# HG changeset patch # User wenzelm # Date 1210158252 -7200 # Node ID 81308d44fe0a380d70ec8173531b28092721d374 # Parent 6ac51a2f48e1377ce63f7d71f911003b28ff291f updated generated file; diff -r 6ac51a2f48e1 -r 81308d44fe0a doc-src/IsarRef/Thy/document/Generic.tex --- a/doc-src/IsarRef/Thy/document/Generic.tex Wed May 07 12:56:11 2008 +0200 +++ b/doc-src/IsarRef/Thy/document/Generic.tex Wed May 07 13:04:12 2008 +0200 @@ -38,7 +38,7 @@ \indexdef{}{command}{definition}\mbox{\isa{\isacommand{definition}}} & : & \isarkeep{local{\dsh}theory} \\ \indexdef{}{attribute}{defn}\mbox{\isa{defn}} & : & \isaratt \\ \indexdef{}{command}{abbreviation}\mbox{\isa{\isacommand{abbreviation}}} & : & \isarkeep{local{\dsh}theory} \\ - \indexdef{}{command}{print-abbrevs}\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-abbrevs}\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \indexdef{}{command}{notation}\mbox{\isa{\isacommand{notation}}} & : & \isarkeep{local{\dsh}theory} \\ \indexdef{}{command}{no-notation}\mbox{\isa{\isacommand{no{\isacharunderscore}notation}}} & : & \isarkeep{local{\dsh}theory} \\ \end{matharray} @@ -68,7 +68,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{axiomatization}}}~\isa{c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub m\ {\isasymWHERE}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n}] introduces several constants + \item [\mbox{\isa{\isacommand{axiomatization}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub m\ {\isasymWHERE}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}] introduces several constants simultaneously and states axiomatic properties for these. The constants are marked as being specified once and for all, which prevents additional specifications being issued later on. @@ -77,20 +77,20 @@ declaring a new logical system. Normal applications should only use definitional mechanisms! - \item [\mbox{\isa{\isacommand{definition}}}~\isa{c\ {\isasymWHERE}\ eq}] produces an - internal definition \isa{c\ {\isasymequiv}\ t} according to the specification + \item [\mbox{\isa{\isacommand{definition}}}~\isa{{\isachardoublequote}c\ {\isasymWHERE}\ eq{\isachardoublequote}}] produces an + internal definition \isa{{\isachardoublequote}c\ {\isasymequiv}\ t{\isachardoublequote}} according to the specification given as \isa{eq}, which is then turned into a proven fact. The given proposition may deviate from internal meta-level equality according to the rewrite rules declared as \mbox{\isa{defn}} by the - object-logic. This usually covers object-level equality \isa{x\ {\isacharequal}\ y} and equivalence \isa{A\ {\isasymleftrightarrow}\ B}. End-users normally need not + object-logic. This usually covers object-level equality \isa{{\isachardoublequote}x\ {\isacharequal}\ y{\isachardoublequote}} and equivalence \isa{{\isachardoublequote}A\ {\isasymleftrightarrow}\ B{\isachardoublequote}}. End-users normally need not change the \mbox{\isa{defn}} setup. Definitions may be presented with explicit arguments on the LHS, as - well as additional conditions, e.g.\ \isa{f\ x\ y\ {\isacharequal}\ t} instead of - \isa{f\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t} and \isa{y\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ g\ x\ y\ {\isacharequal}\ u} instead of an - unrestricted \isa{g\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ u}. + well as additional conditions, e.g.\ \isa{{\isachardoublequote}f\ x\ y\ {\isacharequal}\ t{\isachardoublequote}} instead of + \isa{{\isachardoublequote}f\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t{\isachardoublequote}} and \isa{{\isachardoublequote}y\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ g\ x\ y\ {\isacharequal}\ u{\isachardoublequote}} instead of an + unrestricted \isa{{\isachardoublequote}g\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ u{\isachardoublequote}}. - \item [\mbox{\isa{\isacommand{abbreviation}}}~\isa{c\ {\isasymWHERE}\ eq}] introduces + \item [\mbox{\isa{\isacommand{abbreviation}}}~\isa{{\isachardoublequote}c\ {\isasymWHERE}\ eq{\isachardoublequote}}] introduces a syntactic constant which is associated with a certain term according to the meta-level equality \isa{eq}. @@ -110,7 +110,7 @@ \item [\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}] prints all constant abbreviations of the current context. - \item [\mbox{\isa{\isacommand{notation}}}~\isa{c\ {\isacharparenleft}mx{\isacharparenright}}] associates mixfix + \item [\mbox{\isa{\isacommand{notation}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}}] associates mixfix syntax with an existing constant or fixed variable. This is a robust interface to the underlying \mbox{\isa{\isacommand{syntax}}} primitive (\secref{sec:syn-trans}). Type declaration and internal syntactic @@ -180,7 +180,7 @@ variables) and assumptions (hypotheses). Definitions and theorems depending on the context may be added incrementally later on. Named contexts refer to locales (cf.\ \secref{sec:locale}) or type classes - (cf.\ \secref{sec:class}); the name ``\isa{{\isacharminus}}'' signifies the + (cf.\ \secref{sec:class}); the name ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' signifies the global theory context. \begin{matharray}{rcll} @@ -199,7 +199,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{context}}}~\isa{c\ {\isasymBEGIN}}] recommences an + \item [\mbox{\isa{\isacommand{context}}}~\isa{{\isachardoublequote}c\ {\isasymBEGIN}{\isachardoublequote}}] recommences an existing locale or class context \isa{c}. Note that locale and class definitions allow to include the \indexref{}{keyword}{begin}\mbox{\isa{\isakeyword{begin}}} keyword as well, in order to continue the local theory immediately @@ -210,10 +210,10 @@ \mbox{\isa{\isacommand{end}}} has a different meaning: it concludes the theory itself (\secref{sec:begin-thy}). - \item [\isa{{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}}] given after any local theory command - specifies an immediate target, e.g.\ ``\mbox{\isa{\isacommand{definition}}}~\isa{{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}}'' or ``\mbox{\isa{\isacommand{theorem}}}~\isa{{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}}''. This works both in a local or + \item [\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}{\isachardoublequote}}] given after any local theory command + specifies an immediate target, e.g.\ ``\mbox{\isa{\isacommand{definition}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}{\isachardoublequote}}'' or ``\mbox{\isa{\isacommand{theorem}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}{\isachardoublequote}}''. This works both in a local or global theory context; the current target context will be suspended - for this command only. Note that ``\isa{{\isacharparenleft}{\isasymIN}\ {\isacharminus}{\isacharparenright}}'' will + for this command only. Note that ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ {\isacharminus}{\isacharparenright}{\isachardoublequote}}'' will always produce a global result independently of the current target context. @@ -222,19 +222,19 @@ The exact meaning of results produced within a local theory context depends on the underlying target infrastructure (locale, type class etc.). The general idea is as follows, considering a context named - \isa{c} with parameter \isa{x} and assumption \isa{A{\isacharbrackleft}x{\isacharbrackright}}. + \isa{c} with parameter \isa{x} and assumption \isa{{\isachardoublequote}A{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}}. Definitions are exported by introducing a global version with additional arguments; a syntactic abbreviation links the long form with the abstract version of the target context. For example, - \isa{a\ {\isasymequiv}\ t{\isacharbrackleft}x{\isacharbrackright}} becomes \isa{c{\isachardot}a\ {\isacharquery}x\ {\isasymequiv}\ t{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}} at the theory - level (for arbitrary \isa{{\isacharquery}x}), together with a local - abbreviation \isa{c\ {\isasymequiv}\ c{\isachardot}a\ x} in the target context (for the + \isa{{\isachardoublequote}a\ {\isasymequiv}\ t{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} becomes \isa{{\isachardoublequote}c{\isachardot}a\ {\isacharquery}x\ {\isasymequiv}\ t{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}{\isachardoublequote}} at the theory + level (for arbitrary \isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}}), together with a local + abbreviation \isa{{\isachardoublequote}c\ {\isasymequiv}\ c{\isachardot}a\ x{\isachardoublequote}} in the target context (for the fixed parameter \isa{x}). Theorems are exported by discharging the assumptions and - generalizing the parameters of the context. For example, \isa{a{\isacharcolon}\ B{\isacharbrackleft}x{\isacharbrackright}} becomes \isa{c{\isachardot}a{\isacharcolon}\ A{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}\ {\isasymLongrightarrow}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}, again for arbitrary - \isa{{\isacharquery}x}.% + generalizing the parameters of the context. For example, \isa{{\isachardoublequote}a{\isacharcolon}\ B{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} becomes \isa{{\isachardoublequote}c{\isachardot}a{\isacharcolon}\ A{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}\ {\isasymLongrightarrow}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}{\isachardoublequote}}, again for arbitrary + \isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}}.% \end{isamarkuptext}% \isamarkuptrue% % @@ -256,8 +256,8 @@ \begin{isamarkuptext}% \begin{matharray}{rcl} \indexdef{}{command}{locale}\mbox{\isa{\isacommand{locale}}} & : & \isartrans{theory}{local{\dsh}theory} \\ - \indexdef{}{command}{print-locale}\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ - \indexdef{}{command}{print-locales}\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-locale}\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-locales}\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \indexdef{}{method}{intro-locales}\mbox{\isa{intro{\isacharunderscore}locales}} & : & \isarmeth \\ \indexdef{}{method}{unfold-locales}\mbox{\isa{unfold{\isacharunderscore}locales}} & : & \isarmeth \\ \end{matharray} @@ -294,7 +294,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{locale}}}~\isa{loc\ {\isacharequal}\ import\ {\isacharplus}\ body}] defines a + \item [\mbox{\isa{\isacommand{locale}}}~\isa{{\isachardoublequote}loc\ {\isacharequal}\ import\ {\isacharplus}\ body{\isachardoublequote}}] defines a new locale \isa{loc} as a context consisting of a certain view of existing locales (\isa{import}) plus some additional elements (\isa{body}). Both \isa{import} and \isa{body} are optional; @@ -306,11 +306,11 @@ The \isa{import} consists of a structured context expression, consisting of references to existing locales, renamed contexts, or - merged contexts. Renaming uses positional notation: \isa{c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n} means that (a prefix of) the fixed - parameters of context \isa{c} are named \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub n}; a ``\isa{{\isacharunderscore}}'' (underscore) means to skip that + merged contexts. Renaming uses positional notation: \isa{{\isachardoublequote}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isachardoublequote}} means that (a prefix of) the fixed + parameters of context \isa{c} are named \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub n{\isachardoublequote}}; a ``\isa{{\isacharunderscore}}'' (underscore) means to skip that position. Renaming by default deletes concrete syntax, but new syntax may by specified with a mixfix annotation. An exeption of - this rule is the special syntax declared with ``\isa{{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}}'' (see below), which is neither deleted nor can it + this rule is the special syntax declared with ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}{\isachardoublequote}}'' (see below), which is neither deleted nor can it be changed. Merging proceeds from left-to-right, suppressing any duplicates stemming from different paths through the import hierarchy. @@ -320,26 +320,26 @@ \begin{descr} - \item [\mbox{\isa{\isakeyword{fixes}}}~\isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isacharparenleft}mx{\isacharparenright}}] declares a local + \item [\mbox{\isa{\isakeyword{fixes}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}}] declares a local parameter of type \isa{{\isasymtau}} and mixfix annotation \isa{mx} (both - are optional). The special syntax declaration ``\isa{{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}}'' means that \isa{x} may be referenced + are optional). The special syntax declaration ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}{\isachardoublequote}}'' means that \isa{x} may be referenced implicitly in this context. - \item [\mbox{\isa{\isakeyword{constrains}}}~\isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}] introduces a type + \item [\mbox{\isa{\isakeyword{constrains}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}}] introduces a type constraint \isa{{\isasymtau}} on the local parameter \isa{x}. - \item [\mbox{\isa{\isakeyword{assumes}}}~\isa{a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n}] + \item [\mbox{\isa{\isakeyword{assumes}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}] introduces local premises, similar to \mbox{\isa{\isacommand{assume}}} within a proof (cf.\ \secref{sec:proof-context}). - \item [\mbox{\isa{\isakeyword{defines}}}~\isa{a{\isacharcolon}\ x\ {\isasymequiv}\ t}] defines a previously + \item [\mbox{\isa{\isakeyword{defines}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}}] defines a previously declared parameter. This is similar to \mbox{\isa{\isacommand{def}}} within a proof (cf.\ \secref{sec:proof-context}), but \mbox{\isa{\isakeyword{defines}}} takes an equational proposition instead of variable-term pair. The left-hand side of the equation may have additional arguments, e.g.\ - ``\mbox{\isa{\isakeyword{defines}}}~\isa{f\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ t}''. + ``\mbox{\isa{\isakeyword{defines}}}~\isa{{\isachardoublequote}f\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ t{\isachardoublequote}}''. - \item [\mbox{\isa{\isakeyword{notes}}}~\isa{a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n}] + \item [\mbox{\isa{\isakeyword{notes}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}] reconsiders facts within a local context. Most notably, this may include arbitrary declarations in any attribute specifications included here, e.g.\ a local \mbox{\isa{simp}} rule. @@ -355,7 +355,7 @@ \end{descr} - Note that ``\isa{{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}}'' patterns given + Note that ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}'' patterns given in the syntax of \mbox{\isa{\isakeyword{assumes}}} and \mbox{\isa{\isakeyword{defines}}} above are illegal in locale definitions. In the long goal format of \secref{sec:goals}, term bindings may be included as expected, @@ -374,21 +374,21 @@ these predicates operate at the meta-level in theory, but the locale packages attempts to internalize statements according to the object-logic setup (e.g.\ replacing \isa{{\isasymAnd}} by \isa{{\isasymforall}}, and - \isa{{\isasymLongrightarrow}} by \isa{{\isasymlongrightarrow}} in HOL; see also + \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} by \isa{{\isachardoublequote}{\isasymlongrightarrow}{\isachardoublequote}} in HOL; see also \secref{sec:object-logic}). Separate introduction rules \isa{loc{\isacharunderscore}axioms{\isachardot}intro} and \isa{loc{\isachardot}intro} are provided as well. - The \isa{{\isacharparenleft}open{\isacharparenright}} option of a locale specification prevents both + The \isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}} option of a locale specification prevents both the current \isa{loc{\isacharunderscore}axioms} and cumulative \isa{loc} predicate constructions. Predicates are also omitted for empty specification texts. - \item [\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}~\isa{import\ {\isacharplus}\ body}] prints the + \item [\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}~\isa{{\isachardoublequote}import\ {\isacharplus}\ body{\isachardoublequote}}] prints the specified locale expression in a flattened form. The notable special case \mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}~\isa{loc} just prints the contents of the named locale, but keep in mind that type-inference will normalize type variables according to the usual alphabetical order. The command omits \mbox{\isa{\isakeyword{notes}}} elements by default. - Use \mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}\isa{{\isacharbang}} to get them included. + Use \mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} to get them included. \item [\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}] prints the names of all locales of the current theory. @@ -421,7 +421,7 @@ \begin{matharray}{rcl} \indexdef{}{command}{interpretation}\mbox{\isa{\isacommand{interpretation}}} & : & \isartrans{theory}{proof(prove)} \\ \indexdef{}{command}{interpret}\mbox{\isa{\isacommand{interpret}}} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\ - \indexdef{}{command}{print-interps}\mbox{\isa{\isacommand{print{\isacharunderscore}interps}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-interps}\mbox{\isa{\isacommand{print{\isacharunderscore}interps}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \end{matharray} \indexouternonterm{interp} @@ -441,7 +441,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{interpretation}}}~\isa{expr\ insts\ {\isasymWHERE}\ eqns}] + \item [\mbox{\isa{\isacommand{interpretation}}}~\isa{{\isachardoublequote}expr\ insts\ {\isasymWHERE}\ eqns{\isachardoublequote}}] The first form of \mbox{\isa{\isacommand{interpretation}}} interprets \isa{expr} in the theory. The instantiation is given as a list of terms \isa{insts} and is positional. All parameters must receive an @@ -480,7 +480,7 @@ interpretations dynamically participate in any facts added to locales. - \item [\mbox{\isa{\isacommand{interpretation}}}~\isa{name\ {\isasymsubseteq}\ expr}] + \item [\mbox{\isa{\isacommand{interpretation}}}~\isa{{\isachardoublequote}name\ {\isasymsubseteq}\ expr{\isachardoublequote}}] This form of the command interprets \isa{expr} in the locale \isa{name}. It requires a proof that the specification of \isa{name} implies the specification of \isa{expr}. As in the @@ -507,7 +507,7 @@ prefix and attributes, although only for fragments of \isa{expr} that are not interpreted in the theory already. - \item [\mbox{\isa{\isacommand{interpret}}}~\isa{expr\ insts\ {\isasymWHERE}\ eqns}] + \item [\mbox{\isa{\isacommand{interpret}}}~\isa{{\isachardoublequote}expr\ insts\ {\isasymWHERE}\ eqns{\isachardoublequote}}] interprets \isa{expr} in the proof context and is otherwise similar to interpretation in theories. @@ -560,7 +560,7 @@ \indexdef{}{command}{instantiation}\mbox{\isa{\isacommand{instantiation}}} & : & \isartrans{theory}{local{\dsh}theory} \\ \indexdef{}{command}{instance}\mbox{\isa{\isacommand{instance}}} & : & \isartrans{local{\dsh}theory}{local{\dsh}theory} \\ \indexdef{}{command}{subclass}\mbox{\isa{\isacommand{subclass}}} & : & \isartrans{local{\dsh}theory}{local{\dsh}theory} \\ - \indexdef{}{command}{print-classes}\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-classes}\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \indexdef{}{method}{intro-classes}\mbox{\isa{intro{\isacharunderscore}classes}} & : & \isarmeth \\ \end{matharray} @@ -583,24 +583,24 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{class}}}~\isa{c\ {\isacharequal}\ superclasses\ {\isacharplus}\ body}] defines + \item [\mbox{\isa{\isacommand{class}}}~\isa{{\isachardoublequote}c\ {\isacharequal}\ superclasses\ {\isacharplus}\ body{\isachardoublequote}}] defines a new class \isa{c}, inheriting from \isa{superclasses}. This introduces a locale \isa{c} with import of all locales \isa{superclasses}. Any \mbox{\isa{\isakeyword{fixes}}} in \isa{body} are lifted to the global - theory level (\emph{class operations} \isa{f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n} of class \isa{c}), mapping the local type parameter - \isa{{\isasymalpha}} to a schematic type variable \isa{{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c}. + theory level (\emph{class operations} \isa{{\isachardoublequote}f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n{\isachardoublequote}} of class \isa{c}), mapping the local type parameter + \isa{{\isasymalpha}} to a schematic type variable \isa{{\isachardoublequote}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isachardoublequote}}. Likewise, \mbox{\isa{\isakeyword{assumes}}} in \isa{body} are also lifted, - mapping each local parameter \isa{f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} to its - corresponding global constant \isa{f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}}. The + mapping each local parameter \isa{{\isachardoublequote}f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} to its + corresponding global constant \isa{{\isachardoublequote}f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}. The corresponding introduction rule is provided as \isa{c{\isacharunderscore}class{\isacharunderscore}axioms{\isachardot}intro}. This rule should be rarely needed directly --- the \mbox{\isa{intro{\isacharunderscore}classes}} method takes care of the details of class membership proofs. - \item [\mbox{\isa{\isacommand{instantiation}}}~\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}\ s\ {\isasymBEGIN}}] opens a theory target (cf.\ - \secref{sec:target}) which allows to specify class operations \isa{f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n} corresponding to sort \isa{s} at the - particular type instance \isa{{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ s\isactrlsub n{\isacharparenright}\ t}. A plain \mbox{\isa{\isacommand{instance}}} command + \item [\mbox{\isa{\isacommand{instantiation}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}\ s\ {\isasymBEGIN}{\isachardoublequote}}] opens a theory target (cf.