doc-src/IsarImplementation/Thy/prelim.thy
author wenzelm
Wed Sep 13 21:41:25 2006 +0200 (2006-09-13)
changeset 20530 448594cbd82b
parent 20488 121bc2135bd3
child 20547 796ae7fa1049
permissions -rw-r--r--
renamed NameSpace.drop_base to NameSpace.qualifier;
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(* $Id$ *)
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theory prelim imports base begin
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chapter {* Preliminaries *}
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section {* Contexts \label{sec:context} *}
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text {*
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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 @{text "\<Gamma> \<turnstile>\<^sub>\<Theta> \<phi>"}, which means that a
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  proposition @{text "\<phi>"} is derivable from hypotheses @{text "\<Gamma>"}
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  within the theory @{text "\<Theta>"}.  There are logical reasons for
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  keeping @{text "\<Theta>"} and @{text "\<Gamma>"} 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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  @{text "\<Gamma> \<turnstile> \<phi>"} 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.\ @{text "\<Gamma> \<turnstile>\<^sub>\<Theta>
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  \<phi>"} implies @{text "\<Gamma>' \<turnstile>\<^sub>\<Theta>\<^sub>' \<phi>"} for contexts @{text "\<Theta>'
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  \<supseteq> \<Theta>"} and @{text "\<Gamma>' \<supseteq> \<Gamma>"}.
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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.\ @{text "\<Gamma>' \<turnstile>\<^sub>\<Theta> \<phi>"}
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  implies @{text "\<Gamma> \<turnstile>\<^sub>\<Theta> \<Delta> \<Longrightarrow> \<phi>"} where @{text "\<Gamma>' \<supseteq> \<Gamma>"} and
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  @{text "\<Delta> = \<Gamma>' - \<Gamma>"}.  Note that @{text "\<Theta>"} remains unchanged here,
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  only the @{text "\<Gamma>"} 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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  @{text "\<Theta>"} and @{text "\<Gamma>"} 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 @{text
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  "\<Theta>"} and @{text "\<Gamma>"} 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 @{text "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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*}
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subsection {* Theory context \label{sec:context-theory} *}
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text {*
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  \glossary{Theory}{FIXME}
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  A \emph{theory} is a data container with explicit named 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 @{text "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 @{text "begin"} operation starts a new theory by importing
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  several parent theories and entering a special @{text "draft"} mode,
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  which is sustained until the final @{text "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 @{text "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 @{text "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 @{text "Pure"}, with theory @{text "Length"}
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  importing @{text "Nat"} and @{text "List"}.  The body of @{text
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  "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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        &            & @{text "Pure"} \\
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        &            & @{text "\<down>"} \\
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        &            & @{text "FOL"} \\
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        & $\swarrow$ &              & $\searrow$ & \\
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  $Nat$ &            &              &            & @{text "List"} \\
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        & $\searrow$ &              & $\swarrow$ \\
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        &            & @{text "Length"} \\
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        &            & \multicolumn{3}{l}{~~$\isarkeyword{imports}$} \\
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        &            & \multicolumn{3}{l}{~~$\isarkeyword{begin}$} \\
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        &            & $\vdots$~~ \\
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        &            & @{text "\<bullet>"}~~ \\
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        &            & $\vdots$~~ \\
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        &            & @{text "\<bullet>"}~~ \\
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        &            & $\vdots$~~ \\
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        &            & \multicolumn{3}{l}{~~$\isarkeyword{end}$} \\
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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 @{text "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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*}
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text %mlref {*
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  \begin{mldecls}
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  @{index_ML_type theory} \\
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  @{index_ML Theory.subthy: "theory * theory -> bool"} \\
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  @{index_ML Theory.merge: "theory * theory -> theory"} \\
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  @{index_ML Theory.checkpoint: "theory -> theory"} \\
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  @{index_ML Theory.copy: "theory -> theory"} \\[1ex]
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  @{index_ML_type theory_ref} \\
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  @{index_ML Theory.self_ref: "theory -> theory_ref"} \\
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  @{index_ML Theory.deref: "theory_ref -> theory"} \\
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  \end{mldecls}
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  \begin{description}
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  \item @{ML_type 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 @{ML "Theory.subthy"}~@{text "(thy\<^sub>1, thy\<^sub>2)"}
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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 (@{text "\<subseteq>"}) of the corresponding content.
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  \item @{ML "Theory.merge"}~@{text "(thy\<^sub>1, thy\<^sub>2)"}
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  absorbs one theory into the other.  This fails for unrelated
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  theories!
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  \item @{ML "Theory.checkpoint"}~@{text "thy"} produces a safe
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  stepping stone in the linear development of @{text "thy"}.  The next
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  update will result in two related, valid theories.
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  \item @{ML "Theory.copy"}~@{text "thy"} produces a variant of @{text
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  "thy"} that holds a copy of the same data.  The result is not
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  related to the original; the original is unchanched.
