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}%