\ + \secref{sec:target}) which allows to specify class operations \isa{{\isachardoublequote}f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n{\isachardoublequote}} corresponding to sort \isa{s} at the + particular type instance \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ s\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}}. A plain \mbox{\isa{\isacommand{instance}}} command in the target body poses a goal stating these type arities. The target is concluded by an \indexref{}{command}{end}\mbox{\isa{\isacommand{end}}} command. @@ -645,15 +645,15 @@ \begin{itemize} - \item Local constant declarations \isa{g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} referring to the - local type parameter \isa{{\isasymalpha}} and local parameters \isa{f{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} - are accompanied by theory-level constants \isa{g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}} - referring to theory-level class operations \isa{f{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}}. + \item Local constant declarations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} referring to the + local type parameter \isa{{\isasymalpha}} and local parameters \isa{{\isachardoublequote}f{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} + are accompanied by theory-level constants \isa{{\isachardoublequote}g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}} + referring to theory-level class operations \isa{{\isachardoublequote}f{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}. \item Local theorem bindings are lifted as are assumptions. - \item Local syntax refers to local operations \isa{g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} and - global operations \isa{g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}} uniformly. Type inference + \item Local syntax refers to local operations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} and + global operations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}} uniformly. Type inference resolves ambiguities. In rare cases, manual type annotations are needed. @@ -685,7 +685,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{axclass}}}~\isa{c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ axms}] defines an axiomatic type class as the intersection of + \item [\mbox{\isa{\isacommand{axclass}}}~\isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ axms{\isachardoublequote}}] defines an axiomatic type class as the intersection of existing classes, with additional axioms holding. Class axioms may not contain more than one type variable. The class axioms (with implicit sort constraints added) are bound to the given names. @@ -693,11 +693,11 @@ \isa{c{\isacharunderscore}class{\isachardot}intro}); this rule is employed by method \mbox{\isa{intro{\isacharunderscore}classes}} to support instantiation proofs of this class. The ``class axioms'' are stored as theorems according to the given - name specifications, adding \isa{c{\isacharunderscore}class} as name space prefix; + name specifications, adding \isa{{\isachardoublequote}c{\isacharunderscore}class{\isachardoublequote}} as name space prefix; the same facts are also stored collectively as \isa{c{\isacharunderscore}class{\isachardot}axioms}. - \item [\mbox{\isa{\isacommand{instance}}}~\isa{c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}} and - \mbox{\isa{\isacommand{instance}}}~\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}\ s}] + \item [\mbox{\isa{\isacommand{instance}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} and + \mbox{\isa{\isacommand{instance}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}\ s{\isachardoublequote}}] setup a goal stating a class relation or type arity. The proof would usually proceed by \mbox{\isa{intro{\isacharunderscore}classes}}, and then establish the characteristic theorems of the type classes involved. After @@ -732,16 +732,16 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{overloading}}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isasymequiv}\ c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub n\ {\isasymBEGIN}}] + \item [\mbox{\isa{\isacommand{overloading}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymequiv}\ c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub n\ {\isasymBEGIN}{\isachardoublequote}}] opens a theory target (cf.\ \secref{sec:target}) which allows to specify constants with overloaded definitions. These are identified - by an explicitly given mapping from variable names \isa{x\isactrlsub i} to constants \isa{c\isactrlsub i} at particular type + by an explicitly given mapping from variable names \isa{{\isachardoublequote}x\isactrlsub i{\isachardoublequote}} to constants \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} at particular type instances. The definitions themselves are established using common - specification tools, using the names \isa{x\isactrlsub i} as + specification tools, using the names \isa{{\isachardoublequote}x\isactrlsub i{\isachardoublequote}} as reference to the corresponding constants. The target is concluded by \mbox{\isa{\isacommand{end}}}. - A \isa{{\isacharparenleft}unchecked{\isacharparenright}} option disables global dependency checks for + A \isa{{\isachardoublequote}{\isacharparenleft}unchecked{\isacharparenright}{\isachardoublequote}} option disables global dependency checks for the corresponding definition, which is occasionally useful for exotic overloading. It is at the discretion of the user to avoid malformed theory specifications! @@ -781,7 +781,7 @@ \item [\mbox{\isa{\isacommand{print{\isacharunderscore}configs}}}] prints the available configuration options, with names, types, and current values. - \item [\isa{name\ {\isacharequal}\ value}] as an attribute expression modifies + \item [\isa{{\isachardoublequote}name\ {\isacharequal}\ value{\isachardoublequote}}] as an attribute expression modifies the named option, with the syntax of the value depending on the option's type. For \verb|bool| the default value is \isa{true}. Any attempt to change a global option in a local context is ignored. @@ -801,7 +801,7 @@ \begin{isamarkuptext}% \begin{matharray}{rcl} \indexdef{}{command}{obtain}\mbox{\isa{\isacommand{obtain}}} & : & \isartrans{proof(state)}{proof(prove)} \\ - \indexdef{}{command}{guess}\mbox{\isa{\isacommand{guess}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isartrans{proof(state)}{proof(prove)} \\ + \indexdef{}{command}{guess}\mbox{\isa{\isacommand{guess}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isartrans{proof(state)}{proof(prove)} \\ \end{matharray} Generalized elimination means that additional elements with certain @@ -823,19 +823,19 @@ \end{rail} The derived Isar command \mbox{\isa{\isacommand{obtain}}} is defined as follows - (where \isa{b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub k} shall refer to (optional) + (where \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub k{\isachardoublequote}} shall refer to (optional) facts indicated for forward chaining). \begin{matharray}{l} - \isa{{\isasymlangle}using\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k{\isasymrangle}}~~\mbox{\isa{\isacommand{obtain}}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ \ {\isasymlangle}proof{\isasymrangle}\ {\isasymequiv}} \\[1ex] - \quad \mbox{\isa{\isacommand{have}}}~\isa{{\isasymAnd}thesis{\isachardot}\ {\isacharparenleft}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isacharparenright}\ {\isasymLongrightarrow}\ thesis} \\ + \isa{{\isachardoublequote}{\isasymlangle}using\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k{\isasymrangle}{\isachardoublequote}}~~\mbox{\isa{\isacommand{obtain}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ \ {\isasymlangle}proof{\isasymrangle}\ {\isasymequiv}{\isachardoublequote}} \\[1ex] + \quad \mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}{\isasymAnd}thesis{\isachardot}\ {\isacharparenleft}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isacharparenright}\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\ \quad \mbox{\isa{\isacommand{proof}}}~\isa{succeed} \\ \qquad \mbox{\isa{\isacommand{fix}}}~\isa{thesis} \\ - \qquad \mbox{\isa{\isacommand{assume}}}~\isa{that\ {\isacharbrackleft}Pure{\isachardot}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis} \\ + \qquad \mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}that\ {\isacharbrackleft}Pure{\isachardot}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\ \qquad \mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{show}}}~\isa{thesis} \\ \quad\qquad \mbox{\isa{\isacommand{apply}}}~\isa{{\isacharminus}} \\ - \quad\qquad \mbox{\isa{\isacommand{using}}}~\isa{b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k\ \ {\isasymlangle}proof{\isasymrangle}} \\ + \quad\qquad \mbox{\isa{\isacommand{using}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k\ \ {\isasymlangle}proof{\isasymrangle}{\isachardoublequote}} \\ \quad \mbox{\isa{\isacommand{qed}}} \\ - \quad \mbox{\isa{\isacommand{fix}}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m}~\mbox{\isa{\isacommand{assume}}}\isa{\isactrlsup {\isacharasterisk}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n} \\ + \quad \mbox{\isa{\isacommand{fix}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\mbox{\isa{\isacommand{assume}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}} \\ \end{matharray} Typically, the soundness proof is relatively straight-forward, often @@ -859,9 +859,9 @@ \medskip The improper variant \mbox{\isa{\isacommand{guess}}} is similar to \mbox{\isa{\isacommand{obtain}}}, but derives the obtained statement from the course of reasoning! The proof starts with a fixed goal \isa{thesis}. The subsequent proof may refine this to anything of the - form like \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis}, but must not introduce new subgoals. The + form like \isa{{\isachardoublequote}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}}, but must not introduce new subgoals. The final goal state is then used as reduction rule for the obtain - scheme described above. Obtained parameters \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m} are marked as internal by default, which prevents the + scheme described above. Obtained parameters \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} are marked as internal by default, which prevents the proof context from being polluted by ad-hoc variables. The variable names and type constraints given as arguments for \mbox{\isa{\isacommand{guess}}} specify a prefix of obtained parameters explicitly in the text. @@ -881,15 +881,15 @@ \indexdef{}{command}{finally}\mbox{\isa{\isacommand{finally}}} & : & \isartrans{proof(state)}{proof(chain)} \\ \indexdef{}{command}{moreover}\mbox{\isa{\isacommand{moreover}}} & : & \isartrans{proof(state)}{proof(state)} \\ \indexdef{}{command}{ultimately}\mbox{\isa{\isacommand{ultimately}}} & : & \isartrans{proof(state)}{proof(chain)} \\ - \indexdef{}{command}{print-trans-rules}\mbox{\isa{\isacommand{print{\isacharunderscore}trans{\isacharunderscore}rules}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-trans-rules}\mbox{\isa{\isacommand{print{\isacharunderscore}trans{\isacharunderscore}rules}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \mbox{\isa{trans}} & : & \isaratt \\ \mbox{\isa{sym}} & : & \isaratt \\ \mbox{\isa{symmetric}} & : & \isaratt \\ \end{matharray} Calculational proof is forward reasoning with implicit application - of transitivity rules (such those of \isa{{\isacharequal}}, \isa{{\isasymle}}, - \isa{{\isacharless}}). Isabelle/Isar maintains an auxiliary fact register + of transitivity rules (such those of \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymle}{\isachardoublequote}}, + \isa{{\isachardoublequote}{\isacharless}{\isachardoublequote}}). Isabelle/Isar maintains an auxiliary fact register \indexref{}{fact}{calculation}\mbox{\isa{calculation}} for accumulating results obtained by transitivity composed with the current result. Command \mbox{\isa{\isacommand{also}}} updates \mbox{\isa{calculation}} involving \mbox{\isa{this}}, while \mbox{\isa{\isacommand{finally}}} exhibits the final \mbox{\isa{calculation}} by @@ -900,7 +900,7 @@ but only collect further results in \mbox{\isa{calculation}} without applying any rules yet. - Also note that the implicit term abbreviation ``\isa{{\isasymdots}}'' has + Also note that the implicit term abbreviation ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' has its canonical application with calculational proofs. It refers to the argument of the preceding statement. (The argument of a curried infix expression happens to be its right-hand side.) @@ -917,10 +917,10 @@ handling of block-structure.} \begin{matharray}{rcl} - \mbox{\isa{\isacommand{also}}}\isa{\isactrlsub {\isadigit{0}}} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ this} \\ - \mbox{\isa{\isacommand{also}}}\isa{\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}} \\[0.5ex] + \mbox{\isa{\isacommand{also}}}\isa{{\isachardoublequote}\isactrlsub {\isadigit{0}}{\isachardoublequote}} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ this{\isachardoublequote}} \\ + \mbox{\isa{\isacommand{also}}}\isa{{\isachardoublequote}\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}{\isachardoublequote}} \\[0.5ex] \mbox{\isa{\isacommand{finally}}} & \equiv & \mbox{\isa{\isacommand{also}}}~\mbox{\isa{\isacommand{from}}}~\isa{calculation} \\[0.5ex] - \mbox{\isa{\isacommand{moreover}}} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ calculation\ this} \\ + \mbox{\isa{\isacommand{moreover}}} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ calculation\ this{\isachardoublequote}} \\ \mbox{\isa{\isacommand{ultimately}}} & \equiv & \mbox{\isa{\isacommand{moreover}}}~\mbox{\isa{\isacommand{from}}}~\isa{calculation} \\ \end{matharray} @@ -933,7 +933,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{also}}}~\isa{{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}}] + \item [\mbox{\isa{\isacommand{also}}}~\isa{{\isachardoublequote}{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}}] maintains the auxiliary \mbox{\isa{calculation}} register as follows. The first occurrence of \mbox{\isa{\isacommand{also}}} in some calculational thread initializes \mbox{\isa{calculation}} by \mbox{\isa{this}}. Any @@ -943,7 +943,7 @@ rules are picked from the current context, unless alternative rules are given as explicit arguments. - \item [\mbox{\isa{\isacommand{finally}}}~\isa{{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}}] + \item [\mbox{\isa{\isacommand{finally}}}~\isa{{\isachardoublequote}{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}}] maintaining \mbox{\isa{calculation}} in the same way as \mbox{\isa{\isacommand{also}}}, and concludes the current calculational thread. The final result is exhibited as fact for forward chaining towards the next goal. Basically, \mbox{\isa{\isacommand{finally}}} just abbreviates \mbox{\isa{\isacommand{also}}}~\mbox{\isa{\isacommand{from}}}~\mbox{\isa{calculation}}. Typical idioms for @@ -965,11 +965,11 @@ \item [\mbox{\isa{symmetric}}] resolves a theorem with some rule declared as \mbox{\isa{sym}} in the current context. For example, - ``\mbox{\isa{\isacommand{assume}}}~\isa{{\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcolon}\ x\ {\isacharequal}\ y}'' produces a + ``\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}{\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcolon}\ x\ {\isacharequal}\ y{\isachardoublequote}}'' produces a swapped fact derived from that assumption. In structured proof texts it is often more appropriate to use an - explicit single-step elimination proof, such as ``\mbox{\isa{\isacommand{assume}}}~\isa{x\ {\isacharequal}\ y}~\mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{have}}}~\isa{y\ {\isacharequal}\ x}~\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}''. + explicit single-step elimination proof, such as ``\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ y{\isachardoublequote}}~\mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}y\ {\isacharequal}\ x{\isachardoublequote}}~\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}''. \end{descr}% \end{isamarkuptext}% @@ -988,9 +988,9 @@ \indexdef{}{method}{unfold}\mbox{\isa{unfold}} & : & \isarmeth \\ \indexdef{}{method}{fold}\mbox{\isa{fold}} & : & \isarmeth \\ \indexdef{}{method}{insert}\mbox{\isa{insert}} & : & \isarmeth \\[0.5ex] - \indexdef{}{method}{erule}\mbox{\isa{erule}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{drule}\mbox{\isa{drule}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{frule}\mbox{\isa{frule}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ + \indexdef{}{method}{erule}\mbox{\isa{erule}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{drule}\mbox{\isa{drule}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{frule}\mbox{\isa{frule}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ \indexdef{}{method}{succeed}\mbox{\isa{succeed}} & : & \isarmeth \\ \indexdef{}{method}{fail}\mbox{\isa{fail}} & : & \isarmeth \\ \end{matharray} @@ -1004,15 +1004,15 @@ \begin{descr} - \item [\mbox{\isa{unfold}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n} and \mbox{\isa{fold}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] expand (or fold back) the + \item [\mbox{\isa{unfold}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} and \mbox{\isa{fold}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] expand (or fold back) the given definitions throughout all goals; any chained facts provided are inserted into the goal and subject to rewriting as well. - \item [\mbox{\isa{insert}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] inserts + \item [\mbox{\isa{insert}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] inserts theorems as facts into all goals of the proof state. Note that current facts indicated for forward chaining are ignored. - \item [\mbox{\isa{erule}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}, \mbox{\isa{drule}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}, and \mbox{\isa{frule}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] are similar to the basic \mbox{\isa{rule}} + \item [\mbox{\isa{erule}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}, \mbox{\isa{drule}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}, and \mbox{\isa{frule}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] are similar to the basic \mbox{\isa{rule}} method (see \secref{sec:pure-meth-att}), but apply rules by elim-resolution, destruct-resolution, and forward-resolution, respectively \cite{isabelle-ref}. The optional natural number @@ -1028,11 +1028,11 @@ facts. \item [\mbox{\isa{succeed}}] yields a single (unchanged) result; it is - the identity of the ``\isa{{\isacharcomma}}'' method combinator (cf.\ + the identity of the ``\isa{{\isachardoublequote}{\isacharcomma}{\isachardoublequote}}'' method combinator (cf.\ \secref{sec:syn-meth}). \item [\mbox{\isa{fail}}] yields an empty result sequence; it is the - identity of the ``\isa{{\isacharbar}}'' method combinator (cf.\ + identity of the ``\isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}}'' method combinator (cf.\ \secref{sec:syn-meth}). \end{descr} @@ -1046,8 +1046,8 @@ \indexdef{}{attribute}{folded}\mbox{\isa{folded}} & : & \isaratt \\[0.5ex] \indexdef{}{attribute}{rotated}\mbox{\isa{rotated}} & : & \isaratt \\ \indexdef{Pure}{attribute}{elim-format}\mbox{\isa{elim{\isacharunderscore}format}} & : & \isaratt \\ - \indexdef{}{attribute}{standard}\mbox{\isa{standard}}\isa{\isactrlsup {\isacharasterisk}} & : & \isaratt \\ - \indexdef{}{attribute}{no-vars}\mbox{\isa{no{\isacharunderscore}vars}}\isa{\isactrlsup {\isacharasterisk}} & : & \isaratt \\ + \indexdef{}{attribute}{standard}\mbox{\isa{standard}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\ + \indexdef{}{attribute}{no-vars}\mbox{\isa{no{\isacharunderscore}vars}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\ \end{matharray} \begin{rail} @@ -1064,7 +1064,7 @@ \begin{descr} - \item [\mbox{\isa{tagged}}~\isa{name\ arg} and \mbox{\isa{untagged}}~\isa{name}] add and remove \emph{tags} of some theorem. + \item [\mbox{\isa{tagged}}~\isa{{\isachardoublequote}name\ arg{\isachardoublequote}} and \mbox{\isa{untagged}}~\isa{name}] add and remove \emph{tags} of some theorem. Tags may be any list of string pairs that serve as formal comment. The first string is considered the tag name, the second its argument. Note that \mbox{\isa{untagged}} removes any tags of the @@ -1074,11 +1074,11 @@ compose rules by resolution. \mbox{\isa{THEN}} resolves with the first premise of \isa{a} (an alternative position may be also specified); the \mbox{\isa{COMP}} version skips the automatic - lifting process that is normally intended (cf.\ \verb|op RS| and - \verb|op COMP| in \cite[\S5]{isabelle-ref}). + lifting process that is normally intended (cf.\ \verb|"op RS"| and + \verb|"op COMP"| in \cite[\S5]{isabelle-ref}). - \item [\mbox{\isa{unfolded}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n} and - \mbox{\isa{folded}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] expand and fold + \item [\mbox{\isa{unfolded}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} and + \mbox{\isa{folded}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] expand and fold back again the given definitions throughout a rule. \item [\mbox{\isa{rotated}}~\isa{n}] rotate the premises of a @@ -1135,16 +1135,16 @@ \secref{sec:pure-meth-att}). \begin{matharray}{rcl} - \indexdef{}{method}{rule-tac}\mbox{\isa{rule{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{erule-tac}\mbox{\isa{erule{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{drule-tac}\mbox{\isa{drule{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{frule-tac}\mbox{\isa{frule{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{cut-tac}\mbox{\isa{cut{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{thin-tac}\mbox{\isa{thin{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{subgoal-tac}\mbox{\isa{subgoal{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{rename-tac}\mbox{\isa{rename{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{rotate-tac}\mbox{\isa{rotate{\isacharunderscore}tac}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{tactic}\mbox{\isa{tactic}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ + \indexdef{}{method}{rule-tac}\mbox{\isa{rule{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{erule-tac}\mbox{\isa{erule{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{drule-tac}\mbox{\isa{drule{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{frule-tac}\mbox{\isa{frule{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{cut-tac}\mbox{\isa{cut{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{thin-tac}\mbox{\isa{thin{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{subgoal-tac}\mbox{\isa{subgoal{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{rename-tac}\mbox{\isa{rename{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{rotate-tac}\mbox{\isa{rotate{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{tactic}\mbox{\isa{tactic}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ \end{matharray} \begin{rail} @@ -1187,8 +1187,8 @@ \item [\mbox{\isa{subgoal{\isacharunderscore}tac}}~\isa{{\isasymphi}}] adds \isa{{\isasymphi}} as an assumption to a subgoal. See also \verb|subgoal_tac| and \verb|subgoals_tac| in \cite[\S3]{isabelle-ref}. - \item [\mbox{\isa{rename{\isacharunderscore}tac}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n}] renames - parameters of a goal according to the list \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub n}, which refers to the \emph{suffix} of variables. + \item [\mbox{\isa{rename{\isacharunderscore}tac}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isachardoublequote}}] renames + parameters of a goal according to the list \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub n{\isachardoublequote}}, which refers to the \emph{suffix} of variables. \item [\mbox{\isa{rotate{\isacharunderscore}tac}}~\isa{n}] rotates the assumptions of a goal by \isa{n} positions: from right to left if \isa{n} is @@ -1196,7 +1196,7 @@ default value is 1. See also \verb|rotate_tac| in \cite[\S3]{isabelle-ref}. - \item [\mbox{\isa{tactic}}~\isa{text}] produces a proof method from + \item [\mbox{\isa{tactic}}~\isa{{\isachardoublequote}text{\isachardoublequote}}] produces a proof method from any ML text of type \verb|tactic|. Apart from the usual ML environment and the current implicit theory context, the ML code may refer to the following locally bound values: @@ -1272,25 +1272,25 @@ structured proofs this is usually quite well behaved in practice: just the local premises of the actual goal are involved, additional facts may be inserted via explicit forward-chaining (via \mbox{\isa{\isacommand{then}}}, \mbox{\isa{\isacommand{from}}}, \mbox{\isa{\isacommand{using}}} etc.). The full - context of premises is only included if the ``\isa{{\isacharbang}}'' (bang) + context of premises is only included if the ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' (bang) argument is given, which should be used with some care, though. Additional Simplifier options may be specified to tune the behavior further (mostly for unstructured scripts with many accidental local - facts): ``\isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}}'' means assumptions are ignored - completely (cf.