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  \item @{ML_type 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 @{ML "Theory.self_ref"}~@{text "thy"} and @{ML
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  "Theory.deref"}~@{text "thy_ref"} convert between @{ML_type
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  "theory"} and @{ML_type "theory_ref"}.  As the referenced theory
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  evolves monotonically over time, later invocations of @{ML
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  "Theory.deref"} may refer to a larger context.
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  \end{description}
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*}
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subsection {* Proof context \label{sec:context-proof} *}
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text {*
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  \glossary{Proof context}{The static context of a structured proof,
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  acts like a local ``theory'' of the current portion of Isar proof
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  text, generalizes the idea of local hypotheses @{text "\<Gamma>"} in
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  judgments @{text "\<Gamma> \<turnstile> \<phi>"} of natural deduction calculi.  There is a
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  generic notion of introducing and discharging hypotheses.
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  Arbritrary auxiliary context data may be adjoined.}
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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 @{text "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 @{text "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 @{text "\<Gamma> \<turnstile> \<phi>"}, just to make double
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  sure.  Results could still leak into an alien proof context do 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 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, cf.\ \secref{sec:isar-proof-state}.
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*}
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text %mlref {*
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  \begin{mldecls}
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  @{index_ML_type Proof.context} \\
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  @{index_ML ProofContext.init: "theory -> Proof.context"} \\
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  @{index_ML ProofContext.theory_of: "Proof.context -> theory"} \\
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  @{index_ML ProofContext.transfer: "theory -> Proof.context -> Proof.context"} \\
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  \end{mldecls}
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  \begin{description}
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  \item @{ML_type Proof.context} represents proof contexts.  Elements
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  of this type are essentially pure values, with a sliding reference
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  to the background theory.
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  \item @{ML ProofContext.init}~@{text "thy"} produces a proof context
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  derived from @{text "thy"}, initializing all data.
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  \item @{ML ProofContext.theory_of}~@{text "ctxt"} selects the
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  background theory from @{text "ctxt"}, dereferencing its internal
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  @{ML_type theory_ref}.
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  \item @{ML ProofContext.transfer}~@{text "thy ctxt"} promotes the
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  background theory of @{text "ctxt"} to the super theory @{text
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  "thy"}.
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  \end{description}
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*}
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subsection {* Generic contexts \label{sec:generic-context} *}
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text {*
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  A generic context is the disjoint sum of either a theory or proof
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  context.  Occasionally, this enables uniform treatment of generic
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  context data, typically extra-logical information.  Operations on
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  generic contexts include the usual injections, partial selections,
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  and combinators for lifting operations on either component of the
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  disjoint sum.
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  Moreover, there are total operations @{text "theory_of"} and @{text
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  "proof_of"} to convert a generic context into either kind: a theory
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  can always be selected from the sum, while a proof context might
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  have to be constructed by an ad-hoc @{text "init"} operation.
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*}
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text %mlref {*
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  \begin{mldecls}
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  @{index_ML_type Context.generic} \\
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  @{index_ML Context.theory_of: "Context.generic -> theory"} \\
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  @{index_ML Context.proof_of: "Context.generic -> Proof.context"} \\
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  \end{mldecls}
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  \begin{description}
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  \item @{ML_type Context.generic} is the direct sum of @{ML_type
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  "theory"} and @{ML_type "Proof.context"}, with the datatype
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  constructors @{ML "Context.Theory"} and @{ML "Context.Proof"}.
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  \item @{ML Context.theory_of}~@{text "context"} always produces a
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  theory from the generic @{text "context"}, using @{ML
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  "ProofContext.theory_of"} as required.
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  \item @{ML Context.proof_of}~@{text "context"} always produces a
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  proof context from the generic @{text "context"}, using @{ML
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  "ProofContext.init"} as required (note that this re-initializes the
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  context data with each invocation).
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  \end{description}
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*}
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subsection {* Context data \label{sec:context-data} *}
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text {*
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  The main purpose of theory and proof contexts is to manage arbitrary
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  data.  New data types can be declared incrementally at compile time.
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  There are separate declaration mechanisms for any of the three kinds
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  of contexts: theory, proof, generic.
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  \paragraph{Theory data} may refer to destructive entities, which are
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  maintained in direct correspondence to the linear evolution of
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  theory values, including explicit copies.\footnote{Most existing
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  instances of destructive theory data are merely historical relics
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  (e.g.\ the destructive theorem storage, and destructive hints for
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  the Simplifier and Classical rules).}  A theory data declaration
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  needs to implement the following specification (depending on type
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  @{text "T"}):
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  \medskip
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  \begin{tabular}{ll}
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  @{text "name: string"} \\
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  @{text "empty: T"} & initial value \\
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  @{text "copy: T \<rightarrow> T"} & refresh impure data \\
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   327
  @{text "extend: T \<rightarrow> T"} & re-initialize on import \\
wenzelm@20449
   328
  @{text "merge: T \<times> T \<rightarrow> T"} & join on import \\
wenzelm@20449
   329
  @{text "print: T \<rightarrow> unit"} & diagnostic output \\
wenzelm@20449
   330
  \end{tabular}
wenzelm@20449
   331
  \medskip
wenzelm@20449
   332
wenzelm@20449
   333
  \noindent The @{text "name"} acts as a comment for diagnostic
wenzelm@20449
   334
  messages; @{text "copy"} is just the identity for pure data; @{text
wenzelm@20449
   335
  "extend"} is acts like a unitary version of @{text "merge"}, both
wenzelm@20449
   336
  should also include the functionality of @{text "copy"} for impure
wenzelm@20449
   337
  data.
