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%
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\begin{isabellebody}%
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\def\isabellecontext{Spec}%
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%
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\isadelimtheory
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%
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\endisadelimtheory
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%
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\isatagtheory
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\isacommand{theory}\isamarkupfalse%
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\ Spec\isanewline
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\isakeyword{imports}\ Main\isanewline
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\isakeyword{begin}%
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\endisatagtheory
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{\isafoldtheory}%
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%
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\isadelimtheory
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%
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\endisadelimtheory
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%
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\isamarkupchapter{Theory specifications%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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The Isabelle/Isar theory format integrates specifications and
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proofs, supporting interactive development with unlimited undo
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operation. There is an integrated document preparation system (see
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\chref{ch:document-prep}), for typesetting formal developments
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together with informal text. The resulting hyper-linked PDF
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documents can be used both for WWW presentation and printed copies.
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The Isar proof language (see \chref{ch:proofs}) is embedded into the
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theory language as a proper sub-language. Proof mode is entered by
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stating some \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}} or \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}} at the theory
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level, and left again with the final conclusion (e.g.\ via \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}). Some theory specification mechanisms also require a proof,
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such as \hyperlink{command.typedef}{\mbox{\isa{\isacommand{typedef}}}} in HOL, which demands non-emptiness of
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the representing sets.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsection{Defining theories \label{sec:begin-thy}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\begin{matharray}{rcl}
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\indexdef{}{command}{theory}\hypertarget{command.theory}{\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}} & : & \isa{{\isachardoublequote}toplevel\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
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\indexdef{global}{command}{end}\hypertarget{command.global.end}{\hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ toplevel{\isachardoublequote}} \\
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\end{matharray}
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Isabelle/Isar theories are defined via theory files, which may
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contain both specifications and proofs; occasionally definitional
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mechanisms also require some explicit proof. The theory body may be
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sub-structured by means of \emph{local theory targets}, such as
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\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}} and \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}.
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The first proper command of a theory is \hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}, which
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indicates imports of previous theories and optional dependencies on
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other source files (usually in ML). Just preceding the initial
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\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}} command there may be an optional \hyperlink{command.header}{\mbox{\isa{\isacommand{header}}}} declaration, which is only relevant to document
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preparation: see also the other section markup commands in
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\secref{sec:markup}.
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A theory is concluded by a final \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} command,
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one that does not belong to a local theory target. No further
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commands may follow such a global \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}},
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although some user-interfaces might pretend that trailing input is
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admissible.
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\begin{rail}
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'theory' name 'imports' (name +) uses? 'begin'
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;
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uses: 'uses' ((name | parname) +);
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\end{rail}
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\begin{description}
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\item \hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}~\isa{{\isachardoublequote}A\ {\isasymIMPORTS}\ B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n\ {\isasymBEGIN}{\isachardoublequote}}
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starts a new theory \isa{A} based on the merge of existing
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theories \isa{{\isachardoublequote}B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n{\isachardoublequote}}.
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Due to the possibility to import more than one ancestor, the
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resulting theory structure of an Isabelle session forms a directed
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acyclic graph (DAG). Isabelle's theory loader ensures that the
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sources contributing to the development graph are always up-to-date:
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changed files are automatically reloaded whenever a theory header
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specification is processed.
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The optional \indexdef{}{keyword}{uses}\hypertarget{keyword.uses}{\hyperlink{keyword.uses}{\mbox{\isa{\isakeyword{uses}}}}} specification declares additional
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dependencies on extra files (usually ML sources). Files will be
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loaded immediately (as ML), unless the name is parenthesized. The
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latter case records a dependency that needs to be resolved later in
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the text, usually via explicit \indexref{}{command}{use}\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}} for ML files;
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other file formats require specific load commands defined by the
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corresponding tools or packages.
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\item \hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} concludes the current theory
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definition. Note that local theory targets involve a local
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\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}, which is clear from the nesting.
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\end{description}%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsection{Local theory targets \label{sec:target}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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A local theory target is a context managed separately within the
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enclosing theory. Contexts may introduce parameters (fixed
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variables) and assumptions (hypotheses). Definitions and theorems
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depending on the context may be added incrementally later on. Named
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contexts refer to locales (cf.\ \secref{sec:locale}) or type classes
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(cf.\ \secref{sec:class}); the name ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' signifies the
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global theory context.
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\begin{matharray}{rcll}
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\indexdef{}{command}{context}\hypertarget{command.context}{\hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
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\indexdef{local}{command}{end}\hypertarget{command.local.end}{\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
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\end{matharray}
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\indexouternonterm{target}
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\begin{rail}
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'context' name 'begin'
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;
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target: '(' 'in' name ')'
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;
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\end{rail}
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\begin{description}
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\item \hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}~\isa{{\isachardoublequote}c\ {\isasymBEGIN}{\isachardoublequote}} recommences an
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existing locale or class context \isa{c}. Note that locale and
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class definitions allow to include the \hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}} keyword as
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well, in order to continue the local theory immediately after the
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initial specification.
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\item \hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}} concludes the current local theory
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and continues the enclosing global theory. Note that a global
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\hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} has a different meaning: it concludes the
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theory itself (\secref{sec:begin-thy}).
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\item \isa{{\isachardoublequote}{\isacharparenleft}{\isachardoublequote}}\indexdef{}{keyword}{in}\hypertarget{keyword.in}{\hyperlink{keyword.in}{\mbox{\isa{\isakeyword{in}}}}}~\isa{{\isachardoublequote}c{\isacharparenright}{\isachardoublequote}} given after any
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local theory command specifies an immediate target, e.g.\
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``\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}{\isachardoublequote}}'' or ``\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}{\isachardoublequote}}''. This works both in a local or
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global theory context; the current target context will be suspended
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for this command only. Note that ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ {\isacharminus}{\isacharparenright}{\isachardoublequote}}'' will
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always produce a global result independently of the current target
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context.
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\end{description}
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The exact meaning of results produced within a local theory context
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depends on the underlying target infrastructure (locale, type class
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etc.). The general idea is as follows, considering a context named
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\isa{c} with parameter \isa{x} and assumption \isa{{\isachardoublequote}A{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}}.
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Definitions are exported by introducing a global version with
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additional arguments; a syntactic abbreviation links the long form
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with the abstract version of the target context. For example,
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\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
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level (for arbitrary \isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}}), together with a local
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abbreviation \isa{{\isachardoublequote}c\ {\isasymequiv}\ c{\isachardot}a\ x{\isachardoublequote}} in the target context (for the
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fixed parameter \isa{x}).
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Theorems are exported by discharging the assumptions and
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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
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\isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}}.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsection{Basic specification elements%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\begin{matharray}{rcll}
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\indexdef{}{command}{axiomatization}\hypertarget{command.axiomatization}{\hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!)\\
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\indexdef{}{command}{definition}\hypertarget{command.definition}{\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
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\indexdef{}{attribute}{defn}\hypertarget{attribute.defn}{\hyperlink{attribute.defn}{\mbox{\isa{defn}}}} & : & \isa{attribute} \\
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\indexdef{}{command}{abbreviation}\hypertarget{command.abbreviation}{\hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
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\indexdef{}{command}{print\_abbrevs}\hypertarget{command.print-abbrevs}{\hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}\ {\isachardoublequote}} \\
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\end{matharray}
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These specification mechanisms provide a slightly more abstract view
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than the underlying primitives of \hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}, \hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}} (see \secref{sec:consts}), and \hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}} (see
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\secref{sec:axms-thms}). In particular, type-inference is commonly
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available, and result names need not be given.
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\begin{rail}
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'axiomatization' target? fixes? ('where' specs)?
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;
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'definition' target? (decl 'where')? thmdecl? prop
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;
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'abbreviation' target? mode? (decl 'where')? prop
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;
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fixes: ((name ('::' type)? mixfix? | vars) + 'and')
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;
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specs: (thmdecl? props + 'and')
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;
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decl: name ('::' type)? mixfix?
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;
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\end{rail}
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\begin{description}
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\item \hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub m\ {\isasymWHERE}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}
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introduces several constants simultaneously and states axiomatic
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properties for these. The constants are marked as being specified
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once and for all, which prevents additional specifications being
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issued later on.
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Note that axiomatic specifications are only appropriate when
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declaring a new logical system; axiomatic specifications are
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restricted to global theory contexts. Normal applications should
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only use definitional mechanisms!
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\item \hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isachardoublequote}c\ {\isasymWHERE}\ eq{\isachardoublequote}} produces an
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internal definition \isa{{\isachardoublequote}c\ {\isasymequiv}\ t{\isachardoublequote}} according to the specification
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given as \isa{eq}, which is then turned into a proven fact. The
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given proposition may deviate from internal meta-level equality
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according to the rewrite rules declared as \hyperlink{attribute.defn}{\mbox{\isa{defn}}} by the
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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
|
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|
229 |
change the \hyperlink{attribute.defn}{\mbox{\isa{defn}}} setup.
|
wenzelm@27042
|
230 |
|
wenzelm@27042
|
231 |
Definitions may be presented with explicit arguments on the LHS, as
|
wenzelm@27042
|
232 |
well as additional conditions, e.g.\ \isa{{\isachardoublequote}f\ x\ y\ {\isacharequal}\ t{\isachardoublequote}} instead of
|
wenzelm@27042
|
233 |
\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
|
wenzelm@27042
|
234 |
unrestricted \isa{{\isachardoublequote}g\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ u{\isachardoublequote}}.
|
wenzelm@27042
|
235 |
|
wenzelm@28788
|
236 |
\item \hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}~\isa{{\isachardoublequote}c\ {\isasymWHERE}\ eq{\isachardoublequote}} introduces a
|
wenzelm@28788
|
237 |
syntactic constant which is associated with a certain term according
|
wenzelm@28788
|
238 |
to the meta-level equality \isa{eq}.
|
wenzelm@27042
|
239 |
|
wenzelm@27042
|
240 |
Abbreviations participate in the usual type-inference process, but
|
wenzelm@27042
|
241 |
are expanded before the logic ever sees them. Pretty printing of
|
wenzelm@27042
|
242 |
terms involves higher-order rewriting with rules stemming from
|
wenzelm@27042
|
243 |
reverted abbreviations. This needs some care to avoid overlapping
|
wenzelm@27042
|
244 |
or looping syntactic replacements!
|
wenzelm@27042
|
245 |
|
wenzelm@27042
|
246 |
The optional \isa{mode} specification restricts output to a
|
wenzelm@27042
|
247 |
particular print mode; using ``\isa{input}'' here achieves the
|
wenzelm@27042
|
248 |
effect of one-way abbreviations. The mode may also include an
|
wenzelm@27042
|
249 |
``\hyperlink{keyword.output}{\mbox{\isa{\isakeyword{output}}}}'' qualifier that affects the concrete syntax
|
wenzelm@27042
|
250 |
declared for abbreviations, cf.\ \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}} in
|
wenzelm@27042
|
251 |
\secref{sec:syn-trans}.
|
wenzelm@27042
|
252 |
|
wenzelm@28788
|
253 |
\item \hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}} prints all constant abbreviations
|
wenzelm@27042
|
254 |
of the current context.