\ \verb|simp_tac|), ``\isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}}'' means + facts): ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}}'' means assumptions are ignored + completely (cf.\ \verb|simp_tac|), ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}}'' means assumptions are used in the simplification of the conclusion but are - not themselves simplified (cf.\ \verb|asm_simp_tac|), and ``\isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}}'' means assumptions are simplified but are not used + not themselves simplified (cf.\ \verb|asm_simp_tac|), and ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}{\isachardoublequote}}'' means assumptions are simplified but are not used in the simplification of each other or the conclusion (cf.\ \verb|full_simp_tac|). For compatibility reasons, there is also an option - ``\isa{{\isacharparenleft}asm{\isacharunderscore}lr{\isacharparenright}}'', which means that an assumption is only used + ``\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharunderscore}lr{\isacharparenright}{\isachardoublequote}}'', which means that an assumption is only used for simplifying assumptions which are to the right of it (cf.\ \verb|asm_lr_simp_tac|). - Giving an option ``\isa{{\isacharparenleft}depth{\isacharunderscore}limit{\isacharcolon}\ n{\isacharparenright}}'' limits the number of + Giving an option ``\isa{{\isachardoublequote}{\isacharparenleft}depth{\isacharunderscore}limit{\isacharcolon}\ n{\isacharparenright}{\isachardoublequote}}'' limits the number of recursive invocations of the simplifier during conditional rewriting. \medskip The Splitter package is usually configured to work as part - of the Simplifier. The effect of repeatedly applying \verb|split_tac| can be simulated by ``\isa{{\isacharparenleft}simp\ only{\isacharcolon}\ split{\isacharcolon}\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}}''. There is also a separate \isa{split} + of the Simplifier. The effect of repeatedly applying \verb|split_tac| can be simulated by ``\isa{{\isachardoublequote}{\isacharparenleft}simp\ only{\isacharcolon}\ split{\isacharcolon}\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. There is also a separate \isa{split} method available for single-step case splitting.% \end{isamarkuptext}% \isamarkuptrue% @@ -1301,7 +1301,7 @@ % \begin{isamarkuptext}% \begin{matharray}{rcl} - \indexdef{}{command}{print-simpset}\mbox{\isa{\isacommand{print{\isacharunderscore}simpset}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-simpset}\mbox{\isa{\isacommand{print{\isacharunderscore}simpset}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \indexdef{}{attribute}{simp}\mbox{\isa{simp}} & : & \isaratt \\ \indexdef{}{attribute}{cong}\mbox{\isa{cong}} & : & \isaratt \\ \indexdef{}{attribute}{split}\mbox{\isa{split}} & : & \isaratt \\ @@ -1351,8 +1351,8 @@ \item [\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}] defines a named simplification procedure that is invoked by the Simplifier whenever any of the given term patterns match the current redex. The implementation, - which is provided as ML source text, needs to be of type \verb|morphism -> simpset -> cterm -> thm option|, where the \verb|cterm| represents the current redex \isa{r} and the result is - supposed to be some proven rewrite rule \isa{r\ {\isasymequiv}\ r{\isacharprime}} (or a + which is provided as ML source text, needs to be of type \verb|"morphism -> simpset -> cterm -> thm option"|, where the \verb|cterm| represents the current redex \isa{r} and the result is + supposed to be some proven rewrite rule \isa{{\isachardoublequote}r\ {\isasymequiv}\ r{\isacharprime}{\isachardoublequote}} (or a generalized version), or \verb|NONE| to indicate failure. The \verb|simpset| argument holds the full context of the current Simplifier invocation, including the actual Isar proof context. The @@ -1365,7 +1365,7 @@ Morphisms and identifiers are only relevant for simprocs that are defined within a local target context, e.g.\ in a locale. - \item [\isa{simproc\ add{\isacharcolon}\ name} and \isa{simproc\ del{\isacharcolon}\ name}] + \item [\isa{{\isachardoublequote}simproc\ add{\isacharcolon}\ name{\isachardoublequote}} and \isa{{\isachardoublequote}simproc\ del{\isacharcolon}\ name{\isachardoublequote}}] add or delete named simprocs to the current Simplifier context. The default is to add a simproc. Note that \mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}} already adds the new simproc to the subsequent context. @@ -1393,9 +1393,9 @@ \begin{descr} - \item [\mbox{\isa{simplified}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] + \item [\mbox{\isa{simplified}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] causes a theorem to be simplified, either by exactly the specified - rules \isa{a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n}, or the implicit Simplifier + rules \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}}, or the implicit Simplifier context if no arguments are given. The result is fully simplified by default, including assumptions and conclusion; the options \isa{no{\isacharunderscore}asm} etc.\ tune the Simplifier in the same way as the for the \isa{simp} method. @@ -1415,9 +1415,9 @@ % \begin{isamarkuptext}% \begin{matharray}{rcl} - \indexdef{}{method}{subst}\mbox{\isa{subst}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{hypsubst}\mbox{\isa{hypsubst}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ - \indexdef{}{method}{split}\mbox{\isa{split}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarmeth \\ + \indexdef{}{method}{subst}\mbox{\isa{subst}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{hypsubst}\mbox{\isa{hypsubst}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ + \indexdef{}{method}{split}\mbox{\isa{split}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\ \end{matharray} \begin{rail} @@ -1440,33 +1440,33 @@ step using rule \isa{eq}, which may be either a meta or object equality. - \item [\mbox{\isa{subst}}~\isa{{\isacharparenleft}asm{\isacharparenright}\ eq}] substitutes in an + \item [\mbox{\isa{subst}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}\ eq{\isachardoublequote}}] substitutes in an assumption. - \item [\mbox{\isa{subst}}~\isa{{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq}] performs several + \item [\mbox{\isa{subst}}~\isa{{\isachardoublequote}{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq{\isachardoublequote}}] performs several substitutions in the conclusion. The numbers \isa{i} to \isa{j} indicate the positions to substitute at. Positions are ordered from the top of the term tree moving down from left to right. For - example, in \isa{{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}} there are three positions - where commutativity of \isa{{\isacharplus}} is applicable: 1 refers to the - whole term, 2 to \isa{a\ {\isacharplus}\ b} and 3 to \isa{c\ {\isacharplus}\ d}. + example, in \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}{\isachardoublequote}} there are three positions + where commutativity of \isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}} is applicable: 1 refers to the + whole term, 2 to \isa{{\isachardoublequote}a\ {\isacharplus}\ b{\isachardoublequote}} and 3 to \isa{{\isachardoublequote}c\ {\isacharplus}\ d{\isachardoublequote}}. - If the positions in the list \isa{{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}} are non-overlapping - (e.g.\ \isa{{\isacharparenleft}{\isadigit{2}}\ {\isadigit{3}}{\isacharparenright}} in \isa{{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}}) you may + If the positions in the list \isa{{\isachardoublequote}{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}{\isachardoublequote}} are non-overlapping + (e.g.\ \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}\ {\isadigit{3}}{\isacharparenright}{\isachardoublequote}} in \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}{\isachardoublequote}}) you may assume all substitutions are performed simultaneously. Otherwise the behaviour of \isa{subst} is not specified. - \item [\mbox{\isa{subst}}~\isa{{\isacharparenleft}asm{\isacharparenright}\ {\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq}] performs the - substitutions in the assumptions. Positions \isa{{\isadigit{1}}\ {\isasymdots}\ i\isactrlsub {\isadigit{1}}} - refer to assumption 1, positions \isa{i\isactrlsub {\isadigit{1}}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymdots}\ i\isactrlsub {\isadigit{2}}} + \item [\mbox{\isa{subst}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}\ {\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq{\isachardoublequote}}] performs the + substitutions in the assumptions. Positions \isa{{\isachardoublequote}{\isadigit{1}}\ {\isasymdots}\ i\isactrlsub {\isadigit{1}}{\isachardoublequote}} + refer to assumption 1, positions \isa{{\isachardoublequote}i\isactrlsub {\isadigit{1}}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymdots}\ i\isactrlsub {\isadigit{2}}{\isachardoublequote}} to assumption 2, and so on. \item [\mbox{\isa{hypsubst}}] performs substitution using some - assumption; this only works for equations of the form \isa{x\ {\isacharequal}\ t} where \isa{x} is a free or bound variable. + assumption; this only works for equations of the form \isa{{\isachardoublequote}x\ {\isacharequal}\ t{\isachardoublequote}} where \isa{x} is a free or bound variable. - \item [\mbox{\isa{split}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] performs + \item [\mbox{\isa{split}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] performs single-step case splitting using the given rules. By default, - splitting is performed in the conclusion of a goal; the \isa{{\isacharparenleft}asm{\isacharparenright}} option indicates to operate on assumptions instead. + splitting is performed in the conclusion of a goal; the \isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}{\isachardoublequote}} option indicates to operate on assumptions instead. Note that the \mbox{\isa{simp}} method already involves repeated application of split rules as declared in the current context. @@ -1510,7 +1510,7 @@ Isabelle/Pure (\secref{sec:pure-meth-att}). \item [\mbox{\isa{contradiction}}] solves some goal by contradiction, - deriving any result from both \isa{{\isasymnot}\ A} and \isa{A}. Chained + deriving any result from both \isa{{\isachardoublequote}{\isasymnot}\ A{\isachardoublequote}} and \isa{A}. Chained facts, which are guaranteed to participate, may appear in either order. @@ -1564,7 +1564,7 @@ Any of the above methods support additional modifiers of the context of classical rules. Their semantics is analogous to the attributes given before. Facts provided by forward chaining are inserted into - the goal before commencing proof search. The ``\isa{{\isacharbang}}''~argument causes the full context of assumptions to be + the goal before commencing proof search. The ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}''~argument causes the full context of assumptions to be included as well.% \end{isamarkuptext}% \isamarkuptrue% @@ -1608,7 +1608,7 @@ here. Facts provided by forward chaining are inserted into the goal before - doing the search. The ``\isa{{\isacharbang}}'' argument causes the full + doing the search. The ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' argument causes the full context of assumptions to be included as well. \end{descr}% @@ -1621,7 +1621,7 @@ % \begin{isamarkuptext}% \begin{matharray}{rcl} - \indexdef{}{command}{print-claset}\mbox{\isa{\isacommand{print{\isacharunderscore}claset}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-claset}\mbox{\isa{\isacommand{print{\isacharunderscore}claset}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \indexdef{}{attribute}{intro}\mbox{\isa{intro}} & : & \isaratt \\ \indexdef{}{attribute}{elim}\mbox{\isa{elim}} & : & \isaratt \\ \indexdef{}{attribute}{dest}\mbox{\isa{dest}} & : & \isaratt \\ @@ -1647,8 +1647,8 @@ \item [\mbox{\isa{intro}}, \mbox{\isa{elim}}, and \mbox{\isa{dest}}] declare introduction, elimination, and destruction rules, respectively. By default, rules are considered as \emph{unsafe} - (i.e.\ not applied blindly without backtracking), while ``\isa{{\isacharbang}}'' classifies as \emph{safe}. Rule declarations marked by - ``\isa{{\isacharquery}}'' coincide with those of Isabelle/Pure, cf.\ + (i.e.\ not applied blindly without backtracking), while ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' classifies as \emph{safe}. Rule declarations marked by + ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' coincide with those of Isabelle/Pure, cf.\ \secref{sec:pure-meth-att} (i.e.\ are only applied in single steps of the \mbox{\isa{rule}} method). The optional natural number specifies an explicit weight argument, which is ignored by automated @@ -1661,9 +1661,9 @@ Simplifier and the Classical reasoner at the same time. Non-conditional rules result in a ``safe'' introduction and elimination pair; conditional ones are considered ``unsafe''. Rules - with negative conclusion are automatically inverted (using \isa{{\isasymnot}}-elimination internally). + with negative conclusion are automatically inverted (using \isa{{\isachardoublequote}{\isasymnot}{\isachardoublequote}}-elimination internally). - The ``\isa{{\isacharquery}}'' version of \mbox{\isa{iff}} declares rules to + The ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' version of \mbox{\isa{iff}} declares rules to the Isabelle/Pure context only, and omits the Simplifier declaration. @@ -1683,7 +1683,7 @@ \begin{descr} \item [\mbox{\isa{swapped}}] turns an introduction rule into an - elimination, by resolving with the classical swap principle \isa{{\isacharparenleft}{\isasymnot}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymLongrightarrow}\ B{\isacharparenright}}. + elimination, by resolving with the classical swap principle \isa{{\isachardoublequote}{\isacharparenleft}{\isasymnot}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymLongrightarrow}\ B{\isacharparenright}{\isachardoublequote}}. \end{descr}% \end{isamarkuptext}% @@ -1700,7 +1700,7 @@ \begin{isamarkuptext}% \begin{matharray}{rcl} \indexdef{}{command}{case}\mbox{\isa{\isacommand{case}}} & : & \isartrans{proof(state)}{proof(state)} \\ - \indexdef{}{command}{print-cases}\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{proof} \\ + \indexdef{}{command}{print-cases}\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{proof} \\ \indexdef{}{attribute}{case-names}\mbox{\isa{case{\isacharunderscore}names}} & : & \isaratt \\ \indexdef{}{attribute}{case-conclusion}\mbox{\isa{case{\isacharunderscore}conclusion}} & : & \isaratt \\ \indexdef{}{attribute}{params}\mbox{\isa{params}} & : & \isaratt \\ @@ -1716,20 +1716,20 @@ The \mbox{\isa{\isacommand{case}}} command provides a shorthand to refer to a local context symbolically: certain proof methods provide an - environment of named ``cases'' of the form \isa{c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub n}; the effect of ``\mbox{\isa{\isacommand{case}}}~\isa{c}'' is then equivalent to ``\mbox{\isa{\isacommand{fix}}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m}~\mbox{\isa{\isacommand{assume}}}~\isa{c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n}''. Term bindings may be covered as well, notably + environment of named ``cases'' of the form \isa{{\isachardoublequote}c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}; the effect of ``\mbox{\isa{\isacommand{case}}}~\isa{c}'' is then equivalent to ``\mbox{\isa{\isacommand{fix}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}''. Term bindings may be covered as well, notably \mbox{\isa{{\isacharquery}case}} for the main conclusion. - By default, the ``terminology'' \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m} of + By default, the ``terminology'' \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} of a case value is marked as hidden, i.e.\ there is no way to refer to such parameters in the subsequent proof text. After all, original rule parameters stem from somewhere outside of the current proof - text. By using the explicit form ``\mbox{\isa{\isacommand{case}}}~\isa{{\isacharparenleft}c\ y\isactrlsub {\isadigit{1}}\ {\isasymdots}\ y\isactrlsub m{\isacharparenright}}'' instead, the proof author is able to + text. By using the explicit form ``\mbox{\isa{\isacommand{case}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ y\isactrlsub {\isadigit{1}}\ {\isasymdots}\ y\isactrlsub m{\isacharparenright}{\isachardoublequote}}'' instead, the proof author is able to chose local names that fit nicely into the current context. \medskip It is important to note that proper use of \mbox{\isa{\isacommand{case}}} does not provide means to peek at the current goal state, which is not directly observable in Isar! Nonetheless, goal - refinement commands do provide named cases \isa{goal\isactrlsub i} - for each subgoal \isa{i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n} of the resulting goal state. + refinement commands do provide named cases \isa{{\isachardoublequote}goal\isactrlsub i{\isachardoublequote}} + for each subgoal \isa{{\isachardoublequote}i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n{\isachardoublequote}} of the resulting goal state. Using this extra feature requires great care, because some bits of the internal tactical machinery intrude the proof text. In particular, parameter names stemming from the left-over of automated @@ -1765,30 +1765,30 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{case}}}~\isa{{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}}] - invokes a named local context \isa{c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub m}, as provided by an appropriate + \item [\mbox{\isa{\isacommand{case}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}{\isachardoublequote}}] + invokes a named local context \isa{{\isachardoublequote}c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub m{\isachardoublequote}}, as provided by an appropriate proof method (such as \indexref{}{method}{cases}\mbox{\isa{cases}} and \indexref{}{method}{induct}\mbox{\isa{induct}}). - The command ``\mbox{\isa{\isacommand{case}}}~\isa{{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}}'' abbreviates ``\mbox{\isa{\isacommand{fix}}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m}~\mbox{\isa{\isacommand{assume}}}~\isa{c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n}''. + The command ``\mbox{\isa{\isacommand{case}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}{\isachardoublequote}}'' abbreviates ``\mbox{\isa{\isacommand{fix}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}''. \item [\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}] prints all local contexts of the current state, using Isar proof language notation. - \item [\mbox{\isa{case{\isacharunderscore}names}}~\isa{c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub k}] + \item [\mbox{\isa{case{\isacharunderscore}names}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub k{\isachardoublequote}}] declares names for the local contexts of premises of a theorem; - \isa{c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub k} refers to the \emph{suffix} of the + \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub k{\isachardoublequote}} refers to the \emph{suffix} of the list of premises. - \item [\mbox{\isa{case{\isacharunderscore}conclusion}}~\isa{c\ d\isactrlsub {\isadigit{1}}\ {\isasymdots}\ d\isactrlsub k}] declares names for the conclusions of a named premise - \isa{c}; here \isa{d\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ d\isactrlsub k} refers to the + \item [\mbox{\isa{case{\isacharunderscore}conclusion}}~\isa{{\isachardoublequote}c\ d\isactrlsub {\isadigit{1}}\ {\isasymdots}\ d\isactrlsub k{\isachardoublequote}}] declares names for the conclusions of a named premise + \isa{c}; here \isa{{\isachardoublequote}d\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ d\isactrlsub k{\isachardoublequote}} refers to the prefix of arguments of a logical formula built by nesting a binary - connective (e.g.\ \isa{{\isasymor}}). + connective (e.g.\ \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}). Note that proof methods such as \mbox{\isa{induct}} and \mbox{\isa{coinduct}} already provide a default name for the conclusion as a whole. The need to name subformulas only arises with cases that split into several sub-cases, as in common co-induction rules. - \item [\mbox{\isa{params}}~\isa{p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n}] renames the innermost parameters of - premises \isa{{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n} of some theorem. An empty list of names + \item [\mbox{\isa{params}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n{\isachardoublequote}}] renames the innermost parameters of + premises \isa{{\isachardoublequote}{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n{\isachardoublequote}} of some theorem. An empty list of names may be given to skip positions, leaving the present parameters unchanged. @@ -1798,7 +1798,7 @@ \item [\mbox{\isa{consumes}}~\isa{n}] declares the number of ``major premises'' of a rule, i.e.\ the number of facts to be consumed when it is applied by an appropriate proof method. The - default value of \mbox{\isa{consumes}} is \isa{n\ {\isacharequal}\ {\isadigit{1}}}, which is + default value of \mbox{\isa{consumes}} is \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}}, which is appropriate for the usual kind of cases and induction rules for inductive sets (cf.