wenzelm@20449
   338
wenzelm@20451
   339
  \paragraph{Proof context data} is purely functional.  A declaration
wenzelm@20451
   340
  needs to implement the following specification:
wenzelm@20449
   341
wenzelm@20449
   342
  \medskip
wenzelm@20449
   343
  \begin{tabular}{ll}
wenzelm@20449
   344
  @{text "name: string"} \\
wenzelm@20449
   345
  @{text "init: theory \<rightarrow> T"} & produce initial value \\
wenzelm@20449
   346
  @{text "print: T \<rightarrow> unit"} & diagnostic output \\
wenzelm@20449
   347
  \end{tabular}
wenzelm@20449
   348
  \medskip
wenzelm@20449
   349
wenzelm@20449
   350
  \noindent The @{text "init"} operation is supposed to produce a pure
wenzelm@20451
   351
  value from the given background theory.  The remainder is analogous
wenzelm@20451
   352
  to theory data.
wenzelm@20449
   353
wenzelm@20451
   354
  \paragraph{Generic data} provides a hybrid interface for both theory
wenzelm@20451
   355
  and proof data.  The declaration is essentially the same as for
wenzelm@20451
   356
  (pure) theory data, without @{text "copy"}, though.  The @{text
wenzelm@20451
   357
  "init"} operation for proof contexts merely selects the current data
wenzelm@20451
   358
  value from the background theory.
wenzelm@20449
   359
wenzelm@20449
   360
  \bigskip In any case, a data declaration of type @{text "T"} results
wenzelm@20449
   361
  in the following interface:
wenzelm@20449
   362
wenzelm@20449
   363
  \medskip
wenzelm@20449
   364
  \begin{tabular}{ll}
wenzelm@20449
   365
  @{text "init: theory \<rightarrow> theory"} \\
wenzelm@20449
   366
  @{text "get: context \<rightarrow> T"} \\
wenzelm@20449
   367
  @{text "put: T \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   368
  @{text "map: (T \<rightarrow> T) \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   369
  @{text "print: context \<rightarrow> unit"}
wenzelm@20449
   370
  \end{tabular}
wenzelm@20449
   371
  \medskip
wenzelm@20449
   372
wenzelm@20449
   373
  \noindent Here @{text "init"} needs to be applied to the current
wenzelm@20449
   374
  theory context once, in order to register the initial setup.  The
wenzelm@20449
   375
  other operations provide access for the particular kind of context
wenzelm@20449
   376
  (theory, proof, or generic context).  Note that this is a safe
wenzelm@20449
   377
  interface: there is no other way to access the corresponding data
wenzelm@20451
   378
  slot of a context.  By keeping these operations private, a component
wenzelm@20451
   379
  may maintain abstract values authentically, without other components
wenzelm@20451
   380
  interfering.
wenzelm@20447
   381
*}
wenzelm@20447
   382
wenzelm@20450
   383
text %mlref {*
wenzelm@20450
   384
  \begin{mldecls}
wenzelm@20450
   385
  @{index_ML_functor TheoryDataFun} \\
wenzelm@20450
   386
  @{index_ML_functor ProofDataFun} \\
wenzelm@20450
   387
  @{index_ML_functor GenericDataFun} \\
wenzelm@20450
   388
  \end{mldecls}
wenzelm@20450
   389
wenzelm@20450
   390
  \begin{description}
wenzelm@20450
   391
wenzelm@20450
   392
  \item @{ML_functor TheoryDataFun}@{text "(spec)"} declares data for
wenzelm@20450
   393
  type @{ML_type theory} according to the specification provided as
wenzelm@20451
   394
  argument structure.  The resulting structure provides data init and
wenzelm@20451
   395
  access operations as described above.
wenzelm@20450
   396
wenzelm@20470
   397
  \item @{ML_functor ProofDataFun}@{text "(spec)"} is analogous to
wenzelm@20470
   398
  @{ML_functor TheoryDataFun} for type @{ML_type Proof.context}.
wenzelm@20450
   399
wenzelm@20470
   400
  \item @{ML_functor GenericDataFun}@{text "(spec)"} is analogous to
wenzelm@20470
   401
  @{ML_functor TheoryDataFun} for type @{ML_type Context.generic}.
