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\begin{isabellebody}%
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\def\isabellecontext{Prelim}%
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
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\isacommand{theory}\isamarkupfalse%
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\ Prelim\isanewline
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\isakeyword{imports}\ Base\isanewline
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\isakeyword{begin}%
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\endisatagtheory
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{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
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%
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\isamarkupchapter{Preliminaries%
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}
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\isamarkuptrue%
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%
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\isamarkupsection{Contexts \label{sec:context}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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A logical context represents the background that is required for
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formulating statements and composing proofs. It acts as a medium to
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produce formal content, depending on earlier material (declarations,
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results etc.).
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For example, derivations within the Isabelle/Pure logic can be
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described as a judgment \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}, which means that a
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proposition \isa{{\isasymphi}} is derivable from hypotheses \isa{{\isasymGamma}}
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within the theory \isa{{\isasymTheta}}. There are logical reasons for
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keeping \isa{{\isasymTheta}} and \isa{{\isasymGamma}} separate: theories can be
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liberal about supporting type constructors and schematic
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polymorphism of constants and axioms, while the inner calculus of
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\isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}} is strictly limited to Simple Type Theory (with
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fixed type variables in the assumptions).
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\medskip Contexts and derivations are linked by the following key
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principles:
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\begin{itemize}
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\item Transfer: monotonicity of derivations admits results to be
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transferred into a \emph{larger} context, i.e.\ \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}} implies \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\isactrlsub {\isacharprime}\ {\isasymphi}} for contexts \isa{{\isasymTheta}{\isacharprime}\ {\isasymsupseteq}\ {\isasymTheta}} and \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}}.
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\item Export: discharge of hypotheses admits results to be exported
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into a \emph{smaller} context, i.e.\ \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}
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implies \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymDelta}\ {\isasymLongrightarrow}\ {\isasymphi}} where \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}} and
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\isa{{\isasymDelta}\ {\isacharequal}\ {\isasymGamma}{\isacharprime}\ {\isacharminus}\ {\isasymGamma}}. Note that \isa{{\isasymTheta}} remains unchanged here,
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only the \isa{{\isasymGamma}} part is affected.
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\end{itemize}
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\medskip By modeling the main characteristics of the primitive
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\isa{{\isasymTheta}} and \isa{{\isasymGamma}} above, and abstracting over any
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particular logical content, we arrive at the fundamental notions of
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\emph{theory context} and \emph{proof context} in Isabelle/Isar.
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These implement a certain policy to manage arbitrary \emph{context
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data}. There is a strongly-typed mechanism to declare new kinds of
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data at compile time.
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The internal bootstrap process of Isabelle/Pure eventually reaches a
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stage where certain data slots provide the logical content of \isa{{\isasymTheta}} and \isa{{\isasymGamma}} sketched above, but this does not stop there!
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Various additional data slots support all kinds of mechanisms that
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are not necessarily part of the core logic.
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For example, there would be data for canonical introduction and
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elimination rules for arbitrary operators (depending on the
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object-logic and application), which enables users to perform
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standard proof steps implicitly (cf.\ the \isa{rule} method
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\cite{isabelle-isar-ref}).
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\medskip Thus Isabelle/Isar is able to bring forth more and more
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concepts successively. In particular, an object-logic like
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Isabelle/HOL continues the Isabelle/Pure setup by adding specific
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components for automated reasoning (classical reasoner, tableau
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prover, structured induction etc.) and derived specification
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mechanisms (inductive predicates, recursive functions etc.). All of
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this is ultimately based on the generic data management by theory
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and proof contexts introduced here.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{Theory context \label{sec:context-theory}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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A \emph{theory} is a data container with explicit name and unique
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identifier. Theories are related by a (nominal) sub-theory
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relation, which corresponds to the dependency graph of the original
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construction; each theory is derived from a certain sub-graph of
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ancestor theories.
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The \isa{merge} operation produces the least upper bound of two
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theories, which actually degenerates into absorption of one theory
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into the other (due to the nominal sub-theory relation).
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The \isa{begin} operation starts a new theory by importing
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several parent theories and entering a special \isa{draft} mode,
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which is sustained until the final \isa{end} operation. A draft
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theory acts like a linear type, where updates invalidate earlier
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versions. An invalidated draft is called ``stale''.
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The \isa{checkpoint} operation produces an intermediate stepping
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stone that will survive the next update: both the original and the
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changed theory remain valid and are related by the sub-theory
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relation. Checkpointing essentially recovers purely functional
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theory values, at the expense of some extra internal bookkeeping.
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The \isa{copy} operation produces an auxiliary version that has
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the same data content, but is unrelated to the original: updates of
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the copy do not affect the original, neither does the sub-theory
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relation hold.
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\medskip The example in \figref{fig:ex-theory} below shows a theory
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graph derived from \isa{Pure}, with theory \isa{Length}
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importing \isa{Nat} and \isa{List}. The body of \isa{Length} consists of a sequence of updates, working mostly on
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drafts. Intermediate checkpoints may occur as well, due to the
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history mechanism provided by the Isar top-level, cf.\
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\secref{sec:isar-toplevel}.
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\begin{figure}[htb]
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\begin{center}
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\begin{tabular}{rcccl}
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& & \isa{Pure} \\
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& & \isa{{\isasymdown}} \\
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& & \isa{FOL} \\
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& $\swarrow$ & & $\searrow$ & \\
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\isa{Nat} & & & & \isa{List} \\
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& $\searrow$ & & $\swarrow$ \\
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& & \isa{Length} \\
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& & \multicolumn{3}{l}{~~\hyperlink{keyword.imports}{\mbox{\isa{\isakeyword{imports}}}}} \\
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& & \multicolumn{3}{l}{~~\hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}}} \\
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& & $\vdots$~~ \\
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& & \isa{{\isasymbullet}}~~ \\
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& & $\vdots$~~ \\
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& & \isa{{\isasymbullet}}~~ \\
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& & $\vdots$~~ \\
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& & \multicolumn{3}{l}{~~\hyperlink{command.end}{\mbox{\isa{\isacommand{end}}}}} \\
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\end{tabular}
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\caption{A theory definition depending on ancestors}\label{fig:ex-theory}
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\end{center}
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\end{figure}
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\medskip There is a separate notion of \emph{theory reference} for
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maintaining a live link to an evolving theory context: updates on
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drafts are propagated automatically. Dynamic updating stops after
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an explicit \isa{end} only.
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Derived entities may store a theory reference in order to indicate
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the context they belong to. This implicitly assumes monotonic
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reasoning, because the referenced context may become larger without
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further notice.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isadelimmlref
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\endisadelimmlref
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\isatagmlref
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%
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\begin{isamarkuptext}%
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\begin{mldecls}
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\indexdef{}{ML type}{theory}\verb|type theory| \\
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\indexdef{}{ML}{Theory.subthy}\verb|Theory.subthy: theory * theory -> bool| \\
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\indexdef{}{ML}{Theory.merge}\verb|Theory.merge: theory * theory -> theory| \\
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\indexdef{}{ML}{Theory.checkpoint}\verb|Theory.checkpoint: theory -> theory| \\
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\indexdef{}{ML}{Theory.copy}\verb|Theory.copy: theory -> theory| \\
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\end{mldecls}
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\begin{mldecls}
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\indexdef{}{ML type}{theory\_ref}\verb|type theory_ref| \\
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\indexdef{}{ML}{Theory.deref}\verb|Theory.deref: theory_ref -> theory| \\
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\indexdef{}{ML}{Theory.check\_thy}\verb|Theory.check_thy: theory -> theory_ref| \\
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\end{mldecls}
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\begin{description}
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\item \verb|theory| represents theory contexts. This is
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essentially a linear type! Most operations destroy the original
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version, which then becomes ``stale''.