\ \secref{sec:hol-inductive}). Rules without any \mbox{\isa{consumes}} declaration given are treated as if @@ -1861,7 +1861,7 @@ \begin{descr} - \item [\mbox{\isa{cases}}~\isa{insts\ R}] applies method \mbox{\isa{rule}} with an appropriate case distinction theorem, instantiated to + \item [\mbox{\isa{cases}}~\isa{{\isachardoublequote}insts\ R{\isachardoublequote}}] applies method \mbox{\isa{rule}} with an appropriate case distinction theorem, instantiated to the subjects \isa{insts}. Symbolic case names are bound according to the rule's local contexts. @@ -1873,8 +1873,8 @@ facts & & arguments & rule \\\hline & \mbox{\isa{cases}} & & classical case split \\ & \mbox{\isa{cases}} & \isa{t} & datatype exhaustion (type of \isa{t}) \\ - \isa{{\isasymturnstile}\ A\ t} & \mbox{\isa{cases}} & \isa{{\isasymdots}} & inductive predicate/set elimination (of \isa{A}) \\ - \isa{{\isasymdots}} & \mbox{\isa{cases}} & \isa{{\isasymdots}\ rule{\isacharcolon}\ R} & explicit rule \isa{R} \\ + \isa{{\isachardoublequote}{\isasymturnstile}\ A\ t{\isachardoublequote}} & \mbox{\isa{cases}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & inductive predicate/set elimination (of \isa{A}) \\ + \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \mbox{\isa{cases}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\ \end{tabular} \medskip @@ -1884,28 +1884,28 @@ term needs to be specified; this refers to the first variable of the last premise (it is usually the same for all cases). - \item [\mbox{\isa{induct}}~\isa{insts\ R}] is analogous to the + \item [\mbox{\isa{induct}}~\isa{{\isachardoublequote}insts\ R{\isachardoublequote}}] is analogous to the \mbox{\isa{cases}} method, but refers to induction rules, which are determined as follows: \medskip \begin{tabular}{llll} facts & & arguments & rule \\\hline - & \mbox{\isa{induct}} & \isa{P\ x} & datatype induction (type of \isa{x}) \\ - \isa{{\isasymturnstile}\ A\ x} & \mbox{\isa{induct}} & \isa{{\isasymdots}} & predicate/set induction (of \isa{A}) \\ - \isa{{\isasymdots}} & \mbox{\isa{induct}} & \isa{{\isasymdots}\ rule{\isacharcolon}\ R} & explicit rule \isa{R} \\ + & \mbox{\isa{induct}} & \isa{{\isachardoublequote}P\ x{\isachardoublequote}} & datatype induction (type of \isa{x}) \\ + \isa{{\isachardoublequote}{\isasymturnstile}\ A\ x{\isachardoublequote}} & \mbox{\isa{induct}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & predicate/set induction (of \isa{A}) \\ + \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \mbox{\isa{induct}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\ \end{tabular} \medskip Several instantiations may be given, each referring to some part of a mutual inductive definition or datatype --- only related partial induction rules may be used together, though. Any of the lists of - terms \isa{P{\isacharcomma}\ x{\isacharcomma}\ {\isasymdots}} refers to the \emph{suffix} of variables + terms \isa{{\isachardoublequote}P{\isacharcomma}\ x{\isacharcomma}\ {\isasymdots}{\isachardoublequote}} refers to the \emph{suffix} of variables present in the induction rule. This enables the writer to specify only induction variables, or both predicates and variables, for example. - Instantiations may be definitional: equations \isa{x\ {\isasymequiv}\ t} + Instantiations may be definitional: equations \isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}} introduce local definitions, which are inserted into the claim and discharged after applying the induction rule. Equalities reappear in the inductive cases, but have been transformed according to the @@ -1913,19 +1913,19 @@ practically useful induction hypotheses, some variables occurring in \isa{t} need to be fixed (see below). - The optional ``\isa{arbitrary{\isacharcolon}\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m}'' - specification generalizes variables \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m} of the original goal before applying induction. Thus + The optional ``\isa{{\isachardoublequote}arbitrary{\isacharcolon}\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}'' + specification generalizes variables \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} of the original goal before applying induction. Thus induction hypotheses may become sufficiently general to get the proof through. Together with definitional instantiations, one may effectively perform induction over expressions of a certain structure. - The optional ``\isa{taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n}'' + The optional ``\isa{{\isachardoublequote}taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}'' specification provides additional instantiations of a prefix of pending variables in the rule. Such schematic induction rules rarely occur in practice, though. - \item [\mbox{\isa{coinduct}}~\isa{inst\ R}] is analogous to the + \item [\mbox{\isa{coinduct}}~\isa{{\isachardoublequote}inst\ R{\isachardoublequote}}] is analogous to the \mbox{\isa{induct}} method, but refers to coinduction rules, which are determined as follows: @@ -1933,20 +1933,20 @@ \begin{tabular}{llll} goal & & arguments & rule \\\hline & \mbox{\isa{coinduct}} & \isa{x} & type coinduction (type of \isa{x}) \\ - \isa{A\ x} & \mbox{\isa{coinduct}} & \isa{{\isasymdots}} & predicate/set coinduction (of \isa{A}) \\ - \isa{{\isasymdots}} & \mbox{\isa{coinduct}} & \isa{{\isasymdots}\ rule{\isacharcolon}\ R} & explicit rule \isa{R} \\ + \isa{{\isachardoublequote}A\ x{\isachardoublequote}} & \mbox{\isa{coinduct}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & predicate/set coinduction (of \isa{A}) \\ + \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \mbox{\isa{coinduct}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\ \end{tabular} Coinduction is the dual of induction. Induction essentially - eliminates \isa{A\ x} towards a generic result \isa{P\ x}, - while coinduction introduces \isa{A\ x} starting with \isa{B\ x}, for a suitable ``bisimulation'' \isa{B}. The cases of a + eliminates \isa{{\isachardoublequote}A\ x{\isachardoublequote}} towards a generic result \isa{{\isachardoublequote}P\ x{\isachardoublequote}}, + while coinduction introduces \isa{{\isachardoublequote}A\ x{\isachardoublequote}} starting with \isa{{\isachardoublequote}B\ x{\isachardoublequote}}, for a suitable ``bisimulation'' \isa{B}. The cases of a coinduct rule are typically named after the predicates or sets being covered, while the conclusions consist of several alternatives being named after the individual destructor patterns. The given instantiation refers to the \emph{suffix} of variables occurring in the rule's major premise, or conclusion if unavailable. - An additional ``\isa{taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n}'' + An additional ``\isa{{\isachardoublequote}taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}'' specification may be required in order to specify the bisimulation to be used in the coinduction step. @@ -1966,7 +1966,7 @@ \medskip Despite the additional infrastructure, both \mbox{\isa{cases}} and \mbox{\isa{coinduct}} merely apply a certain rule, after instantiation, while conforming due to the usual way of monotonic - natural deduction: the context of a structured statement \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ {\isasymdots}} + natural deduction: the context of a structured statement \isa{{\isachardoublequote}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ {\isasymdots}{\isachardoublequote}} reappears unchanged after the case split. The \mbox{\isa{induct}} method is fundamentally different in this @@ -2000,7 +2000,7 @@ % \begin{isamarkuptext}% \begin{matharray}{rcl} - \indexdef{}{command}{print-induct-rules}\mbox{\isa{\isacommand{print{\isacharunderscore}induct{\isacharunderscore}rules}}}\isa{\isactrlsup {\isacharasterisk}} & : & \isarkeep{theory~|~proof} \\ + \indexdef{}{command}{print-induct-rules}\mbox{\isa{\isacommand{print{\isacharunderscore}induct{\isacharunderscore}rules}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\ \indexdef{}{attribute}{cases}\mbox{\isa{cases}} & : & \isaratt \\ \indexdef{}{attribute}{induct}\mbox{\isa{induct}} & : & \isaratt \\ \indexdef{}{attribute}{coinduct}\mbox{\isa{coinduct}} & : & \isaratt \\ @@ -2054,13 +2054,13 @@ The very starting point for any Isabelle object-logic is a ``truth judgment'' that links object-level statements to the meta-logic (with its minimal language of \isa{prop} that covers universal - quantification \isa{{\isasymAnd}} and implication \isa{{\isasymLongrightarrow}}). + quantification \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and implication \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}). Common object-logics are sufficiently expressive to internalize rule - statements over \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} within their own + statements over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} within their own language. This is useful in certain situations where a rule needs to be viewed as an atomic statement from the meta-level perspective, - e.g.\ \isa{{\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymLongrightarrow}\ P\ x} versus \isa{{\isasymforall}x\ {\isasymin}\ A{\isachardot}\ P\ x}. + e.g.\ \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymLongrightarrow}\ P\ x{\isachardoublequote}} versus \isa{{\isachardoublequote}{\isasymforall}x\ {\isasymin}\ A{\isachardot}\ P\ x{\isachardoublequote}}. From the following language elements, only the \mbox{\isa{atomize}} method and \mbox{\isa{rule{\isacharunderscore}format}} attribute are occasionally @@ -2082,11 +2082,11 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{judgment}}}~\isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isacharparenleft}mx{\isacharparenright}}] declares + \item [\mbox{\isa{\isacommand{judgment}}}~\isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}}] declares constant \isa{c} as the truth judgment of the current object-logic. Its type \isa{{\isasymsigma}} should specify a coercion of the category of object-level propositions to \isa{prop} of the Pure - meta-logic; the mixfix annotation \isa{{\isacharparenleft}mx{\isacharparenright}} would typically + meta-logic; the mixfix annotation \isa{{\isachardoublequote}{\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} would typically just link the object language (internally of syntactic category \isa{logic}) with that of \isa{prop}. Only one \mbox{\isa{\isacommand{judgment}}} declaration may be given in any theory development. @@ -2094,25 +2094,25 @@ premises of a sub-goal, using the meta-level equations declared via \mbox{\isa{atomize}} (as an attribute) beforehand. As a result, heavily nested goals become amenable to fundamental operations such - as resolution (cf.\ the \mbox{\isa{rule}} method). Giving the ``\isa{{\isacharparenleft}full{\isacharparenright}}'' option here means to turn the whole subgoal into an + as resolution (cf.\ the \mbox{\isa{rule}} method). Giving the ``\isa{{\isachardoublequote}{\isacharparenleft}full{\isacharparenright}{\isachardoublequote}}'' option here means to turn the whole subgoal into an object-statement (if possible), including the outermost parameters and assumptions as well. A typical collection of \mbox{\isa{atomize}} rules for a particular object-logic would provide an internalization for each of the - connectives of \isa{{\isasymAnd}}, \isa{{\isasymLongrightarrow}}, and \isa{{\isasymequiv}}. + connectives of \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}, and \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}}. Meta-level conjunction should be covered as well (this is particularly important for locales, see \secref{sec:locale}). \item [\mbox{\isa{rule{\isacharunderscore}format}}] rewrites a theorem by the equalities declared as \mbox{\isa{rulify}} rules in the current object-logic. By default, the result is fully normalized, including - assumptions and conclusions at any depth. The \isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}} + assumptions and conclusions at any depth. The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}} option restricts the transformation to the conclusion of a rule. In common object-logics (HOL, FOL, ZF), the effect of \mbox{\isa{rule{\isacharunderscore}format}} is to replace (bounded) universal quantification - (\isa{{\isasymforall}}) and implication (\isa{{\isasymlongrightarrow}}) by the corresponding - rule statements over \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}}. + (\isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}}) and implication (\isa{{\isachardoublequote}{\isasymlongrightarrow}{\isachardoublequote}}) by the corresponding + rule statements over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}. \end{descr}% \end{isamarkuptext}% diff -r 6ac51a2f48e1 -r 81308d44fe0a doc-src/IsarRef/Thy/document/HOLCF_Specific.tex --- a/doc-src/IsarRef/Thy/document/HOLCF_Specific.tex Wed May 07 12:56:11 2008 +0200 +++ b/doc-src/IsarRef/Thy/document/HOLCF_Specific.tex Wed May 07 13:04:12 2008 +0200 @@ -12,17 +12,85 @@ \isacommand{theory}\isamarkupfalse% \ HOLCF{\isacharunderscore}Specific\isanewline \isakeyword{imports}\ HOLCF\isanewline -\isakeyword{begin}\isanewline -\isanewline +\isakeyword{begin}% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory +% +\isamarkupchapter{HOLCF specific elements% +} +\isamarkuptrue% +% +\isamarkupsection{Mixfix syntax for continuous operations% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{matharray}{rcl} + \indexdef{HOLCF}{command}{consts}\mbox{\isa{\isacommand{consts}}} & : & \isartrans{theory}{theory} \\ + \end{matharray} + + HOLCF provides a separate type for continuous functions \isa{{\isachardoublequote}{\isasymalpha}\ {\isasymrightarrow}\ {\isasymbeta}{\isachardoublequote}}, with an explicit application operator \isa{{\isachardoublequote}f\ {\isasymcdot}\ x{\isachardoublequote}}. + Isabelle mixfix syntax normally refers directly to the pure + meta-level function type \isa{{\isachardoublequote}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymbeta}{\isachardoublequote}}, with application \isa{{\isachardoublequote}f\ x{\isachardoublequote}}. + + The HOLCF variant of \mbox{\isa{\isacommand{consts}}} modifies that of + Pure Isabelle (cf.\ \secref{sec:consts}) such that declarations + involving continuous function types are treated specifically. Any + given syntax template is transformed internally, generating + translation rules for the abstract and concrete representation of + continuous application. Note that mixing of HOLCF and Pure + application is \emph{not} supported!% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsection{Recursive domains% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +\begin{matharray}{rcl} + \indexdef{HOLCF}{command}{domain}\mbox{\isa{\isacommand{domain}}} & : & \isartrans{theory}{theory} \\ + \end{matharray} + + \begin{rail} + 'domain' parname? (dmspec + 'and') + ; + + dmspec: typespec '=' (cons + '|') + ; + cons: name (type *) mixfix? + ; + dtrules: 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs + \end{rail} + + Recursive domains in HOLCF are analogous to datatypes in classical + HOL (cf.\ \secref{sec:hol-datatype}). Mutual recursion is + supported, but no nesting nor arbitrary branching. Domain + constructors may be strict (default) or lazy, the latter admits to + introduce infinitary objects in the typical LCF manner (e.g.\ lazy + lists). See also \cite{MuellerNvOS99} for a general discussion of + HOLCF domains.% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isadelimtheory +% +\endisadelimtheory +% +\isatagtheory \isacommand{end}\isamarkupfalse% % \endisatagtheory {\isafoldtheory}% % \isadelimtheory -\isanewline % \endisadelimtheory +\isanewline \end{isabellebody}% %%% Local Variables: %%% mode: latex diff -r 6ac51a2f48e1 -r 81308d44fe0a doc-src/IsarRef/Thy/document/Quick_Reference.tex --- a/doc-src/IsarRef/Thy/document/Quick_Reference.tex Wed May 07 12:56:11 2008 +0200 +++ b/doc-src/IsarRef/Thy/document/Quick_Reference.tex Wed May 07 13:04:12 2008 +0200 @@ -34,36 +34,36 @@ % \begin{isamarkuptext}% \begin{tabular}{ll} - \mbox{\isa{\isacommand{fix}}}~\isa{x} & augment context by \isa{{\isasymAnd}x{\isachardot}\ {\isasymbox}} \\ - \mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & augment context by \isa{{\isasymphi}\ {\isasymLongrightarrow}\ {\isasymbox}} \\ + \mbox{\isa{\isacommand{fix}}}~\isa{x} & augment context by \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ {\isasymbox}{\isachardoublequote}} \\ + \mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & augment context by \isa{{\isachardoublequote}{\isasymphi}\ {\isasymLongrightarrow}\ {\isasymbox}{\isachardoublequote}} \\ \mbox{\isa{\isacommand{then}}} & indicate forward chaining of facts \\ - \mbox{\isa{\isacommand{have}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & prove local result \\ - \mbox{\isa{\isacommand{show}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & prove local result, refining some goal \\ + \mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & prove local result \\ + \mbox{\isa{\isacommand{show}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & prove local result, refining some goal \\ \mbox{\isa{\isacommand{using}}}~\isa{a} & indicate use of additional facts \\ \mbox{\isa{\isacommand{unfolding}}}~\isa{a} & unfold definitional equations \\ - \mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}}~\dots~\mbox{\isa{\isacommand{qed}}}~\isa{m\isactrlsub {\isadigit{2}}} & indicate proof structure and refinements \\ + \mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\dots~\mbox{\isa{\isacommand{qed}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} & indicate proof structure and refinements \\ \mbox{\isa{\isacommand{{\isacharbraceleft}}}}~\dots~\mbox{\isa{\isacommand{{\isacharbraceright}}}} & indicate explicit blocks \\ \mbox{\isa{\isacommand{next}}} & switch blocks \\ - \mbox{\isa{\isacommand{note}}}~\isa{a\ {\isacharequal}\ b} & reconsider facts \\ - \mbox{\isa{\isacommand{let}}}~\isa{p\ {\isacharequal}\ t} & abbreviate terms by higher-order matching \\ + \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b{\isachardoublequote}} & reconsider facts \\ + \mbox{\isa{\isacommand{let}}}~\isa{{\isachardoublequote}p\ {\isacharequal}\ t{\isachardoublequote}} & abbreviate terms by higher-order matching \\ \end{tabular} \begin{matharray}{rcl} - \isa{theory{\isasymdash}stmt} & = & \mbox{\isa{\isacommand{theorem}}}~\isa{name{\isacharcolon}\ props\ proof} \Or \mbox{\isa{\isacommand{definition}}}~\dots \Or \dots \\[1ex] - \isa{proof} & = & \isa{prfx\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{proof}}}~\isa{method\ stmt\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{qed}}}~\isa{method} \\ - & \Or & \isa{prfx\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{done}}} \\[1ex] + \isa{{\isachardoublequote}theory{\isasymdash}stmt{\isachardoublequote}} & = & \mbox{\isa{\isacommand{theorem}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \Or \mbox{\isa{\isacommand{definition}}}~\dots \Or \dots \\[1ex] + \isa{{\isachardoublequote}proof{\isachardoublequote}} & = & \isa{{\isachardoublequote}prfx\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}method\ stmt\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\mbox{\isa{\isacommand{qed}}}~\isa{method} \\ + & \Or & \isa{{\isachardoublequote}prfx\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\mbox{\isa{\isacommand{done}}} \\[1ex] \isa{prfx} & = & \mbox{\isa{\isacommand{apply}}}~\isa{method} \\ - & \Or & \mbox{\isa{\isacommand{using}}}~\isa{facts} \\ - & \Or & \mbox{\isa{\isacommand{unfolding}}}~\isa{facts} \\ - \isa{stmt} & = & \mbox{\isa{\isacommand{{\isacharbraceleft}}}}~\isa{stmt\isactrlsup {\isacharasterisk}}~\mbox{\isa{\isacommand{{\isacharbraceright}}}} \\ + & \Or & \mbox{\isa{\isacommand{using}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} \\ + & \Or & \mbox{\isa{\isacommand{unfolding}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} \\ + \isa{stmt} & = & \mbox{\isa{\isacommand{{\isacharbraceleft}}}}~\isa{{\isachardoublequote}stmt\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\mbox{\isa{\isacommand{{\isacharbraceright}}}} \\ & \Or & \mbox{\isa{\isacommand{next}}} \\ - & \Or & \mbox{\isa{\isacommand{note}}}~\isa{name\ {\isacharequal}\ facts} \\ - & \Or & \mbox{\isa{\isacommand{let}}}~\isa{term\ {\isacharequal}\ term} \\ - & \Or & \mbox{\isa{\isacommand{fix}}}~\isa{var\isactrlsup {\isacharplus}} \\ - & \Or & \mbox{\isa{\isacommand{assume}}}~\isa{name{\isacharcolon}\ props} \\ - & \Or & \mbox{\isa{\isacommand{then}}}\isa{\isactrlsup {\isacharquery}}~\isa{goal} \\ - \isa{goal} & = & \mbox{\isa{\isacommand{have}}}~\isa{name{\isacharcolon}\ props\ proof} \\ - & \Or & \mbox{\isa{\isacommand{show}}}~\isa{name{\isacharcolon}\ props\ proof} \\ + & \Or & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ facts{\isachardoublequote}} \\ + & \Or & \mbox{\isa{\isacommand{let}}}~\isa{{\isachardoublequote}term\ {\isacharequal}\ term{\isachardoublequote}} \\ + & \Or & \mbox{\isa{\isacommand{fix}}}~\isa{{\isachardoublequote}var\isactrlsup {\isacharplus}{\isachardoublequote}} \\ + & \Or & \mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props{\isachardoublequote}} \\ + & \Or & \mbox{\isa{\isacommand{then}}}\isa{{\isachardoublequote}\isactrlsup {\isacharquery}{\isachardoublequote}}~\isa{goal} \\ + \isa{goal} & = & \mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \\ + & \Or & \mbox{\isa{\isacommand{show}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \\ \end{matharray}% \end{isamarkuptext}% \isamarkuptrue% @@ -74,13 +74,13 @@ % \begin{isamarkuptext}% \begin{matharray}{rcl} - \mbox{\isa{\isacommand{by}}}~\isa{m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}} & \equiv & \mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}}~\mbox{\isa{\isacommand{qed}}}~\isa{m\isactrlsub {\isadigit{2}}} \\ + \mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} & \equiv & \mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\mbox{\isa{\isacommand{qed}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} \\ \mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}} & \equiv & \mbox{\isa{\isacommand{by}}}~\isa{rule} \\ \mbox{\isa{\isacommand{{\isachardot}}}} & \equiv & \mbox{\isa{\isacommand{by}}}~\isa{this} \\ \mbox{\isa{\isacommand{hence}}} & \equiv & \mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{have}}} \\ \mbox{\isa{\isacommand{thus}}} & \equiv & \mbox{\isa{\isacommand{then}}}~\mbox{\isa{\isacommand{show}}} \\ \mbox{\isa{\isacommand{from}}}~\isa{a} & \equiv & \mbox{\isa{\isacommand{note}}}~\isa{a}~\mbox{\isa{\isacommand{then}}} \\ - \mbox{\isa{\isacommand{with}}}~\isa{a} & \equiv & \mbox{\isa{\isacommand{from}}}~\isa{a\ {\isasymAND}\ this} \\[1ex] + \mbox{\isa{\isacommand{with}}}~\isa{a} & \equiv & \mbox{\isa{\isacommand{from}}}~\isa{{\isachardoublequote}a\ {\isasymAND}\ this{\isachardoublequote}} \\[1ex] \mbox{\isa{\isacommand{from}}}~\isa{this} & \equiv & \mbox{\isa{\isacommand{then}}} \\ \mbox{\isa{\isacommand{from}}}~\isa{this}~\mbox{\isa{\isacommand{have}}} & \equiv & \mbox{\isa{\isacommand{hence}}} \\ \mbox{\isa{\isacommand{from}}}~\isa{this}~\mbox{\isa{\isacommand{show}}} & \equiv & \mbox{\isa{\isacommand{thus}}} \\ @@ -94,15 +94,15 @@ % \begin{isamarkuptext}% \begin{matharray}{rcl} - \mbox{\isa{\isacommand{also}}}\isa{\isactrlsub {\isadigit{0}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ this} \\ - \mbox{\isa{\isacommand{also}}}\isa{\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}} \\ + \mbox{\isa{\isacommand{also}}}\isa{{\isachardoublequote}\isactrlsub {\isadigit{0}}{\isachardoublequote}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ this{\isachardoublequote}} \\ + \mbox{\isa{\isacommand{also}}}\isa{{\isachardoublequote}\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}{\isachardoublequote}} \\ \mbox{\isa{\isacommand{finally}}} & \approx & \mbox{\isa{\isacommand{also}}}~\mbox{\isa{\isacommand{from}}}~\isa{calculation} \\[0.5ex] - \mbox{\isa{\isacommand{moreover}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{calculation\ {\isacharequal}\ calculation\ this} \\ + \mbox{\isa{\isacommand{moreover}}} & \approx & \mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ calculation\ this{\isachardoublequote}} \\ \mbox{\isa{\isacommand{ultimately}}} & \approx & \mbox{\isa{\isacommand{moreover}}}~\mbox{\isa{\isacommand{from}}}~\isa{calculation} \\[0.5ex] - \mbox{\isa{\isacommand{presume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} & \approx & \mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} \\ - \mbox{\isa{\isacommand{def}}}~\isa{a{\isacharcolon}\ x\ {\isasymequiv}\ t} & \approx & \mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ x\ {\isasymequiv}\ t} \\ - \mbox{\isa{\isacommand{obtain}}}~\isa{x\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}} & \approx & \dots~\mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} \\ - \mbox{\isa{\isacommand{case}}}~\isa{c} & \approx & \mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{c{\isacharcolon}\ {\isasymphi}} \\ + \mbox{\isa{\isacommand{presume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & \approx & \mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} \\ + \mbox{\isa{\isacommand{def}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}} & \approx & \mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}} \\ + \mbox{\isa{\isacommand{obtain}}}~\isa{{\isachardoublequote}x\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & \approx & \dots~\mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} \\ + \mbox{\isa{\isacommand{case}}}~\isa{c} & \approx & \mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} \\ \mbox{\isa{\isacommand{sorry}}} & \approx & \mbox{\isa{\isacommand{by}}}~\isa{cheating} \\ \end{matharray}% \end{isamarkuptext}% @@ -134,7 +134,7 @@ \mbox{\isa{this}} & apply current facts \\ \mbox{\isa{rule}}~\isa{a} & apply some rule \\ \mbox{\isa{rule}} & apply standard rule (default for \mbox{\isa{\isacommand{proof}}}) \\ - \mbox{\isa{contradiction}} & apply \isa{{\isasymnot}} elimination rule (any order) \\ + \mbox{\isa{contradiction}} & apply \isa{{\isachardoublequote}{\isasymnot}{\isachardoublequote}} elimination rule (any order) \\ \mbox{\isa{cases}}~\isa{t} & case analysis (provides cases) \\ \mbox{\isa{induct}}~\isa{x} & proof by induction (provides cases) \\[2ex] @@ -164,7 +164,7 @@ \multicolumn{2}{l}{\textbf{Operations}} \\[0.5ex] \mbox{\isa{OF}}~\isa{a} & rule resolved with facts (skipping ``\isa{{\isacharunderscore}}'') \\ \mbox{\isa{of}}~\isa{t} & rule instantiated with terms (skipping ``\isa{{\isacharunderscore}}'') \\ - \mbox{\isa{where}}~\isa{x\ {\isacharequal}\ t} & rule instantiated with terms, by variable name \\ + \mbox{\isa{where}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ t{\isachardoublequote}} & rule instantiated with terms, by variable name \\ \mbox{\isa{symmetric}} & resolution with symmetry rule \\ \mbox{\isa{THEN}}~\isa{b} & resolution with another rule \\ \mbox{\isa{rule{\isacharunderscore}format}} & result put into standard rule format \\ @@ -190,26 +190,26 @@ & \mbox{\isa{rule}} & \mbox{\isa{iprover}} & \mbox{\isa{blast}} & \mbox{\isa{simp}} & \mbox{\isa{auto}} \\ & & & \mbox{\isa{fast}} & \mbox{\isa{simp{\isacharunderscore}all}} & \mbox{\isa{force}} \\ \hline - \mbox{\isa{Pure{\isachardot}elim}}\isa{{\isacharbang}} \mbox{\isa{Pure{\isachardot}intro}}\isa{{\isacharbang}} - & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + \mbox{\isa{Pure{\isachardot}elim}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} \mbox{\isa{Pure{\isachardot}intro}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \mbox{\isa{Pure{\isachardot}elim}} \mbox{\isa{Pure{\isachardot}intro}} - & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ - \mbox{\isa{elim}}\isa{{\isacharbang}} \mbox{\isa{intro}}\isa{{\isacharbang}} - & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} \\ + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ + \mbox{\isa{elim}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} \mbox{\isa{intro}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \mbox{\isa{elim}} \mbox{\isa{intro}} - & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} \\ + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \mbox{\isa{iff}} - & \isa{{\isasymtimes}} & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ - \mbox{\isa{iff}}\isa{{\isacharquery}} - & \isa{{\isasymtimes}} \\ - \mbox{\isa{elim}}\isa{{\isacharquery}} \mbox{\isa{intro}}\isa{{\isacharquery}} - & \isa{{\isasymtimes}} \\ + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ + \mbox{\isa{iff}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}} + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ + \mbox{\isa{elim}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}} \mbox{\isa{intro}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}} + & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \mbox{\isa{simp}} - & & & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + & & & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \mbox{\isa{cong}} - & & & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + & & & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \mbox{\isa{split}} - & & & & \isa{{\isasymtimes}} & \isa{{\isasymtimes}} \\ + & & & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\ \end{tabular}% \end{isamarkuptext}% \isamarkuptrue% @@ -249,7 +249,7 @@ \mbox{\isa{subgoal{\isacharunderscore}tac}}~\isa{{\isasymphi}} & new claims \\ \mbox{\isa{rename{\isacharunderscore}tac}}~\isa{x} & rename innermost goal parameters \\ \mbox{\isa{rotate{\isacharunderscore}tac}}~\isa{n} & rotate assumptions of goal \\ - \mbox{\isa{tactic}}~\isa{text} & arbitrary ML tactic \\ + \mbox{\isa{tactic}}~\isa{{\isachardoublequote}text{\isachardoublequote}} & arbitrary ML tactic \\ \mbox{\isa{case{\isacharunderscore}tac}}~\isa{t} & exhaustion (datatypes) \\ \mbox{\isa{induct{\isacharunderscore}tac}}~\isa{x} & induction (datatypes) \\ \mbox{\isa{ind{\isacharunderscore}cases}}~\isa{t} & exhaustion + simplification (inductive predicates) \\ diff -r 6ac51a2f48e1 -r 81308d44fe0a doc-src/IsarRef/Thy/document/intro.tex --- a/doc-src/IsarRef/Thy/document/intro.tex Wed May 07 12:56:11 2008 +0200 +++ b/doc-src/IsarRef/Thy/document/intro.tex Wed May 07 13:04:12 2008 +0200 @@ -195,7 +195,7 @@ \medskip Using proper mathematical symbols in Isabelle theories can be very convenient for readability of large formulas. On the other hand, the plain ASCII sources easily become somewhat unintelligible. - For example, \isa{{\isasymLongrightarrow}} would appear as \verb|\| according + For example, \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} would appear as \verb|\| according the default set of Isabelle symbols. Nevertheless, the Isabelle document preparation system (see \secref{sec:document-prep}) will be happy to print non-ASCII symbols properly. It is even possible to diff -r 6ac51a2f48e1 -r 81308d44fe0a doc-src/IsarRef/Thy/document/pure.tex --- a/doc-src/IsarRef/Thy/document/pure.tex Wed May 07 12:56:11 2008 +0200 +++ b/doc-src/IsarRef/Thy/document/pure.tex Wed May 07 13:04:12 2008 +0200 @@ -37,7 +37,7 @@ constructors, or \emph{improper commands}. Some proof methods and attributes introduced later are classified as improper as well. Improper Isar language elements, which are subsequently marked by - ``\isa{\isactrlsup {\isacharasterisk}}'', are often helpful when developing proof + ``\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}'', are often helpful when developing proof documents, while their use is discouraged for the final human-readable outcome. Typical examples are diagnostic commands that print terms or theorems according to the current context; other @@ -84,14 +84,14 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{header}}}~\isa{text}] provides plain text + \item [\mbox{\isa{\isacommand{header}}}~\isa{{\isachardoublequote}text{\isachardoublequote}}] provides plain text markup just preceding the formal beginning of a theory. In actual document preparation the corresponding {\LaTeX} macro \verb|\isamarkupheader| may be redefined to produce chapter or section headings. See also \secref{sec:markup-thy} and \secref{sec:markup-prf} for further markup commands. - \item [\mbox{\isa{\isacommand{theory}}}~\isa{A\ {\isasymIMPORTS}\ B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n\ {\isasymBEGIN}}] starts a new theory \isa{A} based on the - merge of existing theories \isa{B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n}. + \item [\mbox{\isa{\isacommand{theory}}}~\isa{{\isachardoublequote}A\ {\isasymIMPORTS}\ B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n\ {\isasymBEGIN}{\isachardoublequote}}] starts a new theory \isa{A} based on the + merge of existing theories \isa{{\isachardoublequote}B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n{\isachardoublequote}}. Due to inclusion of several ancestors, the overall theory structure emerging in an Isabelle session forms a directed acyclic graph @@ -153,17 +153,17 @@ \end{descr} - The \isa{text} argument of these markup commands (except for + The \isa{{\isachardoublequote}text{\isachardoublequote}} argument of these markup commands (except for \mbox{\isa{\isacommand{text{\isacharunderscore}raw}}}) may contain references to formal entities (``antiquotations'', see also \secref{sec:antiq}). These are - interpreted in the present theory context, or the named \isa{target}. + interpreted in the present theory context, or the named \isa{{\isachardoublequote}target{\isachardoublequote}}. Any of these markup elements corresponds to a {\LaTeX} command with the name prefixed by \verb|\isamarkup|. For the sectioning commands this is a plain macro with a single argument, e.g.\ - \verb|\isamarkupchapter{|\isa{{\isasymdots}}\verb|}| for + \verb|\isamarkupchapter{|\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}\verb|}| for \mbox{\isa{\isacommand{chapter}}}. The \mbox{\isa{\isacommand{text}}} markup results in a - {\LaTeX} environment \verb|\begin{isamarkuptext}| \isa{{\isasymdots}} \verb|\end{isamarkuptext}|, while \mbox{\isa{\isacommand{text{\isacharunderscore}raw}}} + {\LaTeX} environment \verb|\begin{isamarkuptext}| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|\end{isamarkuptext}|, while \mbox{\isa{\isacommand{text{\isacharunderscore}raw}}} causes the text to be inserted directly into the {\LaTeX} source. \medskip Additional markup commands are available for proofs (see @@ -195,12 +195,12 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{classes}}}~\isa{c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n}] - declares class \isa{c} to be a subclass of existing classes \isa{c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n}. Cyclic class structures are not permitted. + \item [\mbox{\isa{\isacommand{classes}}}~\isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isachardoublequote}}] + declares class \isa{c} to be a subclass of existing classes \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isachardoublequote}}. Cyclic class structures are not permitted. - \item [\mbox{\isa{\isacommand{classrel}}}~\isa{c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}}] states - subclass relations between existing classes \isa{c\isactrlsub {\isadigit{1}}} and - \isa{c\isactrlsub {\isadigit{2}}}. This is done axiomatically! The \indexref{}{command}{instance}\mbox{\isa{\isacommand{instance}}} command (see \secref{sec:axclass}) provides a way to + \item [\mbox{\isa{\isacommand{classrel}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}}] states + subclass relations between existing classes \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isachardoublequote}} and + \isa{{\isachardoublequote}c\isactrlsub {\isadigit{2}}{\isachardoublequote}}. This is done axiomatically! The \indexref{}{command}{instance}\mbox{\isa{\isacommand{instance}}} command (see \secref{sec:axclass}) provides a way to introduce proven class relations. \item [\mbox{\isa{\isacommand{defaultsort}}}~\isa{s}] makes sort \isa{s} the @@ -240,14 +240,14 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{types}}}~\isa{{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t\ {\isacharequal}\ {\isasymtau}}] - introduces \emph{type synonym} \isa{{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t} - for existing type \isa{{\isasymtau}}. Unlike actual type definitions, as + \item [\mbox{\isa{\isacommand{types}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t\ {\isacharequal}\ {\isasymtau}{\isachardoublequote}}] + introduces \emph{type synonym} \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}} + for existing type \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}}. Unlike actual type definitions, as are available in Isabelle/HOL for example, type synonyms are just purely syntactic abbreviations without any logical significance. Internally, type synonyms are fully expanded. - \item [\mbox{\isa{\isacommand{typedecl}}}~\isa{{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t}] + \item [\mbox{\isa{\isacommand{typedecl}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}}] declares a new type constructor \isa{t}, intended as an actual logical type (of the object-logic, if available). @@ -256,7 +256,7 @@ syntactic types, i.e.\ nonterminal symbols of Isabelle's inner syntax of terms or types. - \item [\mbox{\isa{\isacommand{arities}}}~\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}\ s}] augments Isabelle's order-sorted signature of types by new type + \item [\mbox{\isa{\isacommand{arities}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}\ s{\isachardoublequote}}] augments Isabelle's order-sorted signature of types by new type constructor arities. This is done axiomatically! The \indexref{}{command}{instance}\mbox{\isa{\isacommand{instance}}} command (see \S\ref{sec:axclass}) provides a way to introduce proven type arities. @@ -270,12 +270,12 @@ % \begin{isamarkuptext}% Definitions essentially express abbreviations within the logic. The - simplest form of a definition is \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isasymequiv}\ t}, where \isa{c} is a newly declared constant. Isabelle also allows derived forms + simplest form of a definition is \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isasymequiv}\ t{\isachardoublequote}}, where \isa{c} is a newly declared constant. Isabelle also allows derived forms where the arguments of \isa{c} appear on the left, abbreviating a - prefix of \isa{{\isasymlambda}}-abstractions, e.g.\ \isa{c\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t} may be - written more conveniently as \isa{c\ x\ y\ {\isasymequiv}\ t}. Moreover, + prefix of \isa{{\isasymlambda}}-abstractions, e.g.\ \isa{{\isachardoublequote}c\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t{\isachardoublequote}} may be + written more conveniently as \isa{{\isachardoublequote}c\ x\ y\ {\isasymequiv}\ t{\isachardoublequote}}. Moreover, definitions may be weakened by adding arbitrary pre-conditions: - \isa{A\ {\isasymLongrightarrow}\ c\ x\ y\ {\isasymequiv}\ t}. + \isa{{\isachardoublequote}A\ {\isasymLongrightarrow}\ c\ x\ y\ {\isasymequiv}\ t{\isachardoublequote}}. \medskip The built-in well-formedness conditions for definitional specifications are: @@ -288,7 +288,7 @@ left-hand side. \item All type variables on the right-hand side must also appear on - the left-hand side; this prohibits \isa{{\isadigit{0}}\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymequiv}\ length\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ list{\isacharparenright}} for example. + the left-hand side; this prohibits \isa{{\isachardoublequote}{\isadigit{0}}\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymequiv}\ length\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ list{\isacharparenright}{\isachardoublequote}} for example. \item The definition must not be recursive. Most object-logics provide definitional principles that can be used to express @@ -296,13 +296,13 @@ \end{itemize} - Overloading means that a constant being declared as \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ decl} may be defined separately on type instances \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isacharparenright}\ t\ decl} for each type constructor \isa{t}. The right-hand side may mention overloaded constants + Overloading means that a constant being declared as \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ decl{\isachardoublequote}} may be defined separately on type instances \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isacharparenright}\ t\ decl{\isachardoublequote}} for each type constructor \isa{t}. The right-hand side may mention overloaded constants recursively at type instances corresponding to the immediate - argument types \isa{{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n}. Incomplete + argument types \isa{{\isachardoublequote}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isachardoublequote}}. Incomplete specification patterns impose global constraints on all occurrences, - e.g.\ \isa{d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymalpha}} on the left-hand side means that all + e.g.\ \isa{{\isachardoublequote}d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymalpha}{\isachardoublequote}} on the left-hand side means that all corresponding occurrences on some right-hand side need to be an - instance of this, general \isa{d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymbeta}} will be disallowed. + instance of this, general \isa{{\isachardoublequote}d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymbeta}{\isachardoublequote}} will be disallowed. \begin{matharray}{rcl} \indexdef{}{command}{consts}\mbox{\isa{\isacommand{consts}}} & : & \isartrans{theory}{theory} \\ @@ -331,20 +331,20 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{consts}}}~\isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}] declares constant + \item [\mbox{\isa{\isacommand{consts}}}~\isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}{\isachardoublequote}}] declares constant \isa{c} to have any instance of type scheme \isa{{\isasymsigma}}. The optional mixfix annotations may attach concrete syntax to the constants declared. - \item [\mbox{\isa{\isacommand{defs}}}~\isa{name{\isacharcolon}\ eqn}] introduces \isa{eqn} + \item [\mbox{\isa{\isacommand{defs}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ eqn{\isachardoublequote}}] introduces \isa{eqn} as a definitional axiom for some existing constant. - The \isa{{\isacharparenleft}unchecked{\isacharparenright}} option disables global dependency checks + The \isa{{\isachardoublequote}{\isacharparenleft}unchecked{\isacharparenright}{\isachardoublequote}} option disables global dependency checks for this definition, which is occasionally useful for exotic overloading. It is at the discretion of the user to avoid malformed theory specifications! - The \isa{{\isacharparenleft}overloaded{\isacharparenright}} option declares definitions to be + The \isa{{\isachardoublequote}{\isacharparenleft}overloaded{\isacharparenright}{\isachardoublequote}} option declares definitions to be potentially overloaded. Unless this option is given, a warning message would be issued for any definitional equation with a more special type than that of the corresponding constant declaration. @@ -362,8 +362,8 @@ specifications is processed in a strictly sequential manner, with type-checking being performed independently. - An optional initial context of \isa{{\isacharparenleft}structure{\isacharparenright}} declarations - admits use of indexed syntax, using the special symbol \verb|\| (printed as ``\isa{{\isasymindex}}''). The latter concept is + An optional initial context of \isa{{\isachardoublequote}{\isacharparenleft}structure{\isacharparenright}{\isachardoublequote}} declarations + admits use of indexed syntax, using the special symbol \verb|\| (printed as ``\isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}}''). The latter concept is particularly useful with locales (see also \S\ref{sec:locale}). \end{descr}% @@ -396,7 +396,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{syntax}}}~\isa{{\isacharparenleft}mode{\isacharparenright}\ decls}] is similar to + \item [\mbox{\isa{\isacommand{syntax}}}~\isa{{\isachardoublequote}{\isacharparenleft}mode{\isacharparenright}\ decls{\isachardoublequote}}] is similar to \mbox{\isa{\isacommand{consts}}}~\isa{decls}, except that the actual logical signature extension is omitted. Thus the context free grammar of Isabelle's inner syntax may be augmented in arbitrary ways, @@ -404,12 +404,12 @@ print mode that the grammar rules belong; unless the \indexref{}{keyword}{output}\mbox{\isa{\isakeyword{output}}} indicator is given, all productions are added both to the input and output grammar. - \item [\mbox{\isa{\isacommand{no{\isacharunderscore}syntax}}}~\isa{{\isacharparenleft}mode{\isacharparenright}\ decls}] removes + \item [\mbox{\isa{\isacommand{no{\isacharunderscore}syntax}}}~\isa{{\isachardoublequote}{\isacharparenleft}mode{\isacharparenright}\ decls{\isachardoublequote}}] removes grammar declarations (and translations) resulting from \isa{decls}, which are interpreted in the same manner as for \mbox{\isa{\isacommand{syntax}}} above. \item [\mbox{\isa{\isacommand{translations}}}~\isa{rules}] specifies syntactic - translation rules (i.e.\ macros): parse~/ print rules (\isa{{\isasymrightleftharpoons}}), - parse rules (\isa{{\isasymrightharpoonup}}), or print rules (\isa{{\isasymleftharpoondown}}). + translation rules (i.e.\ macros): parse~/ print rules (\isa{{\isachardoublequote}{\isasymrightleftharpoons}{\isachardoublequote}}), + parse rules (\isa{{\isachardoublequote}{\isasymrightharpoonup}{\isachardoublequote}}), or print rules (\isa{{\isachardoublequote}{\isasymleftharpoondown}{\isachardoublequote}}). Translation patterns may be prefixed by the syntactic category to be used for parsing; the default is \isa{logic}. @@ -441,7 +441,7 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{axioms}}}~\isa{a{\isacharcolon}\ {\isasymphi}}] introduces arbitrary + \item [\mbox{\isa{\isacommand{axioms}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}] introduces arbitrary statements as axioms of the meta-logic. In fact, axioms are ``axiomatic theorems'', and may be referred later just as any other theorem. @@ -450,7 +450,7 @@ systems. Everyday work is typically done the hard way, with proper definitions and proven theorems. - \item [\mbox{\isa{\isacommand{lemmas}}}~\isa{a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n}] + \item [\mbox{\isa{\isacommand{lemmas}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}] retrieves and stores existing facts in the theory context, or the specified target context (see also \secref{sec:target}). Typical applications would also involve attributes, to declare Simplifier @@ -496,15 +496,15 @@ Note that global names are prone to get hidden accidently later, when qualified names of the same base name are introduced. - \item [\mbox{\isa{\isacommand{hide}}}~\isa{space\ names}] fully removes - declarations from a given name space (which may be \isa{class}, - \isa{type}, \isa{const}, or \isa{fact}); with the \isa{{\isacharparenleft}open{\isacharparenright}} option, only the base name is hidden. Global + \item [\mbox{\isa{\isacommand{hide}}}~\isa{{\isachardoublequote}space\ names{\isachardoublequote}}] fully removes + declarations from a given name space (which may be \isa{{\isachardoublequote}class{\isachardoublequote}}, + \isa{{\isachardoublequote}type{\isachardoublequote}}, \isa{{\isachardoublequote}const{\isachardoublequote}}, or \isa{{\isachardoublequote}fact{\isachardoublequote}}); with the \isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}} option, only the base name is hidden. Global (unqualified) names may never be hidden. Note that hiding name space accesses has no impact on logical declarations -- they remain valid internally. Entities that are no longer accessible to the user are printed with the special qualifier - ``\isa{{\isacharquery}{\isacharquery}}'' prefixed to the full internal name. + ``\isa{{\isachardoublequote}{\isacharquery}{\isacharquery}{\isachardoublequote}}'' prefixed to the full internal name. \end{descr}% \end{isamarkuptext}% @@ -535,28 +535,28 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{use}}}~\isa{file}] reads and executes ML - commands from \isa{file}. The current theory context is passed - down to the ML toplevel and may be modified, using \verb|Context.