doc-src/IsarImplementation/Thy/Prelim.thy
author wenzelm
Fri Sep 24 15:53:13 2010 +0200 (2010-09-24)
changeset 39687 4e9b6ada3a21
parent 37533 d775bd70f571
child 39821 bf164c153d10
permissions -rw-r--r--
modernized structure Ord_List;
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theory Prelim
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imports Base
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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 {* A \emph{theory} is a data container with explicit name and
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  unique 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.  To this end, the system maintains a set of
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  symbolic ``identification stamps'' within each theory.
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  In order to avoid the full-scale overhead of explicit sub-theory
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  identification of arbitrary intermediate stages, a theory is
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  switched into @{text "draft"} mode under certain circumstances.  A
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  draft theory acts like a linear type, where updates invalidate
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  earlier versions.  An invalidated draft is called \emph{stale}.
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  The @{text "checkpoint"} operation produces a safe stepping stone
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  that will survive the next update without becoming stale: both the
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  old and the new theory remain valid and are related by the
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  sub-theory relation.  Checkpointing essentially recovers purely
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  functional theory values, at the expense of some extra internal
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  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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  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 (according 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 mode of nameless
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  incremental updates, until the final @{text "end"} operation is
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  performed.
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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 internally, while transaction boundaries of Isar top-level
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  commands (\secref{sec:isar-toplevel}) are guaranteed to be safe
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  checkpoints.
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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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  @{text "Nat"} &    &              &            & @{text "List"} \\
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        & $\searrow$ &              & $\swarrow$ \\
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        &            & @{text "Length"} \\
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        &            & \multicolumn{3}{l}{~~@{keyword "imports"}} \\
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        &            & \multicolumn{3}{l}{~~@{keyword "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}{~~@{command "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.checkpoint: "theory -> theory"} \\
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  @{index_ML Theory.copy: "theory -> theory"} \\
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  @{index_ML Theory.merge: "theory * theory -> theory"} \\
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  @{index_ML Theory.begin_theory: "string -> theory list -> theory"} \\
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  \end{mldecls}
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  \begin{mldecls}
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  @{index_ML_type theory_ref} \\
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  @{index_ML Theory.deref: "theory_ref -> theory"} \\
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  @{index_ML Theory.check_thy: "theory -> theory_ref"} \\
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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, with explicit runtime checking!  Most
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  internal theory operations destroy the original version, which then
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  becomes ``stale''.
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  \item @{ML "Theory.subthy"}~@{text "(thy\<^sub>1, thy\<^sub>2)"} compares theories
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  according to the intrinsic graph structure of the construction.
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  This sub-theory relation is a nominal approximation of inclusion
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  (@{text "\<subseteq>"}) of the corresponding content (according to the
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  semantics of the ML modules that implement the data).
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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"}.  This
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  changes the old theory, but the next update will result in two
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  related, valid theories.
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  \item @{ML "Theory.copy"}~@{text "thy"} produces a variant of @{text
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  "thy"} with the same data.  The copy is not related to the original,
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  but the original is unchanged.
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  \item @{ML "Theory.merge"}~@{text "(thy\<^sub>1, thy\<^sub>2)"} absorbs one theory
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  into the other, without changing @{text "thy\<^sub>1"} or @{text "thy\<^sub>2"}.
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  This version of ad-hoc theory merge fails for unrelated theories!
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  \item @{ML "Theory.begin_theory"}~@{text "name parents"} constructs
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  a new theory based on the given parents.  This {\ML} function is
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  normally not invoked directly.
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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.deref"}~@{text "thy_ref"} turns a @{ML_type
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  "theory_ref"} into an @{ML_type "theory"} value.  As the referenced
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  theory evolves monotonically over time, later invocations of @{ML
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  "Theory.deref"} may refer to a larger context.
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  \item @{ML "Theory.check_thy"}~@{text "thy"} produces a @{ML_type
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  "theory_ref"} from a valid @{ML_type "theory"} value.
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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 {* A proof context is a container for pure data with a
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  back-reference to the theory it belongs to.  The @{text "init"}
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  operation creates a proof context from a given theory.
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  Modifications to draft theories are propagated to the proof context
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  as usual, but there is also an explicit @{text "transfer"} operation
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  to force resynchronization with more substantial updates to the
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  underlying theory.
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  Entities derived in a proof context need to record logical
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  requirements explicitly, since there is no separate context
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  identification or symbolic inclusion as for theories.  For example,
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  hypotheses used in primitive derivations (cf.\ \secref{sec:thms})
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  are recorded separately within the sequent @{text "\<Gamma> \<turnstile> \<phi>"}, just to
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  make double sure.  Results could still leak into an alien proof
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  context due to programming errors, but Isabelle/Isar includes some
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  extra validity checks in critical positions, notably at the end of a
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  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 an Isar proof state models
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  block-structured reasoning explicitly, using a stack of proof
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  contexts internally.  For various technical reasons, the background
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  theory of an Isar proof state must not be changed while the proof is
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  still under construction!
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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_global: "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_global}~@{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, which
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  incurs a small runtime overhead.
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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_global"} 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 {* The main purpose of theory and proof contexts is to manage
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  arbitrary (pure) data.  New data types can be declared incrementally
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  at compile time.  There are separate declaration mechanisms for any
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  of the three kinds of contexts: theory, proof, generic.
