |
\begin{isamarkuptext}% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1199 |
The class relation together with the collection of |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1200 |
type-constructor arities must obey the principle of |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1201 |
\emph{co-regularity} as defined below. |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1202 |
|
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1203 |
\medskip For the subsequent formulation of co-regularity we assume |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1204 |
that the class relation is closed by transitivity and reflexivity. |
40406 | 1205 |
Moreover the collection of arities \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{22}{\isachardoublequote}}} is |
1206 |
completed such that \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} |
|
1207 |
implies \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} for all such declarations. |
|
37768
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1208 |
|
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1209 |
Treating sorts as finite sets of classes (meaning the intersection), |
40406 | 1210 |
the class relation \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} is extended to sorts as |
37768
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1211 |
follows: |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1212 |
\[ |
40406 | 1213 |
\isa{{\isaliteral{22}{\isachardoublequote}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} |
37768
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1214 |
\] |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1215 |
|
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1216 |
This relation on sorts is further extended to tuples of sorts (of |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1217 |
the same length) in the component-wise way. |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1218 |
|
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1219 |
\smallskip Co-regularity of the class relation together with the |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1220 |
arities relation means: |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1221 |
\[ |
40406 | 1222 |
\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} |
37768
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1223 |
\] |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1224 |
\noindent for all such arities. In other words, whenever the result |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1225 |
classes of some type-constructor arities are related, then the |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1226 |
argument sorts need to be related in the same way. |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1227 |
|
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1228 |
\medskip Co-regularity is a very fundamental property of the |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1229 |
order-sorted algebra of types. For example, it entails principle |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1230 |
types and most general unifiers, e.g.\ see \cite{nipkow-prehofer}.% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1231 |
\end{isamarkuptext}% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1232 |
\isamarkuptrue% |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1233 |
% |
27042 | 1234 |
\isamarkupsection{Unrestricted overloading% |
1235 |
} |
|
1236 |
\isamarkuptrue% |
|
1237 |
% |
|
1238 |
\begin{isamarkuptext}% |
|
47483 | 1239 |
\begin{matharray}{rcl} |
1240 |
\indexdef{}{command}{overloading}\hypertarget{command.overloading}{\hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1241 |
\end{matharray} |
|
1242 |
||
1243 |
Isabelle/Pure's definitional schemes support certain forms of |
|
31047 | 1244 |
overloading (see \secref{sec:consts}). Overloading means that a |
40406 | 1245 |
constant being declared as \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ decl{\isaliteral{22}{\isachardoublequote}}} may be |
31047 | 1246 |
defined separately on type instances |
40406 | 1247 |
\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t\ decl{\isaliteral{22}{\isachardoublequote}}} |
31047 | 1248 |
for each type constructor \isa{t}. At most occassions |
27042 | 1249 |
overloading will be used in a Haskell-like fashion together with |
1250 |
type classes by means of \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}} (see |
|
1251 |
\secref{sec:class}). Sometimes low-level overloading is desirable. |
|
1252 |
The \hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}} target provides a convenient view for |
|
1253 |
end-users. |
|
1254 |
||
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|
1255 |
\begin{railoutput} |
42704 | 1256 |
\rail@begin{2}{} |
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1257 |
\rail@term{\hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}}[] |
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1258 |
\rail@plus |
42704 | 1259 |
\rail@nont{\isa{spec}}[] |
1260 |
\rail@nextplus{1} |
|
1261 |
\rail@endplus |
|
1262 |
\rail@term{\isa{\isakeyword{begin}}}[] |
|
1263 |
\rail@end |
|
1264 |
\rail@begin{2}{\isa{spec}} |
|
42617 | 1265 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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|
1266 |
\rail@bar |
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|
1267 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}}}[] |
42704 | 1268 |
\rail@nextbar{1} |
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1269 |
\rail@term{\isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}}}[] |
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1270 |
\rail@endbar |
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|
1271 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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|
1272 |
\rail@bar |
42704 | 1273 |
\rail@nextbar{1} |
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|
1274 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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1275 |
\rail@term{\isa{\isakeyword{unchecked}}}[] |