wenzelm@20450
   402
wenzelm@20450
   403
  \end{description}
wenzelm@20450
   404
*}
wenzelm@20450
   405
wenzelm@20447
   406
wenzelm@20476
   407
section {* Names *}
wenzelm@20451
   408
wenzelm@20476
   409
text {*
wenzelm@20476
   410
  In principle, a name is just a string, but there are various
wenzelm@20488
   411
  convention for encoding additional structure.  For example, ``@{text
wenzelm@20488
   412
  "Foo.bar.baz"}'' is considered as a qualified name consisting of
wenzelm@20488
   413
  three basic name components.  The individual constituents of a name
wenzelm@20488
   414
  may have further substructure, e.g.\ the string
wenzelm@20488
   415
  ``\verb,\,\verb,<alpha>,'' encodes as a single symbol.
wenzelm@20451
   416
*}
wenzelm@20437
   417
wenzelm@20437
   418
wenzelm@20437
   419
subsection {* Strings of symbols *}
wenzelm@20437
   420
wenzelm@20476
   421
text {*
wenzelm@20476
   422
  \glossary{Symbol}{The smallest unit of text in Isabelle, subsumes
wenzelm@20476
   423
  plain ASCII characters as well as an infinite collection of named
wenzelm@20476
   424
  symbols (for greek, math etc.).}
wenzelm@20470
   425
wenzelm@20476
   426
  A \emph{symbol} constitutes the smallest textual unit in Isabelle
wenzelm@20488
   427
  --- raw characters are normally not encountered at all.  Isabelle
wenzelm@20488
   428
  strings consist of a sequence of symbols, represented as a packed
wenzelm@20488
   429
  string or a list of strings.  Each symbol is in itself a small
wenzelm@20488
   430
  string, which has either one of the following forms:
wenzelm@20437
   431
wenzelm@20451
   432
  \begin{enumerate}
wenzelm@20437
   433
wenzelm@20488
   434
  \item a single ASCII character ``@{text "c"}'', for example
wenzelm@20488
   435
  ``\verb,a,'',
wenzelm@20437
   436
wenzelm@20488
   437
  \item a regular symbol ``\verb,\,\verb,<,@{text "ident"}\verb,>,'',
wenzelm@20476
   438
  for example ``\verb,\,\verb,<alpha>,'',
wenzelm@20437
   439
wenzelm@20488
   440
  \item a control symbol ``\verb,\,\verb,<^,@{text "ident"}\verb,>,'',
wenzelm@20476
   441
  for example ``\verb,\,\verb,<^bold>,'',
wenzelm@20437
   442
wenzelm@20488
   443
  \item a raw symbol ``\verb,\,\verb,<^raw:,@{text text}\verb,>,''
wenzelm@20488
   444
  where @{text text} constists of printable characters excluding
wenzelm@20476
   445
  ``\verb,.,'' and ``\verb,>,'', for example
wenzelm@20476
   446
  ``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
wenzelm@20437
   447
wenzelm@20488
   448
  \item a numbered raw control symbol ``\verb,\,\verb,<^raw,@{text
wenzelm@20476
   449
  n}\verb,>, where @{text n} consists of digits, for example
wenzelm@20451
   450
  ``\verb,\,\verb,<^raw42>,''.
wenzelm@20437
   451
wenzelm@20451
   452
  \end{enumerate}
wenzelm@20437
   453
wenzelm@20476
   454
  \noindent The @{text "ident"} syntax for symbol names is @{text
wenzelm@20476
   455
  "letter (letter | digit)\<^sup>*"}, where @{text "letter =
wenzelm@20476
   456
  A..Za..z"} and @{text "digit = 0..9"}.  There are infinitely many
wenzelm@20476
   457
  regular symbols and control symbols, but a fixed collection of
wenzelm@20476
   458
  standard symbols is treated specifically.  For example,
wenzelm@20488
   459
  ``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it
wenzelm@20488
   460
  may occur within regular Isabelle identifiers.
wenzelm@20437
   461
wenzelm@20488
   462
  Since the character set underlying Isabelle symbols is 7-bit ASCII
wenzelm@20488
   463
  and 8-bit characters are passed through transparently, Isabelle may
wenzelm@20488
   464
  also process Unicode/UCS data in UTF-8 encoding.  Unicode provides
wenzelm@20488
   465
  its own collection of mathematical symbols, but there is no built-in
wenzelm@20488
   466
  link to the standard collection of Isabelle.
wenzelm@20476
   467
wenzelm@20476
   468
  \medskip Output of Isabelle symbols depends on the print mode
wenzelm@20476
   469
  (\secref{FIXME}).  For example, the standard {\LaTeX} setup of the
wenzelm@20476
   470
  Isabelle document preparation system would present
wenzelm@20451
   471
  ``\verb,\,\verb,<alpha>,'' as @{text "\<alpha>"}, and
wenzelm@20451
   472
  ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as @{text
wenzelm@20451
   473
  "\<^bold>\<alpha>"}.