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  \paragraph{Theory data} declarations need to implement the following
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  SML signature:
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  \medskip
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  \begin{tabular}{ll}
wenzelm@22869
   327
  @{text "\<type> T"} & representing type \\
wenzelm@22869
   328
  @{text "\<val> empty: T"} & empty default value \\
wenzelm@22869
   329
  @{text "\<val> extend: T \<rightarrow> T"} & re-initialize on import \\
wenzelm@22869
   330
  @{text "\<val> merge: T \<times> T \<rightarrow> T"} & join on import \\
wenzelm@20449
   331
  \end{tabular}
wenzelm@20449
   332
  \medskip
wenzelm@20449
   333
wenzelm@22869
   334
  \noindent The @{text "empty"} value acts as initial default for
wenzelm@22869
   335
  \emph{any} theory that does not declare actual data content; @{text
wenzelm@33524
   336
  "extend"} is acts like a unitary version of @{text "merge"}.
wenzelm@20449
   337
wenzelm@34921
   338
  Implementing @{text "merge"} can be tricky.  The general idea is
wenzelm@34921
   339
  that @{text "merge (data\<^sub>1, data\<^sub>2)"} inserts those parts of @{text
wenzelm@34921
   340
  "data\<^sub>2"} into @{text "data\<^sub>1"} that are not yet present, while
wenzelm@34921
   341
  keeping the general order of things.  The @{ML Library.merge}
wenzelm@34921
   342
  function on plain lists may serve as canonical template.
wenzelm@34921
   343
wenzelm@34921
   344
  Particularly note that shared parts of the data must not be
wenzelm@34921
   345
  duplicated by naive concatenation, or a theory graph that is like a
wenzelm@34921
   346
  chain of diamonds would cause an exponential blowup!
wenzelm@34921
   347
wenzelm@33524
   348
  \paragraph{Proof context data} declarations need to implement the
wenzelm@33524
   349
  following SML signature:
wenzelm@20449
   350
wenzelm@20449
   351
  \medskip
wenzelm@20449
   352
  \begin{tabular}{ll}
wenzelm@22869
   353
  @{text "\<type> T"} & representing type \\
wenzelm@22869
   354
  @{text "\<val> init: theory \<rightarrow> T"} & produce initial value \\
wenzelm@20449
   355
  \end{tabular}
wenzelm@20449
   356
  \medskip
wenzelm@20449
   357
wenzelm@20449
   358
  \noindent The @{text "init"} operation is supposed to produce a pure
wenzelm@34921
   359
  value from the given background theory and should be somehow
wenzelm@34921
   360
  ``immediate''.  Whenever a proof context is initialized, which
wenzelm@34921
   361
  happens frequently, the the system invokes the @{text "init"}
wenzelm@34921
   362
  operation of \emph{all} theory data slots ever declared.
wenzelm@20449
   363
wenzelm@20451
   364
  \paragraph{Generic data} provides a hybrid interface for both theory
wenzelm@33524
   365
  and proof data.  The @{text "init"} operation for proof contexts is
wenzelm@33524
   366
  predefined to select the current data value from the background
wenzelm@33524
   367
  theory.
wenzelm@20449
   368
wenzelm@34921
   369
  \bigskip Any of these data declaration over type @{text "T"} result
wenzelm@34921
   370
  in an ML structure with the following signature:
wenzelm@20449
   371
wenzelm@20449
   372
  \medskip
wenzelm@20449
   373
  \begin{tabular}{ll}
wenzelm@20449
   374
  @{text "get: context \<rightarrow> T"} \\
wenzelm@20449
   375
  @{text "put: T \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   376
  @{text "map: (T \<rightarrow> T) \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   377
  \end{tabular}
wenzelm@20449
   378
  \medskip
wenzelm@20449
   379
wenzelm@34921
   380
  \noindent These other operations provide exclusive access for the
wenzelm@34921
   381
  particular kind of context (theory, proof, or generic context).
wenzelm@34921
   382
  This interface fully observes the ML discipline for types and
wenzelm@34921
   383
  scopes: there is no other way to access the corresponding data slot
wenzelm@34921
   384
  of a context.  By keeping these operations private, an Isabelle/ML
wenzelm@34921
   385
  module may maintain abstract values authentically.
wenzelm@20447
   386
*}
wenzelm@20447
   387
wenzelm@20450
   388
text %mlref {*
wenzelm@20450
   389
  \begin{mldecls}
wenzelm@33524
   390
  @{index_ML_functor Theory_Data} \\
wenzelm@33524
   391
  @{index_ML_functor Proof_Data} \\
wenzelm@33524
   392
  @{index_ML_functor Generic_Data} \\
wenzelm@20450
   393
  \end{mldecls}
wenzelm@20450
   394
wenzelm@20450
   395
  \begin{description}
wenzelm@20450
   396
wenzelm@33524
   397
  \item @{ML_functor Theory_Data}@{text "(spec)"} declares data for
wenzelm@20450
   398
  type @{ML_type theory} according to the specification provided as
wenzelm@20451
   399
  argument structure.  The resulting structure provides data init and
wenzelm@20451
   400
  access operations as described above.
wenzelm@20450
   401
wenzelm@33524
   402
  \item @{ML_functor Proof_Data}@{text "(spec)"} is analogous to
wenzelm@33524
   403
  @{ML_functor Theory_Data} for type @{ML_type Proof.context}.
wenzelm@20450
   404
wenzelm@33524
   405
  \item @{ML_functor Generic_Data}@{text "(spec)"} is analogous to
wenzelm@33524
   406
  @{ML_functor Theory_Data} for type @{ML_type Context.generic}.