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\item \verb|Theory.subthy|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}}
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compares theories according to the inherent graph structure of the
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construction. This sub-theory relation is a nominal approximation
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of inclusion (\isa{{\isasymsubseteq}}) of the corresponding content.
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\item \verb|Theory.merge|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}}
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absorbs one theory into the other. This fails for unrelated
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theories!
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\item \verb|Theory.checkpoint|~\isa{thy} produces a safe
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stepping stone in the linear development of \isa{thy}. The next
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update will result in two related, valid theories.
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\item \verb|Theory.copy|~\isa{thy} produces a variant of \isa{thy} with the same data. The result is not related to the
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original; the original is unchanged.
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\item \verb|theory_ref| represents a sliding reference to an
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always valid theory; updates on the original are propagated
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automatically.
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\item \verb|Theory.deref|~\isa{thy{\isacharunderscore}ref} turns a \verb|theory_ref| into an \verb|theory| value. As the referenced
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theory evolves monotonically over time, later invocations of \verb|Theory.deref| may refer to a larger context.
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\item \verb|Theory.check_thy|~\isa{thy} produces a \verb|theory_ref| from a valid \verb|theory| value.
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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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\endisatagmlref
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{\isafoldmlref}%
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%
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\isadelimmlref
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%
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\endisadelimmlref
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%
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\isamarkupsubsection{Proof context \label{sec:context-proof}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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A proof context is a container for pure data with a back-reference
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to the theory it belongs to. The \isa{init} operation creates a
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proof context from a given theory. Modifications to draft theories
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are propagated to the proof context as usual, but there is also an
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explicit \isa{transfer} operation to force resynchronization
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with more substantial updates to the underlying theory. The actual
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context data does not require any special bookkeeping, thanks to the
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lack of destructive features.
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Entities derived in a proof context need to record inherent logical
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requirements explicitly, since there is no separate context
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identification as for theories. For example, hypotheses used in
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primitive derivations (cf.\ \secref{sec:thms}) are recorded
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separately within the sequent \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}}, just to make double
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sure. Results could still leak into an alien proof context due to
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programming errors, but Isabelle/Isar includes some extra validity
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checks in critical positions, notably at the end of a sub-proof.
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Proof contexts may be manipulated arbitrarily, although the common
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discipline is to follow block structure as a mental model: a given
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context is extended consecutively, and results are exported back
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into the original context. Note that the Isar proof states model
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block-structured reasoning explicitly, using a stack of proof
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contexts internally.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isadelimmlref
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%
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\endisadelimmlref
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|
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%
|
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|
263 |
\isatagmlref
|
wenzelm@30296
|
264 |
%
|
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|
265 |
\begin{isamarkuptext}%
|
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|
266 |
\begin{mldecls}
|
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|
267 |
\indexdef{}{ML type}{Proof.context}\verb|type Proof.context| \\
|
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|
268 |
\indexdef{}{ML}{ProofContext.init}\verb|ProofContext.init: theory -> Proof.context| \\
|
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|
269 |
\indexdef{}{ML}{ProofContext.theory\_of}\verb|ProofContext.theory_of: Proof.context -> theory| \\
|
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|
270 |
\indexdef{}{ML}{ProofContext.transfer}\verb|ProofContext.transfer: theory -> Proof.context -> Proof.context| \\
|
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|
271 |
\end{mldecls}
|
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|
272 |
|
wenzelm@30296
|
273 |
\begin{description}
|
wenzelm@30296
|
274 |
|
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|
275 |
\item \verb|Proof.context| represents proof contexts. Elements
|
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|
276 |
of this type are essentially pure values, with a sliding reference
|
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|
277 |
to the background theory.
|
wenzelm@30296
|
278 |
|
wenzelm@30296
|
279 |
\item \verb|ProofContext.init|~\isa{thy} produces a proof context
|
wenzelm@30296
|
280 |
derived from \isa{thy}, initializing all data.
|
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|
281 |
|
wenzelm@30296
|
282 |
\item \verb|ProofContext.theory_of|~\isa{ctxt} selects the
|
wenzelm@30296
|
283 |
background theory from \isa{ctxt}, dereferencing its internal
|
wenzelm@30296
|
284 |
\verb|theory_ref|.
|
wenzelm@30296
|
285 |
|
wenzelm@30296
|
286 |
\item \verb|ProofContext.transfer|~\isa{thy\ ctxt} promotes the
|
wenzelm@30296
|
287 |
background theory of \isa{ctxt} to the super theory \isa{thy}.
|
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|
288 |
|
wenzelm@30296
|
289 |
\end{description}%
|
wenzelm@30296
|
290 |
\end{isamarkuptext}%
|
wenzelm@30296
|
291 |
\isamarkuptrue%
|
wenzelm@30296
|
292 |
%
|
wenzelm@30296
|
293 |
\endisatagmlref
|
wenzelm@30296
|
294 |
{\isafoldmlref}%
|
wenzelm@30296
|
295 |
%
|
wenzelm@30296
|
296 |
\isadelimmlref
|
wenzelm@30296
|
297 |
%
|
wenzelm@30296
|
298 |
\endisadelimmlref
|
wenzelm@30296
|
299 |
%
|
wenzelm@30296
|
300 |
\isamarkupsubsection{Generic contexts \label{sec:generic-context}%
|
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|
301 |
}
|
wenzelm@30296
|
302 |
\isamarkuptrue%
|
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|
303 |
%
|
wenzelm@30296
|
304 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
305 |
A generic context is the disjoint sum of either a theory or proof
|
wenzelm@30296
|
306 |
context. Occasionally, this enables uniform treatment of generic
|
wenzelm@30296
|
307 |
context data, typically extra-logical information. Operations on
|
wenzelm@30296
|
308 |
generic contexts include the usual injections, partial selections,
|
wenzelm@30296
|
309 |
and combinators for lifting operations on either component of the
|
wenzelm@30296
|
310 |
disjoint sum.
|
wenzelm@30296
|
311 |
|
wenzelm@30296
|
312 |
Moreover, there are total operations \isa{theory{\isacharunderscore}of} and \isa{proof{\isacharunderscore}of} to convert a generic context into either kind: a theory
|
wenzelm@30296
|
313 |
can always be selected from the sum, while a proof context might
|
wenzelm@30296
|
314 |
have to be constructed by an ad-hoc \isa{init} operation.%
|
wenzelm@30296
|
315 |
\end{isamarkuptext}%
|
wenzelm@30296
|
316 |
\isamarkuptrue%
|
wenzelm@30296
|
317 |
%
|
wenzelm@30296
|
318 |
\isadelimmlref
|
wenzelm@30296
|
319 |
%
|
wenzelm@30296
|
320 |
\endisadelimmlref
|
wenzelm@30296
|
321 |
%
|
wenzelm@30296
|
322 |
\isatagmlref
|
wenzelm@30296
|
323 |
%
|
wenzelm@30296
|
324 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
325 |
\begin{mldecls}
|
wenzelm@30296
|
326 |
\indexdef{}{ML type}{Context.generic}\verb|type Context.generic| \\
|
wenzelm@30296
|
327 |
\indexdef{}{ML}{Context.theory\_of}\verb|Context.theory_of: Context.generic -> theory| \\
|
wenzelm@30296
|
328 |
\indexdef{}{ML}{Context.proof\_of}\verb|Context.proof_of: Context.generic -> Proof.context| \\
|
wenzelm@30296
|
329 |
\end{mldecls}
|
wenzelm@30296
|
330 |
|
wenzelm@30296
|
331 |
\begin{description}
|
wenzelm@30296
|
332 |
|
wenzelm@30296
|
333 |
\item \verb|Context.generic| is the direct sum of \verb|theory| and \verb|Proof.context|, with the datatype
|
wenzelm@30296
|
334 |
constructors \verb|Context.Theory| and \verb|Context.Proof|.