wenzelm@20451
   474
*}
wenzelm@20437
   475
wenzelm@20437
   476
text %mlref {*
wenzelm@20437
   477
  \begin{mldecls}
wenzelm@20437
   478
  @{index_ML_type "Symbol.symbol"} \\
wenzelm@20437
   479
  @{index_ML Symbol.explode: "string -> Symbol.symbol list"} \\
wenzelm@20437
   480
  @{index_ML Symbol.is_letter: "Symbol.symbol -> bool"} \\
wenzelm@20437
   481
  @{index_ML Symbol.is_digit: "Symbol.symbol -> bool"} \\
wenzelm@20437
   482
  @{index_ML Symbol.is_quasi: "Symbol.symbol -> bool"} \\
wenzelm@20451
   483
  @{index_ML Symbol.is_blank: "Symbol.symbol -> bool"} \\[1ex]
wenzelm@20437
   484
  @{index_ML_type "Symbol.sym"} \\
wenzelm@20437
   485
  @{index_ML Symbol.decode: "Symbol.symbol -> Symbol.sym"} \\
wenzelm@20437
   486
  \end{mldecls}
wenzelm@20437
   487
wenzelm@20437
   488
  \begin{description}
wenzelm@20437
   489
wenzelm@20488
   490
  \item @{ML_type "Symbol.symbol"} represents individual Isabelle
wenzelm@20488
   491
  symbols; this is an alias for @{ML_type "string"}.
wenzelm@20437
   492
wenzelm@20476
   493
  \item @{ML "Symbol.explode"}~@{text "str"} produces a symbol list
wenzelm@20488
   494
  from the packed form.  This function supercedes @{ML
wenzelm@20476
   495
  "String.explode"} for virtually all purposes of manipulating text in
wenzelm@20476
   496
  Isabelle!
wenzelm@20437
   497
wenzelm@20437
   498
  \item @{ML "Symbol.is_letter"}, @{ML "Symbol.is_digit"}, @{ML
wenzelm@20476
   499
  "Symbol.is_quasi"}, @{ML "Symbol.is_blank"} classify standard
wenzelm@20476
   500
  symbols according to fixed syntactic conventions of Isabelle, cf.\
wenzelm@20476
   501
  \cite{isabelle-isar-ref}.
wenzelm@20437
   502
wenzelm@20437
   503
  \item @{ML_type "Symbol.sym"} is a concrete datatype that represents
wenzelm@20488
   504
  the different kinds of symbols explicitly, with constructors @{ML
wenzelm@20488
   505
  "Symbol.Char"}, @{ML "Symbol.Sym"}, @{ML "Symbol.Ctrl"}, @{ML
wenzelm@20451
   506
  "Symbol.Raw"}.
wenzelm@20437
   507
wenzelm@20437
   508
  \item @{ML "Symbol.decode"} converts the string representation of a
wenzelm@20451
   509
  symbol into the datatype version.
wenzelm@20437
   510
wenzelm@20437
   511
  \end{description}
wenzelm@20437
   512
*}
wenzelm@20437
   513
wenzelm@20437
   514
wenzelm@20476
   515
subsection {* Basic names \label{sec:basic-names} *}
wenzelm@20476
   516
wenzelm@20476
   517
text {*
wenzelm@20476
   518
  A \emph{basic name} essentially consists of a single Isabelle
wenzelm@20476
   519
  identifier.  There are conventions to mark separate classes of basic
wenzelm@20476
   520
  names, by attaching a suffix of underscores (@{text "_"}): one
wenzelm@20476
   521
  underscore means \emph{internal name}, two underscores means
wenzelm@20476
   522
  \emph{Skolem name}, three underscores means \emph{internal Skolem
wenzelm@20476
   523
  name}.
wenzelm@20476
   524
wenzelm@20476
   525
  For example, the basic name @{text "foo"} has the internal version
wenzelm@20476
   526
  @{text "foo_"}, with Skolem versions @{text "foo__"} and @{text
wenzelm@20476
   527
  "foo___"}, respectively.
wenzelm@20476
   528
wenzelm@20488
   529
  These special versions provide copies of the basic name space, apart
wenzelm@20488
   530
  from anything that normally appears in the user text.  For example,
wenzelm@20488
   531
  system generated variables in Isar proof contexts are usually marked
wenzelm@20488
   532
  as internal, which prevents mysterious name references like @{text
wenzelm@20488
   533
  "xaa"} to appear in the text.
wenzelm@20476
   534
wenzelm@20488
   535
  \medskip Manipulating binding scopes often requires on-the-fly
wenzelm@20488
   536
  renamings.  A \emph{name context} contains a collection of already
wenzelm@20488
   537
  used names.  The @{text "declare"} operation adds names to the
wenzelm@20488
   538
  context.
wenzelm@20476
   539
wenzelm@20488
   540
  The @{text "invents"} operation derives a number of fresh names from
wenzelm@20488
   541
  a given starting point.  For example, the first three names derived
wenzelm@20488
   542
  from @{text "a"} are @{text "a"}, @{text "b"}, @{text "c"}.