wenzelm@20450
   407
wenzelm@20450
   408
  \end{description}
wenzelm@20450
   409
*}
wenzelm@20450
   410
wenzelm@34928
   411
text %mlex {*
wenzelm@34928
   412
  The following artificial example demonstrates theory
wenzelm@34928
   413
  data: we maintain a set of terms that are supposed to be wellformed
wenzelm@34928
   414
  wrt.\ the enclosing theory.  The public interface is as follows:
wenzelm@34928
   415
*}
wenzelm@34928
   416
wenzelm@34928
   417
ML {*
wenzelm@34928
   418
  signature WELLFORMED_TERMS =
wenzelm@34928
   419
  sig
wenzelm@34928
   420
    val get: theory -> term list
wenzelm@34928
   421
    val add: term -> theory -> theory
wenzelm@34928
   422
  end;
wenzelm@34928
   423
*}
wenzelm@34928
   424
wenzelm@34928
   425
text {* \noindent The implementation uses private theory data
wenzelm@34928
   426
  internally, and only exposes an operation that involves explicit
wenzelm@34928
   427
  argument checking wrt.\ the given theory. *}
wenzelm@34928
   428
wenzelm@34928
   429
ML {*
wenzelm@34928
   430
  structure Wellformed_Terms: WELLFORMED_TERMS =
wenzelm@34928
   431
  struct
wenzelm@34928
   432
wenzelm@34928
   433
  structure Terms = Theory_Data
wenzelm@34928
   434
  (
wenzelm@39687
   435
    type T = term Ord_List.T;
wenzelm@34928
   436
    val empty = [];
wenzelm@34928
   437
    val extend = I;
wenzelm@34928
   438
    fun merge (ts1, ts2) =
wenzelm@39687
   439
      Ord_List.union Term_Ord.fast_term_ord ts1 ts2;
wenzelm@34928
   440
  )
wenzelm@34928
   441
wenzelm@34928
   442
  val get = Terms.get;
wenzelm@34928
   443
wenzelm@34928
   444
  fun add raw_t thy =
wenzelm@34928
   445
    let val t = Sign.cert_term thy raw_t
wenzelm@39687
   446
    in Terms.map (Ord_List.insert Term_Ord.fast_term_ord t) thy end;
wenzelm@34928
   447
wenzelm@34928
   448
  end;
wenzelm@34928
   449
*}
wenzelm@34928
   450
wenzelm@39687
   451
text {* We use @{ML_type "term Ord_List.T"} for reasonably efficient
wenzelm@34928
   452
  representation of a set of terms: all operations are linear in the
wenzelm@34928
   453
  number of stored elements.  Here we assume that our users do not
wenzelm@34928
   454
  care about the declaration order, since that data structure forces
wenzelm@34928
   455
  its own arrangement of elements.
wenzelm@34928
   456
wenzelm@34928
   457
  Observe how the @{verbatim merge} operation joins the data slots of
wenzelm@39687
   458
  the two constituents: @{ML Ord_List.union} prevents duplication of
wenzelm@34928
   459
  common data from different branches, thus avoiding the danger of
wenzelm@34928
   460
  exponential blowup.  (Plain list append etc.\ must never be used for
wenzelm@34928
   461
  theory data merges.)
wenzelm@34928
   462
wenzelm@34928
   463
  \medskip Our intended invariant is achieved as follows:
wenzelm@34928
   464
  \begin{enumerate}
wenzelm@34928
   465
wenzelm@34928
   466
  \item @{ML Wellformed_Terms.add} only admits terms that have passed
wenzelm@34928
   467
  the @{ML Sign.cert_term} check of the given theory at that point.
wenzelm@34928
   468
wenzelm@34928
   469
  \item Wellformedness in the sense of @{ML Sign.cert_term} is
wenzelm@34928
   470
  monotonic wrt.\ the sub-theory relation.  So our data can move
wenzelm@34928
   471
  upwards in the hierarchy (via extension or merges), and maintain
wenzelm@34928
   472
  wellformedness without further checks.
wenzelm@34928
   473
wenzelm@34928
   474
  \end{enumerate}
wenzelm@34928
   475
wenzelm@34928
   476
  Note that all basic operations of the inference kernel (which
wenzelm@34928
   477
  includes @{ML Sign.cert_term}) observe this monotonicity principle,
wenzelm@34928
   478
  but other user-space tools don't.  For example, fully-featured
wenzelm@34928
   479
  type-inference via @{ML Syntax.check_term} (cf.\
wenzelm@34928
   480
  \secref{sec:term-check}) is not necessarily monotonic wrt.\ the
wenzelm@34928
   481
  background theory, since constraints of term constants can be
wenzelm@34928
   482
  strengthened by later declarations, for example.
wenzelm@34928
   483
wenzelm@34928
   484
  In most cases, user-space context data does not have to take such
wenzelm@34928
   485
  invariants too seriously.  The situation is different in the
wenzelm@34928
   486
  implementation of the inference kernel itself, which uses the very
wenzelm@34928
   487
  same data mechanisms for types, constants, axioms etc.