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1276 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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|
1277 |
\rail@endbar |
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|
1278 |
\rail@end |
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|
1279 |
\end{railoutput} |
42617 | 1280 |
|
27042 | 1281 |
|
28788 | 1282 |
\begin{description} |
27042 | 1283 |
|
40406 | 1284 |
\item \hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} |
27042 | 1285 |
opens a theory target (cf.\ \secref{sec:target}) which allows to |
1286 |
specify constants with overloaded definitions. These are identified |
|
40406 | 1287 |
by an explicitly given mapping from variable names \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} to |
1288 |
constants \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} at particular type instances. The |
|
28788 | 1289 |
definitions themselves are established using common specification |
40406 | 1290 |
tools, using the names \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} as reference to the |
28788 | 1291 |
corresponding constants. The target is concluded by \hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}. |
27042 | 1292 |
|
40406 | 1293 |
A \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}unchecked{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option disables global dependency checks for |
27042 | 1294 |
the corresponding definition, which is occasionally useful for |
31047 | 1295 |
exotic overloading (see \secref{sec:consts} for a precise description). |
1296 |
It is at the discretion of the user to avoid |
|
27042 | 1297 |
malformed theory specifications! |
1298 |
||
28788 | 1299 |
\end{description}% |
27042 | 1300 |
\end{isamarkuptext}% |
1301 |
\isamarkuptrue% |
|
1302 |
% |
|
1303 |
\isamarkupsection{Incorporating ML code \label{sec:ML}% |
|
1304 |
} |
|
1305 |
\isamarkuptrue% |
|
1306 |
% |
|
1307 |
\begin{isamarkuptext}% |
|
1308 |
\begin{matharray}{rcl} |
|
40406 | 1309 |
\indexdef{}{command}{use}\hypertarget{command.use}{\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
1310 |
\indexdef{}{command}{ML}\hypertarget{command.ML}{\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1311 |
\indexdef{}{command}{ML\_prf}\hypertarget{command.ML-prf}{\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1312 |
\indexdef{}{command}{ML\_val}\hypertarget{command.ML-val}{\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1313 |
\indexdef{}{command}{ML\_command}\hypertarget{command.ML-command}{\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1314 |
\indexdef{}{command}{setup}\hypertarget{command.setup}{\hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1315 |
\indexdef{}{command}{local\_setup}\hypertarget{command.local-setup}{\hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1316 |
\indexdef{}{command}{attribute\_setup}\hypertarget{command.attribute-setup}{\hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
27042 | 1317 |
\end{matharray} |
1318 |
||
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|
1319 |
\begin{railoutput} |
42662 | 1320 |
\rail@begin{1}{} |
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|
1321 |
\rail@term{\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}}[] |
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|
1322 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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|
1323 |
\rail@end |
42662 | 1324 |
\rail@begin{6}{} |
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changeset
|
1325 |
\rail@bar |
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|
1326 |
\rail@term{\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}}[] |
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|
1327 |
\rail@nextbar{1} |
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|
1328 |
\rail@term{\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}}}[] |
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|
1329 |
\rail@nextbar{2} |
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|
1330 |
\rail@term{\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}}}[] |
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|
1331 |
\rail@nextbar{3} |
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|
1332 |
\rail@term{\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}}}[] |
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|
1333 |
\rail@nextbar{4} |
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|
1334 |
\rail@term{\hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}}[] |
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|
1335 |
\rail@nextbar{5} |
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|
1336 |
\rail@term{\hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isaliteral{5F}{\isacharunderscore}}setup}}}}}[] |
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|
1337 |
\rail@endbar |
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|
1338 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
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|
1339 |
\rail@end |
42813
6c841fa92fa2
optional description for 'attribute_setup' and 'method_setup';
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|
1340 |
\rail@begin{2}{} |
42596
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|
1341 |
\rail@term{\hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}}}[] |
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|
1342 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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|
1343 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
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|
1344 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
42813
6c841fa92fa2
optional description for 'attribute_setup' and 'method_setup';
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|
1345 |
\rail@bar |
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optional description for 'attribute_setup' and 'method_setup';
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|
1346 |
\rail@nextbar{1} |
42596
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diff