>>| or derived ML commands. The file name is checked with + \item [\mbox{\isa{\isacommand{use}}}~\isa{{\isachardoublequote}file{\isachardoublequote}}] reads and executes ML + commands from \isa{{\isachardoublequote}file{\isachardoublequote}}. The current theory context is passed + down to the ML toplevel and may be modified, using \verb|"Context.>>"| or derived ML commands. The file name is checked with the \indexref{}{keyword}{uses}\mbox{\isa{\isakeyword{uses}}} dependency declaration given in the theory header (see also \secref{sec:begin-thy}). - \item [\mbox{\isa{\isacommand{ML}}}~\isa{text}] is similar to \mbox{\isa{\isacommand{use}}}, but executes ML commands directly from the given \isa{text}. + \item [\mbox{\isa{\isacommand{ML}}}~\isa{{\isachardoublequote}text{\isachardoublequote}}] is similar to \mbox{\isa{\isacommand{use}}}, but executes ML commands directly from the given \isa{{\isachardoublequote}text{\isachardoublequote}}. \item [\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}} and \mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}] are diagnostic versions of \mbox{\isa{\isacommand{ML}}}, which means that the context may not be updated. \mbox{\isa{\isacommand{ML{\isacharunderscore}val}}} echos the bindings produced at the ML toplevel, but \mbox{\isa{\isacommand{ML{\isacharunderscore}command}}} is silent. - \item [\mbox{\isa{\isacommand{setup}}}~\isa{text}] changes the current theory - context by applying \isa{text}, which refers to an ML expression - of type \verb|theory -> theory|. This enables to initialize + \item [\mbox{\isa{\isacommand{setup}}}~\isa{{\isachardoublequote}text{\isachardoublequote}}] changes the current theory + context by applying \isa{{\isachardoublequote}text{\isachardoublequote}}, which refers to an ML expression + of type \verb|"theory -> theory"|. This enables to initialize any object-logic specific tools and packages written in ML, for example. - \item [\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}~\isa{name\ {\isacharequal}\ text\ description}] - defines a proof method in the current theory. The given \isa{text} has to be an ML expression of type \verb|Args.src ->|\isasep\isanewline% -\verb| Proof.context -> Proof.method|. Parsing concrete method syntax + \item [\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ text\ description{\isachardoublequote}}] + defines a proof method in the current theory. The given \isa{{\isachardoublequote}text{\isachardoublequote}} has to be an ML expression of type \verb|"Args.src ->|\isasep\isanewline% +\verb| Proof.context -> Proof.method"|. Parsing concrete method syntax from \verb|Args.src| input can be quite tedious in general. The following simple examples are for methods without any explicit arguments, or a list of theorems, respectively. @@ -622,7 +622,7 @@ (string * string * (string -> string * real)) list \end{ttbox} - If the \isa{{\isacharparenleft}advanced{\isacharparenright}} option is given, the corresponding + If the \isa{{\isachardoublequote}{\isacharparenleft}advanced{\isacharparenright}{\isachardoublequote}} option is given, the corresponding translation functions may depend on the current theory or proof context. This allows to implement advanced syntax mechanisms, as translations functions may refer to specific theory declarations or @@ -661,7 +661,7 @@ specification of axioms -- there is no internal check of the correctness of the results! The inference kernel records oracle invocations within the internal derivation object of theorems, and - the pretty printer attaches ``\isa{{\isacharbrackleft}{\isacharbang}{\isacharbrackright}}'' to indicate results + the pretty printer attaches ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' to indicate results that are not fully checked by Isabelle inferences. \begin{rail} @@ -671,11 +671,11 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{oracle}}}~\isa{name\ {\isacharparenleft}type{\isacharparenright}\ {\isacharequal}\ text}] turns the - given ML expression \isa{text} of type - \verb|theory ->|~\isa{type}~\verb|-> term| into an + \item [\mbox{\isa{\isacommand{oracle}}}~\isa{{\isachardoublequote}name\ {\isacharparenleft}type{\isacharparenright}\ {\isacharequal}\ text{\isachardoublequote}}] turns the + given ML expression \isa{{\isachardoublequote}text{\isachardoublequote}} of type + \verb|theory ->|~\isa{{\isachardoublequote}type{\isachardoublequote}}~\verb|-> term| into an ML function of type - \verb|theory ->|~\isa{type}~\verb|-> thm|, which is + \verb|theory ->|~\isa{{\isachardoublequote}type{\isachardoublequote}}~\verb|-> thm|, which is bound to the global identifier \verb|name|. \end{descr}% @@ -695,16 +695,16 @@ \begin{descr} - \item [\isa{proof{\isacharparenleft}prove{\isacharparenright}}] means that a new goal has just been + \item [\isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}] means that a new goal has just been stated that is now to be \emph{proven}; the next command may refine it by some proof method, and enter a sub-proof to establish the actual result. - \item [\isa{proof{\isacharparenleft}state{\isacharparenright}}] is like a nested theory mode: the + \item [\isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}}] is like a nested theory mode: the context may be augmented by \emph{stating} additional assumptions, intermediate results etc. - \item [\isa{proof{\isacharparenleft}chain{\isacharparenright}}] is intermediate between \isa{proof{\isacharparenleft}state{\isacharparenright}} and \isa{proof{\isacharparenleft}prove{\isacharparenright}}: existing facts (i.e.\ + \item [\isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}}] is intermediate between \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} and \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}: existing facts (i.e.\ the contents of the special ``\indexref{}{fact}{this}\mbox{\isa{this}}'' register) have been just picked up in order to be used when refining the goal claimed next. @@ -762,16 +762,16 @@ logical framework. Introducing some \emph{arbitrary, but fixed} variable via ``\mbox{\isa{\isacommand{fix}}}~\isa{x}'' results in a local value that may be used in the subsequent proof as any other variable or - constant. Furthermore, any result \isa{{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}} exported from + constant. Furthermore, any result \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} exported from the context will be universally closed wrt.\ \isa{x} at the - outermost level: \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}} (this is expressed in normal + outermost level: \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} (this is expressed in normal form using Isabelle's meta-variables). Similarly, introducing some assumption \isa{{\isasymchi}} has two effects. On the one hand, a local theorem is created that may be used as a fact in subsequent proof steps. On the other hand, any result - \isa{{\isasymchi}\ {\isasymturnstile}\ {\isasymphi}} exported from the context becomes conditional wrt.\ - the assumption: \isa{{\isasymturnstile}\ {\isasymchi}\ {\isasymLongrightarrow}\ {\isasymphi}}. Thus, solving an enclosing goal + \isa{{\isachardoublequote}{\isasymchi}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} exported from the context becomes conditional wrt.\ + the assumption: \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymchi}\ {\isasymLongrightarrow}\ {\isasymphi}{\isachardoublequote}}. Thus, solving an enclosing goal using such a result would basically introduce a new subgoal stemming from the assumption. How this situation is handled depends on the version of assumption command used: while \mbox{\isa{\isacommand{assume}}} @@ -779,10 +779,10 @@ the goal, \mbox{\isa{\isacommand{presume}}} leaves the subgoal unchanged in order to be proved later by the user. - Local definitions, introduced by ``\mbox{\isa{\isacommand{def}}}~\isa{x\ {\isasymequiv}\ t}'', are achieved by combining ``\mbox{\isa{\isacommand{fix}}}~\isa{x}'' with + Local definitions, introduced by ``\mbox{\isa{\isacommand{def}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'', are achieved by combining ``\mbox{\isa{\isacommand{fix}}}~\isa{x}'' with another version of assumption that causes any hypothetical equation - \isa{x\ {\isasymequiv}\ t} to be eliminated by the reflexivity rule. Thus, - exporting some result \isa{x\ {\isasymequiv}\ t\ {\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}} yields \isa{{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}t{\isacharbrackright}}. + \isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}} to be eliminated by the reflexivity rule. Thus, + exporting some result \isa{{\isachardoublequote}x\ {\isasymequiv}\ t\ {\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} yields \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}t{\isacharbrackright}{\isachardoublequote}}. \begin{rail} 'fix' (vars + 'and') @@ -800,7 +800,7 @@ \item [\mbox{\isa{\isacommand{fix}}}~\isa{x}] introduces a local variable \isa{x} that is \emph{arbitrary, but fixed.} - \item [\mbox{\isa{\isacommand{assume}}}~\isa{a{\isacharcolon}\ {\isasymphi}} and \mbox{\isa{\isacommand{presume}}}~\isa{a{\isacharcolon}\ {\isasymphi}}] introduce a local fact \isa{{\isasymphi}\ {\isasymturnstile}\ {\isasymphi}} by + \item [\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} and \mbox{\isa{\isacommand{presume}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}] introduce a local fact \isa{{\isachardoublequote}{\isasymphi}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} by assumption. Subsequent results applied to an enclosing goal (e.g.\ by \indexref{}{command}{show}\mbox{\isa{\isacommand{show}}}) are handled as follows: \mbox{\isa{\isacommand{assume}}} expects to be able to unify with existing premises in the goal, while \mbox{\isa{\isacommand{presume}}} leaves \isa{{\isasymphi}} as new subgoals. @@ -809,9 +809,9 @@ \indexref{}{keyword}{and}\mbox{\isa{\isakeyword{and}}}; the resulting list of current facts consists of all of these concatenated. - \item [\mbox{\isa{\isacommand{def}}}~\isa{x\ {\isasymequiv}\ t}] introduces a local + \item [\mbox{\isa{\isacommand{def}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}] introduces a local (non-polymorphic) definition. In results exported from the context, - \isa{x} is replaced by \isa{t}. Basically, ``\mbox{\isa{\isacommand{def}}}~\isa{x\ {\isasymequiv}\ t}'' abbreviates ``\mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{x\ {\isasymequiv}\ t}'', with the resulting + \isa{x} is replaced by \isa{t}. Basically, ``\mbox{\isa{\isacommand{def}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'' abbreviates ``\mbox{\isa{\isacommand{fix}}}~\isa{x}~\mbox{\isa{\isacommand{assume}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'', with the resulting hypothetical equation solved by reflexivity. The default name for the definitional equation is \isa{x{\isacharunderscore}def}. @@ -859,8 +859,8 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{note}}}~\isa{a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n}] - recalls existing facts \isa{b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub n}, binding + \item [\mbox{\isa{\isacommand{note}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}] + recalls existing facts \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub n{\isachardoublequote}}, binding the result as \isa{a}. Note that attributes may be involved as well, both on the left and right hand sides. @@ -877,31 +877,31 @@ \item [\mbox{\isa{\isacommand{from}}}~\isa{b}] abbreviates ``\mbox{\isa{\isacommand{note}}}~\isa{b}~\mbox{\isa{\isacommand{then}}}''; thus \mbox{\isa{\isacommand{then}}} is equivalent to ``\mbox{\isa{\isacommand{from}}}~\isa{this}''. - \item [\mbox{\isa{\isacommand{with}}}~\isa{b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n}] - abbreviates ``\mbox{\isa{\isacommand{from}}}~\isa{b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n\ {\isasymAND}\ this}''; thus the forward chaining is from earlier facts together + \item [\mbox{\isa{\isacommand{with}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}] + abbreviates ``\mbox{\isa{\isacommand{from}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n\ {\isasymAND}\ this{\isachardoublequote}}''; thus the forward chaining is from earlier facts together with the current ones. - \item [\mbox{\isa{\isacommand{using}}}~\isa{b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n}] augments + \item [\mbox{\isa{\isacommand{using}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}] augments the facts being currently indicated for use by a subsequent refinement step (such as \indexref{}{command}{apply}\mbox{\isa{\isacommand{apply}}} or \indexref{}{command}{proof}\mbox{\isa{\isacommand{proof}}}). - \item [\mbox{\isa{\isacommand{unfolding}}}~\isa{b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n}] is + \item [\mbox{\isa{\isacommand{unfolding}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}] is structurally similar to \mbox{\isa{\isacommand{using}}}, but unfolds definitional - equations \isa{b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ b\isactrlsub n} throughout the goal state + equations \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} throughout the goal state and facts. \end{descr} Forward chaining with an empty list of theorems is the same as not chaining at all. Thus ``\mbox{\isa{\isacommand{from}}}~\isa{nothing}'' has no - effect apart from entering \isa{prove{\isacharparenleft}chain{\isacharparenright}} mode, since + effect apart from entering \isa{{\isachardoublequote}prove{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode, since \indexref{}{fact}{nothing}\mbox{\isa{nothing}} is bound to the empty list of theorems. Basic proof methods (such as \indexref{}{method}{rule}\mbox{\isa{rule}}) expect multiple facts to be given in their proper order, corresponding to a prefix of the premises of the rule involved. Note that positions may be - easily skipped using something like \mbox{\isa{\isacommand{from}}}~\isa{{\isacharunderscore}\ {\isasymAND}\ a\ {\isasymAND}\ b}, for example. This involves the trivial rule - \isa{PROP\ {\isasympsi}\ {\isasymLongrightarrow}\ PROP\ {\isasympsi}}, which is bound in Isabelle/Pure as + easily skipped using something like \mbox{\isa{\isacommand{from}}}~\isa{{\isachardoublequote}{\isacharunderscore}\ {\isasymAND}\ a\ {\isasymAND}\ b{\isachardoublequote}}, for example. This involves the trivial rule + \isa{{\isachardoublequote}PROP\ {\isasympsi}\ {\isasymLongrightarrow}\ PROP\ {\isasympsi}{\isachardoublequote}}, which is bound in Isabelle/Pure as ``\indexref{}{fact}{-}\mbox{\isa{{\isacharunderscore}}}'' (underscore). Automated methods (such as \mbox{\isa{simp}} or \mbox{\isa{auto}}) just @@ -937,7 +937,7 @@ Goals may consist of multiple statements, resulting in a list of facts eventually. A pending multi-goal is internally represented as - a meta-level conjunction (printed as \isa{{\isacharampersand}{\isacharampersand}}), which is usually + a meta-level conjunction (printed as \isa{{\isachardoublequote}{\isacharampersand}{\isacharampersand}{\isachardoublequote}}), which is usually split into the corresponding number of sub-goals prior to an initial method application, via \indexref{}{command}{proof}\mbox{\isa{\isacommand{proof}}} (\secref{sec:proof-steps}) or \indexref{}{command}{apply}\mbox{\isa{\isacommand{apply}}} @@ -979,25 +979,25 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{lemma}}}~\isa{a{\isacharcolon}\ {\isasymphi}}] enters proof mode with - \isa{{\isasymphi}} as main goal, eventually resulting in some fact \isa{{\isasymturnstile}\ {\isasymphi}} to be put back into the target context. An additional + \item [\mbox{\isa{\isacommand{lemma}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}] enters proof mode with + \isa{{\isasymphi}} as main goal, eventually resulting in some fact \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} to be put back into the target context. An additional \railnonterm{context} specification may build up an initial proof context for the subsequent claim; this includes local definitions and syntax as well, see the definition of \mbox{\isa{contextelem}} in \secref{sec:locale}. - \item [\mbox{\isa{\isacommand{theorem}}}~\isa{a{\isacharcolon}\ {\isasymphi}} and \mbox{\isa{\isacommand{corollary}}}~\isa{a{\isacharcolon}\ {\isasymphi}}] are essentially the same as \mbox{\isa{\isacommand{lemma}}}~\isa{a{\isacharcolon}\ {\isasymphi}}, but the facts are internally marked as + \item [\mbox{\isa{\isacommand{theorem}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} and \mbox{\isa{\isacommand{corollary}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}] are essentially the same as \mbox{\isa{\isacommand{lemma}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}, but the facts are internally marked as being of a different kind. This discrimination acts like a formal comment. - \item [\mbox{\isa{\isacommand{have}}}~\isa{a{\isacharcolon}\ {\isasymphi}}] claims a local goal, + \item [\mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}] claims a local goal, eventually resulting in a fact within the current logical context. This operation is completely independent of any pending sub-goals of an enclosing goal statements, so \mbox{\isa{\isacommand{have}}} may be freely used for experimental exploration of potential results within a proof body. - \item [\mbox{\isa{\isacommand{show}}}~\isa{a{\isacharcolon}\ {\isasymphi}}] is like \mbox{\isa{\isacommand{have}}}~\isa{a{\isacharcolon}\ {\isasymphi}} plus a second stage to refine some pending + \item [\mbox{\isa{\isacommand{show}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}] is like \mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} plus a second stage to refine some pending sub-goal for each one of the finished result, after having been exported into the corresponding context (at the head of the sub-proof of this \mbox{\isa{\isacommand{show}}} command). @@ -1079,12 +1079,12 @@ \begin{enumerate} - \item An \emph{initial} refinement step \indexref{}{command}{proof}\mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}} reduces a newly stated goal to a number + \item An \emph{initial} refinement step \indexref{}{command}{proof}\mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} reduces a newly stated goal to a number of sub-goals that are to be solved later. Facts are passed to - \isa{m\isactrlsub {\isadigit{1}}} for forward chaining, if so indicated by \isa{proof{\isacharparenleft}chain{\isacharparenright}} mode. + \isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} for forward chaining, if so indicated by \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode. - \item A \emph{terminal} conclusion step \indexref{}{command}{qed}\mbox{\isa{\isacommand{qed}}}~\isa{m\isactrlsub {\isadigit{2}}} is intended to solve remaining goals. No facts are - passed to \isa{m\isactrlsub {\isadigit{2}}}. + \item A \emph{terminal} conclusion step \indexref{}{command}{qed}\mbox{\isa{\isacommand{qed}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} is intended to solve remaining goals. No facts are + passed to \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}. \end{enumerate} @@ -1120,16 +1120,16 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}}] refines the goal by - proof method \isa{m\isactrlsub {\isadigit{1}}}; facts for forward chaining are - passed if so indicated by \isa{proof{\isacharparenleft}chain{\isacharparenright}} mode. + \item [\mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}] refines the goal by + proof method \isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}; facts for forward chaining are + passed if so indicated by \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode. - \item [\mbox{\isa{\isacommand{qed}}}~\isa{m\isactrlsub {\isadigit{2}}}] refines any remaining - goals by proof method \isa{m\isactrlsub {\isadigit{2}}} and concludes the - sub-proof by assumption. If the goal had been \isa{show} (or - \isa{thus}), some pending sub-goal is solved as well by the rule + \item [\mbox{\isa{\isacommand{qed}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}] refines any remaining + goals by proof method \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} and concludes the + sub-proof by assumption. If the goal had been \isa{{\isachardoublequote}show{\isachardoublequote}} (or + \isa{{\isachardoublequote}thus{\isachardoublequote}}), some pending sub-goal is solved as well by the rule resulting from the result \emph{exported} into the enclosing goal - context. Thus \isa{qed} may fail for two reasons: either \isa{m\isactrlsub {\isadigit{2}}} fails, or the resulting rule does not fit to any + context. Thus \isa{{\isachardoublequote}qed{\isachardoublequote}} may fail for two reasons: either \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} fails, or the resulting rule does not fit to any pending goal\footnote{This includes any additional ``strong'' assumptions as introduced by \mbox{\isa{\isacommand{assume}}}.