|
wenzelm@27042
|
255 |
|
wenzelm@28788
|
256 |
\end{description}%
|
wenzelm@27042
|
257 |
\end{isamarkuptext}%
|
wenzelm@27042
|
258 |
\isamarkuptrue%
|
wenzelm@27042
|
259 |
%
|
wenzelm@27042
|
260 |
\isamarkupsection{Generic declarations%
|
wenzelm@27042
|
261 |
}
|
wenzelm@27042
|
262 |
\isamarkuptrue%
|
wenzelm@27042
|
263 |
%
|
wenzelm@27042
|
264 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
265 |
Arbitrary operations on the background context may be wrapped-up as
|
wenzelm@27042
|
266 |
generic declaration elements. Since the underlying concept of local
|
wenzelm@27042
|
267 |
theories may be subject to later re-interpretation, there is an
|
wenzelm@27042
|
268 |
additional dependency on a morphism that tells the difference of the
|
wenzelm@27042
|
269 |
original declaration context wrt.\ the application context
|
wenzelm@27042
|
270 |
encountered later on. A fact declaration is an important special
|
wenzelm@27042
|
271 |
case: it consists of a theorem which is applied to the context by
|
wenzelm@27042
|
272 |
means of an attribute.
|
wenzelm@27042
|
273 |
|
wenzelm@27042
|
274 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
275 |
\indexdef{}{command}{declaration}\hypertarget{command.declaration}{\hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
276 |
\indexdef{}{command}{declare}\hypertarget{command.declare}{\hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@27042
|
277 |
\end{matharray}
|
wenzelm@27042
|
278 |
|
wenzelm@27042
|
279 |
\begin{rail}
|
wenzelm@27042
|
280 |
'declaration' target? text
|
wenzelm@27042
|
281 |
;
|
wenzelm@27042
|
282 |
'declare' target? (thmrefs + 'and')
|
wenzelm@27042
|
283 |
;
|
wenzelm@27042
|
284 |
\end{rail}
|
wenzelm@27042
|
285 |
|
wenzelm@28788
|
286 |
\begin{description}
|
wenzelm@27042
|
287 |
|
wenzelm@28788
|
288 |
\item \hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}~\isa{d} adds the declaration
|
wenzelm@27042
|
289 |
function \isa{d} of ML type \verb|declaration|, to the current
|
wenzelm@27042
|
290 |
local theory under construction. In later application contexts, the
|
wenzelm@27042
|
291 |
function is transformed according to the morphisms being involved in
|
wenzelm@27042
|
292 |
the interpretation hierarchy.
|
wenzelm@27042
|
293 |
|
wenzelm@28788
|
294 |
\item \hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}~\isa{thms} declares theorems to the
|
wenzelm@27042
|
295 |
current local theory context. No theorem binding is involved here,
|
wenzelm@27042
|
296 |
unlike \hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}} or \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}} (cf.\
|
wenzelm@27042
|
297 |
\secref{sec:axms-thms}), so \hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}} only has the effect
|
wenzelm@27042
|
298 |
of applying attributes as included in the theorem specification.
|
wenzelm@27042
|
299 |
|
wenzelm@28788
|
300 |
\end{description}%
|
wenzelm@27042
|
301 |
\end{isamarkuptext}%
|
wenzelm@27042
|
302 |
\isamarkuptrue%
|
wenzelm@27042
|
303 |
%
|
wenzelm@27042
|
304 |
\isamarkupsection{Locales \label{sec:locale}%
|
wenzelm@27042
|
305 |
}
|
wenzelm@27042
|
306 |
\isamarkuptrue%
|
wenzelm@27042
|
307 |
%
|
wenzelm@27042
|
308 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
309 |
Locales are named local contexts, consisting of a list of
|
wenzelm@27042
|
310 |
declaration elements that are modeled after the Isar proof context
|
wenzelm@27042
|
311 |
commands (cf.\ \secref{sec:proof-context}).%
|
wenzelm@27042
|
312 |
\end{isamarkuptext}%
|
wenzelm@27042
|
313 |
\isamarkuptrue%
|
wenzelm@27042
|
314 |
%
|
wenzelm@27042
|
315 |
\isamarkupsubsection{Locale specifications%
|
wenzelm@27042
|
316 |
}
|
wenzelm@27042
|
317 |
\isamarkuptrue%
|
wenzelm@27042
|
318 |
%
|
wenzelm@27042
|
319 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
320 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
321 |
\indexdef{}{command}{locale}\hypertarget{command.locale}{\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
322 |
\indexdef{}{command}{print\_locale}\hypertarget{command.print-locale}{\hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
|
wenzelm@28788
|
323 |
\indexdef{}{command}{print\_locales}\hypertarget{command.print-locales}{\hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
|
wenzelm@28788
|
324 |
\indexdef{}{method}{intro\_locales}\hypertarget{method.intro-locales}{\hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}}} & : & \isa{method} \\
|
wenzelm@28788
|
325 |
\indexdef{}{method}{unfold\_locales}\hypertarget{method.unfold-locales}{\hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}}} & : & \isa{method} \\
|
wenzelm@27042
|
326 |
\end{matharray}
|
wenzelm@27042
|
327 |
|
wenzelm@27042
|
328 |
\indexouternonterm{contextexpr}\indexouternonterm{contextelem}
|
wenzelm@27042
|
329 |
\indexisarelem{fixes}\indexisarelem{constrains}\indexisarelem{assumes}
|
wenzelm@28788
|
330 |
\indexisarelem{defines}\indexisarelem{notes}
|
wenzelm@27042
|
331 |
\begin{rail}
|
wenzelm@27834
|
332 |
'locale' name ('=' localeexpr)? 'begin'?
|
wenzelm@27042
|
333 |
;
|
wenzelm@27042
|
334 |
'print\_locale' '!'? localeexpr
|
wenzelm@27042
|
335 |
;
|
wenzelm@27042
|
336 |
localeexpr: ((contextexpr '+' (contextelem+)) | contextexpr | (contextelem+))
|
wenzelm@27042
|
337 |
;
|
wenzelm@27042
|
338 |
|
wenzelm@27042
|
339 |
contextexpr: nameref | '(' contextexpr ')' |
|
wenzelm@27042
|
340 |
(contextexpr (name mixfix? +)) | (contextexpr + '+')
|
wenzelm@27042
|
341 |
;
|
wenzelm@27042
|
342 |
contextelem: fixes | constrains | assumes | defines | notes
|
wenzelm@27042
|
343 |
;
|
wenzelm@27042
|
344 |
fixes: 'fixes' ((name ('::' type)? structmixfix? | vars) + 'and')
|
wenzelm@27042
|
345 |
;
|
wenzelm@27042
|
346 |
constrains: 'constrains' (name '::' type + 'and')
|
wenzelm@27042
|
347 |
;
|
wenzelm@27042
|
348 |
assumes: 'assumes' (thmdecl? props + 'and')
|
wenzelm@27042
|
349 |
;
|
wenzelm@27042
|
350 |
defines: 'defines' (thmdecl? prop proppat? + 'and')
|
wenzelm@27042
|
351 |
;
|
wenzelm@27042
|
352 |
notes: 'notes' (thmdef? thmrefs + 'and')
|
wenzelm@27042
|
353 |
;
|
wenzelm@27042
|
354 |
\end{rail}
|
wenzelm@27042
|
355 |
|
wenzelm@28788
|
356 |
\begin{description}
|
wenzelm@27042
|
357 |
|
wenzelm@28788
|
358 |
\item \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}~\isa{{\isachardoublequote}loc\ {\isacharequal}\ import\ {\isacharplus}\ body{\isachardoublequote}} defines a
|
wenzelm@27042
|
359 |
new locale \isa{loc} as a context consisting of a certain view of
|
wenzelm@27042
|
360 |
existing locales (\isa{import}) plus some additional elements
|
wenzelm@27042
|
361 |
(\isa{body}). Both \isa{import} and \isa{body} are optional;
|
wenzelm@27042
|
362 |
the degenerate form \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}~\isa{loc} defines an empty
|
wenzelm@27042
|
363 |
locale, which may still be useful to collect declarations of facts
|
wenzelm@27042
|
364 |
later on. Type-inference on locale expressions automatically takes
|
wenzelm@27042
|
365 |
care of the most general typing that the combined context elements
|
wenzelm@27042
|
366 |
may acquire.
|
wenzelm@27042
|
367 |
|
wenzelm@27042
|
368 |
The \isa{import} consists of a structured context expression,
|
wenzelm@27042
|
369 |
consisting of references to existing locales, renamed contexts, or
|
wenzelm@27042
|
370 |
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
|
wenzelm@27042
|
371 |
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
|
wenzelm@27042
|
372 |
position. Renaming by default deletes concrete syntax, but new
|
wenzelm@27042
|
373 |
syntax may by specified with a mixfix annotation. An exeption of
|
wenzelm@27042
|
374 |
this rule is the special syntax declared with ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}{\isachardoublequote}}'' (see below), which is neither deleted nor can it
|
wenzelm@27042
|
375 |
be changed. Merging proceeds from left-to-right, suppressing any
|
wenzelm@27042
|
376 |
duplicates stemming from different paths through the import
|
wenzelm@27042
|
377 |
hierarchy.
|
wenzelm@27042
|
378 |
|
wenzelm@27042
|
379 |
The \isa{body} consists of basic context elements, further context
|
wenzelm@27042
|
380 |
expressions may be included as well.
|
wenzelm@27042
|
381 |
|
wenzelm@28788
|
382 |
\begin{description}
|
wenzelm@27042
|
383 |
|
wenzelm@28788
|
384 |
\item \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} declares a local
|
wenzelm@27042
|
385 |
parameter of type \isa{{\isasymtau}} and mixfix annotation \isa{mx} (both
|
wenzelm@27042
|
386 |
are optional). The special syntax declaration ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}{\isachardoublequote}}'' means that \isa{x} may be referenced
|
wenzelm@27042
|
387 |
implicitly in this context.
|
wenzelm@27042
|
388 |
|
wenzelm@28788
|
389 |
\item \hyperlink{element.constrains}{\mbox{\isa{\isakeyword{constrains}}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}} introduces a type
|
wenzelm@27042
|
390 |
constraint \isa{{\isasymtau}} on the local parameter \isa{x}.
|
wenzelm@27042
|
391 |
|
wenzelm@28788
|
392 |
\item \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}
|
wenzelm@27042
|
393 |
introduces local premises, similar to \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} within a
|
wenzelm@27042
|
394 |
proof (cf.\ \secref{sec:proof-context}).
|
wenzelm@27042
|
395 |
|
wenzelm@28788
|
396 |
\item \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}} defines a previously
|
wenzelm@27042
|
397 |
declared parameter. This is similar to \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}} within a
|
wenzelm@27042
|
398 |
proof (cf.\ \secref{sec:proof-context}), but \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}
|
wenzelm@27042
|
399 |
takes an equational proposition instead of variable-term pair. The
|
wenzelm@27042
|
400 |
left-hand side of the equation may have additional arguments, e.g.\
|
wenzelm@27042
|
401 |
``\hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isachardoublequote}f\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ t{\isachardoublequote}}''.
|
wenzelm@27042
|
402 |
|
wenzelm@28788
|
403 |
\item \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}
|
wenzelm@27042
|
404 |
reconsiders facts within a local context. Most notably, this may
|
wenzelm@27042
|
405 |
include arbitrary declarations in any attribute specifications
|
wenzelm@27042
|
406 |
included here, e.g.\ a local \hyperlink{attribute.simp}{\mbox{\isa{simp}}} rule.
|
wenzelm@27042
|
407 |
|
wenzelm@28788
|
408 |
The initial \isa{import} specification of a locale expression
|
wenzelm@28788
|
409 |
maintains a dynamic relation to the locales being referenced
|
wenzelm@28788
|
410 |
(benefiting from any later fact declarations in the obvious manner).