changeset
|
1347 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
42813
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optional description for 'attribute_setup' and 'method_setup';
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|
1348 |
\rail@endbar |
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|
1349 |
\rail@end |
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|
1350 |
\end{railoutput} |
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changeset
|
1351 |
|
27042 | 1352 |
|
28788 | 1353 |
\begin{description} |
27042 | 1354 |
|
40406 | 1355 |
\item \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}} reads and executes ML |
1356 |
commands from \isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}. The current theory context is passed |
|
28788 | 1357 |
down to the ML toplevel and may be modified, using \verb|Context.>>| or derived ML commands. The file name is checked with |
27042 | 1358 |
the \indexref{}{keyword}{uses}\hyperlink{keyword.uses}{\mbox{\isa{\isakeyword{uses}}}} dependency declaration given in the theory |
1359 |
header (see also \secref{sec:begin-thy}). |
|
28281 | 1360 |
|
1361 |
Top-level ML bindings are stored within the (global or local) theory |
|
1362 |
context. |
|
27042 | 1363 |
|
40406 | 1364 |
\item \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} is similar to \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}, |
1365 |
but executes ML commands directly from the given \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}}. |
|
28788 | 1366 |
Top-level ML bindings are stored within the (global or local) theory |
1367 |
context. |
|
28281 | 1368 |
|
40406 | 1369 |
\item \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}} is analogous to \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}} but works |
28788 | 1370 |
within a proof context. |
28281 | 1371 |
|
1372 |
Top-level ML bindings are stored within the proof context in a |
|
1373 |
purely sequential fashion, disregarding the nested proof structure. |
|
40406 | 1374 |
ML bindings introduced by \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}} are discarded at the |
28281 | 1375 |
end of the proof. |
27042 | 1376 |
|
40406 | 1377 |
\item \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} and \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}} are diagnostic |
28788 | 1378 |
versions of \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}, which means that the context may not be |
40406 | 1379 |
updated. \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} echos the bindings produced at the ML |
1380 |
toplevel, but \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}} is silent. |
|
27042 | 1381 |
|
40406 | 1382 |
\item \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} changes the current theory |
1383 |
context by applying \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}}, which refers to an ML expression |
|
30463 | 1384 |
of type \verb|theory -> theory|. This enables to initialize |
1385 |
any object-logic specific tools and packages written in ML, for |
|
1386 |
example. |
|
1387 |
||
40406 | 1388 |
\item \hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isaliteral{5F}{\isacharunderscore}}setup}}}} is similar to \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}} for |
30463 | 1389 |
a local theory context, and an ML expression of type \verb|local_theory -> local_theory|. This allows to |
1390 |
invoke local theory specification packages without going through |
|
1391 |
concrete outer syntax, for example. |
|
27042 | 1392 |
|
40406 | 1393 |
\item \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ text\ description{\isaliteral{22}{\isachardoublequote}}} |
1394 |
defines an attribute in the current theory. The given \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} has to be an ML expression of type |
|
30527 | 1395 |
\verb|attribute context_parser|, cf.\ basic parsers defined in |
1396 |
structure \verb|Args| and \verb|Attrib|. |
|
1397 |
||
1398 |
In principle, attributes can operate both on a given theorem and the |
|
1399 |
implicit context, although in practice only one is modified and the |
|
1400 |
other serves as parameter. Here are examples for these two cases: |
|
1401 |
||
1402 |
\end{description}% |
|
1403 |
\end{isamarkuptext}% |
|
1404 |
\isamarkuptrue% |
|
1405 |
% |
|
1406 |
\isadelimML |
|
42704 | 1407 |
\ \ % |
30527 | 1408 |
\endisadelimML |
1409 |
% |
|
1410 |
\isatagML |
|
40406 | 1411 |
\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse% |
1412 |
\ my{\isaliteral{5F}{\isacharunderscore}}rule\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline |
|
42704 | 1413 |
\ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ ths\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline |
1414 |
\ \ \ \ \ \ Thm{\isaliteral{2E}{\isachardot}}rule{\isaliteral{5F}{\isacharunderscore}}attribute\isanewline |
|
1415 |
\ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}fn\ context{\isaliteral{3A}{\isacharcolon}}\ Context{\isaliteral{2E}{\isachardot}}generic\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ th{\isaliteral{3A}{\isacharcolon}}\ thm\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline |
|
40406 | 1416 |
\ \ \ \ \ \ \ \ \ \ let\ val\ th{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ th\ OF\ ths\isanewline |
42936 | 1417 |
\ \ \ \ \ \ \ \ \ \ in\ th{\isaliteral{27}{\isacharprime}}\ end{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline |
30527 | 1418 |
\isanewline |
42704 | 1419 |
\ \ \isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse% |
40406 | 1420 |
\ my{\isaliteral{5F}{\isacharunderscore}}declaration\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline |
42704 | 1421 |
\ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ ths\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline |
1422 |
\ \ \ \ \ \ Thm{\isaliteral{2E}{\isachardot}}declaration{\isaliteral{5F}{\isacharunderscore}}attribute\isanewline |
|
1423 |
\ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}fn\ th{\isaliteral{3A}{\isacharcolon}}\ thm\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ context{\isaliteral{3A}{\isacharcolon}}\ Context{\isaliteral{2E}{\isachardot}}generic\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline |
|
40406 | 1424 |
\ \ \ \ \ \ \ \ \ \ let\ val\ context{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ context\isanewline |
42936 | 1425 |
\ \ \ \ \ \ \ \ \ \ in\ context{\isaliteral{27}{\isacharprime}}\ end{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}% |
30527 | 1426 |
\endisatagML |
1427 |
{\isafoldML}% |
|
1428 |
% |
|
1429 |
\isadelimML |
|
1430 |
% |
|
1431 |
\endisadelimML |
|
1432 |
% |
|
27042 | 1433 |
\isamarkupsection{Primitive specification elements% |
1434 |
} |
|
1435 |
\isamarkuptrue% |
|
1436 |
% |
|
1437 |
\isamarkupsubsection{Type classes and sorts \label{sec:classes}% |
|
1438 |
} |
|
1439 |
\isamarkuptrue% |
|
1440 |
% |
|
1441 |
\begin{isamarkuptext}% |
|
1442 |
\begin{matharray}{rcll} |
|
40406 | 1443 |
\indexdef{}{command}{classes}\hypertarget{command.classes}{\hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
1444 |
\indexdef{}{command}{classrel}\hypertarget{command.classrel}{\hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\ |
|
1445 |
\indexdef{}{command}{default\_sort}\hypertarget{command.default-sort}{\hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isaliteral{5F}{\isacharunderscore}}sort}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} |
|
27042 | 1446 |
\end{matharray} |
1447 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1448 |
\begin{railoutput} |
42662 | 1449 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1450 |
\rail@term{\hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1451 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1452 |
\rail@nont{\hyperlink{syntax.classdecl}{\mbox{\isa{classdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1453 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1454 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1455 |
\rail@end |
42662 | 1456 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1457 |
\rail@term{\hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1458 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1459 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1460 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1461 |
\rail@term{\isa{{\isaliteral{3C}{\isacharless}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1462 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1463 |
\rail@term{\isa{{\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1464 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1465 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1466 |
\rail@nextplus{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1467 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1468 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1469 |
\rail@end |
42662 | 1470 |
\rail@begin{1}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1471 |
\rail@term{\hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isaliteral{5F}{\isacharunderscore}}sort}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1472 |
\rail@nont{\hyperlink{syntax.sort}{\mbox{\isa{sort}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1473 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1474 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1475 |
|
27042 | 1476 |
|
28788 | 1477 |
\begin{description} |
27042 | 1478 |
|
40406 | 1479 |
\item \hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} declares class |
1480 |
\isa{c} to be a subclass of existing classes \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}. |
|
28788 | 1481 |
Isabelle implicitly maintains the transitive closure of the class |
1482 |
hierarchy. Cyclic class structures are not permitted. |
|
1483 |
||
40406 | 1484 |
\item \hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} states subclass |
1485 |
relations between existing classes \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}. |
|
37768
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1486 |
This is done axiomatically! The \indexref{}{command}{subclass}\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}} and |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1487 |
\indexref{}{command}{instance}\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} commands (see \secref{sec:class}) provide |
e86221f3bac7
moved co-regularity to class section; avoid duplicated class_deps
haftmann
parents:
37115
diff
changeset
|
1488 |
a way to introduce proven class relations. |
27042 | 1489 |
|
40406 | 1490 |
\item \hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isaliteral{5F}{\isacharunderscore}}sort}}}}~\isa{s} makes sort \isa{s} the |
28788 | 1491 |
new default sort for any type variable that is given explicitly in |
1492 |
the text, but lacks a sort constraint (wrt.\ the current context). |
|
1493 |
Type variables generated by type inference are not affected. |
|
27042 | 1494 |
|
28788 | 1495 |
Usually the default sort is only changed when defining a new |
1496 |
object-logic. For example, the default sort in Isabelle/HOL is |
|
39831 | 1497 |
\isa{type}, the class of all HOL types. |
27042 | 1498 |
|
28788 | 1499 |
When merging theories, the default sorts of the parents are |
1500 |
logically intersected, i.e.\ the representations as lists of classes |
|
1501 |
are joined. |
|
1502 |
||
1503 |
\end{description}% |
|
27042 | 1504 |
\end{isamarkuptext}% |
1505 |
\isamarkuptrue% |
|
1506 |
% |
|
1507 |
\isamarkupsubsection{Types and type abbreviations \label{sec:types-pure}% |
|
1508 |
} |
|
1509 |
\isamarkuptrue% |
|
1510 |
% |
|
1511 |
\begin{isamarkuptext}% |
|
1512 |
\begin{matharray}{rcll} |
|
41249
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1513 |
\indexdef{}{command}{type\_synonym}\hypertarget{command.type-synonym}{\hyperlink{command.type-synonym}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}synonym}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
40406 | 1514 |
\indexdef{}{command}{typedecl}\hypertarget{command.typedecl}{\hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
1515 |
\indexdef{}{command}{arities}\hypertarget{command.arities}{\hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\ |
|