wenzelm@20476
   543
wenzelm@20476
   544
  The @{text "variants"} operation produces fresh names by
wenzelm@20488
   545
  incrementing tentative names as base-26 numbers (with digits @{text
wenzelm@20488
   546
  "a..z"}) until all clashes are resolved.  For example, name @{text
wenzelm@20488
   547
  "foo"} results in variants @{text "fooa"}, @{text "foob"}, @{text
wenzelm@20488
   548
  "fooc"}, \dots, @{text "fooaa"}, @{text "fooab"} etc.; each renaming
wenzelm@20488
   549
  step picks the next unused variant from this sequence.
wenzelm@20476
   550
*}
wenzelm@20476
   551
wenzelm@20476
   552
text %mlref {*
wenzelm@20476
   553
  \begin{mldecls}
wenzelm@20476
   554
  @{index_ML Name.internal: "string -> string"} \\
wenzelm@20476
   555
  @{index_ML Name.skolem: "string -> string"} \\[1ex]
wenzelm@20476
   556
  @{index_ML_type Name.context} \\
wenzelm@20476
   557
  @{index_ML Name.context: Name.context} \\
wenzelm@20476
   558
  @{index_ML Name.declare: "string -> Name.context -> Name.context"} \\
wenzelm@20476
   559
  @{index_ML Name.invents: "Name.context -> string -> int -> string list"} \\
wenzelm@20476
   560
  @{index_ML Name.variants: "string list -> Name.context -> string list * Name.context"} \\
wenzelm@20476
   561
  \end{mldecls}
wenzelm@20476
   562
wenzelm@20476
   563
  \begin{description}
wenzelm@20476
   564
wenzelm@20476
   565
  \item @{ML Name.internal}~@{text "name"} produces an internal name
wenzelm@20476
   566
  by adding one underscore.
wenzelm@20476
   567
wenzelm@20476
   568
  \item @{ML Name.skolem}~@{text "name"} produces a Skolem name by
wenzelm@20476
   569
  adding two underscores.
wenzelm@20476
   570
wenzelm@20476
   571
  \item @{ML_type Name.context} represents the context of already used
wenzelm@20476
   572
  names; the initial value is @{ML "Name.context"}.
wenzelm@20476
   573
wenzelm@20488
   574
  \item @{ML Name.declare}~@{text "name"} enters a used name into the
wenzelm@20488
   575
  context.
wenzelm@20437
   576
wenzelm@20488
   577
  \item @{ML Name.invents}~@{text "context name n"} produces @{text
wenzelm@20488
   578
  "n"} fresh names derived from @{text "name"}.
wenzelm@20488
   579
wenzelm@20488
   580
  \item @{ML Name.variants}~@{text "names context"} produces fresh
wenzelm@20488
   581
  varians of @{text "names"}; the result is entered into the context.
wenzelm@20476
   582
wenzelm@20476
   583
  \end{description}
wenzelm@20476
   584
*}
wenzelm@20476
   585
wenzelm@20476
   586
wenzelm@20476
   587
subsection {* Indexed names *}
wenzelm@20476
   588
wenzelm@20476
   589
text {*
wenzelm@20476
   590
  An \emph{indexed name} (or @{text "indexname"}) is a pair of a basic
wenzelm@20488
   591
  name and a natural number.  This representation allows efficient
wenzelm@20488
   592
  renaming by incrementing the second component only.  The canonical
wenzelm@20488
   593
  way to rename two collections of indexnames apart from each other is
wenzelm@20488
   594
  this: determine the maximum index @{text "maxidx"} of the first
wenzelm@20488
   595
  collection, then increment all indexes of the second collection by
wenzelm@20488
   596
  @{text "maxidx + 1"}; the maximum index of an empty collection is
wenzelm@20488
   597
  @{text "-1"}.
wenzelm@20476
   598
wenzelm@20488
   599
  Occasionally, basic names and indexed names are injected into the
wenzelm@20488
   600
  same pair type: the (improper) indexname @{text "(x, -1)"} is used
wenzelm@20488
   601
  to encode basic names.
wenzelm@20488
   602
wenzelm@20488
   603
  \medskip Isabelle syntax observes the following rules for
wenzelm@20488
   604
  representing an indexname @{text "(x, i)"} as a packed string:
wenzelm@20476
   605
wenzelm@20476
   606
  \begin{itemize}
wenzelm@20476
   607
wenzelm@20479
   608
  \item @{text "?x"} if @{text "x"} does not end with a digit and @{text "i = 0"},
wenzelm@20476
   609
wenzelm@20476
   610
  \item @{text "?xi"} if @{text "x"} does not end with a digit,
wenzelm@20476
   611
wenzelm@20488
   612
  \item @{text "?x.i"} otherwise.
wenzelm@20476
   613
wenzelm@20476
   614
  \end{itemize}
wenzelm@20470
   615
wenzelm@20488
   616
  Indexnames may acquire large index numbers over time.  Results are
wenzelm@20488
   617
  normalized towards @{text "0"} at certain checkpoints, notably at
wenzelm@20488
   618
  the end of a proof.  This works by producing variants of the
wenzelm@20488
   619
  corresponding basic name components.  For example, the collection
wenzelm@20488
   620
  @{text "?x1, ?x7, ?x42"} becomes @{text "?x, ?xa, ?xb"}.