|
wenzelm@27042
|
411 |
|
wenzelm@28788
|
412 |
\end{description}
|
wenzelm@27042
|
413 |
|
wenzelm@27042
|
414 |
Note that ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}'' patterns given
|
wenzelm@27042
|
415 |
in the syntax of \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} and \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}} above
|
wenzelm@27042
|
416 |
are illegal in locale definitions. In the long goal format of
|
wenzelm@27042
|
417 |
\secref{sec:goals}, term bindings may be included as expected,
|
wenzelm@27042
|
418 |
though.
|
wenzelm@27042
|
419 |
|
wenzelm@27042
|
420 |
\medskip By default, locale specifications are ``closed up'' by
|
wenzelm@27042
|
421 |
turning the given text into a predicate definition \isa{loc{\isacharunderscore}axioms} and deriving the original assumptions as local lemmas
|
wenzelm@27042
|
422 |
(modulo local definitions). The predicate statement covers only the
|
wenzelm@27042
|
423 |
newly specified assumptions, omitting the content of included locale
|
wenzelm@27042
|
424 |
expressions. The full cumulative view is only provided on export,
|
wenzelm@27042
|
425 |
involving another predicate \isa{loc} that refers to the complete
|
wenzelm@27042
|
426 |
specification text.
|
wenzelm@27042
|
427 |
|
wenzelm@27042
|
428 |
In any case, the predicate arguments are those locale parameters
|
wenzelm@27042
|
429 |
that actually occur in the respective piece of text. Also note that
|
wenzelm@27042
|
430 |
these predicates operate at the meta-level in theory, but the locale
|
wenzelm@27042
|
431 |
packages attempts to internalize statements according to the
|
wenzelm@27042
|
432 |
object-logic setup (e.g.\ replacing \isa{{\isasymAnd}} by \isa{{\isasymforall}}, and
|
wenzelm@27042
|
433 |
\isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} by \isa{{\isachardoublequote}{\isasymlongrightarrow}{\isachardoublequote}} in HOL; see also
|
wenzelm@27042
|
434 |
\secref{sec:object-logic}). Separate introduction rules \isa{loc{\isacharunderscore}axioms{\isachardot}intro} and \isa{loc{\isachardot}intro} are provided as well.
|
wenzelm@27042
|
435 |
|
wenzelm@28788
|
436 |
\item \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}~\isa{{\isachardoublequote}import\ {\isacharplus}\ body{\isachardoublequote}} prints the
|
wenzelm@27042
|
437 |
specified locale expression in a flattened form. The notable
|
wenzelm@27042
|
438 |
special case \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}~\isa{loc} just prints the
|
wenzelm@27042
|
439 |
contents of the named locale, but keep in mind that type-inference
|
wenzelm@27042
|
440 |
will normalize type variables according to the usual alphabetical
|
wenzelm@27042
|
441 |
order. The command omits \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}} elements by default.
|
wenzelm@27042
|
442 |
Use \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} to get them included.
|
wenzelm@27042
|
443 |
|
wenzelm@28788
|
444 |
\item \hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}} prints the names of all locales
|
wenzelm@27042
|
445 |
of the current theory.
|
wenzelm@27042
|
446 |
|
wenzelm@28788
|
447 |
\item \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}} and \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}}
|
wenzelm@27042
|
448 |
repeatedly expand all introduction rules of locale predicates of the
|
wenzelm@27042
|
449 |
theory. While \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}} only applies the \isa{loc{\isachardot}intro} introduction rules and therefore does not decend to
|
wenzelm@27042
|
450 |
assumptions, \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}} is more aggressive and applies
|
wenzelm@27042
|
451 |
\isa{loc{\isacharunderscore}axioms{\isachardot}intro} as well. Both methods are aware of locale
|
ballarin@28728
|
452 |
specifications entailed by the context, both from target statements,
|
ballarin@28728
|
453 |
and from interpretations (see below). New goals that are entailed
|
ballarin@28728
|
454 |
by the current context are discharged automatically.
|
wenzelm@27042
|
455 |
|
wenzelm@28788
|
456 |
\end{description}%
|
wenzelm@27042
|
457 |
\end{isamarkuptext}%
|
wenzelm@27042
|
458 |
\isamarkuptrue%
|
wenzelm@27042
|
459 |
%
|
wenzelm@27042
|
460 |
\isamarkupsubsection{Interpretation of locales%
|
wenzelm@27042
|
461 |
}
|
wenzelm@27042
|
462 |
\isamarkuptrue%
|
wenzelm@27042
|
463 |
%
|
wenzelm@27042
|
464 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
465 |
Locale expressions (more precisely, \emph{context expressions}) may
|
wenzelm@27042
|
466 |
be instantiated, and the instantiated facts added to the current
|
wenzelm@27042
|
467 |
context. This requires a proof of the instantiated specification
|
wenzelm@27042
|
468 |
and is called \emph{locale interpretation}. Interpretation is
|
wenzelm@27042
|
469 |
possible in theories and locales (command \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}) and also within a proof body (command \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}).
|
wenzelm@27042
|
470 |
|
wenzelm@27042
|
471 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
472 |
\indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
|
wenzelm@28788
|
473 |
\indexdef{}{command}{interpret}\hypertarget{command.interpret}{\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
|
wenzelm@27042
|
474 |
\end{matharray}
|
wenzelm@27042
|
475 |
|
wenzelm@27042
|
476 |
\indexouternonterm{interp}
|
wenzelm@27042
|
477 |
\begin{rail}
|
wenzelm@27042
|
478 |
'interpretation' (interp | name ('<' | subseteq) contextexpr)
|
wenzelm@27042
|
479 |
;
|
wenzelm@27042
|
480 |
'interpret' interp
|
wenzelm@27042
|
481 |
;
|
wenzelm@27042
|
482 |
instantiation: ('[' (inst+) ']')?
|
wenzelm@27042
|
483 |
;
|
ballarin@28085
|
484 |
interp: (name ':')? \\ (contextexpr instantiation |
|
wenzelm@27042
|
485 |
name instantiation 'where' (thmdecl? prop + 'and'))
|
wenzelm@27042
|
486 |
;
|
wenzelm@27042
|
487 |
\end{rail}
|
wenzelm@27042
|
488 |
|
wenzelm@28788
|
489 |
\begin{description}
|
wenzelm@27042
|
490 |
|
wenzelm@28788
|
491 |
\item \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}~\isa{{\isachardoublequote}expr\ insts\ {\isasymWHERE}\ eqns{\isachardoublequote}}
|
wenzelm@27042
|
492 |
|
wenzelm@27042
|
493 |
The first form of \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}} interprets \isa{expr} in the theory. The instantiation is given as a list of terms
|
wenzelm@27042
|
494 |
\isa{insts} and is positional. All parameters must receive an
|
wenzelm@27042
|
495 |
instantiation term --- with the exception of defined parameters.
|
wenzelm@27042
|
496 |
These are, if omitted, derived from the defining equation and other
|
wenzelm@27042
|
497 |
instantiations. Use ``\isa{{\isacharunderscore}}'' to omit an instantiation term.
|
wenzelm@27042
|
498 |
|
wenzelm@27042
|
499 |
The command generates proof obligations for the instantiated
|
wenzelm@27042
|
500 |
specifications (assumes and defines elements). Once these are
|
wenzelm@27042
|
501 |
discharged by the user, instantiated facts are added to the theory
|
wenzelm@27042
|
502 |
in a post-processing phase.
|
wenzelm@27042
|
503 |
|
wenzelm@27042
|
504 |
Additional equations, which are unfolded in facts during
|
wenzelm@27042
|
505 |
post-processing, may be given after the keyword \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}}.
|
wenzelm@27042
|
506 |
This is useful for interpreting concepts introduced through
|
wenzelm@27042
|
507 |
definition specification elements. The equations must be proved.
|
wenzelm@27042
|
508 |
Note that if equations are present, the context expression is
|
wenzelm@27042
|
509 |
restricted to a locale name.
|
wenzelm@27042
|
510 |
|
wenzelm@27042
|
511 |
The command is aware of interpretations already active in the
|
ballarin@28085
|
512 |
theory, but does not simplify the goal automatically. In order to
|
ballarin@28085
|
513 |
simplify the proof obligations use methods \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}}
|
ballarin@28085
|
514 |
or \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}}. Post-processing is not applied to
|
ballarin@28085
|
515 |
facts of interpretations that are already active. This avoids
|
ballarin@28085
|
516 |
duplication of interpreted facts, in particular. Note that, in the
|
ballarin@28085
|
517 |
case of a locale with import, parts of the interpretation may
|
ballarin@28085
|
518 |
already be active. The command will only process facts for new
|
ballarin@28085
|
519 |
parts.
|
wenzelm@27042
|
520 |
|
ballarin@28085
|
521 |
The context expression may be preceded by a name, which takes effect
|
ballarin@28085
|
522 |
in the post-processing of facts. It is used to prefix fact names,
|
ballarin@28085
|
523 |
for example to avoid accidental hiding of other facts.
|
wenzelm@27042
|
524 |
|
wenzelm@27042
|
525 |
Adding facts to locales has the effect of adding interpreted facts
|
wenzelm@27042
|
526 |
to the theory for all active interpretations also. That is,
|
wenzelm@27042
|
527 |
interpretations dynamically participate in any facts added to
|
wenzelm@27042
|
528 |
locales.
|
wenzelm@27042
|
529 |
|
wenzelm@28788
|
530 |
\item \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}~\isa{{\isachardoublequote}name\ {\isasymsubseteq}\ expr{\isachardoublequote}}
|
wenzelm@27042
|
531 |
|
wenzelm@27042
|
532 |
This form of the command interprets \isa{expr} in the locale
|
wenzelm@27042
|
533 |
\isa{name}. It requires a proof that the specification of \isa{name} implies the specification of \isa{expr}. As in the
|
wenzelm@27042
|
534 |
localized version of the theorem command, the proof is in the
|
wenzelm@27042
|
535 |
context of \isa{name}. After the proof obligation has been
|
wenzelm@27042
|
536 |
dischared, the facts of \isa{expr} become part of locale \isa{name} as \emph{derived} context elements and are available when the
|
wenzelm@27042
|
537 |
context \isa{name} is subsequently entered. Note that, like
|
wenzelm@27042
|
538 |
import, this is dynamic: facts added to a locale part of \isa{expr} after interpretation become also available in \isa{name}.
|
wenzelm@27042
|
539 |
Like facts of renamed context elements, facts obtained by
|
wenzelm@27042
|
540 |
interpretation may be accessed by prefixing with the parameter
|
wenzelm@27042
|
541 |
renaming (where the parameters are separated by ``\isa{{\isacharunderscore}}'').
|
wenzelm@27042
|
542 |
|
wenzelm@27042
|
543 |
Unlike interpretation in theories, instantiation is confined to the
|
wenzelm@27042
|
544 |
renaming of parameters, which may be specified as part of the
|
wenzelm@27042
|
545 |
context expression \isa{expr}. Using defined parameters in \isa{name} one may achieve an effect similar to instantiation, though.
|
wenzelm@27042
|
546 |
|
wenzelm@27042
|
547 |
Only specification fragments of \isa{expr} that are not already
|
wenzelm@27042
|
548 |
part of \isa{name} (be it imported, derived or a derived fragment
|
wenzelm@27042
|
549 |
of the import) are considered by interpretation. This enables
|
wenzelm@27042
|
550 |
circular interpretations.
|
wenzelm@27042
|
551 |
|
wenzelm@27042
|
552 |
If interpretations of \isa{name} exist in the current theory, the
|
wenzelm@27042
|
553 |
command adds interpretations for \isa{expr} as well, with the same
|
wenzelm@27042
|
554 |
prefix and attributes, although only for fragments of \isa{expr}
|
wenzelm@27042
|
555 |
that are not interpreted in the theory already.