27042 | 1516 |
\end{matharray} |
1517 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1518 |
\begin{railoutput} |
42662 | 1519 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1520 |
\rail@term{\hyperlink{command.type-synonym}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}synonym}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1521 |
\rail@nont{\hyperlink{syntax.typespec}{\mbox{\isa{typespec}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1522 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1523 |
\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1524 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1525 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1526 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1527 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1528 |
\rail@end |
42662 | 1529 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1530 |
\rail@term{\hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1531 |
\rail@nont{\hyperlink{syntax.typespec}{\mbox{\isa{typespec}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1532 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1533 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1534 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1535 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1536 |
\rail@end |
42662 | 1537 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1538 |
\rail@term{\hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1539 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1540 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1541 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1542 |
\rail@nont{\hyperlink{syntax.arity}{\mbox{\isa{arity}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1543 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1544 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1545 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1546 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1547 |
|
27042 | 1548 |
|
28788 | 1549 |
\begin{description} |
27042 | 1550 |
|
41249
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1551 |
\item \hyperlink{command.type-synonym}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}synonym}}}}~\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}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} |
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1552 |
introduces a \emph{type synonym} \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}}} for the |
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1553 |
existing type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}}. Unlike actual type definitions, as are |
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1554 |
available in Isabelle/HOL for example, type synonyms are merely |
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1555 |
syntactic abbreviations without any logical significance. |
26f12f98f50a
Command 'type_synonym' (with single argument) supersedes 'types' (legacy feature);
wenzelm
parents:
40802
diff
changeset
|
1556 |
Internally, type synonyms are fully expanded. |
27042 | 1557 |
|
40406 | 1558 |
\item \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\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}}} declares a new |
28788 | 1559 |
type constructor \isa{t}. If the object-logic defines a base sort |
1560 |
\isa{s}, then the constructor is declared to operate on that, via |
|
40406 | 1561 |
the axiomatic specification \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}s{\isaliteral{22}{\isachardoublequote}}}. |
28788 | 1562 |
|
40406 | 1563 |
\item \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}s{\isaliteral{22}{\isachardoublequote}}} augments |
28788 | 1564 |
Isabelle's order-sorted signature of types by new type constructor |
35282
8fd9d555d04d
dropped references to old axclass from documentation
haftmann
parents:
33868
diff
changeset
|
1565 |
arities. This is done axiomatically! The \indexref{}{command}{instantiation}\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}} |
8fd9d555d04d
dropped references to old axclass from documentation
haftmann
parents:
33868
diff
changeset
|
1566 |
target (see \secref{sec:class}) provides a way to introduce |
28788 | 1567 |
proven type arities. |
1568 |
||
1569 |
\end{description}% |
|
1570 |
\end{isamarkuptext}% |
|
1571 |
\isamarkuptrue% |
|
1572 |
% |
|
27042 | 1573 |
\isamarkupsubsection{Constants and definitions \label{sec:consts}% |
1574 |
} |
|
1575 |
\isamarkuptrue% |
|
1576 |
% |
|
1577 |
\begin{isamarkuptext}% |
|
47483 | 1578 |
\begin{matharray}{rcl} |
1579 |
\indexdef{}{command}{consts}\hypertarget{command.consts}{\hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1580 |
\indexdef{}{command}{defs}\hypertarget{command.defs}{\hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1581 |
\end{matharray} |
|
1582 |
||
1583 |
Definitions essentially express abbreviations within the logic. The |
|
40406 | 1584 |
simplest form of a definition is \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}, where \isa{c} is a newly declared constant. Isabelle also allows derived forms |
27042 | 1585 |
where the arguments of \isa{c} appear on the left, abbreviating a |
40406 | 1586 |
prefix of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-abstractions, e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{22}{\isachardoublequote}}} may be |
1587 |
written more conveniently as \isa{{\isaliteral{22}{\isachardoublequote}}c\ x\ y\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}. Moreover, |
|
27042 | 1588 |
definitions may be weakened by adding arbitrary pre-conditions: |
40406 | 1589 |
\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ c\ x\ y\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}. |
27042 | 1590 |
|
1591 |
\medskip The built-in well-formedness conditions for definitional |
|
1592 |
specifications are: |
|
1593 |
||
1594 |
\begin{itemize} |
|
1595 |
||
1596 |
\item Arguments (on the left-hand side) must be distinct variables. |
|
1597 |
||
1598 |
\item All variables on the right-hand side must also appear on the |
|
1599 |
left-hand side. |
|
1600 |
||
1601 |