wenzelm@20476
   621
*}
wenzelm@20476
   622
wenzelm@20476
   623
text %mlref {*
wenzelm@20476
   624
  \begin{mldecls}
wenzelm@20476
   625
  @{index_ML_type indexname} \\
wenzelm@20476
   626
  \end{mldecls}
wenzelm@20476
   627
wenzelm@20476
   628
  \begin{description}
wenzelm@20476
   629
wenzelm@20476
   630
  \item @{ML_type indexname} represents indexed names.  This is an
wenzelm@20476
   631
  abbreviation for @{ML_type "string * int"}.  The second component is
wenzelm@20476
   632
  usually non-negative, except for situations where @{text "(x, -1)"}
wenzelm@20488
   633
  is used to embed basic names into this type.
wenzelm@20476
   634
wenzelm@20476
   635
  \end{description}
wenzelm@20476
   636
*}
wenzelm@20476
   637
wenzelm@20476
   638
wenzelm@20476
   639
subsection {* Qualified names and name spaces *}
wenzelm@20476
   640
wenzelm@20476
   641
text {*
wenzelm@20476
   642
  A \emph{qualified name} consists of a non-empty sequence of basic
wenzelm@20488
   643
  name components.  The packed representation uses a dot as separator,
wenzelm@20488
   644
  as in ``@{text "A.b.c"}''.  The last component is called \emph{base}
wenzelm@20488
   645
  name, the remaining prefix \emph{qualifier} (which may be empty).
wenzelm@20488
   646
  The idea of qualified names is to encode nested structures by
wenzelm@20488
   647
  recording the access paths as qualifiers.  For example, an item
wenzelm@20488
   648
  named ``@{text "A.b.c"}'' may be understood as a local entity @{text
wenzelm@20488
   649
  "c"}, within a local structure @{text "b"}, within a global
wenzelm@20488
   650
  structure @{text "A"}.  Typically, name space hierarchies consist of
wenzelm@20488
   651
  1--2 levels of qualification, but this need not be always so.
wenzelm@20437
   652
wenzelm@20476
   653
  The empty name is commonly used as an indication of unnamed
wenzelm@20488
   654
  entities, whenever this makes any sense.  The basic operations on
wenzelm@20488
   655
  qualified names are smart enough to pass through such improper names
wenzelm@20476
   656
  unchanged.
wenzelm@20476
   657
wenzelm@20476
   658
  \medskip A @{text "naming"} policy tells how to turn a name
wenzelm@20476
   659
  specification into a fully qualified internal name (by the @{text
wenzelm@20488
   660
  "full"} operation), and how fully qualified names may be accessed
wenzelm@20488
   661
  externally.  For example, the default naming policy is to prefix an
wenzelm@20488
   662
  implicit path: @{text "full x"} produces @{text "path.x"}, and the
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  standard accesses for @{text "path.x"} include both @{text "x"} and
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  @{text "path.x"}.  Normally, the naming is implicit in the theory or
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  proof context; there are separate versions of the corresponding.
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  \medskip A @{text "name space"} manages a collection of fully
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  internalized names, together with a mapping between external names
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  and internal names (in both directions).  The corresponding @{text
wenzelm@20476
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  "intern"} and @{text "extern"} operations are mostly used for
wenzelm@20476
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  parsing and printing only!  The @{text "declare"} operation augments
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  a name space according to the accesses determined by the naming
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  policy.
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   674
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  \medskip As a general principle, there is a separate name space for
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  each kind of formal entity, e.g.\ logical constant, type
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  constructor, type class, theorem.  It is usually clear from the
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  occurrence in concrete syntax (or from the scope) which kind of
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  entity a name refers to.  For example, the very same name @{text
wenzelm@20488
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  "c"} may be used uniformly for a constant, type constructor, and
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  type class.
wenzelm@20476
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  There are common schemes to name theorems systematically, according
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  to the name of the main logical entity involved, e.g.\ @{text
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  "c.intro"} for a canonical theorem related to constant @{text "c"}.
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  This technique of mapping names from one space into another requires
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  some care in order to avoid conflicts.  In particular, theorem names
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  derived from a type constructor or type class are better suffixed in
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  addition to the usual qualification, e.g.\ @{text "c_type.intro"}
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  and @{text "c_class.intro"} for theorems related to type @{text "c"}
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  and class @{text "c"}, respectively.