|
wenzelm@27042
|
556 |
|
wenzelm@28788
|
557 |
\item \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}~\isa{{\isachardoublequote}expr\ insts\ {\isasymWHERE}\ eqns{\isachardoublequote}}
|
wenzelm@27042
|
558 |
interprets \isa{expr} in the proof context and is otherwise
|
wenzelm@27042
|
559 |
similar to interpretation in theories.
|
wenzelm@27042
|
560 |
|
wenzelm@28788
|
561 |
\end{description}
|
wenzelm@27042
|
562 |
|
wenzelm@27042
|
563 |
\begin{warn}
|
wenzelm@27042
|
564 |
Since attributes are applied to interpreted theorems,
|
wenzelm@27042
|
565 |
interpretation may modify the context of common proof tools, e.g.\
|
wenzelm@27042
|
566 |
the Simplifier or Classical Reasoner. Since the behavior of such
|
wenzelm@27042
|
567 |
automated reasoning tools is \emph{not} stable under
|
wenzelm@27042
|
568 |
interpretation morphisms, manual declarations might have to be
|
wenzelm@27042
|
569 |
issued.
|
wenzelm@27042
|
570 |
\end{warn}
|
wenzelm@27042
|
571 |
|
wenzelm@27042
|
572 |
\begin{warn}
|
wenzelm@27042
|
573 |
An interpretation in a theory may subsume previous
|
wenzelm@27042
|
574 |
interpretations. This happens if the same specification fragment
|
wenzelm@27042
|
575 |
is interpreted twice and the instantiation of the second
|
wenzelm@27042
|
576 |
interpretation is more general than the interpretation of the
|
wenzelm@27042
|
577 |
first. A warning is issued, since it is likely that these could
|
wenzelm@27042
|
578 |
have been generalized in the first place. The locale package does
|
wenzelm@27042
|
579 |
not attempt to remove subsumed interpretations.
|
wenzelm@27042
|
580 |
\end{warn}%
|
wenzelm@27042
|
581 |
\end{isamarkuptext}%
|
wenzelm@27042
|
582 |
\isamarkuptrue%
|
wenzelm@27042
|
583 |
%
|
wenzelm@27042
|
584 |
\isamarkupsection{Classes \label{sec:class}%
|
wenzelm@27042
|
585 |
}
|
wenzelm@27042
|
586 |
\isamarkuptrue%
|
wenzelm@27042
|
587 |
%
|
wenzelm@27042
|
588 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
589 |
A class is a particular locale with \emph{exactly one} type variable
|
wenzelm@27042
|
590 |
\isa{{\isasymalpha}}. Beyond the underlying locale, a corresponding type class
|
wenzelm@27042
|
591 |
is established which is interpreted logically as axiomatic type
|
wenzelm@27042
|
592 |
class \cite{Wenzel:1997:TPHOL} whose logical content are the
|
wenzelm@27042
|
593 |
assumptions of the locale. Thus, classes provide the full
|
wenzelm@27042
|
594 |
generality of locales combined with the commodity of type classes
|
wenzelm@27042
|
595 |
(notably type-inference). See \cite{isabelle-classes} for a short
|
wenzelm@27042
|
596 |
tutorial.
|
wenzelm@27042
|
597 |
|
wenzelm@27042
|
598 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
599 |
\indexdef{}{command}{class}\hypertarget{command.class}{\hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
600 |
\indexdef{}{command}{instantiation}\hypertarget{command.instantiation}{\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
601 |
\indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
602 |
\indexdef{}{command}{subclass}\hypertarget{command.subclass}{\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
603 |
\indexdef{}{command}{print\_classes}\hypertarget{command.print-classes}{\hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
|
haftmann@29706
|
604 |
\indexdef{}{command}{class\_deps}\hypertarget{command.class-deps}{\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
|
wenzelm@28788
|
605 |
\indexdef{}{method}{intro\_classes}\hypertarget{method.intro-classes}{\hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}}} & : & \isa{method} \\
|
wenzelm@27042
|
606 |
\end{matharray}
|
wenzelm@27042
|
607 |
|
wenzelm@27042
|
608 |
\begin{rail}
|
wenzelm@27042
|
609 |
'class' name '=' ((superclassexpr '+' (contextelem+)) | superclassexpr | (contextelem+)) \\
|
wenzelm@27042
|
610 |
'begin'?
|
wenzelm@27042
|
611 |
;
|
wenzelm@27042
|
612 |
'instantiation' (nameref + 'and') '::' arity 'begin'
|
wenzelm@27042
|
613 |
;
|
wenzelm@27042
|
614 |
'instance'
|
wenzelm@27042
|
615 |
;
|
wenzelm@27042
|
616 |
'subclass' target? nameref
|
wenzelm@27042
|
617 |
;
|
wenzelm@27042
|
618 |
'print\_classes'
|
wenzelm@27042
|
619 |
;
|
haftmann@29706
|
620 |
'class\_deps'
|
haftmann@29706
|
621 |
;
|
wenzelm@27042
|
622 |
|
wenzelm@27042
|
623 |
superclassexpr: nameref | (nameref '+' superclassexpr)
|
wenzelm@27042
|
624 |
;
|
wenzelm@27042
|
625 |
\end{rail}
|
wenzelm@27042
|
626 |
|
wenzelm@28788
|
627 |
\begin{description}
|
wenzelm@27042
|
628 |
|
wenzelm@28788
|
629 |
\item \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}~\isa{{\isachardoublequote}c\ {\isacharequal}\ superclasses\ {\isacharplus}\ body{\isachardoublequote}} defines
|
wenzelm@27042
|
630 |
a new class \isa{c}, inheriting from \isa{superclasses}. This
|
wenzelm@27042
|
631 |
introduces a locale \isa{c} with import of all locales \isa{superclasses}.
|
wenzelm@27042
|
632 |
|
wenzelm@27042
|
633 |
Any \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}} in \isa{body} are lifted to the global
|
wenzelm@27042
|
634 |
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
|
wenzelm@27042
|
635 |
\isa{{\isasymalpha}} to a schematic type variable \isa{{\isachardoublequote}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isachardoublequote}}.
|
wenzelm@27042
|
636 |
|
wenzelm@27042
|
637 |
Likewise, \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} in \isa{body} are also lifted,
|
wenzelm@27042
|
638 |
mapping each local parameter \isa{{\isachardoublequote}f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} to its
|
wenzelm@27042
|
639 |
corresponding global constant \isa{{\isachardoublequote}f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}. The
|
wenzelm@27042
|
640 |
corresponding introduction rule is provided as \isa{c{\isacharunderscore}class{\isacharunderscore}axioms{\isachardot}intro}. This rule should be rarely needed directly
|
wenzelm@27042
|
641 |
--- the \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} method takes care of the details of
|
wenzelm@27042
|
642 |
class membership proofs.
|
wenzelm@27042
|
643 |
|
wenzelm@28788
|
644 |
\item \hyperlink{command.instantiation}{\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
|
wenzelm@28788
|
645 |
allows to specify class operations \isa{{\isachardoublequote}f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n{\isachardoublequote}} corresponding
|
wenzelm@28788
|
646 |
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 \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} command in the
|
wenzelm@28788
|
647 |
target body poses a goal stating these type arities. The target is
|
wenzelm@28788
|
648 |
concluded by an \indexref{local}{command}{end}\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}} command.
|
wenzelm@27042
|
649 |
|
wenzelm@27042
|
650 |
Note that a list of simultaneous type constructors may be given;
|
wenzelm@27042
|
651 |
this corresponds nicely to mutual recursive type definitions, e.g.\
|
wenzelm@27042
|
652 |
in Isabelle/HOL.
|
wenzelm@27042
|
653 |
|
wenzelm@28788
|
654 |
\item \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} in an instantiation target body sets
|
wenzelm@27042
|
655 |
up a goal stating the type arities claimed at the opening \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}. The proof would usually proceed by \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}}, and then establish the characteristic theorems of
|
wenzelm@27042
|
656 |
the type classes involved. After finishing the proof, the
|
wenzelm@27042
|
657 |
background theory will be augmented by the proven type arities.
|
wenzelm@27042
|
658 |
|
wenzelm@28788
|
659 |
\item \hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}~\isa{c} in a class context for class
|
wenzelm@27042
|
660 |
\isa{d} sets up a goal stating that class \isa{c} is logically
|
wenzelm@27042
|
661 |
contained in class \isa{d}. After finishing the proof, class
|
wenzelm@27042
|
662 |
\isa{d} is proven to be subclass \isa{c} and the locale \isa{c} is interpreted into \isa{d} simultaneously.
|
wenzelm@27042
|
663 |
|
wenzelm@28788
|
664 |
\item \hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}} prints all classes in the current
|
wenzelm@27042
|
665 |
theory.
|
wenzelm@27042
|
666 |
|
haftmann@29706
|
667 |
\item \hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}} visualizes all classes and their
|
haftmann@29706
|
668 |
subclass relations as a Hasse diagram.
|
haftmann@29706
|
669 |
|
wenzelm@28788
|
670 |
\item \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} repeatedly expands all class
|
wenzelm@27042
|
671 |
introduction rules of this theory. Note that this method usually
|
wenzelm@27042
|
672 |
needs not be named explicitly, as it is already included in the
|
wenzelm@27042
|
673 |
default proof step (e.g.\ of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}). In particular,
|
wenzelm@27042
|
674 |
instantiation of trivial (syntactic) classes may be performed by a
|
wenzelm@27042
|
675 |
single ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' proof step.
|
wenzelm@27042
|
676 |
|
wenzelm@28788
|
677 |
\end{description}%
|
wenzelm@27042
|
678 |
\end{isamarkuptext}%
|
wenzelm@27042
|
679 |
\isamarkuptrue%
|
wenzelm@27042
|
680 |
%
|
wenzelm@27042
|
681 |
\isamarkupsubsection{The class target%
|
wenzelm@27042
|
682 |
}
|
wenzelm@27042
|
683 |
\isamarkuptrue%
|
wenzelm@27042
|
684 |
%
|
wenzelm@27042
|
685 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
686 |
%FIXME check
|
wenzelm@27042
|
687 |
|
wenzelm@27042
|
688 |
A named context may refer to a locale (cf.\ \secref{sec:target}).
|
wenzelm@27042
|
689 |
If this locale is also a class \isa{c}, apart from the common
|
wenzelm@27042
|
690 |
locale target behaviour the following happens.
|
wenzelm@27042
|
691 |
|
wenzelm@27042
|
692 |
\begin{itemize}
|
wenzelm@27042
|
693 |
|
wenzelm@27042
|
694 |
\item Local constant declarations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} referring to the
|
wenzelm@27042
|
695 |
local type parameter \isa{{\isasymalpha}} and local parameters \isa{{\isachardoublequote}f{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}}
|
wenzelm@27042
|
696 |
are accompanied by theory-level constants \isa{{\isachardoublequote}g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}
|
wenzelm@27042
|
697 |
referring to theory-level class operations \isa{{\isachardoublequote}f{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}.
|
wenzelm@27042
|
698 |
|
wenzelm@27042
|
699 |
\item Local theorem bindings are lifted as are assumptions.
|
wenzelm@27042
|
700 |
|
wenzelm@27042
|
701 |
\item Local syntax refers to local operations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} and
|
wenzelm@27042
|
702 |
global operations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}} uniformly. Type inference
|
wenzelm@27042
|
703 |
resolves ambiguities. In rare cases, manual type annotations are
|
wenzelm@27042
|
704 |
needed.