\item All type variables on the right-hand side must also appear on |
|
40406 | 1602 |
the left-hand side; this prohibits \isa{{\isaliteral{22}{\isachardoublequote}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ length\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ list{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} for example. |
27042 | 1603 |
|
1604 |
\item The definition must not be recursive. Most object-logics |
|
1605 |
provide definitional principles that can be used to express |
|
1606 |
recursion safely. |
|
1607 |
||
1608 |
\end{itemize} |
|
1609 |
||
31047 | 1610 |
The right-hand side of overloaded definitions may mention overloaded constants |
27042 | 1611 |
recursively at type instances corresponding to the immediate |
40406 | 1612 |
argument types \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}. Incomplete |
27042 | 1613 |
specification patterns impose global constraints on all occurrences, |
40406 | 1614 |
e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}d\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}} on the left-hand side means that all |
27042 | 1615 |
corresponding occurrences on some right-hand side need to be an |
40406 | 1616 |
instance of this, general \isa{{\isaliteral{22}{\isachardoublequote}}d\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequote}}} will be disallowed. |
27042 | 1617 |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1618 |
\begin{railoutput} |
42662 | 1619 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1620 |
\rail@term{\hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1621 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1622 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1623 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1624 |
\rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1625 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1626 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1627 |
\rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1628 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1629 |
\rail@nextplus{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1630 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1631 |
\rail@end |
42704 | 1632 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1633 |
\rail@term{\hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1634 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1635 |
\rail@nextbar{1} |
42704 | 1636 |
\rail@nont{\isa{opt}}[] |
1637 |
\rail@endbar |
|
1638 |
\rail@plus |
|
1639 |
\rail@nont{\hyperlink{syntax.axmdecl}{\mbox{\isa{axmdecl}}}}[] |
|
1640 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
|
1641 |
\rail@nextplus{1} |
|
1642 |
\rail@endplus |
|
1643 |
\rail@end |
|
1644 |
\rail@begin{2}{\isa{opt}} |
|
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1645 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1646 |
\rail@bar |
42704 | 1647 |
\rail@nextbar{1} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1648 |
\rail@term{\isa{\isakeyword{unchecked}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1649 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1650 |
\rail@bar |
42704 | 1651 |
\rail@nextbar{1} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1652 |
\rail@term{\isa{\isakeyword{overloaded}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1653 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1654 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1655 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1656 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1657 |
|
27042 | 1658 |
|
28788 | 1659 |
\begin{description} |
27042 | 1660 |
|
40406 | 1661 |
\item \hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{22}{\isachardoublequote}}} declares constant \isa{c} to have any instance of type scheme \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}}. The optional |
28788 | 1662 |
mixfix annotations may attach concrete syntax to the constants |
1663 |
declared. |
|
27042 | 1664 |
|
40406 | 1665 |
\item \hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ eqn{\isaliteral{22}{\isachardoublequote}}} introduces \isa{eqn} |
27042 | 1666 |
as a definitional axiom for some existing constant. |
1667 |
||
40406 | 1668 |
The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}unchecked{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option disables global dependency checks |
27042 | 1669 |
for this definition, which is occasionally useful for exotic |
1670 |
overloading. It is at the discretion of the user to avoid malformed |
|
1671 |
theory specifications! |
|
1672 |
||
40406 | 1673 |
The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}overloaded{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option declares definitions to be |
27042 | 1674 |
potentially overloaded. Unless this option is given, a warning |
1675 |
message would be issued for any definitional equation with a more |
|
1676 |
special type than that of the corresponding constant declaration. |
|
1677 |
||
28788 | 1678 |
\end{description}% |
27042 | 1679 |
\end{isamarkuptext}% |
1680 |
\isamarkuptrue% |
|
1681 |
% |
|
1682 |
\isamarkupsection{Axioms and theorems \label{sec:axms-thms}% |
|
1683 |
} |
|
1684 |
\isamarkuptrue% |
|
1685 |
% |
|
1686 |
\begin{isamarkuptext}% |
|
1687 |
\begin{matharray}{rcll} |
|
40406 | 1688 |
\indexdef{}{command}{axioms}\hypertarget{command.axioms}{\hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\ |
1689 |
\indexdef{}{command}{lemmas}\hypertarget{command.lemmas}{\hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1690 |
\indexdef{}{command}{theorems}\hypertarget{command.theorems}{\hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
27042 | 1691 |
\end{matharray} |
1692 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1693 |
\begin{railoutput} |
42662 | 1694 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1695 |
\rail@term{\hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1696 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1697 |