wenzelm@34928
   488
*}
wenzelm@34928
   489
wenzelm@20447
   490
wenzelm@26872
   491
section {* Names \label{sec:names} *}
wenzelm@20451
   492
wenzelm@34925
   493
text {* In principle, a name is just a string, but there are various
wenzelm@34925
   494
  conventions for representing additional structure.  For example,
wenzelm@34927
   495
  ``@{text "Foo.bar.baz"}'' is considered as a long name consisting of
wenzelm@34927
   496
  qualifier @{text "Foo.bar"} and base name @{text "baz"}.  The
wenzelm@34927
   497
  individual constituents of a name may have further substructure,
wenzelm@34927
   498
  e.g.\ the string ``\verb,\,\verb,<alpha>,'' encodes as a single
wenzelm@34927
   499
  symbol.
wenzelm@34927
   500
wenzelm@34927
   501
  \medskip Subsequently, we shall introduce specific categories of
wenzelm@34927
   502
  names.  Roughly speaking these correspond to logical entities as
wenzelm@34927
   503
  follows:
wenzelm@34927
   504
  \begin{itemize}
wenzelm@34927
   505
wenzelm@34927
   506
  \item Basic names (\secref{sec:basic-name}): free and bound
wenzelm@34927
   507
  variables.
wenzelm@34927
   508
wenzelm@34927
   509
  \item Indexed names (\secref{sec:indexname}): schematic variables.
wenzelm@34927
   510
wenzelm@34927
   511
  \item Long names (\secref{sec:long-name}): constants of any kind
wenzelm@34927
   512
  (type constructors, term constants, other concepts defined in user
wenzelm@34927
   513
  space).  Such entities are typically managed via name spaces
wenzelm@34927
   514
  (\secref{sec:name-space}).
wenzelm@34927
   515
wenzelm@34927
   516
  \end{itemize}
wenzelm@20451
   517
*}
wenzelm@20437
   518
wenzelm@20437
   519
wenzelm@20437
   520
subsection {* Strings of symbols *}
wenzelm@20437
   521
wenzelm@34925
   522
text {* A \emph{symbol} constitutes the smallest textual unit in
wenzelm@34925
   523
  Isabelle --- raw ML characters are normally not encountered at all!
wenzelm@34925
   524
  Isabelle strings consist of a sequence of symbols, represented as a
wenzelm@34925
   525
  packed string or an exploded list of strings.  Each symbol is in
wenzelm@34925
   526
  itself a small string, which has either one of the following forms:
wenzelm@20437
   527
wenzelm@20451
   528
  \begin{enumerate}
wenzelm@20437
   529
wenzelm@37533
   530
  \item a single ASCII character ``@{text "c"}'', for example
wenzelm@37533
   531
  ``\verb,a,'',
wenzelm@37533
   532
wenzelm@37533
   533
  \item a codepoint according to UTF8 (non-ASCII byte sequence),
wenzelm@20437
   534
wenzelm@20488
   535
  \item a regular symbol ``\verb,\,\verb,<,@{text "ident"}\verb,>,'',
wenzelm@20476
   536
  for example ``\verb,\,\verb,<alpha>,'',
wenzelm@20437
   537
wenzelm@20488
   538
  \item a control symbol ``\verb,\,\verb,<^,@{text "ident"}\verb,>,'',
wenzelm@20476
   539
  for example ``\verb,\,\verb,<^bold>,'',
wenzelm@20437
   540
wenzelm@20488
   541
  \item a raw symbol ``\verb,\,\verb,<^raw:,@{text text}\verb,>,''
wenzelm@34925
   542
  where @{text text} consists of printable characters excluding
wenzelm@20476
   543
  ``\verb,.,'' and ``\verb,>,'', for example
wenzelm@20476
   544
  ``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
wenzelm@20437
   545
wenzelm@20488
   546
  \item a numbered raw control symbol ``\verb,\,\verb,<^raw,@{text
wenzelm@20476
   547
  n}\verb,>, where @{text n} consists of digits, for example
wenzelm@20451
   548
  ``\verb,\,\verb,<^raw42>,''.
wenzelm@20437
   549
wenzelm@20451
   550
  \end{enumerate}
wenzelm@20437
   551
wenzelm@20476
   552
  \noindent The @{text "ident"} syntax for symbol names is @{text
wenzelm@20476
   553
  "letter (letter | digit)\<^sup>*"}, where @{text "letter =
wenzelm@20476
   554
  A..Za..z"} and @{text "digit = 0..9"}.  There are infinitely many
wenzelm@20476
   555
  regular symbols and control symbols, but a fixed collection of
wenzelm@20476
   556
  standard symbols is treated specifically.  For example,
wenzelm@20488
   557
  ``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it
wenzelm@20488
   558
  may occur within regular Isabelle identifiers.
wenzelm@20437
   559
wenzelm@37533
   560
  The character set underlying Isabelle symbols is 7-bit ASCII, but
wenzelm@37533
   561
  8-bit character sequences are passed-through unchanged.  Unicode/UCS
wenzelm@37533
   562
  data in UTF-8 encoding is processed in a non-strict fashion, such
wenzelm@37533
   563
  that well-formed code sequences are recognized
wenzelm@37533
   564
  accordingly.\footnote{Note that ISO-Latin-1 differs from UTF-8 only
wenzelm@37533
   565
  in some special punctuation characters that even have replacements
wenzelm@37533
   566
  within the standard collection of Isabelle symbols.  Text consisting
wenzelm@37533
   567
  of ASCII plus accented letters can be processed in either encoding.}
wenzelm@37533
   568
  Unicode provides its own collection of mathematical symbols, but
wenzelm@37533
   569
  within the core Isabelle/ML world there is no link to the standard
wenzelm@37533
   570
  collection of Isabelle regular symbols.