|
wenzelm@30296
|
335 |
|
wenzelm@30296
|
336 |
\item \verb|Context.theory_of|~\isa{context} always produces a
|
wenzelm@30296
|
337 |
theory from the generic \isa{context}, using \verb|ProofContext.theory_of| as required.
|
wenzelm@30296
|
338 |
|
wenzelm@30296
|
339 |
\item \verb|Context.proof_of|~\isa{context} always produces a
|
wenzelm@30296
|
340 |
proof context from the generic \isa{context}, using \verb|ProofContext.init| as required (note that this re-initializes the
|
wenzelm@30296
|
341 |
context data with each invocation).
|
wenzelm@30296
|
342 |
|
wenzelm@30296
|
343 |
\end{description}%
|
wenzelm@30296
|
344 |
\end{isamarkuptext}%
|
wenzelm@30296
|
345 |
\isamarkuptrue%
|
wenzelm@30296
|
346 |
%
|
wenzelm@30296
|
347 |
\endisatagmlref
|
wenzelm@30296
|
348 |
{\isafoldmlref}%
|
wenzelm@30296
|
349 |
%
|
wenzelm@30296
|
350 |
\isadelimmlref
|
wenzelm@30296
|
351 |
%
|
wenzelm@30296
|
352 |
\endisadelimmlref
|
wenzelm@30296
|
353 |
%
|
wenzelm@30296
|
354 |
\isamarkupsubsection{Context data \label{sec:context-data}%
|
wenzelm@30296
|
355 |
}
|
wenzelm@30296
|
356 |
\isamarkuptrue%
|
wenzelm@30296
|
357 |
%
|
wenzelm@30296
|
358 |
\begin{isamarkuptext}%
|
wenzelm@33526
|
359 |
The main purpose of theory and proof contexts is to manage
|
wenzelm@33526
|
360 |
arbitrary (pure) data. New data types can be declared incrementally
|
wenzelm@33526
|
361 |
at compile time. There are separate declaration mechanisms for any
|
wenzelm@33526
|
362 |
of the three kinds of contexts: theory, proof, generic.
|
wenzelm@30296
|
363 |
|
wenzelm@33526
|
364 |
\paragraph{Theory data} declarations need to implement the following
|
wenzelm@33526
|
365 |
SML signature:
|
wenzelm@30296
|
366 |
|
wenzelm@30296
|
367 |
\medskip
|
wenzelm@30296
|
368 |
\begin{tabular}{ll}
|
wenzelm@30296
|
369 |
\isa{{\isasymtype}\ T} & representing type \\
|
wenzelm@30296
|
370 |
\isa{{\isasymval}\ empty{\isacharcolon}\ T} & empty default value \\
|
wenzelm@30296
|
371 |
\isa{{\isasymval}\ extend{\isacharcolon}\ T\ {\isasymrightarrow}\ T} & re-initialize on import \\
|
wenzelm@30296
|
372 |
\isa{{\isasymval}\ merge{\isacharcolon}\ T\ {\isasymtimes}\ T\ {\isasymrightarrow}\ T} & join on import \\
|
wenzelm@30296
|
373 |
\end{tabular}
|
wenzelm@30296
|
374 |
\medskip
|
wenzelm@30296
|
375 |
|
wenzelm@30296
|
376 |
\noindent The \isa{empty} value acts as initial default for
|
wenzelm@33526
|
377 |
\emph{any} theory that does not declare actual data content; \isa{extend} is acts like a unitary version of \isa{merge}.
|
wenzelm@30296
|
378 |
|
wenzelm@33526
|
379 |
\paragraph{Proof context data} declarations need to implement the
|
wenzelm@33526
|
380 |
following SML signature:
|
wenzelm@30296
|
381 |
|
wenzelm@30296
|
382 |
\medskip
|
wenzelm@30296
|
383 |
\begin{tabular}{ll}
|
wenzelm@30296
|
384 |
\isa{{\isasymtype}\ T} & representing type \\
|
wenzelm@30296
|
385 |
\isa{{\isasymval}\ init{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} & produce initial value \\
|
wenzelm@30296
|
386 |
\end{tabular}
|
wenzelm@30296
|
387 |
\medskip
|
wenzelm@30296
|
388 |
|
wenzelm@30296
|
389 |
\noindent The \isa{init} operation is supposed to produce a pure
|
wenzelm@30296
|
390 |
value from the given background theory.
|
wenzelm@30296
|
391 |
|
wenzelm@30296
|
392 |
\paragraph{Generic data} provides a hybrid interface for both theory
|
wenzelm@33526
|
393 |
and proof data. The \isa{init} operation for proof contexts is
|
wenzelm@33526
|
394 |
predefined to select the current data value from the background
|
wenzelm@33526
|
395 |
theory.
|
wenzelm@30296
|
396 |
|
wenzelm@30296
|
397 |
\bigskip A data declaration of type \isa{T} results in the
|
wenzelm@30296
|
398 |
following interface:
|
wenzelm@30296
|
399 |
|
wenzelm@30296
|
400 |
\medskip
|
wenzelm@30296
|
401 |
\begin{tabular}{ll}
|
wenzelm@30296
|
402 |
\isa{get{\isacharcolon}\ context\ {\isasymrightarrow}\ T} \\
|
wenzelm@30296
|
403 |
\isa{put{\isacharcolon}\ T\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
|
wenzelm@30296
|
404 |
\isa{map{\isacharcolon}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
|
wenzelm@30296
|
405 |
\end{tabular}
|
wenzelm@30296
|
406 |
\medskip
|
wenzelm@30296
|
407 |
|
wenzelm@33526
|
408 |
\noindent These other operations provide access for the particular
|
wenzelm@33526
|
409 |
kind of context (theory, proof, or generic context). Note that this
|
wenzelm@33526
|
410 |
is a safe interface: there is no other way to access the
|
wenzelm@33526
|
411 |
corresponding data slot of a context. By keeping these operations
|
wenzelm@33526
|
412 |
private, a component may maintain abstract values authentically,
|
wenzelm@33526
|
413 |
without other components interfering.%
|
wenzelm@30296
|
414 |
\end{isamarkuptext}%
|
wenzelm@30296
|
415 |
\isamarkuptrue%
|
wenzelm@30296
|
416 |
%
|
wenzelm@30296
|
417 |
\isadelimmlref
|
wenzelm@30296
|
418 |
%
|
wenzelm@30296
|
419 |
\endisadelimmlref
|
wenzelm@30296
|
420 |
%
|
wenzelm@30296
|
421 |
\isatagmlref
|
wenzelm@30296
|
422 |
%
|
wenzelm@30296
|
423 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
424 |
\begin{mldecls}
|
wenzelm@33526
|
425 |
\indexdef{}{ML functor}{Theory\_Data}\verb|functor Theory_Data| \\
|
wenzelm@33526
|
426 |
\indexdef{}{ML functor}{Proof\_Data}\verb|functor Proof_Data| \\
|
wenzelm@33526
|
427 |
\indexdef{}{ML functor}{Generic\_Data}\verb|functor Generic_Data| \\
|
wenzelm@30296
|
428 |
\end{mldecls}
|
wenzelm@30296
|
429 |
|
wenzelm@30296
|
430 |
\begin{description}
|
wenzelm@30296
|
431 |
|
wenzelm@33526
|
432 |
\item \verb|Theory_Data|\isa{{\isacharparenleft}spec{\isacharparenright}} declares data for
|
wenzelm@30296
|
433 |
type \verb|theory| according to the specification provided as
|
wenzelm@30296
|
434 |
argument structure. The resulting structure provides data init and
|
wenzelm@30296
|
435 |
access operations as described above.