\rail@nont{\hyperlink{syntax.axmdecl}{\mbox{\isa{axmdecl}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1698 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1699 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1700 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1701 |
\rail@end |
45600
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1702 |
\rail@begin{6}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1703 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1704 |
\rail@term{\hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1705 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1706 |
\rail@term{\hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1707 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1708 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1709 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1710 |
\rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1711 |
\rail@endbar |
45600
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1712 |
\rail@cr{3} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1713 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1714 |
\rail@bar |
45600
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1715 |
\rail@nextbar{4} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1716 |
\rail@nont{\hyperlink{syntax.thmdef}{\mbox{\isa{thmdef}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1717 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1718 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
45600
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
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diff
changeset
|
1719 |
\rail@nextplus{5} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1720 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1721 |
\rail@endplus |
45600
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1722 |
\rail@bar |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1723 |
\rail@nextbar{4} |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1724 |
\rail@term{\isa{\isakeyword{for}}}[] |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1725 |
\rail@plus |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1726 |
\rail@nont{\hyperlink{syntax.vars}{\mbox{\isa{vars}}}}[] |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1727 |
\rail@nextplus{5} |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1728 |
\rail@cterm{\isa{\isakeyword{and}}}[] |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1729 |
\rail@endplus |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1730 |
\rail@endbar |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1731 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1732 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1733 |
|
27042 | 1734 |
|
28788 | 1735 |
\begin{description} |
27042 | 1736 |
|
40406 | 1737 |
\item \hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} introduces arbitrary |
27042 | 1738 |
statements as axioms of the meta-logic. In fact, axioms are |
1739 |
``axiomatic theorems'', and may be referred later just as any other |
|
1740 |
theorem. |
|
1741 |
||
1742 |
Axioms are usually only introduced when declaring new logical |
|
1743 |
systems. Everyday work is typically done the hard way, with proper |
|
1744 |
definitions and proven theorems. |
|
1745 |
||
45600
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1746 |
\item \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}~\indexdef{}{keyword}{for}\hypertarget{keyword.for}{\hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} evaluates given facts (with attributes) in |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1747 |
the current context, which may be augmented by local variables. |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1748 |
Results are standardized before being stored, i.e.\ schematic |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1749 |
variables are renamed to enforce index \isa{{\isaliteral{22}{\isachardoublequote}}{\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} uniformly. |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1750 |
|
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1751 |
\item \hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}} is the same as \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}, but |
1bbbac9a0cb0
'lemmas' / 'theorems' commands allow 'for' fixes and standardize the result before storing;
wenzelm
parents:
42936
diff
changeset
|
1752 |
marks the result as a different kind of facts. |
27042 | 1753 |
|
28788 | 1754 |
\end{description}% |
27042 | 1755 |
\end{isamarkuptext}% |
1756 |
\isamarkuptrue% |
|
1757 |
% |
|
1758 |
\isamarkupsection{Oracles% |
|
1759 |
} |
|
1760 |
\isamarkuptrue% |
|
1761 |
% |
|
1762 |
\begin{isamarkuptext}% |
|
47483 | 1763 |
\begin{matharray}{rcll} |
1764 |
\indexdef{}{command}{oracle}\hypertarget{command.oracle}{\hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\ |
|
1765 |
\end{matharray} |
|
1766 |
||
1767 |
Oracles allow Isabelle to take advantage of external reasoners such |
|
1768 |
as arithmetic decision procedures, model checkers, fast tautology |
|
1769 |
checkers or computer algebra systems. Invoked as an oracle, an |
|
1770 |
external reasoner can create arbitrary Isabelle theorems. |
|
27042 | 1771 |
|
28788 | 1772 |
It is the responsibility of the user to ensure that the external |
1773 |
reasoner is as trustworthy as the application requires. Another |
|
1774 |
typical source of errors is the linkup between Isabelle and the |
|
1775 |
external tool, not just its concrete implementation, but also the |
|
1776 |
required translation between two different logical environments. |
|
1777 |
||
1778 |
Isabelle merely guarantees well-formedness of the propositions being |
|
1779 |
asserted, and records within the internal derivation object how |
|
1780 |
presumed theorems depend on unproven suppositions. |
|
1781 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1782 |
\begin{railoutput} |
42662 | 1783 |
\rail@begin{1}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1784 |
\rail@term{\hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1785 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1786 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1787 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1788 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1789 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1790 |