wenzelm@20476
   571
wenzelm@20476
   572
  \medskip Output of Isabelle symbols depends on the print mode
wenzelm@29758
   573
  (\secref{print-mode}).  For example, the standard {\LaTeX} setup of
wenzelm@29758
   574
  the Isabelle document preparation system would present
wenzelm@20451
   575
  ``\verb,\,\verb,<alpha>,'' as @{text "\<alpha>"}, and
wenzelm@20451
   576
  ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as @{text
wenzelm@34925
   577
  "\<^bold>\<alpha>"}.  On-screen rendering usually works by mapping a finite
wenzelm@34925
   578
  subset of Isabelle symbols to suitable Unicode characters.
wenzelm@20451
   579
*}
wenzelm@20437
   580
wenzelm@20437
   581
text %mlref {*
wenzelm@20437
   582
  \begin{mldecls}
wenzelm@34921
   583
  @{index_ML_type "Symbol.symbol": string} \\
wenzelm@20437
   584
  @{index_ML Symbol.explode: "string -> Symbol.symbol list"} \\
wenzelm@20437
   585
  @{index_ML Symbol.is_letter: "Symbol.symbol -> bool"} \\
wenzelm@20437
   586
  @{index_ML Symbol.is_digit: "Symbol.symbol -> bool"} \\
wenzelm@20437
   587
  @{index_ML Symbol.is_quasi: "Symbol.symbol -> bool"} \\
wenzelm@20547
   588
  @{index_ML Symbol.is_blank: "Symbol.symbol -> bool"} \\
wenzelm@20547
   589
  \end{mldecls}
wenzelm@20547
   590
  \begin{mldecls}
wenzelm@20437
   591
  @{index_ML_type "Symbol.sym"} \\
wenzelm@20437
   592
  @{index_ML Symbol.decode: "Symbol.symbol -> Symbol.sym"} \\
wenzelm@20437
   593
  \end{mldecls}
wenzelm@20437
   594
wenzelm@20437
   595
  \begin{description}
wenzelm@20437
   596
wenzelm@20488
   597
  \item @{ML_type "Symbol.symbol"} represents individual Isabelle
wenzelm@34921
   598
  symbols.
wenzelm@20437
   599
wenzelm@20476
   600
  \item @{ML "Symbol.explode"}~@{text "str"} produces a symbol list
wenzelm@20488
   601
  from the packed form.  This function supercedes @{ML
wenzelm@20476
   602
  "String.explode"} for virtually all purposes of manipulating text in
wenzelm@34925
   603
  Isabelle!\footnote{The runtime overhead for exploded strings is
wenzelm@34925
   604
  mainly that of the list structure: individual symbols that happen to
wenzelm@34925
   605
  be a singleton string --- which is the most common case --- do not
wenzelm@34925
   606
  require extra memory in Poly/ML.}
wenzelm@20437
   607
wenzelm@20437
   608
  \item @{ML "Symbol.is_letter"}, @{ML "Symbol.is_digit"}, @{ML
wenzelm@20476
   609
  "Symbol.is_quasi"}, @{ML "Symbol.is_blank"} classify standard
wenzelm@20476
   610
  symbols according to fixed syntactic conventions of Isabelle, cf.\
wenzelm@20476
   611
  \cite{isabelle-isar-ref}.
wenzelm@20437
   612
wenzelm@20437
   613
  \item @{ML_type "Symbol.sym"} is a concrete datatype that represents
wenzelm@20488
   614
  the different kinds of symbols explicitly, with constructors @{ML
wenzelm@37533
   615
  "Symbol.Char"}, @{ML "Symbol.Sym"}, @{ML "Symbol.UTF8"}, @{ML
wenzelm@37533
   616
  "Symbol.Ctrl"}, @{ML "Symbol.Raw"}.
wenzelm@20437
   617
wenzelm@20437
   618
  \item @{ML "Symbol.decode"} converts the string representation of a
wenzelm@20451
   619
  symbol into the datatype version.
wenzelm@20437
   620
wenzelm@20437
   621
  \end{description}
wenzelm@34925
   622
wenzelm@34925
   623
  \paragraph{Historical note.} In the original SML90 standard the
wenzelm@34925
   624
  primitive ML type @{ML_type char} did not exists, and the basic @{ML
wenzelm@34925
   625
  "explode: string -> string list"} operation would produce a list of
wenzelm@34925
   626
  singleton strings as in Isabelle/ML today.  When SML97 came out,
wenzelm@34927
   627
  Isabelle did not adopt its slightly anachronistic 8-bit characters,
wenzelm@34927
   628
  but the idea of exploding a string into a list of small strings was
wenzelm@34925
   629
  extended to ``symbols'' as explained above.  Thus Isabelle sources
wenzelm@34925
   630
  can refer to an infinite store of user-defined symbols, without
wenzelm@34925
   631
  having to worry about the multitude of Unicode encodings.
wenzelm@20437
   632
*}
wenzelm@20437
   633
wenzelm@20437
   634
wenzelm@34927
   635
subsection {* Basic names \label{sec:basic-name} *}
wenzelm@20476
   636
wenzelm@20476
   637
text {*
wenzelm@20476
   638
  A \emph{basic name} essentially consists of a single Isabelle
wenzelm@20476
   639
  identifier.  There are conventions to mark separate classes of basic
wenzelm@29761
   640
  names, by attaching a suffix of underscores: one underscore means
wenzelm@29761
   641
  \emph{internal name}, two underscores means \emph{Skolem name},
wenzelm@29761
   642
  three underscores means \emph{internal Skolem name}.