|
wenzelm@30296
|
436 |
|
wenzelm@33526
|
437 |
\item \verb|Proof_Data|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
|
wenzelm@33526
|
438 |
\verb|Theory_Data| for type \verb|Proof.context|.
|
wenzelm@30296
|
439 |
|
wenzelm@33526
|
440 |
\item \verb|Generic_Data|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
|
wenzelm@33526
|
441 |
\verb|Theory_Data| for type \verb|Context.generic|.
|
wenzelm@30296
|
442 |
|
wenzelm@30296
|
443 |
\end{description}%
|
wenzelm@30296
|
444 |
\end{isamarkuptext}%
|
wenzelm@30296
|
445 |
\isamarkuptrue%
|
wenzelm@30296
|
446 |
%
|
wenzelm@30296
|
447 |
\endisatagmlref
|
wenzelm@30296
|
448 |
{\isafoldmlref}%
|
wenzelm@30296
|
449 |
%
|
wenzelm@30296
|
450 |
\isadelimmlref
|
wenzelm@30296
|
451 |
%
|
wenzelm@30296
|
452 |
\endisadelimmlref
|
wenzelm@30296
|
453 |
%
|
wenzelm@30296
|
454 |
\isamarkupsection{Names \label{sec:names}%
|
wenzelm@30296
|
455 |
}
|
wenzelm@30296
|
456 |
\isamarkuptrue%
|
wenzelm@30296
|
457 |
%
|
wenzelm@30296
|
458 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
459 |
In principle, a name is just a string, but there are various
|
wenzelm@30296
|
460 |
convention for encoding additional structure. For example, ``\isa{Foo{\isachardot}bar{\isachardot}baz}'' is considered as a qualified name consisting of
|
wenzelm@30296
|
461 |
three basic name components. The individual constituents of a name
|
wenzelm@30296
|
462 |
may have further substructure, e.g.\ the string
|
wenzelm@30296
|
463 |
``\verb,\,\verb,<alpha>,'' encodes as a single symbol.%
|
wenzelm@30296
|
464 |
\end{isamarkuptext}%
|
wenzelm@30296
|
465 |
\isamarkuptrue%
|
wenzelm@30296
|
466 |
%
|
wenzelm@30296
|
467 |
\isamarkupsubsection{Strings of symbols%
|
wenzelm@30296
|
468 |
}
|
wenzelm@30296
|
469 |
\isamarkuptrue%
|
wenzelm@30296
|
470 |
%
|
wenzelm@30296
|
471 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
472 |
A \emph{symbol} constitutes the smallest textual unit in Isabelle
|
wenzelm@30296
|
473 |
--- raw characters are normally not encountered at all. Isabelle
|
wenzelm@30296
|
474 |
strings consist of a sequence of symbols, represented as a packed
|
wenzelm@30296
|
475 |
string or a list of strings. Each symbol is in itself a small
|
wenzelm@30296
|
476 |
string, which has either one of the following forms:
|
wenzelm@30296
|
477 |
|
wenzelm@30296
|
478 |
\begin{enumerate}
|
wenzelm@30296
|
479 |
|
wenzelm@30296
|
480 |
\item a single ASCII character ``\isa{c}'', for example
|
wenzelm@30296
|
481 |
``\verb,a,'',
|
wenzelm@30296
|
482 |
|
wenzelm@30296
|
483 |
\item a regular symbol ``\verb,\,\verb,<,\isa{ident}\verb,>,'',
|
wenzelm@30296
|
484 |
for example ``\verb,\,\verb,<alpha>,'',
|
wenzelm@30296
|
485 |
|
wenzelm@30296
|
486 |
\item a control symbol ``\verb,\,\verb,<^,\isa{ident}\verb,>,'',
|
wenzelm@30296
|
487 |
for example ``\verb,\,\verb,<^bold>,'',
|
wenzelm@30296
|
488 |
|
wenzelm@30296
|
489 |
\item a raw symbol ``\verb,\,\verb,<^raw:,\isa{text}\verb,>,''
|
wenzelm@30296
|
490 |
where \isa{text} constists of printable characters excluding
|
wenzelm@30296
|
491 |
``\verb,.,'' and ``\verb,>,'', for example
|
wenzelm@30296
|
492 |
``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
|
wenzelm@30296
|
493 |
|
wenzelm@30296
|
494 |
\item a numbered raw control symbol ``\verb,\,\verb,<^raw,\isa{n}\verb,>, where \isa{n} consists of digits, for example
|
wenzelm@30296
|
495 |
``\verb,\,\verb,<^raw42>,''.
|
wenzelm@30296
|
496 |
|
wenzelm@30296
|
497 |
\end{enumerate}
|
wenzelm@30296
|
498 |
|
wenzelm@30296
|
499 |
\noindent The \isa{ident} syntax for symbol names is \isa{letter\ {\isacharparenleft}letter\ {\isacharbar}\ digit{\isacharparenright}\isactrlsup {\isacharasterisk}}, where \isa{letter\ {\isacharequal}\ A{\isachardot}{\isachardot}Za{\isachardot}{\isachardot}z} and \isa{digit\ {\isacharequal}\ {\isadigit{0}}{\isachardot}{\isachardot}{\isadigit{9}}}. There are infinitely many
|
wenzelm@30296
|
500 |
regular symbols and control symbols, but a fixed collection of
|
wenzelm@30296
|
501 |
standard symbols is treated specifically. For example,
|
wenzelm@30296
|
502 |
``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it
|
wenzelm@30296
|
503 |
may occur within regular Isabelle identifiers.
|
wenzelm@30296
|
504 |
|
wenzelm@30296
|
505 |
Since the character set underlying Isabelle symbols is 7-bit ASCII
|
wenzelm@30296
|
506 |
and 8-bit characters are passed through transparently, Isabelle may
|
wenzelm@30296
|
507 |
also process Unicode/UCS data in UTF-8 encoding. Unicode provides
|
wenzelm@30296
|
508 |
its own collection of mathematical symbols, but there is no built-in
|
wenzelm@30296
|
509 |
link to the standard collection of Isabelle.