|
27042 | 1791 |
|
28788 | 1792 |
\begin{description} |
27042 | 1793 |
|
40406 | 1794 |
\item \hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ text{\isaliteral{22}{\isachardoublequote}}} turns the given ML |
1795 |
expression \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} of type \verb|'a -> cterm| into an |
|
28291 | 1796 |
ML function of type \verb|'a -> thm|, which is bound to the |
28788 | 1797 |
global identifier \verb|name|. This acts like an infinitary |
1798 |
specification of axioms! Invoking the oracle only works within the |
|
1799 |
scope of the resulting theory. |
|
27042 | 1800 |
|
28788 | 1801 |
\end{description} |
1802 |
||
40802 | 1803 |
See \verb|~~/src/HOL/ex/Iff_Oracle.thy| for a worked example of |
28788 | 1804 |
defining a new primitive rule as oracle, and turning it into a proof |
1805 |
method.% |
|
27042 | 1806 |
\end{isamarkuptext}% |
1807 |
\isamarkuptrue% |
|
1808 |
% |
|
1809 |
\isamarkupsection{Name spaces% |
|
1810 |
} |
|
1811 |
\isamarkuptrue% |
|
1812 |
% |
|
1813 |
\begin{isamarkuptext}% |
|
1814 |
\begin{matharray}{rcl} |
|
40406 | 1815 |
\indexdef{}{command}{hide\_class}\hypertarget{command.hide-class}{\hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
1816 |
\indexdef{}{command}{hide\_type}\hypertarget{command.hide-type}{\hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1817 |
\indexdef{}{command}{hide\_const}\hypertarget{command.hide-const}{\hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}const}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
1818 |
\indexdef{}{command}{hide\_fact}\hypertarget{command.hide-fact}{\hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}fact}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
|
27042 | 1819 |
\end{matharray} |
1820 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1821 |
\begin{railoutput} |
42662 | 1822 |
\rail@begin{4}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1823 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1824 |
\rail@nont{\hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1825 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1826 |
\rail@nont{\hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}type}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1827 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1828 |
\rail@nont{\hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}const}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1829 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1830 |
\rail@nont{\hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}fact}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1831 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1832 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1833 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1834 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1835 |
\rail@term{\isa{\isakeyword{open}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1836 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1837 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1838 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1839 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1840 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1841 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1842 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1843 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
41435
diff
changeset
|
1844 |
|
27042 | 1845 |
|
1846 |
Isabelle organizes any kind of name declarations (of types, |
|
1847 |
constants, theorems etc.) by separate hierarchically structured name |
|
1848 |
spaces. Normally the user does not have to control the behavior of |
|
1849 |
name spaces by hand, yet the following commands provide some way to |
|
1850 |
do so. |
|
1851 |
||
28788 | 1852 |
\begin{description} |
27042 | 1853 |
|
40406 | 1854 |
\item \hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}~\isa{names} fully removes class |
1855 |
declarations from a given name space; with the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}open{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} |
|
39977
c9cbc16e93ce
do not mention unqualified names, now that 'global' and 'local' are gone
krauss
parents:
39280
diff
changeset
|
1856 |
option, only the base name is hidden. |
36177
8e0770d2e499
separate commands 'hide_class', 'hide_type', 'hide_const', 'hide_fact';
wenzelm
parents:
35681
diff
changeset
|
1857 |
|
27042 | 1858 |
Note that hiding name space accesses has no impact on logical |
28788 | 1859 |
declarations --- they remain valid internally. Entities that are no |
27042 | 1860 |
longer accessible to the user are printed with the special qualifier |
40406 | 1861 |
``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' prefixed to the full internal name. |
27042 | 1862 |
|
40406 | 1863 |
\item \hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}type}}}}, \hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}const}}}}, and \hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}fact}}}} are similar to \hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}, but hide types, |
36177
8e0770d2e499
separate commands 'hide_class', 'hide_type', 'hide_const', 'hide_fact';
wenzelm
parents:
35681
diff
changeset
|
1864 |
constants, and facts, respectively. |
8e0770d2e499
separate commands 'hide_class', 'hide_type', 'hide_const', 'hide_fact';
wenzelm
parents:
35681
diff
changeset
|
1865 |
|
28788 | 1866 |
\end{description}% |
27042 | 1867 |
\end{isamarkuptext}% |
1868 |
\isamarkuptrue% |
|
1869 |
% |
|
26869 | 1870 |
\isadelimtheory |
1871 |
% |
|
1872 |
\endisadelimtheory |
|
1873 |
% |
|
1874 |
\isatagtheory |
|
1875 |
\isacommand{end}\isamarkupfalse% |
|
1876 |
% |
|
1877 |
\endisatagtheory |
|
1878 |
{\isafoldtheory}% |
|
1879 |
% |
|
1880 |
\isadelimtheory |
|
1881 |
% |
|
1882 |
\endisadelimtheory |
|
1883 |
\isanewline |
|
1884 |
\end{isabellebody}% |
|
1885 |
%%% Local Variables: |
|
1886 |
%%% mode: latex |
|
1887 |
%%% TeX-master: "root" |
|
1888 |
%%% End: |