wenzelm@20476
   643
wenzelm@20476
   644
  For example, the basic name @{text "foo"} has the internal version
wenzelm@20476
   645
  @{text "foo_"}, with Skolem versions @{text "foo__"} and @{text
wenzelm@20476
   646
  "foo___"}, respectively.
wenzelm@20476
   647
wenzelm@20488
   648
  These special versions provide copies of the basic name space, apart
wenzelm@20488
   649
  from anything that normally appears in the user text.  For example,
wenzelm@20488
   650
  system generated variables in Isar proof contexts are usually marked
wenzelm@34926
   651
  as internal, which prevents mysterious names like @{text "xaa"} to
wenzelm@34926
   652
  appear in human-readable text.
wenzelm@20476
   653
wenzelm@20488
   654
  \medskip Manipulating binding scopes often requires on-the-fly
wenzelm@20488
   655
  renamings.  A \emph{name context} contains a collection of already
wenzelm@20488
   656
  used names.  The @{text "declare"} operation adds names to the
wenzelm@20488
   657
  context.
wenzelm@20476
   658
wenzelm@20488
   659
  The @{text "invents"} operation derives a number of fresh names from
wenzelm@20488
   660
  a given starting point.  For example, the first three names derived
wenzelm@20488
   661
  from @{text "a"} are @{text "a"}, @{text "b"}, @{text "c"}.
wenzelm@20476
   662
wenzelm@20476
   663
  The @{text "variants"} operation produces fresh names by
wenzelm@20488
   664
  incrementing tentative names as base-26 numbers (with digits @{text
wenzelm@20488
   665
  "a..z"}) until all clashes are resolved.  For example, name @{text
wenzelm@20488
   666
  "foo"} results in variants @{text "fooa"}, @{text "foob"}, @{text
wenzelm@20488
   667
  "fooc"}, \dots, @{text "fooaa"}, @{text "fooab"} etc.; each renaming
wenzelm@20488
   668
  step picks the next unused variant from this sequence.
wenzelm@20476
   669
*}
wenzelm@20476
   670
wenzelm@20476
   671
text %mlref {*
wenzelm@20476
   672
  \begin{mldecls}
wenzelm@20476
   673
  @{index_ML Name.internal: "string -> string"} \\
wenzelm@20547
   674
  @{index_ML Name.skolem: "string -> string"} \\
wenzelm@20547
   675
  \end{mldecls}
wenzelm@20547
   676
  \begin{mldecls}
wenzelm@20476
   677
  @{index_ML_type Name.context} \\
wenzelm@20476
   678
  @{index_ML Name.context: Name.context} \\
wenzelm@20476
   679
  @{index_ML Name.declare: "string -> Name.context -> Name.context"} \\
wenzelm@20476
   680
  @{index_ML Name.invents: "Name.context -> string -> int -> string list"} \\
wenzelm@20476
   681
  @{index_ML Name.variants: "string list -> Name.context -> string list * Name.context"} \\
wenzelm@20476
   682
  \end{mldecls}
wenzelm@34926
   683
  \begin{mldecls}
wenzelm@34926
   684
  @{index_ML Variable.names_of: "Proof.context -> Name.context"} \\
wenzelm@34926
   685
  \end{mldecls}
wenzelm@20476
   686
wenzelm@20476
   687
  \begin{description}
wenzelm@20476
   688
wenzelm@20476
   689
  \item @{ML Name.internal}~@{text "name"} produces an internal name
wenzelm@20476
   690
  by adding one underscore.
wenzelm@20476
   691
wenzelm@20476
   692
  \item @{ML Name.skolem}~@{text "name"} produces a Skolem name by
wenzelm@20476
   693
  adding two underscores.
wenzelm@20476
   694
wenzelm@20476
   695
  \item @{ML_type Name.context} represents the context of already used
wenzelm@20476
   696
  names; the initial value is @{ML "Name.context"}.
wenzelm@20476
   697
wenzelm@20488
   698
  \item @{ML Name.declare}~@{text "name"} enters a used name into the
wenzelm@20488
   699
  context.
wenzelm@20437
   700
wenzelm@20488
   701
  \item @{ML Name.invents}~@{text "context name n"} produces @{text
wenzelm@20488
   702
  "n"} fresh names derived from @{text "name"}.
wenzelm@20488
   703
wenzelm@20488
   704
  \item @{ML Name.variants}~@{text "names context"} produces fresh
wenzelm@29761
   705
  variants of @{text "names"}; the result is entered into the context.
wenzelm@20476
   706
wenzelm@34926
   707
  \item @{ML Variable.names_of}~@{text "ctxt"} retrieves the context
wenzelm@34926
   708
  of declared type and term variable names.  Projecting a proof
wenzelm@34926
   709
  context down to a primitive name context is occasionally useful when
wenzelm@34926
   710
  invoking lower-level operations.  Regular management of ``fresh
wenzelm@34926
   711
  variables'' is done by suitable operations of structure @{ML_struct
wenzelm@34926
   712
  Variable}, which is also able to provide an official status of
wenzelm@34926
   713
  ``locally fixed variable'' within the logical environment (cf.\
wenzelm@34926
   714
  \secref{sec:variables}).