|
wenzelm@27042
|
705 |
|
wenzelm@27042
|
706 |
\end{itemize}%
|
wenzelm@27042
|
707 |
\end{isamarkuptext}%
|
wenzelm@27042
|
708 |
\isamarkuptrue%
|
wenzelm@27042
|
709 |
%
|
wenzelm@27054
|
710 |
\isamarkupsubsection{Old-style axiomatic type classes \label{sec:axclass}%
|
wenzelm@27042
|
711 |
}
|
wenzelm@27042
|
712 |
\isamarkuptrue%
|
wenzelm@27042
|
713 |
%
|
wenzelm@27042
|
714 |
\begin{isamarkuptext}%
|
wenzelm@27054
|
715 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
716 |
\indexdef{}{command}{axclass}\hypertarget{command.axclass}{\hyperlink{command.axclass}{\mbox{\isa{\isacommand{axclass}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
717 |
\indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
|
wenzelm@27042
|
718 |
\end{matharray}
|
wenzelm@27042
|
719 |
|
wenzelm@27042
|
720 |
Axiomatic type classes are Isabelle/Pure's primitive
|
wenzelm@27042
|
721 |
\emph{definitional} interface to type classes. For practical
|
wenzelm@27042
|
722 |
applications, you should consider using classes
|
wenzelm@27042
|
723 |
(cf.~\secref{sec:classes}) which provide high level interface.
|
wenzelm@27042
|
724 |
|
wenzelm@27042
|
725 |
\begin{rail}
|
wenzelm@27042
|
726 |
'axclass' classdecl (axmdecl prop +)
|
wenzelm@27042
|
727 |
;
|
wenzelm@27042
|
728 |
'instance' (nameref ('<' | subseteq) nameref | nameref '::' arity)
|
wenzelm@27042
|
729 |
;
|
wenzelm@27042
|
730 |
\end{rail}
|
wenzelm@27042
|
731 |
|
wenzelm@28788
|
732 |
\begin{description}
|
wenzelm@27042
|
733 |
|
wenzelm@28788
|
734 |
\item \hyperlink{command.axclass}{\mbox{\isa{\isacommand{axclass}}}}~\isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ axms{\isachardoublequote}} defines an
|
wenzelm@28788
|
735 |
axiomatic type class as the intersection of existing classes, with
|
wenzelm@28788
|
736 |
additional axioms holding. Class axioms may not contain more than
|
wenzelm@28788
|
737 |
one type variable. The class axioms (with implicit sort constraints
|
wenzelm@28788
|
738 |
added) are bound to the given names. Furthermore a class
|
wenzelm@28788
|
739 |
introduction rule is generated (being bound as \isa{c{\isacharunderscore}class{\isachardot}intro}); this rule is employed by method \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} to support instantiation proofs of this class.
|
wenzelm@27042
|
740 |
|
wenzelm@28788
|
741 |
The ``class axioms'' (which are derived from the internal class
|
wenzelm@28788
|
742 |
definition) are stored as theorems according to the given name
|
wenzelm@28788
|
743 |
specifications; the name space prefix \isa{{\isachardoublequote}c{\isacharunderscore}class{\isachardoublequote}} is added
|
wenzelm@28788
|
744 |
here. The full collection of these facts is also stored as \isa{c{\isacharunderscore}class{\isachardot}axioms}.
|
wenzelm@27042
|
745 |
|
wenzelm@28788
|
746 |
\item \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} and \hyperlink{command.instance}{\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
|
wenzelm@28788
|
747 |
relation or type arity. The proof would usually proceed by \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}}, and then establish the characteristic theorems of
|
wenzelm@28788
|
748 |
the type classes involved. After finishing the proof, the theory
|
wenzelm@28788
|
749 |
will be augmented by a type signature declaration corresponding to
|
wenzelm@28788
|
750 |
the resulting theorem.
|
wenzelm@27042
|
751 |
|
wenzelm@28788
|
752 |
\end{description}%
|
wenzelm@27042
|
753 |
\end{isamarkuptext}%
|
wenzelm@27042
|
754 |
\isamarkuptrue%
|
wenzelm@27042
|
755 |
%
|
wenzelm@27042
|
756 |
\isamarkupsection{Unrestricted overloading%
|
wenzelm@27042
|
757 |
}
|
wenzelm@27042
|
758 |
\isamarkuptrue%
|
wenzelm@27042
|
759 |
%
|
wenzelm@27042
|
760 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
761 |
Isabelle/Pure's definitional schemes support certain forms of
|
wenzelm@27042
|
762 |
overloading (see \secref{sec:consts}). At most occassions
|
wenzelm@27042
|
763 |
overloading will be used in a Haskell-like fashion together with
|
wenzelm@27042
|
764 |
type classes by means of \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}} (see
|
wenzelm@27042
|
765 |
\secref{sec:class}). Sometimes low-level overloading is desirable.
|
wenzelm@27042
|
766 |
The \hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}} target provides a convenient view for
|
wenzelm@27042
|
767 |
end-users.
|
wenzelm@27042
|
768 |
|
wenzelm@27042
|
769 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
770 |
\indexdef{}{command}{overloading}\hypertarget{command.overloading}{\hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@27042
|
771 |
\end{matharray}
|
wenzelm@27042
|
772 |
|
wenzelm@27042
|
773 |
\begin{rail}
|
wenzelm@27042
|
774 |
'overloading' \\
|
wenzelm@27042
|
775 |
( string ( '==' | equiv ) term ( '(' 'unchecked' ')' )? + ) 'begin'
|
wenzelm@27042
|
776 |
\end{rail}
|
wenzelm@27042
|
777 |
|
wenzelm@28788
|
778 |
\begin{description}
|
wenzelm@27042
|
779 |
|
wenzelm@28788
|
780 |
\item \hyperlink{command.overloading}{\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}}
|
wenzelm@27042
|
781 |
opens a theory target (cf.\ \secref{sec:target}) which allows to
|
wenzelm@27042
|
782 |
specify constants with overloaded definitions. These are identified
|
wenzelm@28788
|
783 |
by an explicitly given mapping from variable names \isa{{\isachardoublequote}x\isactrlsub i{\isachardoublequote}} to
|
wenzelm@28788
|
784 |
constants \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} at particular type instances. The
|
wenzelm@28788
|
785 |
definitions themselves are established using common specification
|
wenzelm@28788
|
786 |
tools, using the names \isa{{\isachardoublequote}x\isactrlsub i{\isachardoublequote}} as reference to the
|
wenzelm@28788
|
787 |
corresponding constants. The target is concluded by \hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}.
|
wenzelm@27042
|
788 |
|
wenzelm@27042
|
789 |
A \isa{{\isachardoublequote}{\isacharparenleft}unchecked{\isacharparenright}{\isachardoublequote}} option disables global dependency checks for
|
wenzelm@27042
|
790 |
the corresponding definition, which is occasionally useful for
|
wenzelm@27042
|
791 |
exotic overloading. It is at the discretion of the user to avoid
|
wenzelm@27042
|
792 |
malformed theory specifications!
|
wenzelm@27042
|
793 |
|
wenzelm@28788
|
794 |
\end{description}%
|
wenzelm@27042
|
795 |
\end{isamarkuptext}%
|
wenzelm@27042
|
796 |
\isamarkuptrue%
|
wenzelm@27042
|
797 |
%
|
wenzelm@27042
|
798 |
\isamarkupsection{Incorporating ML code \label{sec:ML}%
|
wenzelm@27042
|
799 |
}
|
wenzelm@27042
|
800 |
\isamarkuptrue%
|
wenzelm@27042
|
801 |
%
|
wenzelm@27042
|
802 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
803 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
804 |
\indexdef{}{command}{use}\hypertarget{command.use}{\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
805 |
\indexdef{}{command}{ML}\hypertarget{command.ML}{\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
806 |
\indexdef{}{command}{ML\_prf}\hypertarget{command.ML-prf}{\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
|
wenzelm@28788
|
807 |
\indexdef{}{command}{ML\_val}\hypertarget{command.ML-val}{\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
|
wenzelm@28788
|
808 |
\indexdef{}{command}{ML\_command}\hypertarget{command.ML-command}{\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
|
wenzelm@28788
|
809 |
\indexdef{}{command}{setup}\hypertarget{command.setup}{\hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@27042
|
810 |
\end{matharray}
|
wenzelm@27042
|
811 |
|
wenzelm@28788
|
812 |
\begin{mldecls}
|
wenzelm@30121
|
813 |
\indexdef{}{ML}{bind\_thms}\verb|bind_thms: string * thm list -> unit| \\
|
wenzelm@30121
|
814 |
\indexdef{}{ML}{bind\_thm}\verb|bind_thm: string * thm -> unit| \\
|
wenzelm@28788
|
815 |
\end{mldecls}
|
wenzelm@28788
|
816 |
|
wenzelm@27042
|
817 |
\begin{rail}
|
wenzelm@27042
|
818 |
'use' name
|
wenzelm@27042
|
819 |
;
|
wenzelm@28788
|
820 |
('ML' | 'ML\_prf' | 'ML\_val' | 'ML\_command' | 'setup') text
|
wenzelm@27042
|
821 |
;
|
wenzelm@27042
|
822 |
\end{rail}
|
wenzelm@27042
|
823 |
|
wenzelm@28788
|
824 |
\begin{description}
|
wenzelm@27042
|
825 |
|
wenzelm@28788
|
826 |
\item \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}~\isa{{\isachardoublequote}file{\isachardoublequote}} reads and executes ML
|
wenzelm@27042
|
827 |
commands from \isa{{\isachardoublequote}file{\isachardoublequote}}. The current theory context is passed
|
wenzelm@28788
|
828 |
down to the ML toplevel and may be modified, using \verb|Context.>>| or derived ML commands. The file name is checked with
|
wenzelm@27042
|
829 |
the \indexref{}{keyword}{uses}\hyperlink{keyword.uses}{\mbox{\isa{\isakeyword{uses}}}} dependency declaration given in the theory
|
wenzelm@27042
|
830 |
header (see also \secref{sec:begin-thy}).
|
wenzelm@28281
|
831 |
|
wenzelm@28281
|
832 |
Top-level ML bindings are stored within the (global or local) theory
|
wenzelm@28281
|
833 |
context.
|
wenzelm@27042
|
834 |
|
wenzelm@28788
|
835 |
\item \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} is similar to \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}},
|
wenzelm@28788
|
836 |
but executes ML commands directly from the given \isa{{\isachardoublequote}text{\isachardoublequote}}.
|
wenzelm@28788
|
837 |
Top-level ML bindings are stored within the (global or local) theory
|
wenzelm@28788
|
838 |
context.
|
wenzelm@28281
|
839 |
|
wenzelm@28788
|
840 |
\item \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}} is analogous to \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}} but works
|
wenzelm@28788
|
841 |
within a proof context.
|
wenzelm@28281
|
842 |
|
wenzelm@28281
|
843 |
Top-level ML bindings are stored within the proof context in a
|
wenzelm@28281
|
844 |
purely sequential fashion, disregarding the nested proof structure.
|
wenzelm@28281
|
845 |
ML bindings introduced by \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}} are discarded at the
|
wenzelm@28281
|
846 |
end of the proof.
|
wenzelm@27042
|
847 |
|
wenzelm@28788
|
848 |
\item \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} and \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}} are diagnostic
|
wenzelm@28788
|
849 |
versions of \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}, which means that the context may not be
|
wenzelm@28788
|
850 |
updated. \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} echos the bindings produced at the ML
|
wenzelm@28788
|
851 |
toplevel, but \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}} is silent.