|
wenzelm@30296
|
510 |
|
wenzelm@30296
|
511 |
\medskip Output of Isabelle symbols depends on the print mode
|
wenzelm@30296
|
512 |
(\secref{print-mode}). For example, the standard {\LaTeX} setup of
|
wenzelm@30296
|
513 |
the Isabelle document preparation system would present
|
wenzelm@30296
|
514 |
``\verb,\,\verb,<alpha>,'' as \isa{{\isasymalpha}}, and
|
wenzelm@30296
|
515 |
``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as \isa{\isactrlbold {\isasymalpha}}.%
|
wenzelm@30296
|
516 |
\end{isamarkuptext}%
|
wenzelm@30296
|
517 |
\isamarkuptrue%
|
wenzelm@30296
|
518 |
%
|
wenzelm@30296
|
519 |
\isadelimmlref
|
wenzelm@30296
|
520 |
%
|
wenzelm@30296
|
521 |
\endisadelimmlref
|
wenzelm@30296
|
522 |
%
|
wenzelm@30296
|
523 |
\isatagmlref
|
wenzelm@30296
|
524 |
%
|
wenzelm@30296
|
525 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
526 |
\begin{mldecls}
|
wenzelm@30296
|
527 |
\indexdef{}{ML type}{Symbol.symbol}\verb|type Symbol.symbol| \\
|
wenzelm@30296
|
528 |
\indexdef{}{ML}{Symbol.explode}\verb|Symbol.explode: string -> Symbol.symbol list| \\
|
wenzelm@30296
|
529 |
\indexdef{}{ML}{Symbol.is\_letter}\verb|Symbol.is_letter: Symbol.symbol -> bool| \\
|
wenzelm@30296
|
530 |
\indexdef{}{ML}{Symbol.is\_digit}\verb|Symbol.is_digit: Symbol.symbol -> bool| \\
|
wenzelm@30296
|
531 |
\indexdef{}{ML}{Symbol.is\_quasi}\verb|Symbol.is_quasi: Symbol.symbol -> bool| \\
|
wenzelm@30296
|
532 |
\indexdef{}{ML}{Symbol.is\_blank}\verb|Symbol.is_blank: Symbol.symbol -> bool| \\
|
wenzelm@30296
|
533 |
\end{mldecls}
|
wenzelm@30296
|
534 |
\begin{mldecls}
|
wenzelm@30296
|
535 |
\indexdef{}{ML type}{Symbol.sym}\verb|type Symbol.sym| \\
|
wenzelm@30296
|
536 |
\indexdef{}{ML}{Symbol.decode}\verb|Symbol.decode: Symbol.symbol -> Symbol.sym| \\
|
wenzelm@30296
|
537 |
\end{mldecls}
|
wenzelm@30296
|
538 |
|
wenzelm@30296
|
539 |
\begin{description}
|
wenzelm@30296
|
540 |
|
wenzelm@30296
|
541 |
\item \verb|Symbol.symbol| represents individual Isabelle
|
wenzelm@30296
|
542 |
symbols; this is an alias for \verb|string|.
|
wenzelm@30296
|
543 |
|
wenzelm@30296
|
544 |
\item \verb|Symbol.explode|~\isa{str} produces a symbol list
|
wenzelm@30296
|
545 |
from the packed form. This function supercedes \verb|String.explode| for virtually all purposes of manipulating text in
|
wenzelm@30296
|
546 |
Isabelle!
|
wenzelm@30296
|
547 |
|
wenzelm@30296
|
548 |
\item \verb|Symbol.is_letter|, \verb|Symbol.is_digit|, \verb|Symbol.is_quasi|, \verb|Symbol.is_blank| classify standard
|
wenzelm@30296
|
549 |
symbols according to fixed syntactic conventions of Isabelle, cf.\
|
wenzelm@30296
|
550 |
\cite{isabelle-isar-ref}.
|
wenzelm@30296
|
551 |
|
wenzelm@30296
|
552 |
\item \verb|Symbol.sym| is a concrete datatype that represents
|
wenzelm@30296
|
553 |
the different kinds of symbols explicitly, with constructors \verb|Symbol.Char|, \verb|Symbol.Sym|, \verb|Symbol.Ctrl|, \verb|Symbol.Raw|.
|
wenzelm@30296
|
554 |
|
wenzelm@30296
|
555 |
\item \verb|Symbol.decode| converts the string representation of a
|
wenzelm@30296
|
556 |
symbol into the datatype version.
|
wenzelm@30296
|
557 |
|
wenzelm@30296
|
558 |
\end{description}%
|
wenzelm@30296
|
559 |
\end{isamarkuptext}%
|
wenzelm@30296
|
560 |
\isamarkuptrue%
|
wenzelm@30296
|
561 |
%
|
wenzelm@30296
|
562 |
\endisatagmlref
|
wenzelm@30296
|
563 |
{\isafoldmlref}%
|
wenzelm@30296
|
564 |
%
|
wenzelm@30296
|
565 |
\isadelimmlref
|
wenzelm@30296
|
566 |
%
|
wenzelm@30296
|
567 |
\endisadelimmlref
|
wenzelm@30296
|
568 |
%
|
wenzelm@30296
|
569 |
\isamarkupsubsection{Basic names \label{sec:basic-names}%
|
wenzelm@30296
|
570 |
}
|
wenzelm@30296
|
571 |
\isamarkuptrue%
|
wenzelm@30296
|
572 |
%
|
wenzelm@30296
|
573 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
574 |
A \emph{basic name} essentially consists of a single Isabelle
|
wenzelm@30296
|
575 |
identifier. There are conventions to mark separate classes of basic
|
wenzelm@30296
|
576 |
names, by attaching a suffix of underscores: one underscore means
|
wenzelm@30296
|
577 |
\emph{internal name}, two underscores means \emph{Skolem name},
|
wenzelm@30296
|
578 |
three underscores means \emph{internal Skolem name}.
|
wenzelm@30296
|
579 |
|
wenzelm@30296
|
580 |
For example, the basic name \isa{foo} has the internal version
|
wenzelm@30296
|
581 |
\isa{foo{\isacharunderscore}}, with Skolem versions \isa{foo{\isacharunderscore}{\isacharunderscore}} and \isa{foo{\isacharunderscore}{\isacharunderscore}{\isacharunderscore}}, respectively.
|
wenzelm@30296
|
582 |
|
wenzelm@30296
|
583 |
These special versions provide copies of the basic name space, apart
|
wenzelm@30296
|
584 |
from anything that normally appears in the user text. For example,
|
wenzelm@30296
|
585 |
system generated variables in Isar proof contexts are usually marked
|
wenzelm@30296
|
586 |
as internal, which prevents mysterious name references like \isa{xaa} to appear in the text.
|
wenzelm@30296
|
587 |
|
wenzelm@30296
|
588 |
\medskip Manipulating binding scopes often requires on-the-fly
|
wenzelm@30296
|
589 |
renamings. A \emph{name context} contains a collection of already
|
wenzelm@30296
|
590 |
used names. The \isa{declare} operation adds names to the
|
wenzelm@30296
|
591 |
context.
|
wenzelm@30296
|
592 |
|
wenzelm@30296
|
593 |
The \isa{invents} operation derives a number of fresh names from
|
wenzelm@30296
|
594 |
a given starting point. For example, the first three names derived
|
wenzelm@30296
|
595 |
from \isa{a} are \isa{a}, \isa{b}, \isa{c}.
|
wenzelm@30296
|
596 |
|
wenzelm@30296
|
597 |
The \isa{variants} operation produces fresh names by
|
wenzelm@30296
|
598 |
incrementing tentative names as base-26 numbers (with digits \isa{a{\isachardot}{\isachardot}z}) until all clashes are resolved. For example, name \isa{foo} results in variants \isa{fooa}, \isa{foob}, \isa{fooc}, \dots, \isa{fooaa}, \isa{fooab} etc.; each renaming
|
wenzelm@30296
|
599 |
step picks the next unused variant from this sequence.%
|
wenzelm@30296
|
600 |
\end{isamarkuptext}%
|
wenzelm@30296
|
601 |
\isamarkuptrue%
|
wenzelm@30296
|
602 |
%
|
wenzelm@30296
|
603 |
\isadelimmlref
|
wenzelm@30296
|
604 |
%
|
wenzelm@30296
|
605 |
\endisadelimmlref
|
wenzelm@30296
|
606 |
%
|
wenzelm@30296
|
607 |
\isatagmlref
|
wenzelm@30296
|
608 |
%
|
wenzelm@30296
|
609 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
610 |
\begin{mldecls}
|
wenzelm@30296
|
611 |
\indexdef{}{ML}{Name.internal}\verb|Name.internal: string -> string| \\
|
wenzelm@30296
|
612 |
\indexdef{}{ML}{Name.skolem}\verb|Name.skolem: string -> string| \\
|
wenzelm@30296
|
613 |
\end{mldecls}
|
wenzelm@30296
|
614 |
\begin{mldecls}
|
wenzelm@30296
|
615 |
\indexdef{}{ML type}{Name.context}\verb|type Name.context| \\
|
wenzelm@30296
|
616 |
\indexdef{}{ML}{Name.context}\verb|Name.context: Name.context| \\
|
wenzelm@30296
|
617 |
\indexdef{}{ML}{Name.declare}\verb|Name.declare: string -> Name.context -> Name.context| \\
|
wenzelm@30296
|
618 |
\indexdef{}{ML}{Name.invents}\verb|Name.invents: Name.context -> string -> int -> string list| \\
|
wenzelm@30296
|
619 |
\indexdef{}{ML}{Name.variants}\verb|Name.variants: string list -> Name.context -> string list * Name.context| \\
|
wenzelm@30296
|
620 |
\end{mldecls}
|
wenzelm@30296
|
621 |
|
wenzelm@30296
|
622 |
\begin{description}
|
wenzelm@30296
|
623 |
|
wenzelm@30296
|
624 |
\item \verb|Name.internal|~\isa{name} produces an internal name
|
wenzelm@30296
|
625 |
by adding one underscore.