wenzelm@34926
   715
wenzelm@20476
   716
  \end{description}
wenzelm@20476
   717
*}
wenzelm@20476
   718
wenzelm@20476
   719
wenzelm@34927
   720
subsection {* Indexed names \label{sec:indexname} *}
wenzelm@20476
   721
wenzelm@20476
   722
text {*
wenzelm@20476
   723
  An \emph{indexed name} (or @{text "indexname"}) is a pair of a basic
wenzelm@20488
   724
  name and a natural number.  This representation allows efficient
wenzelm@20488
   725
  renaming by incrementing the second component only.  The canonical
wenzelm@20488
   726
  way to rename two collections of indexnames apart from each other is
wenzelm@20488
   727
  this: determine the maximum index @{text "maxidx"} of the first
wenzelm@20488
   728
  collection, then increment all indexes of the second collection by
wenzelm@20488
   729
  @{text "maxidx + 1"}; the maximum index of an empty collection is
wenzelm@20488
   730
  @{text "-1"}.
wenzelm@20476
   731
wenzelm@34927
   732
  Occasionally, basic names are injected into the same pair type of
wenzelm@34927
   733
  indexed names: then @{text "(x, -1)"} is used to encode the basic
wenzelm@34927
   734
  name @{text "x"}.
wenzelm@20488
   735
wenzelm@20488
   736
  \medskip Isabelle syntax observes the following rules for
wenzelm@20488
   737
  representing an indexname @{text "(x, i)"} as a packed string:
wenzelm@20476
   738
wenzelm@20476
   739
  \begin{itemize}
wenzelm@20476
   740
wenzelm@20479
   741
  \item @{text "?x"} if @{text "x"} does not end with a digit and @{text "i = 0"},
wenzelm@20476
   742
wenzelm@20476
   743
  \item @{text "?xi"} if @{text "x"} does not end with a digit,
wenzelm@20476
   744
wenzelm@20488
   745
  \item @{text "?x.i"} otherwise.
wenzelm@20476
   746
wenzelm@20476
   747
  \end{itemize}
wenzelm@20470
   748
wenzelm@34927
   749
  Indexnames may acquire large index numbers after several maxidx
wenzelm@34927
   750
  shifts have been applied.  Results are usually normalized towards
wenzelm@34927
   751
  @{text "0"} at certain checkpoints, notably at the end of a proof.
wenzelm@34927
   752
  This works by producing variants of the corresponding basic name
wenzelm@34927
   753
  components.  For example, the collection @{text "?x1, ?x7, ?x42"}
wenzelm@34927
   754
  becomes @{text "?x, ?xa, ?xb"}.
wenzelm@20476
   755
*}
wenzelm@20476
   756
wenzelm@20476
   757
text %mlref {*
wenzelm@20476
   758
  \begin{mldecls}
wenzelm@20476
   759
  @{index_ML_type indexname} \\
wenzelm@20476
   760
  \end{mldecls}
wenzelm@20476
   761
wenzelm@20476
   762
  \begin{description}
wenzelm@20476
   763
wenzelm@20476
   764
  \item @{ML_type indexname} represents indexed names.  This is an
wenzelm@20476
   765
  abbreviation for @{ML_type "string * int"}.  The second component is
wenzelm@20476
   766
  usually non-negative, except for situations where @{text "(x, -1)"}
wenzelm@34926
   767
  is used to inject basic names into this type.  Other negative
wenzelm@34926
   768
  indexes should not be used.
wenzelm@20476
   769
wenzelm@20476
   770
  \end{description}
wenzelm@20476
   771
*}
wenzelm@20476
   772
wenzelm@20476
   773
wenzelm@34927
   774
subsection {* Long names \label{sec:long-name} *}
wenzelm@20476
   775
wenzelm@34927
   776
text {* A \emph{long name} consists of a sequence of non-empty name
wenzelm@34927
   777
  components.  The packed representation uses a dot as separator, as
wenzelm@34927
   778
  in ``@{text "A.b.c"}''.  The last component is called \emph{base
wenzelm@34927
   779
  name}, the remaining prefix is called \emph{qualifier} (which may be
wenzelm@34927
   780
  empty).  The qualifier can be understood as the access path to the
wenzelm@34927
   781
  named entity while passing through some nested block-structure,
wenzelm@34927
   782
  although our free-form long names do not really enforce any strict
wenzelm@34927
   783
  discipline.
wenzelm@34927
   784
wenzelm@34927
   785
  For example, an item named ``@{text "A.b.c"}'' may be understood as
wenzelm@34927
   786
  a local entity @{text "c"}, within a local structure @{text "b"},
wenzelm@34927
   787
  within a global structure @{text "A"}.  In practice, long names
wenzelm@34927
   788
  usually represent 1--3 levels of qualification.  User ML code should
wenzelm@34927
   789
  not make any assumptions about the particular structure of long
wenzelm@34927
   790
  names!
wenzelm@20437
   791
wenzelm@20476
   792
  The empty name is commonly used as an indication of unnamed
wenzelm@34927
   793
  entities, or entities that are not entered into the corresponding
wenzelm@34927
   794
  name space, whenever this makes any sense.  The basic operations on
wenzelm@34927
   795
  long names map empty names again to empty names.