|
wenzelm@27042
|
852 |
|
wenzelm@28788
|
853 |
\item \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} changes the current theory
|
wenzelm@27042
|
854 |
context by applying \isa{{\isachardoublequote}text{\isachardoublequote}}, which refers to an ML expression
|
wenzelm@28788
|
855 |
of type \verb|theory -> theory|. This enables
|
wenzelm@28788
|
856 |
to initialize any object-logic specific tools and packages written
|
wenzelm@28788
|
857 |
in ML, for example.
|
wenzelm@28788
|
858 |
|
wenzelm@28788
|
859 |
\item \verb|bind_thms|~\isa{{\isachardoublequote}{\isacharparenleft}name{\isacharcomma}\ thms{\isacharparenright}{\isachardoublequote}} stores a list of
|
wenzelm@28788
|
860 |
theorems produced in ML both in the theory context and the ML
|
wenzelm@28788
|
861 |
toplevel, associating it with the provided name. Theorems are put
|
wenzelm@28788
|
862 |
into a global ``standard'' format before being stored.
|
wenzelm@28788
|
863 |
|
wenzelm@28788
|
864 |
\item \verb|bind_thm| is similar to \verb|bind_thms| but refers to a
|
wenzelm@28788
|
865 |
singleton theorem.
|
wenzelm@27042
|
866 |
|
wenzelm@28788
|
867 |
\end{description}%
|
wenzelm@27042
|
868 |
\end{isamarkuptext}%
|
wenzelm@27042
|
869 |
\isamarkuptrue%
|
wenzelm@27042
|
870 |
%
|
wenzelm@27042
|
871 |
\isamarkupsection{Primitive specification elements%
|
wenzelm@27042
|
872 |
}
|
wenzelm@27042
|
873 |
\isamarkuptrue%
|
wenzelm@27042
|
874 |
%
|
wenzelm@27042
|
875 |
\isamarkupsubsection{Type classes and sorts \label{sec:classes}%
|
wenzelm@27042
|
876 |
}
|
wenzelm@27042
|
877 |
\isamarkuptrue%
|
wenzelm@27042
|
878 |
%
|
wenzelm@27042
|
879 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
880 |
\begin{matharray}{rcll}
|
wenzelm@28788
|
881 |
\indexdef{}{command}{classes}\hypertarget{command.classes}{\hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
882 |
\indexdef{}{command}{classrel}\hypertarget{command.classrel}{\hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
|
wenzelm@28788
|
883 |
\indexdef{}{command}{defaultsort}\hypertarget{command.defaultsort}{\hyperlink{command.defaultsort}{\mbox{\isa{\isacommand{defaultsort}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
884 |
\indexdef{}{command}{class\_deps}\hypertarget{command.class-deps}{\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
|
wenzelm@27042
|
885 |
\end{matharray}
|
wenzelm@27042
|
886 |
|
wenzelm@27042
|
887 |
\begin{rail}
|
wenzelm@27042
|
888 |
'classes' (classdecl +)
|
wenzelm@27042
|
889 |
;
|
wenzelm@27042
|
890 |
'classrel' (nameref ('<' | subseteq) nameref + 'and')
|
wenzelm@27042
|
891 |
;
|
wenzelm@27042
|
892 |
'defaultsort' sort
|
wenzelm@27042
|
893 |
;
|
wenzelm@27042
|
894 |
\end{rail}
|
wenzelm@27042
|
895 |
|
wenzelm@28788
|
896 |
\begin{description}
|
wenzelm@27042
|
897 |
|
wenzelm@28788
|
898 |
\item \hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}~\isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isachardoublequote}} declares class
|
wenzelm@28788
|
899 |
\isa{c} to be a subclass of existing classes \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isachardoublequote}}.
|
wenzelm@28788
|
900 |
Isabelle implicitly maintains the transitive closure of the class
|
wenzelm@28788
|
901 |
hierarchy. Cyclic class structures are not permitted.
|
wenzelm@27042
|
902 |
|
wenzelm@28788
|
903 |
\item \hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} states subclass
|
wenzelm@28788
|
904 |
relations between existing classes \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isachardoublequote}} and \isa{{\isachardoublequote}c\isactrlsub {\isadigit{2}}{\isachardoublequote}}.
|
wenzelm@28788
|
905 |
This is done axiomatically! The \indexref{}{command}{instance}\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} command
|
wenzelm@28788
|
906 |
(see \secref{sec:axclass}) provides a way to introduce proven class
|
wenzelm@28788
|
907 |
relations.
|
wenzelm@27042
|
908 |
|
wenzelm@28788
|
909 |
\item \hyperlink{command.defaultsort}{\mbox{\isa{\isacommand{defaultsort}}}}~\isa{s} makes sort \isa{s} the
|
wenzelm@28788
|
910 |
new default sort for any type variable that is given explicitly in
|
wenzelm@28788
|
911 |
the text, but lacks a sort constraint (wrt.\ the current context).
|
wenzelm@28788
|
912 |
Type variables generated by type inference are not affected.
|
wenzelm@27042
|
913 |
|
wenzelm@28788
|
914 |
Usually the default sort is only changed when defining a new
|
wenzelm@28788
|
915 |
object-logic. For example, the default sort in Isabelle/HOL is
|
wenzelm@28788
|
916 |
\isa{type}, the class of all HOL types. %FIXME sort antiq?
|
wenzelm@28788
|
917 |
|
wenzelm@28788
|
918 |
When merging theories, the default sorts of the parents are
|
wenzelm@28788
|
919 |
logically intersected, i.e.\ the representations as lists of classes
|
wenzelm@28788
|
920 |
are joined.
|
wenzelm@28788
|
921 |
|
wenzelm@28788
|
922 |
\item \hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}} visualizes the subclass relation,
|
wenzelm@27042
|
923 |
using Isabelle's graph browser tool (see also \cite{isabelle-sys}).
|
wenzelm@27042
|
924 |
|
wenzelm@28788
|
925 |
\end{description}%
|
wenzelm@27042
|
926 |
\end{isamarkuptext}%
|
wenzelm@27042
|
927 |
\isamarkuptrue%
|
wenzelm@27042
|
928 |
%
|
wenzelm@27042
|
929 |
\isamarkupsubsection{Types and type abbreviations \label{sec:types-pure}%
|
wenzelm@27042
|
930 |
}
|
wenzelm@27042
|
931 |
\isamarkuptrue%
|
wenzelm@27042
|
932 |
%
|
wenzelm@27042
|
933 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
934 |
\begin{matharray}{rcll}
|
wenzelm@28788
|
935 |
\indexdef{}{command}{types}\hypertarget{command.types}{\hyperlink{command.types}{\mbox{\isa{\isacommand{types}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
936 |
\indexdef{}{command}{typedecl}\hypertarget{command.typedecl}{\hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
937 |
\indexdef{}{command}{arities}\hypertarget{command.arities}{\hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
|
wenzelm@27042
|
938 |
\end{matharray}
|
wenzelm@27042
|
939 |
|
wenzelm@27042
|
940 |
\begin{rail}
|
wenzelm@27042
|
941 |
'types' (typespec '=' type infix? +)
|
wenzelm@27042
|
942 |
;
|
wenzelm@27042
|
943 |
'typedecl' typespec infix?
|
wenzelm@27042
|
944 |
;
|
wenzelm@27042
|
945 |
'arities' (nameref '::' arity +)
|
wenzelm@27042
|
946 |
;
|
wenzelm@27042
|
947 |
\end{rail}
|
wenzelm@27042
|
948 |
|
wenzelm@28788
|
949 |
\begin{description}
|
wenzelm@27042
|
950 |
|
wenzelm@28788
|
951 |
\item \hyperlink{command.types}{\mbox{\isa{\isacommand{types}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t\ {\isacharequal}\ {\isasymtau}{\isachardoublequote}} introduces a
|
wenzelm@28788
|
952 |
\emph{type synonym} \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}} for the existing type
|
wenzelm@28788
|
953 |
\isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}}. Unlike actual type definitions, as are available in
|
wenzelm@28788
|
954 |
Isabelle/HOL for example, type synonyms are merely syntactic
|
wenzelm@28788
|
955 |
abbreviations without any logical significance. Internally, type
|
wenzelm@28788
|
956 |
synonyms are fully expanded.
|
wenzelm@27042
|
957 |
|
wenzelm@28788
|
958 |
\item \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}} declares a new
|
wenzelm@28788
|
959 |
type constructor \isa{t}. If the object-logic defines a base sort
|
wenzelm@28788
|
960 |
\isa{s}, then the constructor is declared to operate on that, via
|
wenzelm@28788
|
961 |
the axiomatic specification \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s{\isacharparenright}s{\isachardoublequote}}.
|
wenzelm@27042
|
962 |
|
wenzelm@28788
|
963 |
\item \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}s{\isachardoublequote}} augments
|
wenzelm@28788
|
964 |
Isabelle's order-sorted signature of types by new type constructor
|
wenzelm@28788
|
965 |
arities. This is done axiomatically! The \indexref{}{command}{instance}\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}
|
wenzelm@28788
|
966 |
command (see \secref{sec:axclass}) provides a way to introduce
|
wenzelm@28788
|
967 |
proven type arities.
|
wenzelm@27042
|
968 |
|
wenzelm@28788
|
969 |
\end{description}%
|
wenzelm@28788
|
970 |
\end{isamarkuptext}%
|
wenzelm@28788
|
971 |
\isamarkuptrue%
|
wenzelm@28788
|
972 |
%
|
wenzelm@28788
|
973 |
\isamarkupsubsection{Co-regularity of type classes and arities%
|
wenzelm@28788
|
974 |
}
|
wenzelm@28788
|
975 |
\isamarkuptrue%
|
wenzelm@28788
|
976 |
%
|
wenzelm@28788
|
977 |
\begin{isamarkuptext}%
|
wenzelm@28788
|
978 |
The class relation together with the collection of
|
wenzelm@28788
|
979 |
type-constructor arities must obey the principle of
|
wenzelm@28788
|
980 |
\emph{co-regularity} as defined below.
|
wenzelm@27042
|
981 |
|
wenzelm@28788
|
982 |
\medskip For the subsequent formulation of co-regularity we assume
|
wenzelm@28788
|
983 |
that the class relation is closed by transitivity and reflexivity.
|
wenzelm@28788
|
984 |
Moreover the collection of arities \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isachardoublequote}} is
|
wenzelm@28788
|
985 |
completed such that \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isachardoublequote}} and \isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c{\isacharprime}{\isachardoublequote}}
|
wenzelm@28788
|
986 |
implies \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isacharprime}{\isachardoublequote}} for all such declarations.
|
wenzelm@28788
|
987 |
|
wenzelm@28788
|
988 |
Treating sorts as finite sets of classes (meaning the intersection),
|
wenzelm@28788
|
989 |
the class relation \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} is extended to sorts as
|
wenzelm@28788
|
990 |
follows:
|
wenzelm@28788
|
991 |
\[
|
wenzelm@28788
|
992 |
\isa{{\isachardoublequote}s\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ s\isactrlsub {\isadigit{2}}\ {\isasymequiv}\ {\isasymforall}c\isactrlsub {\isadigit{2}}\ {\isasymin}\ s\isactrlsub {\isadigit{2}}{\isachardot}\ {\isasymexists}c\isactrlsub {\isadigit{1}}\ {\isasymin}\ s\isactrlsub {\isadigit{1}}{\isachardot}\ c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}}
|
wenzelm@28788
|
993 |
\]
|
wenzelm@28788
|
994 |
|
wenzelm@28788
|
995 |
This relation on sorts is further extended to tuples of sorts (of
|
wenzelm@28788
|
996 |
the same length) in the component-wise way.