|
wenzelm@30296
|
626 |
|
wenzelm@30296
|
627 |
\item \verb|Name.skolem|~\isa{name} produces a Skolem name by
|
wenzelm@30296
|
628 |
adding two underscores.
|
wenzelm@30296
|
629 |
|
wenzelm@30296
|
630 |
\item \verb|Name.context| represents the context of already used
|
wenzelm@30296
|
631 |
names; the initial value is \verb|Name.context|.
|
wenzelm@30296
|
632 |
|
wenzelm@30296
|
633 |
\item \verb|Name.declare|~\isa{name} enters a used name into the
|
wenzelm@30296
|
634 |
context.
|
wenzelm@30296
|
635 |
|
wenzelm@30296
|
636 |
\item \verb|Name.invents|~\isa{context\ name\ n} produces \isa{n} fresh names derived from \isa{name}.
|
wenzelm@30296
|
637 |
|
wenzelm@30296
|
638 |
\item \verb|Name.variants|~\isa{names\ context} produces fresh
|
wenzelm@30296
|
639 |
variants of \isa{names}; the result is entered into the context.
|
wenzelm@30296
|
640 |
|
wenzelm@30296
|
641 |
\end{description}%
|
wenzelm@30296
|
642 |
\end{isamarkuptext}%
|
wenzelm@30296
|
643 |
\isamarkuptrue%
|
wenzelm@30296
|
644 |
%
|
wenzelm@30296
|
645 |
\endisatagmlref
|
wenzelm@30296
|
646 |
{\isafoldmlref}%
|
wenzelm@30296
|
647 |
%
|
wenzelm@30296
|
648 |
\isadelimmlref
|
wenzelm@30296
|
649 |
%
|
wenzelm@30296
|
650 |
\endisadelimmlref
|
wenzelm@30296
|
651 |
%
|
wenzelm@30296
|
652 |
\isamarkupsubsection{Indexed names%
|
wenzelm@30296
|
653 |
}
|
wenzelm@30296
|
654 |
\isamarkuptrue%
|
wenzelm@30296
|
655 |
%
|
wenzelm@30296
|
656 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
657 |
An \emph{indexed name} (or \isa{indexname}) is a pair of a basic
|
wenzelm@30296
|
658 |
name and a natural number. This representation allows efficient
|
wenzelm@30296
|
659 |
renaming by incrementing the second component only. The canonical
|
wenzelm@30296
|
660 |
way to rename two collections of indexnames apart from each other is
|
wenzelm@30296
|
661 |
this: determine the maximum index \isa{maxidx} of the first
|
wenzelm@30296
|
662 |
collection, then increment all indexes of the second collection by
|
wenzelm@30296
|
663 |
\isa{maxidx\ {\isacharplus}\ {\isadigit{1}}}; the maximum index of an empty collection is
|
wenzelm@30296
|
664 |
\isa{{\isacharminus}{\isadigit{1}}}.
|
wenzelm@30296
|
665 |
|
wenzelm@30296
|
666 |
Occasionally, basic names and indexed names are injected into the
|
wenzelm@30296
|
667 |
same pair type: the (improper) indexname \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}} is used
|
wenzelm@30296
|
668 |
to encode basic names.
|
wenzelm@30296
|
669 |
|
wenzelm@30296
|
670 |
\medskip Isabelle syntax observes the following rules for
|
wenzelm@30296
|
671 |
representing an indexname \isa{{\isacharparenleft}x{\isacharcomma}\ i{\isacharparenright}} as a packed string:
|
wenzelm@30296
|
672 |
|
wenzelm@30296
|
673 |
\begin{itemize}
|
wenzelm@30296
|
674 |
|
wenzelm@30296
|
675 |
\item \isa{{\isacharquery}x} if \isa{x} does not end with a digit and \isa{i\ {\isacharequal}\ {\isadigit{0}}},
|
wenzelm@30296
|
676 |
|
wenzelm@30296
|
677 |
\item \isa{{\isacharquery}xi} if \isa{x} does not end with a digit,
|
wenzelm@30296
|
678 |
|
wenzelm@30296
|
679 |
\item \isa{{\isacharquery}x{\isachardot}i} otherwise.
|
wenzelm@30296
|
680 |
|
wenzelm@30296
|
681 |
\end{itemize}
|
wenzelm@30296
|
682 |
|
wenzelm@30296
|
683 |
Indexnames may acquire large index numbers over time. Results are
|
wenzelm@30296
|
684 |
normalized towards \isa{{\isadigit{0}}} at certain checkpoints, notably at
|
wenzelm@30296
|
685 |
the end of a proof. This works by producing variants of the
|
wenzelm@30296
|
686 |
corresponding basic name components. For example, the collection
|
wenzelm@30296
|
687 |
\isa{{\isacharquery}x{\isadigit{1}}{\isacharcomma}\ {\isacharquery}x{\isadigit{7}}{\isacharcomma}\ {\isacharquery}x{\isadigit{4}}{\isadigit{2}}} becomes \isa{{\isacharquery}x{\isacharcomma}\ {\isacharquery}xa{\isacharcomma}\ {\isacharquery}xb}.%
|
wenzelm@30296
|
688 |
\end{isamarkuptext}%
|
wenzelm@30296
|
689 |
\isamarkuptrue%
|
wenzelm@30296
|
690 |
%
|
wenzelm@30296
|
691 |
\isadelimmlref
|
wenzelm@30296
|
692 |
%
|
wenzelm@30296
|
693 |
\endisadelimmlref
|
wenzelm@30296
|
694 |
%
|
wenzelm@30296
|
695 |
\isatagmlref
|
wenzelm@30296
|
696 |
%
|
wenzelm@30296
|
697 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
698 |
\begin{mldecls}
|
wenzelm@30296
|
699 |
\indexdef{}{ML type}{indexname}\verb|type indexname| \\
|
wenzelm@30296
|
700 |
\end{mldecls}
|
wenzelm@30296
|
701 |
|
wenzelm@30296
|
702 |
\begin{description}
|
wenzelm@30296
|
703 |
|
wenzelm@30296
|
704 |
\item \verb|indexname| represents indexed names. This is an
|
wenzelm@30296
|
705 |
abbreviation for \verb|string * int|. The second component is
|
wenzelm@30296
|
706 |
usually non-negative, except for situations where \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}}
|
wenzelm@30296
|
707 |
is used to embed basic names into this type.