} of the enclosing context. Debugging such a situation might involve temporarily @@ -1137,25 +1137,25 @@ local context by replacing occurrences of \mbox{\isa{\isacommand{assume}}} by \mbox{\isa{\isacommand{presume}}}. - \item [\mbox{\isa{\isacommand{by}}}~\isa{m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}}] is a + \item [\mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}}] is a \emph{terminal proof}\index{proof!terminal}; it abbreviates - \mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}}~\isa{qed}~\isa{m\isactrlsub {\isadigit{2}}}, but with backtracking across both methods. Debugging - an unsuccessful \mbox{\isa{\isacommand{by}}}~\isa{m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}} + \mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\isa{{\isachardoublequote}qed{\isachardoublequote}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}, but with backtracking across both methods. Debugging + an unsuccessful \mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} command can be done by expanding its definition; in many cases - \mbox{\isa{\isacommand{proof}}}~\isa{m\isactrlsub {\isadigit{1}}} (or even \isa{apply}~\isa{m\isactrlsub {\isadigit{1}}}) is already sufficient to see the + \mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} (or even \isa{{\isachardoublequote}apply{\isachardoublequote}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}) is already sufficient to see the problem. \item [``\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}''] is a \emph{default - proof}\index{proof!default}; it abbreviates \mbox{\isa{\isacommand{by}}}~\isa{rule}. + proof}\index{proof!default}; it abbreviates \mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}rule{\isachardoublequote}}. \item [``\mbox{\isa{\isacommand{{\isachardot}}}}''] is a \emph{trivial - proof}\index{proof!trivial}; it abbreviates \mbox{\isa{\isacommand{by}}}~\isa{this}. + proof}\index{proof!trivial}; it abbreviates \mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}this{\isachardoublequote}}. \item [\mbox{\isa{\isacommand{sorry}}}] is a \emph{fake proof}\index{proof!fake} pretending to solve the pending claim without further ado. This only works in interactive development, or if the \verb|quick_and_dirty| flag is enabled (in ML). Facts emerging from fake proofs are not the real thing. Internally, each theorem container - is tainted by an oracle invocation, which is indicated as ``\isa{{\isacharbrackleft}{\isacharbang}{\isacharbrackright}}'' in the printed result. + is tainted by an oracle invocation, which is indicated as ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' in the printed result. The most important application of \mbox{\isa{\isacommand{sorry}}} is to support experimentation and top-down proof development. @@ -1217,17 +1217,17 @@ forward chaining facts as premises into the goal. Note that command \indexref{}{command}{proof}\mbox{\isa{\isacommand{proof}}} without any method actually performs a single reduction step using the \indexref{}{method}{rule}\mbox{\isa{rule}} method; thus a plain - \emph{do-nothing} proof step would be ``\mbox{\isa{\isacommand{proof}}}~\isa{{\isacharminus}}'' rather than \mbox{\isa{\isacommand{proof}}} alone. + \emph{do-nothing} proof step would be ``\mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' rather than \mbox{\isa{\isacommand{proof}}} alone. - \item [\mbox{\isa{fact}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] composes - some fact from \isa{a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n} (or implicitly from + \item [\mbox{\isa{fact}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] composes + some fact from \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}} (or implicitly from the current proof context) modulo unification of schematic type and term variables. The rule structure is not taken into account, i.e.\ meta-level implication is considered atomic. This is the same principle underlying literal facts (cf.\ \secref{sec:syn-att}): - ``\mbox{\isa{\isacommand{have}}}~\isa{{\isasymphi}}~\mbox{\isa{\isacommand{by}}}~\isa{fact}'' is - equivalent to ``\mbox{\isa{\isacommand{note}}}~\verb|`|\isa{{\isasymphi}}\verb|`|'' provided that \isa{{\isasymturnstile}\ {\isasymphi}} is an instance of some known - \isa{{\isasymturnstile}\ {\isasymphi}} in the proof context. + ``\mbox{\isa{\isacommand{have}}}~\isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}~\mbox{\isa{\isacommand{by}}}~\isa{fact}'' is + equivalent to ``\mbox{\isa{\isacommand{note}}}~\verb|`|\isa{{\isasymphi}}\verb|`|'' provided that \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} is an instance of some known + \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} in the proof context. \item [\mbox{\isa{assumption}}] solves some goal by a single assumption step. All given facts are guaranteed to participate in the @@ -1240,7 +1240,7 @@ \item [\mbox{\isa{this}}] applies all of the current facts directly as rules. Recall that ``\mbox{\isa{\isacommand{{\isachardot}}}}'' (dot) abbreviates ``\mbox{\isa{\isacommand{by}}}~\isa{this}''. - \item [\mbox{\isa{rule}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] applies some + \item [\mbox{\isa{rule}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] applies some rule given as argument in backward manner; facts are used to reduce the rule before applying it to the goal. Thus \mbox{\isa{rule}} without facts is plain introduction, while with facts it becomes @@ -1255,12 +1255,12 @@ \item [\mbox{\isa{iprover}}] performs intuitionistic proof search, depending on specifically declared rules from the context, or given as explicit arguments. Chained facts are inserted into the goal - before commencing proof search; ``\mbox{\isa{iprover}}\isa{{\isacharbang}}'' + before commencing proof search; ``\mbox{\isa{iprover}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' means to include the current \mbox{\isa{prems}} as well. - Rules need to be classified as \mbox{\isa{intro}}, \mbox{\isa{elim}}, or \mbox{\isa{dest}}; here the ``\isa{{\isacharbang}}'' indicator + Rules need to be classified as \mbox{\isa{intro}}, \mbox{\isa{elim}}, or \mbox{\isa{dest}}; here the ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' indicator refers to ``safe'' rules, which may be applied aggressively (without - considering back-tracking later). Rules declared with ``\isa{{\isacharquery}}'' are ignored in proof search (the single-step \mbox{\isa{rule}} + considering back-tracking later). Rules declared with ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' are ignored in proof search (the single-step \mbox{\isa{rule}} method still observes these). An explicit weight annotation may be given as well; otherwise the number of rule premises will be taken into account here. @@ -1268,8 +1268,8 @@ \item [\mbox{\isa{intro}}, \mbox{\isa{elim}}, and \mbox{\isa{dest}}] declare introduction, elimination, and destruct rules, to be used with the \mbox{\isa{rule}} and \mbox{\isa{iprover}} methods. Note that - the latter will ignore rules declared with ``\isa{{\isacharquery}}'', while - ``\isa{{\isacharbang}}'' are used most aggressively. + the latter will ignore rules declared with ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'', while + ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' are used most aggressively. The classical reasoner (see \secref{sec:classical}) introduces its own variants of these attributes; use qualified names to access the @@ -1278,21 +1278,21 @@ \item [\mbox{\isa{rule}}~\isa{del}] undeclares introduction, elimination, or destruct rules. - \item [\mbox{\isa{OF}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] applies some - theorem to all of the given rules \isa{a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n} - (in parallel). This corresponds to the \verb|op MRS| operation in + \item [\mbox{\isa{OF}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] applies some + theorem to all of the given rules \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}} + (in parallel). This corresponds to the \verb|"op MRS"| operation in ML, but note the reversed order. Positions may be effectively skipped by including ``\isa{{\isacharunderscore}}'' (underscore) as argument. - \item [\mbox{\isa{of}}~\isa{t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n}] performs - positional instantiation of term variables. The terms \isa{t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n} are substituted for any schematic + \item [\mbox{\isa{of}}~\isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}] performs + positional instantiation of term variables. The terms \isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n{\isachardoublequote}} are substituted for any schematic variables occurring in a theorem from left to right; ``\isa{{\isacharunderscore}}'' (underscore) indicates to skip a position. Arguments following - a ``\mbox{\isa{\isakeyword{concl}}}\isa{{\isacharcolon}}'' specification refer to positions + a ``\mbox{\isa{\isakeyword{concl}}}\isa{{\isachardoublequote}{\isacharcolon}{\isachardoublequote}}'' specification refer to positions of the conclusion of a rule. - \item [\mbox{\isa{where}}~\isa{x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isacharequal}\ t\isactrlsub n}] performs named instantiation of schematic + \item [\mbox{\isa{where}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isacharequal}\ t\isactrlsub n{\isachardoublequote}}] performs named instantiation of schematic type and term variables occurring in a theorem. Schematic variables - have to be specified on the left-hand side (e.g.\ \isa{{\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{3}}}). + have to be specified on the left-hand side (e.g.\ \isa{{\isachardoublequote}{\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{3}}{\isachardoublequote}}). The question mark may be omitted if the variable name is a plain identifier without index. As type instantiations are inferred from term instantiations, explicit type instantiations are seldom @@ -1312,8 +1312,8 @@ \indexdef{}{keyword}{is}\mbox{\isa{\isakeyword{is}}} & : & syntax \\ \end{matharray} - Abbreviations may be either bound by explicit \mbox{\isa{\isacommand{let}}}~\isa{p\ {\isasymequiv}\ t} statements, or by annotating assumptions or - goal statements with a list of patterns ``\isa{{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}}''. In both cases, higher-order matching is invoked to + Abbreviations may be either bound by explicit \mbox{\isa{\isacommand{let}}}~\isa{{\isachardoublequote}p\ {\isasymequiv}\ t{\isachardoublequote}} statements, or by annotating assumptions or + goal statements with a list of patterns ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. In both cases, higher-order matching is invoked to bind extra-logical term variables, which may be either named schematic variables of the form \isa{{\isacharquery}x}, or nameless dummies ``\mbox{\isa{{\isacharunderscore}}}'' (underscore). Note that in the \mbox{\isa{\isacommand{let}}} @@ -1344,10 +1344,10 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{let}}}~\isa{p\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ p\isactrlsub n\ {\isacharequal}\ t\isactrlsub n}] binds any text variables in patterns \isa{p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n} by simultaneous higher-order matching - against terms \isa{t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n}. + \item [\mbox{\isa{\isacommand{let}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ p\isactrlsub n\ {\isacharequal}\ t\isactrlsub n{\isachardoublequote}}] binds any text variables in patterns \isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isachardoublequote}} by simultaneous higher-order matching + against terms \isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n{\isachardoublequote}}. - \item [\isa{{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}}] resembles \mbox{\isa{\isacommand{let}}}, but matches \isa{p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n} against the + \item [\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}] resembles \mbox{\isa{\isacommand{let}}}, but matches \isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isachardoublequote}} against the preceding statement. Also note that \mbox{\isa{\isakeyword{is}}} is not a separate command, but part of others (such as \mbox{\isa{\isacommand{assume}}}, \mbox{\isa{\isacommand{have}}} etc.). @@ -1360,7 +1360,7 @@ abstracted over any meta-level parameters (if present). Likewise, \indexref{}{variable}{this}\mbox{\isa{this}} is bound for fact statements resulting from assumptions or finished goals. In case \mbox{\isa{this}} refers to - an object-logic statement that is an application \isa{f\ t}, then + an object-logic statement that is an application \isa{{\isachardoublequote}f\ t{\isachardoublequote}}, then \isa{t} is bound to the special text variable ``\mbox{\isa{{\isasymdots}}}'' (three dots). The canonical application of this convenience are calculational proofs (see \secref{sec:calculation}).% @@ -1447,7 +1447,7 @@ \item [\mbox{\isa{\isacommand{apply}}}~\isa{m}] applies proof method \isa{m} in initial position, but unlike \mbox{\isa{\isacommand{proof}}} it retains - ``\isa{proof{\isacharparenleft}prove{\isacharparenright}}'' mode. Thus consecutive method + ``\isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}'' mode. Thus consecutive method applications may be given just as in tactic scripts. Facts are passed to \isa{m} as indicated by the goal's @@ -1455,7 +1455,7 @@ further \mbox{\isa{\isacommand{apply}}} command would always work in a purely backward manner. - \item [\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}~\isa{m}] applies proof method + \item [\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}~\isa{{\isachardoublequote}m{\isachardoublequote}}] applies proof method \isa{m} as if in terminal position. Basically, this simulates a multi-step tactic script for \mbox{\isa{\isacommand{qed}}}, but may be given anywhere within the proof body. @@ -1469,7 +1469,7 @@ structured proof commands (e.g.\ ``\mbox{\isa{\isacommand{{\isachardot}}}}'' or \mbox{\isa{\isacommand{sorry}}}) may be used to conclude proof scripts as well. \item [\mbox{\isa{\isacommand{defer}}}~\isa{n} and \mbox{\isa{\isacommand{prefer}}}~\isa{n}] shuffle the list of pending goals: \mbox{\isa{\isacommand{defer}}} puts off - sub-goal \isa{n} to the end of the list (\isa{n\ {\isacharequal}\ {\isadigit{1}}} by + sub-goal \isa{n} to the end of the list (\isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}} by default), while \mbox{\isa{\isacommand{prefer}}} brings sub-goal \isa{n} to the front. @@ -1510,7 +1510,7 @@ preparation tools of Isabelle described in \cite{isabelle-sys}. Thus partial or even wrong proof attempts can be discussed in a logically sound manner. Note that the Isabelle {\LaTeX} macros can - be easily adapted to print something like ``\isa{{\isasymdots}}'' instead of + be easily adapted to print something like ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' instead of the keyword ``\mbox{\isa{\isacommand{oops}}}''. \medskip The \mbox{\isa{\isacommand{oops}}} command is undo-able, unlike @@ -1564,17 +1564,17 @@ \begin{descr} - \item [\mbox{\isa{\isacommand{pr}}}~\isa{goals{\isacharcomma}\ prems}] prints the current + \item [\mbox{\isa{\isacommand{pr}}}~\isa{{\isachardoublequote}goals{\isacharcomma}\ prems{\isachardoublequote}}] prints the current proof state (if present), including the proof context, current facts and goals. The optional limit arguments affect the number of goals and premises to be displayed, which is initially 10 for both. Omitting limit values leaves the current setting unchanged. - \item [\mbox{\isa{\isacommand{thm}}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] retrieves + \item [\mbox{\isa{\isacommand{thm}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] retrieves theorems from the current theory or proof context. Note that any attributes included in the theorem specifications are applied to a temporary context derived from the current theory or proof; the - result is discarded, i.e.\ attributes involved in \isa{a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n} do not have any permanent effect. + result is discarded, i.e.\ attributes involved in \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}} do not have any permanent effect. \item [\mbox{\isa{\isacommand{term}}}~\isa{t} and \mbox{\isa{\isacommand{prop}}}~\isa{{\isasymphi}}] read, type-check and print terms or propositions according to the @@ -1601,7 +1601,7 @@ All of the diagnostic commands above admit a list of \isa{modes} to be specified, which is appended to the current print mode (see also \cite{isabelle-ref}). Thus the output behavior may be modified - according particular print mode features. For example, \mbox{\isa{\isacommand{pr}}}~\isa{{\isacharparenleft}latex\ xsymbols\ symbols{\isacharparenright}} would print the current + according particular print mode features. For example, \mbox{\isa{\isacommand{pr}}}~\isa{{\isachardoublequote}{\isacharparenleft}latex\ xsymbols\ symbols{\isacharparenright}{\isachardoublequote}} would print the current proof state with mathematical symbols and special characters represented in {\LaTeX} source, according to the Isabelle style \cite{isabelle-sys}. @@ -1653,7 +1653,7 @@ syntax, including keywords and command. \item [\mbox{\isa{\isacommand{print{\isacharunderscore}theory}}}] prints the main logical content of - the theory context; the ``\isa{{\isacharbang}}'' option indicates extra + the theory context; the ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' option indicates extra verbosity. \item [\mbox{\isa{\isacommand{print{\isacharunderscore}syntax}}}] prints the inner syntax of types @@ -1673,24 +1673,24 @@ \item [\mbox{\isa{\isacommand{find{\isacharunderscore}theorems}}}~\isa{criteria}] retrieves facts from the theory or proof context matching all of given search - criteria. The criterion \isa{name{\isacharcolon}\ p} selects all theorems + criteria. The criterion \isa{{\isachardoublequote}name{\isacharcolon}\ p{\isachardoublequote}} selects all theorems whose fully qualified name matches pattern \isa{p}, which may - contain ``\isa{{\isacharasterisk}}'' wildcards. The criteria \isa{intro}, + contain ``\isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}'' wildcards. The criteria \isa{intro}, \isa{elim}, and \isa{dest} select theorems that match the current goal as introduction, elimination or destruction rules, - respectively. The criterion \isa{simp{\isacharcolon}\ t} selects all rewrite + respectively. The criterion \isa{{\isachardoublequote}simp{\isacharcolon}\ t{\isachardoublequote}} selects all rewrite rules whose left-hand side matches the given term. The criterion term \isa{t} selects all theorems that contain the pattern \isa{t} -- as usual, patterns may contain occurrences of the dummy ``\isa{{\isacharunderscore}}'', schematic variables, and type constraints. - Criteria can be preceded by ``\isa{{\isacharminus}}'' to select theorems that + Criteria can be preceded by ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' to select theorems that do \emph{not} match. Note that giving the empty list of criteria yields \emph{all} currently known facts. An optional limit for the number of printed facts may be given; the default is 40. By default, duplicates are removed from the search result. Use \mbox{\isa{\isakeyword{with{\isacharunderscore}dups}}} to display duplicates. - \item [\mbox{\isa{\isacommand{thm{\isacharunderscore}deps}}}~\isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}] + \item [\mbox{\isa{\isacommand{thm{\isacharunderscore}deps}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}] visualizes dependencies of facts, using Isabelle's graph browser tool (see also \cite{isabelle-sys}). diff -r 6ac51a2f48e1 -r 81308d44fe0a doc-src/IsarRef/Thy/document/syntax.tex --- a/doc-src/IsarRef/Thy/document/syntax.tex Wed May 07 12:56:11 2008 +0200 +++ b/doc-src/IsarRef/Thy/document/syntax.tex Wed May 07 13:04:12 2008 +0200 @@ -141,7 +141,7 @@ A list of standard Isabelle symbols that work well with these tools is given in \cite[appendix~A]{isabelle-sys}. - Source comments take the form \verb|(*|~\isa{{\isasymdots}}~\verb|*)| and may be nested, although user-interface + Source comments take the form \verb|(*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*)| and may be nested, although user-interface tools might prevent this. Note that this form indicates source comments only, which are stripped after lexical analysis of the input. The Isar document syntax also provides formal comments that @@ -194,7 +194,7 @@ % \begin{isamarkuptext}% Large chunks of plain \railqtok{text} are usually given - \railtok{verbatim}, i.e.\ enclosed in \verb|{|\verb|*|~\isa{{\isasymdots}}~\verb|*|\verb|}|. For convenience, + \railtok{verbatim}, i.e.\ enclosed in \verb|{|\verb|*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*|\verb|}|. For convenience, any of the smaller text units conforming to \railqtok{nameref} are admitted as well. A marginal \railnonterm{comment} is of the form \verb|--| \railqtok{text}. Any number of these may occur @@ -217,7 +217,7 @@ \begin{isamarkuptext}% Classes are specified by plain names. Sorts have a very simple inner syntax, which is either a single class name \isa{c} or a - list \isa{{\isacharbraceleft}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isacharbraceright}} referring to the + list \isa{{\isachardoublequote}{\isacharbraceleft}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isacharbraceright}{\isachardoublequote}} referring to the intersection of these classes. The syntax of type arities is given directly at the outer level. @@ -247,7 +247,7 @@ liberal convention is adopted: quotes may be omitted for any type or term that is already atomic at the outer level. For example, one may just write \verb|x| instead of quoted \verb|"x"|. - Note that symbolic identifiers (e.g.\ \verb|++| or \isa{{\isasymforall}} are available as well, provided these have not been superseded + Note that symbolic identifiers (e.g.\ \verb|++| or \isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}} are available as well, provided these have not been superseded by commands or other keywords already (such as \verb|=| or \verb|+|). @@ -313,13 +313,13 @@ Here the \railtok{string} specifications refer to the actual mixfix template (see also \cite{isabelle-ref}), which may include literal text, spacing, blocks, and arguments (denoted by ``\isa{{\isacharunderscore}}''); the - special symbol ``\verb|\|'' (printed as ``\isa{{\isasymindex}}'') + special symbol ``\verb|\|'' (printed as ``\isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}}'') represents an index argument that specifies an implicit structure reference (see also \secref{sec:locale}). Infix and binder declarations provide common abbreviations for particular mixfix declarations. So in practice, mixfix templates mostly degenerate to literal text for concrete syntax, such as ``\verb|++|'' for - an infix symbol, or ``\verb|++|\isa{{\isasymindex}}'' for an infix of + an infix symbol, or ``\verb|++|\isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}}'' for an infix of an implicit structure.% \end{isamarkuptext}% \isamarkuptrue% @@ -333,7 +333,7 @@ methods via ``\verb|,|'' (sequential composition), ``\verb||\verb,|,\verb||'' (alternative choices), ``\verb|?