|
wenzelm@28788
|
997 |
|
wenzelm@28788
|
998 |
\smallskip Co-regularity of the class relation together with the
|
wenzelm@28788
|
999 |
arities relation means:
|
wenzelm@28788
|
1000 |
\[
|
wenzelm@28788
|
1001 |
\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlsub {\isadigit{1}}{\isacharparenright}c\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlsub {\isadigit{2}}{\isacharparenright}c\isactrlsub {\isadigit{2}}\ {\isasymLongrightarrow}\ c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}\ {\isasymLongrightarrow}\ \isactrlvec s\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ \isactrlvec s\isactrlsub {\isadigit{2}}{\isachardoublequote}}
|
wenzelm@28788
|
1002 |
\]
|
wenzelm@28788
|
1003 |
\noindent for all such arities. In other words, whenever the result
|
wenzelm@28788
|
1004 |
classes of some type-constructor arities are related, then the
|
wenzelm@28788
|
1005 |
argument sorts need to be related in the same way.
|
wenzelm@28788
|
1006 |
|
wenzelm@28788
|
1007 |
\medskip Co-regularity is a very fundamental property of the
|
wenzelm@28788
|
1008 |
order-sorted algebra of types. For example, it entails principle
|
wenzelm@28788
|
1009 |
types and most general unifiers, e.g.\ see \cite{nipkow-prehofer}.%
|
wenzelm@27042
|
1010 |
\end{isamarkuptext}%
|
wenzelm@27042
|
1011 |
\isamarkuptrue%
|
wenzelm@27042
|
1012 |
%
|
wenzelm@27042
|
1013 |
\isamarkupsubsection{Constants and definitions \label{sec:consts}%
|
wenzelm@27042
|
1014 |
}
|
wenzelm@27042
|
1015 |
\isamarkuptrue%
|
wenzelm@27042
|
1016 |
%
|
wenzelm@27042
|
1017 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
1018 |
Definitions essentially express abbreviations within the logic. The
|
wenzelm@27042
|
1019 |
simplest form of a definition is \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isasymequiv}\ t{\isachardoublequote}}, where \isa{c} is a newly declared constant. Isabelle also allows derived forms
|
wenzelm@27042
|
1020 |
where the arguments of \isa{c} appear on the left, abbreviating a
|
wenzelm@27042
|
1021 |
prefix of \isa{{\isasymlambda}}-abstractions, e.g.\ \isa{{\isachardoublequote}c\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t{\isachardoublequote}} may be
|
wenzelm@27042
|
1022 |
written more conveniently as \isa{{\isachardoublequote}c\ x\ y\ {\isasymequiv}\ t{\isachardoublequote}}. Moreover,
|
wenzelm@27042
|
1023 |
definitions may be weakened by adding arbitrary pre-conditions:
|
wenzelm@27042
|
1024 |
\isa{{\isachardoublequote}A\ {\isasymLongrightarrow}\ c\ x\ y\ {\isasymequiv}\ t{\isachardoublequote}}.
|
wenzelm@27042
|
1025 |
|
wenzelm@27042
|
1026 |
\medskip The built-in well-formedness conditions for definitional
|
wenzelm@27042
|
1027 |
specifications are:
|
wenzelm@27042
|
1028 |
|
wenzelm@27042
|
1029 |
\begin{itemize}
|
wenzelm@27042
|
1030 |
|
wenzelm@27042
|
1031 |
\item Arguments (on the left-hand side) must be distinct variables.
|
wenzelm@27042
|
1032 |
|
wenzelm@27042
|
1033 |
\item All variables on the right-hand side must also appear on the
|
wenzelm@27042
|
1034 |
left-hand side.
|
wenzelm@27042
|
1035 |
|
wenzelm@27042
|
1036 |
\item All type variables on the right-hand side must also appear on
|
wenzelm@27042
|
1037 |
the left-hand side; this prohibits \isa{{\isachardoublequote}{\isadigit{0}}\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymequiv}\ length\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ list{\isacharparenright}{\isachardoublequote}} for example.
|
wenzelm@27042
|
1038 |
|
wenzelm@27042
|
1039 |
\item The definition must not be recursive. Most object-logics
|
wenzelm@27042
|
1040 |
provide definitional principles that can be used to express
|
wenzelm@27042
|
1041 |
recursion safely.
|
wenzelm@27042
|
1042 |
|
wenzelm@27042
|
1043 |
\end{itemize}
|
wenzelm@27042
|
1044 |
|
wenzelm@27042
|
1045 |
Overloading means that a constant being declared as \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ decl{\isachardoublequote}} may be defined separately on type instances \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isacharparenright}\ t\ decl{\isachardoublequote}} for each type constructor \isa{t}. The right-hand side may mention overloaded constants
|
wenzelm@27042
|
1046 |
recursively at type instances corresponding to the immediate
|
wenzelm@27042
|
1047 |
argument types \isa{{\isachardoublequote}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isachardoublequote}}. Incomplete
|
wenzelm@27042
|
1048 |
specification patterns impose global constraints on all occurrences,
|
wenzelm@27042
|
1049 |
e.g.\ \isa{{\isachardoublequote}d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymalpha}{\isachardoublequote}} on the left-hand side means that all
|
wenzelm@27042
|
1050 |
corresponding occurrences on some right-hand side need to be an
|
wenzelm@27042
|
1051 |
instance of this, general \isa{{\isachardoublequote}d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymbeta}{\isachardoublequote}} will be disallowed.
|
wenzelm@27042
|
1052 |
|
wenzelm@27042
|
1053 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
1054 |
\indexdef{}{command}{consts}\hypertarget{command.consts}{\hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
1055 |
\indexdef{}{command}{defs}\hypertarget{command.defs}{\hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
1056 |
\indexdef{}{command}{constdefs}\hypertarget{command.constdefs}{\hyperlink{command.constdefs}{\mbox{\isa{\isacommand{constdefs}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@27042
|
1057 |
\end{matharray}
|
wenzelm@27042
|
1058 |
|
wenzelm@27042
|
1059 |
\begin{rail}
|
wenzelm@27042
|
1060 |
'consts' ((name '::' type mixfix?) +)
|
wenzelm@27042
|
1061 |
;
|
wenzelm@27042
|
1062 |
'defs' ('(' 'unchecked'? 'overloaded'? ')')? \\ (axmdecl prop +)
|
wenzelm@27042
|
1063 |
;
|
wenzelm@27042
|
1064 |
\end{rail}
|
wenzelm@27042
|
1065 |
|
wenzelm@27042
|
1066 |
\begin{rail}
|
wenzelm@27042
|
1067 |
'constdefs' structs? (constdecl? constdef +)
|
wenzelm@27042
|
1068 |
;
|
wenzelm@27042
|
1069 |
|
wenzelm@27042
|
1070 |
structs: '(' 'structure' (vars + 'and') ')'
|
wenzelm@27042
|
1071 |
;
|
wenzelm@27042
|
1072 |
constdecl: ((name '::' type mixfix | name '::' type | name mixfix) 'where'?) | name 'where'
|
wenzelm@27042
|
1073 |
;
|
wenzelm@27042
|
1074 |
constdef: thmdecl? prop
|
wenzelm@27042
|
1075 |
;
|
wenzelm@27042
|
1076 |
\end{rail}
|
wenzelm@27042
|
1077 |
|
wenzelm@28788
|
1078 |
\begin{description}
|
wenzelm@27042
|
1079 |
|
wenzelm@28788
|
1080 |
\item \hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}~\isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}{\isachardoublequote}} declares constant \isa{c} to have any instance of type scheme \isa{{\isasymsigma}}. The optional
|
wenzelm@28788
|
1081 |
mixfix annotations may attach concrete syntax to the constants
|
wenzelm@28788
|
1082 |
declared.
|
wenzelm@27042
|
1083 |
|
wenzelm@28788
|
1084 |
\item \hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ eqn{\isachardoublequote}} introduces \isa{eqn}
|
wenzelm@27042
|
1085 |
as a definitional axiom for some existing constant.
|
wenzelm@27042
|
1086 |
|
wenzelm@27042
|
1087 |
The \isa{{\isachardoublequote}{\isacharparenleft}unchecked{\isacharparenright}{\isachardoublequote}} option disables global dependency checks
|
wenzelm@27042
|
1088 |
for this definition, which is occasionally useful for exotic
|
wenzelm@27042
|
1089 |
overloading. It is at the discretion of the user to avoid malformed
|
wenzelm@27042
|
1090 |
theory specifications!
|
wenzelm@27042
|
1091 |
|
wenzelm@27042
|
1092 |
The \isa{{\isachardoublequote}{\isacharparenleft}overloaded{\isacharparenright}{\isachardoublequote}} option declares definitions to be
|
wenzelm@27042
|
1093 |
potentially overloaded. Unless this option is given, a warning
|
wenzelm@27042
|
1094 |
message would be issued for any definitional equation with a more
|
wenzelm@27042
|
1095 |
special type than that of the corresponding constant declaration.
|
wenzelm@27042
|
1096 |
|
wenzelm@28788
|
1097 |
\item \hyperlink{command.constdefs}{\mbox{\isa{\isacommand{constdefs}}}} combines constant declarations and
|
wenzelm@28788
|
1098 |
definitions, with type-inference taking care of the most general
|
wenzelm@28788
|
1099 |
typing of the given specification (the optional type constraint may
|
wenzelm@28788
|
1100 |
refer to type-inference dummies ``\isa{{\isacharunderscore}}'' as usual). The
|
wenzelm@28788
|
1101 |
resulting type declaration needs to agree with that of the
|
wenzelm@28788
|
1102 |
specification; overloading is \emph{not} supported here!
|
wenzelm@27042
|
1103 |
|
wenzelm@27042
|
1104 |
The constant name may be omitted altogether, if neither type nor
|
wenzelm@27042
|
1105 |
syntax declarations are given. The canonical name of the
|
wenzelm@27042
|
1106 |
definitional axiom for constant \isa{c} will be \isa{c{\isacharunderscore}def},
|
wenzelm@27042
|
1107 |
unless specified otherwise. Also note that the given list of
|
wenzelm@27042
|
1108 |
specifications is processed in a strictly sequential manner, with
|
wenzelm@27042
|
1109 |
type-checking being performed independently.
|
wenzelm@27042
|
1110 |
|
wenzelm@27042
|
1111 |
An optional initial context of \isa{{\isachardoublequote}{\isacharparenleft}structure{\isacharparenright}{\isachardoublequote}} declarations
|
wenzelm@27042
|
1112 |
admits use of indexed syntax, using the special symbol \verb|\<index>| (printed as ``\isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}}''). The latter concept is
|
wenzelm@28788
|
1113 |
particularly useful with locales (see also \secref{sec:locale}).