|
wenzelm@30296
|
708 |
|
wenzelm@30296
|
709 |
\end{description}%
|
wenzelm@30296
|
710 |
\end{isamarkuptext}%
|
wenzelm@30296
|
711 |
\isamarkuptrue%
|
wenzelm@30296
|
712 |
%
|
wenzelm@30296
|
713 |
\endisatagmlref
|
wenzelm@30296
|
714 |
{\isafoldmlref}%
|
wenzelm@30296
|
715 |
%
|
wenzelm@30296
|
716 |
\isadelimmlref
|
wenzelm@30296
|
717 |
%
|
wenzelm@30296
|
718 |
\endisadelimmlref
|
wenzelm@30296
|
719 |
%
|
wenzelm@30296
|
720 |
\isamarkupsubsection{Qualified names and name spaces%
|
wenzelm@30296
|
721 |
}
|
wenzelm@30296
|
722 |
\isamarkuptrue%
|
wenzelm@30296
|
723 |
%
|
wenzelm@30296
|
724 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
725 |
A \emph{qualified name} consists of a non-empty sequence of basic
|
wenzelm@30296
|
726 |
name components. The packed representation uses a dot as separator,
|
wenzelm@30296
|
727 |
as in ``\isa{A{\isachardot}b{\isachardot}c}''. The last component is called \emph{base}
|
wenzelm@30296
|
728 |
name, the remaining prefix \emph{qualifier} (which may be empty).
|
wenzelm@30296
|
729 |
The idea of qualified names is to encode nested structures by
|
wenzelm@30296
|
730 |
recording the access paths as qualifiers. For example, an item
|
wenzelm@30296
|
731 |
named ``\isa{A{\isachardot}b{\isachardot}c}'' may be understood as a local entity \isa{c}, within a local structure \isa{b}, within a global
|
wenzelm@30296
|
732 |
structure \isa{A}. Typically, name space hierarchies consist of
|
wenzelm@30296
|
733 |
1--2 levels of qualification, but this need not be always so.
|
wenzelm@30296
|
734 |
|
wenzelm@30296
|
735 |
The empty name is commonly used as an indication of unnamed
|
wenzelm@30296
|
736 |
entities, whenever this makes any sense. The basic operations on
|
wenzelm@30296
|
737 |
qualified names are smart enough to pass through such improper names
|
wenzelm@30296
|
738 |
unchanged.
|
wenzelm@30296
|
739 |
|
wenzelm@30296
|
740 |
\medskip A \isa{naming} policy tells how to turn a name
|
wenzelm@30296
|
741 |
specification into a fully qualified internal name (by the \isa{full} operation), and how fully qualified names may be accessed
|
wenzelm@30296
|
742 |
externally. For example, the default naming policy is to prefix an
|
wenzelm@30296
|
743 |
implicit path: \isa{full\ x} produces \isa{path{\isachardot}x}, and the
|
wenzelm@30296
|
744 |
standard accesses for \isa{path{\isachardot}x} include both \isa{x} and
|
wenzelm@30296
|
745 |
\isa{path{\isachardot}x}. Normally, the naming is implicit in the theory or
|
wenzelm@30296
|
746 |
proof context; there are separate versions of the corresponding.
|
wenzelm@30296
|
747 |
|
wenzelm@30296
|
748 |
\medskip A \isa{name\ space} manages a collection of fully
|
wenzelm@30296
|
749 |
internalized names, together with a mapping between external names
|
wenzelm@30296
|
750 |
and internal names (in both directions). The corresponding \isa{intern} and \isa{extern} operations are mostly used for
|
wenzelm@30296
|
751 |
parsing and printing only! The \isa{declare} operation augments
|
wenzelm@30296
|
752 |
a name space according to the accesses determined by the naming
|
wenzelm@30296
|
753 |
policy.
|
wenzelm@30296
|
754 |
|
wenzelm@30296
|
755 |
\medskip As a general principle, there is a separate name space for
|
wenzelm@30296
|
756 |
each kind of formal entity, e.g.\ logical constant, type
|
wenzelm@30296
|
757 |
constructor, type class, theorem. It is usually clear from the
|
wenzelm@30296
|
758 |
occurrence in concrete syntax (or from the scope) which kind of
|
wenzelm@30296
|
759 |
entity a name refers to. For example, the very same name \isa{c} may be used uniformly for a constant, type constructor, and
|
wenzelm@30296
|
760 |
type class.
|
wenzelm@30296
|
761 |
|
wenzelm@30296
|
762 |
There are common schemes to name theorems systematically, according
|
wenzelm@30296
|
763 |
to the name of the main logical entity involved, e.g.\ \isa{c{\isachardot}intro} for a canonical theorem related to constant \isa{c}.
|
wenzelm@30296
|
764 |
This technique of mapping names from one space into another requires
|
wenzelm@30296
|
765 |
some care in order to avoid conflicts. In particular, theorem names
|
wenzelm@30296
|
766 |
derived from a type constructor or type class are better suffixed in
|
wenzelm@30296
|
767 |
addition to the usual qualification, e.g.\ \isa{c{\isacharunderscore}type{\isachardot}intro}
|
wenzelm@30296
|
768 |
and \isa{c{\isacharunderscore}class{\isachardot}intro} for theorems related to type \isa{c}
|
wenzelm@30296
|
769 |
and class \isa{c}, respectively.%
|
wenzelm@30296
|
770 |
\end{isamarkuptext}%
|
wenzelm@30296
|
771 |
\isamarkuptrue%
|
wenzelm@30296
|
772 |
%
|
wenzelm@30296
|
773 |
\isadelimmlref
|
wenzelm@30296
|
774 |
%
|
wenzelm@30296
|
775 |
\endisadelimmlref
|
wenzelm@30296
|
776 |
%
|
wenzelm@30296
|
777 |
\isatagmlref
|
wenzelm@30296
|
778 |
%
|
wenzelm@30296
|
779 |
\begin{isamarkuptext}%
|
wenzelm@30296
|
780 |
\begin{mldecls}
|
wenzelm@30365
|
781 |
\indexdef{}{ML}{Long\_Name.base\_name}\verb|Long_Name.base_name: string -> string| \\
|
wenzelm@30365
|
782 |
\indexdef{}{ML}{Long\_Name.qualifier}\verb|Long_Name.qualifier: string -> string| \\
|
wenzelm@30365
|
783 |
\indexdef{}{ML}{Long\_Name.append}\verb|Long_Name.append: string -> string -> string| \\
|
wenzelm@30365
|
784 |
\indexdef{}{ML}{Long\_Name.implode}\verb|Long_Name.implode: string list -> string| \\
|
wenzelm@30365
|
785 |
\indexdef{}{ML}{Long\_Name.explode}\verb|Long_Name.explode: string -> string list| \\
|
wenzelm@30296
|
786 |
\end{mldecls}
|
wenzelm@30296
|
787 |
\begin{mldecls}
|
haftmann@33174
|
788 |
\indexdef{}{ML type}{Name\_Space.naming}\verb|type Name_Space.naming| \\
|
haftmann@33174
|
789 |
\indexdef{}{ML}{Name\_Space.default\_naming}\verb|Name_Space.default_naming: Name_Space.naming| \\
|
haftmann@33174
|
790 |
\indexdef{}{ML}{Name\_Space.add\_path}\verb|Name_Space.add_path: string -> Name_Space.naming -> Name_Space.naming| \\
|
haftmann@33174
|
791 |
\indexdef{}{ML}{Name\_Space.full\_name}\verb|Name_Space.full_name: Name_Space.naming -> binding -> string| \\
|
wenzelm@30296
|
792 |
\end{mldecls}
|
wenzelm@30296
|
793 |
\begin{mldecls}
|
haftmann@33174
|
794 |
\indexdef{}{ML type}{Name\_Space.T}\verb|type Name_Space.T| \\
|
haftmann@33174
|
795 |
\indexdef{}{ML}{Name\_Space.empty}\verb|Name_Space.empty: string -> Name_Space.T| \\
|
haftmann@33174
|
796 |
\indexdef{}{ML}{Name\_Space.merge}\verb|Name_Space.merge: Name_Space.T * Name_Space.T -> Name_Space.T| \\
|
haftmann@33174
|
797 |
\indexdef{}{ML}{Name\_Space.declare}\verb|Name_Space.declare: bool -> Name_Space.naming -> binding -> Name_Space.T ->|\isasep\isanewline%
|
haftmann@33174
|
798 |
\verb| string * Name_Space.T| \\
|
haftmann@33174
|
799 |
\indexdef{}{ML}{Name\_Space.intern}\verb|Name_Space.intern: Name_Space.T -> string -> string| \\
|
haftmann@33174
|
800 |
\indexdef{}{ML}{Name\_Space.extern}\verb|Name_Space.extern: Name_Space.T -> string -> string| \\
|
wenzelm@30296
|
801 |
\end{mldecls}
|
wenzelm@30296
|
802 |
|
wenzelm@30296
|
803 |
\begin{description}
|
wenzelm@30296
|
804 |
|
wenzelm@30365
|
805 |
\item \verb|Long_Name.base_name|~\isa{name} returns the base name of a
|
wenzelm@30296
|
806 |
qualified name.