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*}
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text %mlref {*
wenzelm@20476
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  \begin{mldecls}
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  @{index_ML NameSpace.base: "string -> string"} \\
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  @{index_ML NameSpace.qualifier: "string -> string"} \\
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  @{index_ML NameSpace.append: "string -> string -> string"} \\
wenzelm@20476
   699
  @{index_ML NameSpace.pack: "string list -> string"} \\
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  @{index_ML NameSpace.unpack: "string -> string list"} \\[1ex]
wenzelm@20476
   701
  @{index_ML_type NameSpace.naming} \\
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  @{index_ML NameSpace.default_naming: NameSpace.naming} \\
wenzelm@20476
   703
  @{index_ML NameSpace.add_path: "string -> NameSpace.naming -> NameSpace.naming"} \\
wenzelm@20476
   704
  @{index_ML NameSpace.full: "NameSpace.naming -> string -> string"} \\[1ex]
wenzelm@20476
   705
  @{index_ML_type NameSpace.T} \\
wenzelm@20476
   706
  @{index_ML NameSpace.empty: NameSpace.T} \\
wenzelm@20476
   707
  @{index_ML NameSpace.merge: "NameSpace.T * NameSpace.T -> NameSpace.T"} \\
wenzelm@20476
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  @{index_ML NameSpace.declare: "NameSpace.naming -> string -> NameSpace.T -> NameSpace.T"} \\
wenzelm@20476
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  @{index_ML NameSpace.intern: "NameSpace.T -> string -> string"} \\
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  @{index_ML NameSpace.extern: "NameSpace.T -> string -> string"} \\
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   711
  \end{mldecls}
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   713
  \begin{description}
wenzelm@20476
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  \item @{ML NameSpace.base}~@{text "name"} returns the base name of a
wenzelm@20476
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  qualified name.
wenzelm@20476
   717
wenzelm@20530
   718
  \item @{ML NameSpace.qualifier}~@{text "name"} returns the qualifier
wenzelm@20476
   719
  of a qualified name.
wenzelm@20437
   720
wenzelm@20476
   721
  \item @{ML NameSpace.append}~@{text "name\<^isub>1 name\<^isub>2"}
wenzelm@20476
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  appends two qualified names.
wenzelm@20437
   723
wenzelm@20488
   724
  \item @{ML NameSpace.pack}~@{text "name"} and @{ML
wenzelm@20488
   725
  NameSpace.unpack}~@{text "names"} convert between the packed string
wenzelm@20488
   726
  representation and the explicit list form of qualified names.
wenzelm@20476
   727
wenzelm@20476
   728
  \item @{ML_type NameSpace.naming} represents the abstract concept of
wenzelm@20476
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  a naming policy.
wenzelm@20437
   730
wenzelm@20476
   731
  \item @{ML NameSpace.default_naming} is the default naming policy.
wenzelm@20476
   732
  In a theory context, this is usually augmented by a path prefix
wenzelm@20476
   733
  consisting of the theory name.
wenzelm@20476
   734
wenzelm@20476
   735
  \item @{ML NameSpace.add_path}~@{text "path naming"} augments the
wenzelm@20488
   736
  naming policy by extending its path component.
wenzelm@20437
   737
wenzelm@20476
   738
  \item @{ML NameSpace.full}@{text "naming name"} turns a name
wenzelm@20476
   739
  specification (usually a basic name) into the fully qualified
wenzelm@20476
   740
  internal version, according to the given naming policy.
wenzelm@20476
   741
wenzelm@20476
   742
  \item @{ML_type NameSpace.T} represents name spaces.
wenzelm@20476
   743
wenzelm@20476
   744
  \item @{ML NameSpace.empty} and @{ML NameSpace.merge}~@{text
wenzelm@20488
   745
  "(space\<^isub>1, space\<^isub>2)"} are the canonical operations for
wenzelm@20488
   746
  maintaining name spaces according to theory data management
wenzelm@20488
   747
  (\secref{sec:context-data}).
wenzelm@20437
   748
wenzelm@20476
   749
  \item @{ML NameSpace.declare}~@{text "naming name space"} enters a
wenzelm@20488
   750
  fully qualified name into the name space, with external accesses
wenzelm@20488
   751
  determined by the naming policy.
wenzelm@20476
   752
wenzelm@20476
   753
  \item @{ML NameSpace.intern}~@{text "space name"} internalizes a
wenzelm@20476
   754
  (partially qualified) external name.
wenzelm@20437
   755
wenzelm@20488
   756
  This operation is mostly for parsing!  Note that fully qualified
wenzelm@20476
   757
  names stemming from declarations are produced via @{ML
wenzelm@20488
   758
  "NameSpace.full"} (or its derivatives for @{ML_type theory} and
wenzelm@20488
   759
  @{ML_type Proof.context}).
wenzelm@20437
   760
wenzelm@20476
   761
  \item @{ML NameSpace.extern}~@{text "space name"} externalizes a
wenzelm@20476
   762
  (fully qualified) internal name.
wenzelm@20476
   763
wenzelm@20488
   764
  This operation is mostly for printing!  Note unqualified names are
wenzelm@20476
   765
  produced via @{ML NameSpace.base}.
wenzelm@20476
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wenzelm@20476
   767
  \end{description}
wenzelm@20476
   768
*}
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   770
end