|
wenzelm@27042
|
1114 |
|
wenzelm@28788
|
1115 |
\end{description}%
|
wenzelm@27042
|
1116 |
\end{isamarkuptext}%
|
wenzelm@27042
|
1117 |
\isamarkuptrue%
|
wenzelm@27042
|
1118 |
%
|
wenzelm@27042
|
1119 |
\isamarkupsection{Axioms and theorems \label{sec:axms-thms}%
|
wenzelm@27042
|
1120 |
}
|
wenzelm@27042
|
1121 |
\isamarkuptrue%
|
wenzelm@27042
|
1122 |
%
|
wenzelm@27042
|
1123 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
1124 |
\begin{matharray}{rcll}
|
wenzelm@28788
|
1125 |
\indexdef{}{command}{axioms}\hypertarget{command.axioms}{\hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
|
wenzelm@28788
|
1126 |
\indexdef{}{command}{lemmas}\hypertarget{command.lemmas}{\hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@28788
|
1127 |
\indexdef{}{command}{theorems}\hypertarget{command.theorems}{\hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
|
wenzelm@27042
|
1128 |
\end{matharray}
|
wenzelm@27042
|
1129 |
|
wenzelm@27042
|
1130 |
\begin{rail}
|
wenzelm@27042
|
1131 |
'axioms' (axmdecl prop +)
|
wenzelm@27042
|
1132 |
;
|
wenzelm@27042
|
1133 |
('lemmas' | 'theorems') target? (thmdef? thmrefs + 'and')
|
wenzelm@27042
|
1134 |
;
|
wenzelm@27042
|
1135 |
\end{rail}
|
wenzelm@27042
|
1136 |
|
wenzelm@28788
|
1137 |
\begin{description}
|
wenzelm@27042
|
1138 |
|
wenzelm@28788
|
1139 |
\item \hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} introduces arbitrary
|
wenzelm@27042
|
1140 |
statements as axioms of the meta-logic. In fact, axioms are
|
wenzelm@27042
|
1141 |
``axiomatic theorems'', and may be referred later just as any other
|
wenzelm@27042
|
1142 |
theorem.
|
wenzelm@27042
|
1143 |
|
wenzelm@27042
|
1144 |
Axioms are usually only introduced when declaring new logical
|
wenzelm@27042
|
1145 |
systems. Everyday work is typically done the hard way, with proper
|
wenzelm@27042
|
1146 |
definitions and proven theorems.
|
wenzelm@27042
|
1147 |
|
wenzelm@28788
|
1148 |
\item \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} retrieves and stores
|
wenzelm@28788
|
1149 |
existing facts in the theory context, or the specified target
|
wenzelm@28788
|
1150 |
context (see also \secref{sec:target}). Typical applications would
|
wenzelm@28788
|
1151 |
also involve attributes, to declare Simplifier rules, for example.
|
wenzelm@27042
|
1152 |
|
wenzelm@28788
|
1153 |
\item \hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}} is essentially the same as \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}, but marks the result as a different kind of facts.
|
wenzelm@27042
|
1154 |
|
wenzelm@28788
|
1155 |
\end{description}%
|
wenzelm@27042
|
1156 |
\end{isamarkuptext}%
|
wenzelm@27042
|
1157 |
\isamarkuptrue%
|
wenzelm@27042
|
1158 |
%
|
wenzelm@27042
|
1159 |
\isamarkupsection{Oracles%
|
wenzelm@27042
|
1160 |
}
|
wenzelm@27042
|
1161 |
\isamarkuptrue%
|
wenzelm@27042
|
1162 |
%
|
wenzelm@27042
|
1163 |
\begin{isamarkuptext}%
|
wenzelm@28788
|
1164 |
Oracles allow Isabelle to take advantage of external reasoners
|
wenzelm@28788
|
1165 |
such as arithmetic decision procedures, model checkers, fast
|
wenzelm@28788
|
1166 |
tautology checkers or computer algebra systems. Invoked as an
|
wenzelm@28788
|
1167 |
oracle, an external reasoner can create arbitrary Isabelle theorems.
|
wenzelm@28788
|
1168 |
|
wenzelm@28788
|
1169 |
It is the responsibility of the user to ensure that the external
|
wenzelm@28788
|
1170 |
reasoner is as trustworthy as the application requires. Another
|
wenzelm@28788
|
1171 |
typical source of errors is the linkup between Isabelle and the
|
wenzelm@28788
|
1172 |
external tool, not just its concrete implementation, but also the
|
wenzelm@28788
|
1173 |
required translation between two different logical environments.
|
wenzelm@28788
|
1174 |
|
wenzelm@28788
|
1175 |
Isabelle merely guarantees well-formedness of the propositions being
|
wenzelm@28788
|
1176 |
asserted, and records within the internal derivation object how
|
wenzelm@28788
|
1177 |
presumed theorems depend on unproven suppositions.
|
wenzelm@28788
|
1178 |
|
wenzelm@28788
|
1179 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
1180 |
\indexdef{}{command}{oracle}\hypertarget{command.oracle}{\hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@27042
|
1181 |
\end{matharray}
|
wenzelm@27042
|
1182 |
|
wenzelm@27042
|
1183 |
\begin{rail}
|
wenzelm@28291
|
1184 |
'oracle' name '=' text
|
wenzelm@27042
|
1185 |
;
|
wenzelm@27042
|
1186 |
\end{rail}
|
wenzelm@27042
|
1187 |
|
wenzelm@28788
|
1188 |
\begin{description}
|
wenzelm@27042
|
1189 |
|
wenzelm@28788
|
1190 |
\item \hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ text{\isachardoublequote}} turns the given ML
|
wenzelm@28291
|
1191 |
expression \isa{{\isachardoublequote}text{\isachardoublequote}} of type \verb|'a -> cterm| into an
|
wenzelm@28291
|
1192 |
ML function of type \verb|'a -> thm|, which is bound to the
|
wenzelm@28788
|
1193 |
global identifier \verb|name|. This acts like an infinitary
|
wenzelm@28788
|
1194 |
specification of axioms! Invoking the oracle only works within the
|
wenzelm@28788
|
1195 |
scope of the resulting theory.
|
wenzelm@27042
|
1196 |
|
wenzelm@28788
|
1197 |
\end{description}
|
wenzelm@28788
|
1198 |
|
wenzelm@30080
|
1199 |
See \hyperlink{file.~~/src/FOL/ex/Iff-Oracle.thy}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}FOL{\isacharslash}ex{\isacharslash}Iff{\isacharunderscore}Oracle{\isachardot}thy}}}} for a worked example of
|
wenzelm@28788
|
1200 |
defining a new primitive rule as oracle, and turning it into a proof
|
wenzelm@28788
|
1201 |
method.%
|
wenzelm@27042
|
1202 |
\end{isamarkuptext}%
|
wenzelm@27042
|
1203 |
\isamarkuptrue%
|
wenzelm@27042
|
1204 |
%
|
wenzelm@27042
|
1205 |
\isamarkupsection{Name spaces%
|
wenzelm@27042
|
1206 |
}
|
wenzelm@27042
|
1207 |
\isamarkuptrue%
|
wenzelm@27042
|
1208 |
%
|
wenzelm@27042
|
1209 |
\begin{isamarkuptext}%
|
wenzelm@27042
|
1210 |
\begin{matharray}{rcl}
|
wenzelm@28788
|
1211 |
\indexdef{}{command}{global}\hypertarget{command.global}{\hyperlink{command.global}{\mbox{\isa{\isacommand{global}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
1212 |
\indexdef{}{command}{local}\hypertarget{command.local}{\hyperlink{command.local}{\mbox{\isa{\isacommand{local}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@28788
|
1213 |
\indexdef{}{command}{hide}\hypertarget{command.hide}{\hyperlink{command.hide}{\mbox{\isa{\isacommand{hide}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
|
wenzelm@27042
|
1214 |
\end{matharray}
|
wenzelm@27042
|
1215 |
|
wenzelm@27042
|
1216 |
\begin{rail}
|
wenzelm@27042
|
1217 |
'hide' ('(open)')? name (nameref + )
|
wenzelm@27042
|
1218 |
;
|
wenzelm@27042
|
1219 |
\end{rail}
|
wenzelm@27042
|
1220 |
|
wenzelm@27042
|
1221 |
Isabelle organizes any kind of name declarations (of types,
|
wenzelm@27042
|
1222 |
constants, theorems etc.) by separate hierarchically structured name
|
wenzelm@27042
|
1223 |
spaces. Normally the user does not have to control the behavior of
|
wenzelm@27042
|
1224 |
name spaces by hand, yet the following commands provide some way to
|
wenzelm@27042
|
1225 |
do so.
|
wenzelm@27042
|
1226 |
|
wenzelm@28788
|
1227 |
\begin{description}
|
wenzelm@27042
|
1228 |
|
wenzelm@28788
|
1229 |
\item \hyperlink{command.global}{\mbox{\isa{\isacommand{global}}}} and \hyperlink{command.local}{\mbox{\isa{\isacommand{local}}}} change the current
|
wenzelm@28788
|
1230 |
name declaration mode. Initially, theories start in \hyperlink{command.local}{\mbox{\isa{\isacommand{local}}}} mode, causing all names to be automatically qualified by
|
wenzelm@28788
|
1231 |
the theory name. Changing this to \hyperlink{command.global}{\mbox{\isa{\isacommand{global}}}} causes all
|
wenzelm@28788
|
1232 |
names to be declared without the theory prefix, until \hyperlink{command.local}{\mbox{\isa{\isacommand{local}}}} is declared again.
|
wenzelm@27042
|
1233 |
|
wenzelm@27042
|
1234 |
Note that global names are prone to get hidden accidently later,
|
wenzelm@27042
|
1235 |
when qualified names of the same base name are introduced.
|
wenzelm@27042
|
1236 |
|
wenzelm@28788
|
1237 |
\item \hyperlink{command.hide}{\mbox{\isa{\isacommand{hide}}}}~\isa{{\isachardoublequote}space\ names{\isachardoublequote}} fully removes
|
wenzelm@27042
|
1238 |
declarations from a given name space (which may be \isa{{\isachardoublequote}class{\isachardoublequote}},
|
wenzelm@27042
|
1239 |
\isa{{\isachardoublequote}type{\isachardoublequote}}, \isa{{\isachardoublequote}const{\isachardoublequote}}, or \isa{{\isachardoublequote}fact{\isachardoublequote}}); with the \isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}} option, only the base name is hidden. Global
|
wenzelm@27042
|
1240 |
(unqualified) names may never be hidden.
|
wenzelm@27042
|
1241 |
|
wenzelm@27042
|
1242 |
Note that hiding name space accesses has no impact on logical
|
wenzelm@28788
|
1243 |
declarations --- they remain valid internally. Entities that are no
|
wenzelm@27042
|
1244 |
longer accessible to the user are printed with the special qualifier
|
wenzelm@27042
|
1245 |
``\isa{{\isachardoublequote}{\isacharquery}{\isacharquery}{\isachardoublequote}}'' prefixed to the full internal name.
|
wenzelm@27042
|
1246 |
|
wenzelm@28788
|
1247 |
\end{description}%
|
wenzelm@27042
|
1248 |
\end{isamarkuptext}%
|
wenzelm@27042
|
1249 |
\isamarkuptrue%
|
wenzelm@27042
|
1250 |
%
|
wenzelm@26869
|
1251 |
\isadelimtheory
|
wenzelm@26869
|
1252 |
%
|
wenzelm@26869
|
1253 |
\endisadelimtheory
|
wenzelm@26869
|
1254 |
%
|
wenzelm@26869
|
1255 |
\isatagtheory
|
wenzelm@26869
|
1256 |
\isacommand{end}\isamarkupfalse%
|
wenzelm@26869
|
1257 |
%
|
wenzelm@26869
|
1258 |
\endisatagtheory
|
wenzelm@26869
|
1259 |
{\isafoldtheory}%
|
wenzelm@26869
|
1260 |
%
|
wenzelm@26869
|
1261 |
\isadelimtheory
|
wenzelm@26869
|
1262 |
%
|
wenzelm@26869
|
1263 |
\endisadelimtheory
|
wenzelm@26869
|
1264 |
\isanewline
|
wenzelm@26869
|
1265 |
\end{isabellebody}%
|
wenzelm@26869
|
1266 |
%%% Local Variables:
|
wenzelm@26869
|
1267 |
%%% mode: latex
|
wenzelm@26869
|
1268 |
%%% TeX-master: "root"
|
wenzelm@26869
|
1269 |
%%% End:
|