|
wenzelm@30296
|
807 |
|
wenzelm@30365
|
808 |
\item \verb|Long_Name.qualifier|~\isa{name} returns the qualifier
|
wenzelm@30296
|
809 |
of a qualified name.
|
wenzelm@30296
|
810 |
|
wenzelm@30365
|
811 |
\item \verb|Long_Name.append|~\isa{name\isactrlisub {\isadigit{1}}\ name\isactrlisub {\isadigit{2}}}
|
wenzelm@30296
|
812 |
appends two qualified names.
|
wenzelm@30296
|
813 |
|
wenzelm@30365
|
814 |
\item \verb|Long_Name.implode|~\isa{names} and \verb|Long_Name.explode|~\isa{name} convert between the packed string
|
wenzelm@30296
|
815 |
representation and the explicit list form of qualified names.
|
wenzelm@30296
|
816 |
|
haftmann@33174
|
817 |
\item \verb|Name_Space.naming| represents the abstract concept of
|
wenzelm@30296
|
818 |
a naming policy.
|
wenzelm@30296
|
819 |
|
haftmann@33174
|
820 |
\item \verb|Name_Space.default_naming| is the default naming policy.
|
wenzelm@30296
|
821 |
In a theory context, this is usually augmented by a path prefix
|
wenzelm@30296
|
822 |
consisting of the theory name.
|
wenzelm@30296
|
823 |
|
haftmann@33174
|
824 |
\item \verb|Name_Space.add_path|~\isa{path\ naming} augments the
|
wenzelm@30296
|
825 |
naming policy by extending its path component.
|
wenzelm@30296
|
826 |
|
haftmann@33174
|
827 |
\item \verb|Name_Space.full_name|~\isa{naming\ binding} turns a
|
wenzelm@30296
|
828 |
name binding (usually a basic name) into the fully qualified
|
wenzelm@30296
|
829 |
internal name, according to the given naming policy.
|
wenzelm@30296
|
830 |
|
haftmann@33174
|
831 |
\item \verb|Name_Space.T| represents name spaces.
|
wenzelm@30296
|
832 |
|
haftmann@33174
|
833 |
\item \verb|Name_Space.empty|~\isa{kind} and \verb|Name_Space.merge|~\isa{{\isacharparenleft}space\isactrlisub {\isadigit{1}}{\isacharcomma}\ space\isactrlisub {\isadigit{2}}{\isacharparenright}} are the canonical operations for
|
wenzelm@30296
|
834 |
maintaining name spaces according to theory data management
|
haftmann@33174
|
835 |
(\secref{sec:context-data}); \isa{kind} is a formal comment
|
haftmann@33174
|
836 |
to characterize the purpose of a name space.
|
wenzelm@30296
|
837 |
|
haftmann@33174
|
838 |
\item \verb|Name_Space.declare|~\isa{strict\ naming\ bindings\ space} enters a name binding as fully qualified internal name into
|
haftmann@33174
|
839 |
the name space, with external accesses determined by the naming
|
haftmann@33174
|
840 |
policy.
|
wenzelm@30296
|
841 |
|
haftmann@33174
|
842 |
\item \verb|Name_Space.intern|~\isa{space\ name} internalizes a
|
wenzelm@30296
|
843 |
(partially qualified) external name.
|
wenzelm@30296
|
844 |
|
wenzelm@30296
|
845 |
This operation is mostly for parsing! Note that fully qualified
|
haftmann@33174
|
846 |
names stemming from declarations are produced via \verb|Name_Space.full_name| and \verb|Name_Space.declare|
|
wenzelm@30296
|
847 |
(or their derivatives for \verb|theory| and
|
wenzelm@30296
|
848 |
\verb|Proof.context|).
|
wenzelm@30296
|
849 |
|
haftmann@33174
|
850 |
\item \verb|Name_Space.extern|~\isa{space\ name} externalizes a
|
wenzelm@30296
|
851 |
(fully qualified) internal name.
|
wenzelm@30296
|
852 |
|
wenzelm@30296
|
853 |
This operation is mostly for printing! User code should not rely on
|
wenzelm@30296
|
854 |
the precise result too much.
|
wenzelm@30296
|
855 |
|
wenzelm@30296
|
856 |
\end{description}%
|
wenzelm@30296
|
857 |
\end{isamarkuptext}%
|
wenzelm@30296
|
858 |
\isamarkuptrue%
|
wenzelm@30296
|
859 |
%
|
wenzelm@30296
|
860 |
\endisatagmlref
|
wenzelm@30296
|
861 |
{\isafoldmlref}%
|
wenzelm@30296
|
862 |
%
|
wenzelm@30296
|
863 |
\isadelimmlref
|
wenzelm@30296
|
864 |
%
|
wenzelm@30296
|
865 |
\endisadelimmlref
|
wenzelm@30296
|
866 |
%
|
wenzelm@30296
|
867 |
\isadelimtheory
|
wenzelm@30296
|
868 |
%
|
wenzelm@30296
|
869 |
\endisadelimtheory
|
wenzelm@30296
|
870 |
%
|
wenzelm@30296
|
871 |
\isatagtheory
|
wenzelm@30296
|
872 |
\isacommand{end}\isamarkupfalse%
|
wenzelm@30296
|
873 |
%
|
wenzelm@30296
|
874 |
\endisatagtheory
|
wenzelm@30296
|
875 |
{\isafoldtheory}%
|
wenzelm@30296
|
876 |
%
|
wenzelm@30296
|
877 |
\isadelimtheory
|
wenzelm@30296
|
878 |
%
|
wenzelm@30296
|
879 |
\endisadelimtheory
|
wenzelm@30296
|
880 |
\isanewline
|
wenzelm@30296
|
881 |
\end{isabellebody}%
|
wenzelm@30296
|
882 |
%%% Local Variables:
|
wenzelm@30296
|
883 |
%%% mode: latex
|
wenzelm@30296
|
884 |
%%% TeX-master: "root"
|
wenzelm@30296
|
885 |
%%% End:
|