|'' (try), ``\verb|+|'' (repeat at least once), ``\verb|[|\isa{n}\verb|]|'' (restriction to first \isa{n} - sub-goals, with default \isa{n\ {\isacharequal}\ {\isadigit{1}}}). In practice, proof + sub-goals, with default \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}}). In practice, proof methods are usually just a comma separated list of \railqtok{nameref}~\railnonterm{args} specifications. Note that parentheses may be dropped for single method specifications (with no @@ -349,18 +349,18 @@ Proper Isar proof methods do \emph{not} admit arbitrary goal addressing, but refer either to the first sub-goal or all sub-goals - uniformly. The goal restriction operator ``\isa{{\isacharbrackleft}n{\isacharbrackright}}'' + uniformly. The goal restriction operator ``\isa{{\isachardoublequote}{\isacharbrackleft}n{\isacharbrackright}{\isachardoublequote}}'' evaluates a method expression within a sandbox consisting of the first \isa{n} sub-goals (which need to exist). For example, the - method ``\isa{simp{\isacharunderscore}all{\isacharbrackleft}{\isadigit{3}}{\isacharbrackright}}'' simplifies the first three - sub-goals, while ``\isa{{\isacharparenleft}rule\ foo{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}{\isacharbrackleft}{\isacharbrackright}}'' simplifies all - new goals that emerge from applying rule \isa{foo} to the + method ``\isa{{\isachardoublequote}simp{\isacharunderscore}all{\isacharbrackleft}{\isadigit{3}}{\isacharbrackright}{\isachardoublequote}}'' simplifies the first three + sub-goals, while ``\isa{{\isachardoublequote}{\isacharparenleft}rule\ foo{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequote}}'' simplifies all + new goals that emerge from applying rule \isa{{\isachardoublequote}foo{\isachardoublequote}} to the originally first one. Improper methods, notably tactic emulations, offer a separate low-level goal addressing scheme as explicit argument to the - individual tactic being involved. Here ``\isa{{\isacharbrackleft}{\isacharbang}{\isacharbrackright}}'' refers to - all goals, and ``\isa{{\isacharbrackleft}n{\isacharminus}{\isacharbrackright}}'' to all goals starting from \isa{n}. + individual tactic being involved. Here ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' refers to + all goals, and ``\isa{{\isachardoublequote}{\isacharbrackleft}n{\isacharminus}{\isacharbrackright}{\isachardoublequote}}'' to all goals starting from \isa{{\isachardoublequote}n{\isachardoublequote}}. \indexouternonterm{goalspec} \begin{rail} @@ -406,12 +406,12 @@ There are three forms of theorem references: \begin{enumerate} - \item named facts \isa{a}, + \item named facts \isa{{\isachardoublequote}a{\isachardoublequote}}, - \item selections from named facts \isa{a{\isacharparenleft}i{\isacharparenright}} or \isa{a{\isacharparenleft}j\ {\isacharminus}\ k{\isacharparenright}}, + \item selections from named facts \isa{{\isachardoublequote}a{\isacharparenleft}i{\isacharparenright}{\isachardoublequote}} or \isa{{\isachardoublequote}a{\isacharparenleft}j\ {\isacharminus}\ k{\isacharparenright}{\isachardoublequote}}, \item literal fact propositions using \indexref{}{syntax}{altstring}\mbox{\isa{altstring}} syntax - \verb|`|\isa{{\isasymphi}}\verb|`| (see also method + \verb|`|\isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}\verb|`| (see also method \indexref{}{method}{fact}\mbox{\isa{fact}} in \secref{sec:pure-meth-att}). \end{enumerate} @@ -422,7 +422,7 @@ not stored within the theorem database of the theory or proof context, but any given attributes are applied nonetheless. - An extra pair of brackets around attributes (like ``\isa{{\isacharbrackleft}{\isacharbrackleft}simproc\ a{\isacharbrackright}{\isacharbrackright}}'') abbreviates a theorem reference involving an + An extra pair of brackets around attributes (like ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbrackleft}simproc\ a{\isacharbrackright}{\isacharbrackright}{\isachardoublequote}}'') abbreviates a theorem reference involving an internal dummy fact, which will be ignored later on. So only the effect of the attribute on the background context will persist. This form of in-place declarations is particularly useful with @@ -458,7 +458,7 @@ \begin{isamarkuptext}% Wherever explicit propositions (or term fragments) occur in a proof text, casual binding of schematic term variables may be given - specified via patterns of the form ``\isa{{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}}''. This works both for \railqtok{term} and \railqtok{prop}. + specified via patterns of the form ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. This works both for \railqtok{term} and \railqtok{prop}. \indexouternonterm{termpat}\indexouternonterm{proppat} \begin{rail} @@ -468,8 +468,8 @@ ; \end{rail} - \medskip Declarations of local variables \isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}} and - logical propositions \isa{a\ {\isacharcolon}\ {\isasymphi}} represent different views on + \medskip Declarations of local variables \isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}} and + logical propositions \isa{{\isachardoublequote}a\ {\isacharcolon}\ {\isasymphi}{\isachardoublequote}} represent different views on the same principle of introducing a local scope. In practice, one may usually omit the typing of \railnonterm{vars} (due to type-inference), and the naming of propositions (due to implicit @@ -486,8 +486,8 @@ The treatment of multiple declarations corresponds to the complementary focus of \railnonterm{vars} versus - \railnonterm{props}. In ``\isa{x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}'' - the typing refers to all variables, while in \isa{a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n} the naming refers to all propositions collectively. + \railnonterm{props}. In ``\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}}'' + the typing refers to all variables, while in \isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}} the naming refers to all propositions collectively. Isar language elements that refer to \railnonterm{vars} or \railnonterm{props} typically admit separate typings or namings via another level of iteration, with explicit \indexref{}{keyword}{and}\mbox{\isa{\isakeyword{and}}} @@ -528,11 +528,11 @@ produced by the Isabelle document preparation system (see also \secref{sec:document-prep}). - Thus embedding of ``\isa{{\isacharat}{\isacharbraceleft}term\ {\isacharbrackleft}show{\isacharunderscore}types{\isacharbrackright}\ {\isachardoublequote}f\ x\ {\isacharequal}\ a\ {\isacharplus}\ x{\isachardoublequote}{\isacharbraceright}}'' + Thus embedding of ``\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}term\ {\isacharbrackleft}show{\isacharunderscore}types{\isacharbrackright}\ {\isachardoublequote}f\ x\ {\isacharequal}\ a\ {\isacharplus}\ x{\isachardoublequote}{\isacharbraceright}{\isachardoublequote}}'' within a text block would cause \isa{{\isacharparenleft}f{\isasymColon}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharplus}\ x} to appear in the final {\LaTeX} document. Also note that theorem antiquotations may involve attributes as well. For example, - \isa{{\isacharat}{\isacharbraceleft}thm\ sym\ {\isacharbrackleft}no{\isacharunderscore}vars{\isacharbrackright}{\isacharbraceright}} would print the theorem's + \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}thm\ sym\ {\isacharbrackleft}no{\isacharunderscore}vars{\isacharbrackright}{\isacharbraceright}{\isachardoublequote}} would print the theorem's statement where all schematic variables have been replaced by fixed ones, which are easier to read. @@ -567,48 +567,48 @@ \end{rail} Note that the syntax of antiquotations may \emph{not} include source - comments \verb|(*|~\isa{{\isasymdots}}~\verb|*)| or verbatim - text \verb|{|\verb|*|~\isa{{\isasymdots}}~\verb|*|\verb|}|. + comments \verb|(*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*)| or verbatim + text \verb|{|\verb|*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*|\verb|}|. \begin{descr} - \item [\isa{{\isacharat}{\isacharbraceleft}theory\ A{\isacharbraceright}}] prints the name \isa{A}, which is + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}theory\ A{\isacharbraceright}{\isachardoublequote}}] prints the name \isa{{\isachardoublequote}A{\isachardoublequote}}, which is guaranteed to refer to a valid ancestor theory in the current context. - \item [\isa{{\isacharat}{\isacharbraceleft}thm\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}}] prints theorems - \isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}. Note that attribute specifications + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}thm\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}}] prints theorems + \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}. Note that attribute specifications may be included as well (see also \secref{sec:syn-att}); the \indexref{}{attribute}{no-vars}\mbox{\isa{no{\isacharunderscore}vars}} rule (see \secref{sec:misc-meth-att}) would be particularly useful to suppress printing of schematic variables. - \item [\isa{{\isacharat}{\isacharbraceleft}prop\ {\isasymphi}{\isacharbraceright}}] prints a well-typed proposition \isa{{\isasymphi}}. + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}prop\ {\isasymphi}{\isacharbraceright}{\isachardoublequote}}] prints a well-typed proposition \isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}. - \item [\isa{{\isacharat}{\isacharbraceleft}term\ t{\isacharbraceright}}] prints a well-typed term \isa{t}. + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}term\ t{\isacharbraceright}{\isachardoublequote}}] prints a well-typed term \isa{{\isachardoublequote}t{\isachardoublequote}}. - \item [\isa{{\isacharat}{\isacharbraceleft}const\ c{\isacharbraceright}}] prints a logical or syntactic constant - \isa{c}. + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}const\ c{\isacharbraceright}{\isachardoublequote}}] prints a logical or syntactic constant + \isa{{\isachardoublequote}c{\isachardoublequote}}. - \item [\isa{{\isacharat}{\isacharbraceleft}abbrev\ c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isacharbraceright}}] prints a constant - abbreviation \isa{c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ rhs} as defined in + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}abbrev\ c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isacharbraceright}{\isachardoublequote}}] prints a constant + abbreviation \isa{{\isachardoublequote}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ rhs{\isachardoublequote}} as defined in the current context. - \item [\isa{{\isacharat}{\isacharbraceleft}typeof\ t{\isacharbraceright}}] prints the type of a well-typed term - \isa{t}. + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}typeof\ t{\isacharbraceright}{\isachardoublequote}}] prints the type of a well-typed term + \isa{{\isachardoublequote}t{\isachardoublequote}}. - \item [\isa{{\isacharat}{\isacharbraceleft}typ\ {\isasymtau}{\isacharbraceright}}] prints a well-formed type \isa{{\isasymtau}}. + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}typ\ {\isasymtau}{\isacharbraceright}{\isachardoublequote}}] prints a well-formed type \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}}. - \item [\isa{{\isacharat}{\isacharbraceleft}thm{\isacharunderscore}style\ s\ a{\isacharbraceright}}] prints theorem \isa{a}, + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}thm{\isacharunderscore}style\ s\ a{\isacharbraceright}{\isachardoublequote}}] prints theorem \isa{a}, previously applying a style \isa{s} to it (see below). - \item [\isa{{\isacharat}{\isacharbraceleft}term{\isacharunderscore}style\ s\ t{\isacharbraceright}}] prints a well-typed term \isa{t} after applying a style \isa{s} to it (see below). + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}term{\isacharunderscore}style\ s\ t{\isacharbraceright}{\isachardoublequote}}] prints a well-typed term \isa{t} after applying a style \isa{s} to it (see below). - \item [\isa{{\isacharat}{\isacharbraceleft}text\ s{\isacharbraceright}}] prints uninterpreted source text \isa{s}. This is particularly useful to print portions of text according + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}text\ s{\isacharbraceright}{\isachardoublequote}}] prints uninterpreted source text \isa{s}. This is particularly useful to print portions of text according to the Isabelle {\LaTeX} output style, without demanding well-formedness (e.g.\ small pieces of terms that should not be parsed or type-checked yet). - \item [\isa{{\isacharat}{\isacharbraceleft}goals{\isacharbraceright}}] prints the current \emph{dynamic} goal + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}goals{\isacharbraceright}{\isachardoublequote}}] prints the current \emph{dynamic} goal state. This is mainly for support of tactic-emulation scripts within Isar --- presentation of goal states does not conform to actual human-readable proof documents. @@ -616,19 +616,19 @@ Please do not include goal states into document output unless you really know what you are doing! - \item [\isa{{\isacharat}{\isacharbraceleft}subgoals{\isacharbraceright}}] is similar to \isa{{\isacharat}{\isacharbraceleft}goals{\isacharbraceright}}, but + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}subgoals{\isacharbraceright}{\isachardoublequote}}] is similar to \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}goals{\isacharbraceright}{\isachardoublequote}}, but does not print the main goal. - \item [\isa{{\isacharat}{\isacharbraceleft}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}}] prints the (compact) - proof terms corresponding to the theorems \isa{a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n}. Note that this requires proof terms to be switched on + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}}] prints the (compact) + proof terms corresponding to the theorems \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}. Note that this requires proof terms to be switched on for the current object logic (see the ``Proof terms'' section of the Isabelle reference manual for information on how to do this). - \item [\isa{{\isacharat}{\isacharbraceleft}full{\isacharunderscore}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}}] is like \isa{{\isacharat}{\isacharbraceleft}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}}, but displays the full proof terms, + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}full{\isacharunderscore}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}}] is like \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}}, but displays the full proof terms, i.e.\ also displays information omitted in the compact proof term, which is denoted by ``\isa{{\isacharunderscore}}'' placeholders there. - \item [\isa{{\isacharat}{\isacharbraceleft}ML\ s{\isacharbraceright}}, \isa{{\isacharat}{\isacharbraceleft}ML{\isacharunderscore}type\ s{\isacharbraceright}}, and \isa{{\isacharat}{\isacharbraceleft}ML{\isacharunderscore}struct\ s{\isacharbraceright}}] check text \isa{s} as ML value, type, and + \item [\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}ML\ s{\isacharbraceright}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}ML{\isacharunderscore}type\ s{\isacharbraceright}{\isachardoublequote}}, and \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}ML{\isacharunderscore}struct\ s{\isacharbraceright}{\isachardoublequote}}] check text \isa{s} as ML value, type, and structure, respectively. The source is displayed verbatim. \end{descr} @@ -644,12 +644,12 @@ \item [\isa{rhs}] is like \isa{lhs}, but extracts the second argument. - \item [\isa{concl}] extracts the conclusion \isa{C} from a rule - in Horn-clause normal form \isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C}. + \item [\isa{{\isachardoublequote}concl{\isachardoublequote}}] extracts the conclusion \isa{C} from a rule + in Horn-clause normal form \isa{{\isachardoublequote}A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C{\isachardoublequote}}. - \item [\isa{prem{\isadigit{1}}}, \dots, \isa{prem{\isadigit{9}}}] extract premise - number \isa{{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isadigit{9}}}, respectively, from from a rule in - Horn-clause normal form \isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C} + \item [\isa{{\isachardoublequote}prem{\isadigit{1}}{\isachardoublequote}}, \dots, \isa{{\isachardoublequote}prem{\isadigit{9}}{\isachardoublequote}}] extract premise + number \isa{{\isachardoublequote}{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isadigit{9}}{\isachardoublequote}}, respectively, from from a rule in + Horn-clause normal form \isa{{\isachardoublequote}A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C{\isachardoublequote}} \end{descr} @@ -659,59 +659,59 @@ \begin{descr} - \item[\isa{show{\isacharunderscore}types\ {\isacharequal}\ bool} and \isa{show{\isacharunderscore}sorts\ {\isacharequal}\ bool}] + \item[\isa{{\isachardoublequote}show{\isacharunderscore}types\ {\isacharequal}\ bool{\isachardoublequote}} and \isa{{\isachardoublequote}show{\isacharunderscore}sorts\ {\isacharequal}\ bool{\isachardoublequote}}] control printing of explicit type and sort constraints. - \item[\isa{show{\isacharunderscore}structs\ {\isacharequal}\ bool}] controls printing of implicit + \item[\isa{{\isachardoublequote}show{\isacharunderscore}structs\ {\isacharequal}\ bool{\isachardoublequote}}] controls printing of implicit structures. - \item[\isa{long{\isacharunderscore}names\ {\isacharequal}\ bool}] forces names of types and + \item[\isa{{\isachardoublequote}long{\isacharunderscore}names\ {\isacharequal}\ bool{\isachardoublequote}}] forces names of types and constants etc.\ to be printed in their fully qualified internal form. - \item[\isa{short{\isacharunderscore}names\ {\isacharequal}\ bool}] forces names of types and + \item[\isa{{\isachardoublequote}short{\isacharunderscore}names\ {\isacharequal}\ bool{\isachardoublequote}}] forces names of types and constants etc.\ to be printed unqualified. Note that internalizing the output again in the current context may well yield a different result. - \item[\isa{unique{\isacharunderscore}names\ {\isacharequal}\ bool}] determines whether the printed + \item[\isa{{\isachardoublequote}unique{\isacharunderscore}names\ {\isacharequal}\ bool{\isachardoublequote}}] determines whether the printed version of qualified names should be made sufficiently long to avoid overlap with names declared further back. Set to \isa{false} for more concise output. - \item[\isa{eta{\isacharunderscore}contract\ {\isacharequal}\ bool}] prints terms in \isa{{\isasymeta}}-contracted form. + \item[\isa{{\isachardoublequote}eta{\isacharunderscore}contract\ {\isacharequal}\ bool{\isachardoublequote}}] prints terms in \isa{{\isasymeta}}-contracted form. - \item[\isa{display\ {\isacharequal}\ bool}] indicates if the text is to be + \item[\isa{{\isachardoublequote}display\ {\isacharequal}\ bool{\isachardoublequote}}] indicates if the text is to be output as multi-line ``display material'', rather than a small piece of text without line breaks (which is the default). - \item[\isa{break\ {\isacharequal}\ bool}] controls line breaks in non-display + \item[\isa{{\isachardoublequote}break\ {\isacharequal}\ bool{\isachardoublequote}}] controls line breaks in non-display material. - \item[\isa{quotes\ {\isacharequal}\ bool}] indicates if the output should be + \item[\isa{{\isachardoublequote}quotes\ {\isacharequal}\ bool{\isachardoublequote}}] indicates if the output should be enclosed in double quotes. - \item[\isa{mode\ {\isacharequal}\ name}] adds \isa{name} to the print mode to + \item[\isa{{\isachardoublequote}mode\ {\isacharequal}\ name{\isachardoublequote}}] adds \isa{name} to the print mode to be used for presentation (see also \cite{isabelle-ref}). Note that the standard setup for {\LaTeX} output is already present by default, including the modes \isa{latex} and \isa{xsymbols}. - \item[\isa{margin\ {\isacharequal}\ nat} and \isa{indent\ {\isacharequal}\ nat}] change the + \item[\isa{{\isachardoublequote}margin\ {\isacharequal}\ nat{\isachardoublequote}} and \isa{{\isachardoublequote}indent\ {\isacharequal}\ nat{\isachardoublequote}}] change the margin or indentation for pretty printing of display material. - \item[\isa{source\ {\isacharequal}\ bool}] prints the source text of the + \item[\isa{{\isachardoublequote}source\ {\isacharequal}\ bool{\isachardoublequote}}] prints the source text of the antiquotation arguments, rather than the actual value. Note that this does not affect well-formedness checks of \mbox{\isa{thm}}, \mbox{\isa{term}}, etc. (only the \mbox{\isa{text}} antiquotation admits arbitrary output). - \item[\isa{goals{\isacharunderscore}limit\ {\isacharequal}\ nat}] determines the maximum number of + \item[\isa{{\isachardoublequote}goals{\isacharunderscore}limit\ {\isacharequal}\ nat{\isachardoublequote}}] determines the maximum number of goals to be printed. - \item[\isa{locale\ {\isacharequal}\ name}] specifies an alternative locale + \item[\isa{{\isachardoublequote}locale\ {\isacharequal}\ name{\isachardoublequote}}] specifies an alternative locale context used for evaluating and printing the subsequent argument. \end{descr} - For boolean flags, ``\isa{name\ {\isacharequal}\ true}'' may be abbreviated as + For boolean flags, ``\isa{{\isachardoublequote}name\ {\isacharequal}\ true{\isachardoublequote}}'' may be abbreviated as ``\isa{name}''. All of the above flags are disabled by default, unless changed from ML. @@ -737,15 +737,15 @@ tag: '\%' (ident | string) \end{rail} - The tags \isa{theory}, \isa{proof}, \isa{ML} are already + The tags \isa{{\isachardoublequote}theory{\isachardoublequote}}, \isa{{\isachardoublequote}proof{\isachardoublequote}}, \isa{{\isachardoublequote}ML{\isachardoublequote}} are already pre-declared for certain classes of commands: \medskip \begin{tabular}{ll} - \isa{theory} & theory begin/end \\ - \isa{proof} & all proof commands \\ - \isa{ML} & all commands involving ML code \\ + \isa{{\isachardoublequote}theory{\isachardoublequote}} & theory begin/end \\ + \isa{{\isachardoublequote}proof{\isachardoublequote}} & all proof commands \\ + \isa{{\isachardoublequote}ML{\isachardoublequote}} & all commands involving ML code \\ \end{tabular} \medskip The Isabelle document preparation system (see also @@ -753,14 +753,14 @@ specifically, e.g.\ to fold proof texts, or drop parts of the text completely. - For example ``\mbox{\isa{\isacommand{by}}}~\isa{{\isacharpercent}invisible\ auto}'' would + For example ``\mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}{\isacharpercent}invisible\ auto{\isachardoublequote}}'' would cause that piece of proof to be treated as \isa{invisible} instead - of \isa{proof} (the default), which may be either show or hidden - depending on the document setup. In contrast, ``\mbox{\isa{\isacommand{by}}}~\isa{{\isacharpercent}visible\ auto}'' would force this text to be shown + of \isa{{\isachardoublequote}proof{\isachardoublequote}} (the default), which may be either show or hidden + depending on the document setup. In contrast, ``\mbox{\isa{\isacommand{by}}}~\isa{{\isachardoublequote}{\isacharpercent}visible\ auto{\isachardoublequote}}'' would force this text to be shown invariably. Explicit tag specifications within a proof apply to all subsequent - commands of the same level of nesting. For example, ``\mbox{\isa{\isacommand{proof}}}~\isa{{\isacharpercent}visible\ {\isasymdots}}~\mbox{\isa{\isacommand{qed}}}'' would force the + commands of the same level of nesting. For example, ``\mbox{\isa{\isacommand{proof}}}~\isa{{\isachardoublequote}{\isacharpercent}visible\ {\isasymdots}{\isachardoublequote}}~\mbox{\isa{\isacommand{qed}}}'' would force the whole sub-proof to be typeset as \isa{visible} (unless some of its parts are tagged differently).% \end{isamarkuptext}%