wenzelm@20437
   796
*}
wenzelm@20437
   797
wenzelm@20476
   798
text %mlref {*
wenzelm@20476
   799
  \begin{mldecls}
wenzelm@30365
   800
  @{index_ML Long_Name.base_name: "string -> string"} \\
wenzelm@30365
   801
  @{index_ML Long_Name.qualifier: "string -> string"} \\
wenzelm@30365
   802
  @{index_ML Long_Name.append: "string -> string -> string"} \\
wenzelm@30365
   803
  @{index_ML Long_Name.implode: "string list -> string"} \\
wenzelm@30365
   804
  @{index_ML Long_Name.explode: "string -> string list"} \\
wenzelm@20547
   805
  \end{mldecls}
wenzelm@34927
   806
wenzelm@34927
   807
  \begin{description}
wenzelm@34927
   808
wenzelm@34927
   809
  \item @{ML Long_Name.base_name}~@{text "name"} returns the base name
wenzelm@34927
   810
  of a long name.
wenzelm@34927
   811
wenzelm@34927
   812
  \item @{ML Long_Name.qualifier}~@{text "name"} returns the qualifier
wenzelm@34927
   813
  of a long name.
wenzelm@34927
   814
wenzelm@34927
   815
  \item @{ML Long_Name.append}~@{text "name\<^isub>1 name\<^isub>2"} appends two long
wenzelm@34927
   816
  names.
wenzelm@34927
   817
wenzelm@34927
   818
  \item @{ML Long_Name.implode}~@{text "names"} and @{ML
wenzelm@34927
   819
  Long_Name.explode}~@{text "name"} convert between the packed string
wenzelm@34927
   820
  representation and the explicit list form of long names.
wenzelm@34927
   821
wenzelm@34927
   822
  \end{description}
wenzelm@34927
   823
*}
wenzelm@34927
   824
wenzelm@34927
   825
wenzelm@34927
   826
subsection {* Name spaces \label{sec:name-space} *}
wenzelm@34927
   827
wenzelm@34927
   828
text {* A @{text "name space"} manages a collection of long names,
wenzelm@34927
   829
  together with a mapping between partially qualified external names
wenzelm@34927
   830
  and fully qualified internal names (in both directions).  Note that
wenzelm@34927
   831
  the corresponding @{text "intern"} and @{text "extern"} operations
wenzelm@34927
   832
  are mostly used for parsing and printing only!  The @{text
wenzelm@34927
   833
  "declare"} operation augments a name space according to the accesses
wenzelm@34927
   834
  determined by a given binding, and a naming policy from the context.
wenzelm@34927
   835
wenzelm@34927
   836
  \medskip A @{text "binding"} specifies details about the prospective
wenzelm@34927
   837
  long name of a newly introduced formal entity.  It consists of a
wenzelm@34927
   838
  base name, prefixes for qualification (separate ones for system
wenzelm@34927
   839
  infrastructure and user-space mechanisms), a slot for the original
wenzelm@34927
   840
  source position, and some additional flags.
wenzelm@34927
   841
wenzelm@34927
   842
  \medskip A @{text "naming"} provides some additional details for
wenzelm@34927
   843
  producing a long name from a binding.  Normally, the naming is
wenzelm@34927
   844
  implicit in the theory or proof context.  The @{text "full"}
wenzelm@34927
   845
  operation (and its variants for different context types) produces a
wenzelm@34927
   846
  fully qualified internal name to be entered into a name space.  The
wenzelm@34927
   847
  main equation of this ``chemical reaction'' when binding new
wenzelm@34927
   848
  entities in a context is as follows:
wenzelm@34927
   849
wenzelm@34927
   850
  \smallskip
wenzelm@34927
   851
  \begin{tabular}{l}
wenzelm@34927
   852
  @{text "binding + naming \<longrightarrow> long name + name space accesses"}
wenzelm@34927
   853
  \end{tabular}
wenzelm@34927
   854
  \smallskip
wenzelm@34927
   855
wenzelm@34927
   856
  \medskip As a general principle, there is a separate name space for
wenzelm@34927
   857
  each kind of formal entity, e.g.\ fact, logical constant, type
wenzelm@34927
   858
  constructor, type class.  It is usually clear from the occurrence in
wenzelm@34927
   859
  concrete syntax (or from the scope) which kind of entity a name
wenzelm@34927
   860
  refers to.  For example, the very same name @{text "c"} may be used
wenzelm@34927
   861
  uniformly for a constant, type constructor, and type class.
wenzelm@34927
   862
wenzelm@34927
   863
  There are common schemes to name derived entities systematically
wenzelm@34927
   864
  according to the name of the main logical entity involved, e.g.\
wenzelm@34927
   865
  fact @{text "c.intro"} for a canonical introduction rule related to
wenzelm@34927
   866
  constant @{text "c"}.  This technique of mapping names from one
wenzelm@34927
   867
  space into another requires some care in order to avoid conflicts.
wenzelm@34927
   868
  In particular, theorem names derived from a type constructor or type
wenzelm@34927
   869
  class are better suffixed in addition to the usual qualification,
wenzelm@34927
   870
  e.g.\ @{text "c_type.intro"} and @{text "c_class.intro"} for
wenzelm@34927
   871
  theorems related to type @{text "c"} and class @{text "c"},
wenzelm@34927
   872
  respectively.
wenzelm@34927
   873
*}
wenzelm@34927
   874
wenzelm@34927
   875
text %mlref {*
wenzelm@34927
   876
  \begin{mldecls}
wenzelm@34927
   877
  @{index_ML_type binding} \\
wenzelm@34927
   878
  @{index_ML Binding.empty: binding} \\
wenzelm@34927
   879
  @{index_ML Binding.name: "string -> binding"} \\
wenzelm@34927
   880
  @{index_ML Binding.qualify: "bool -> string -> binding -> binding"} \\
wenzelm@34927
   881
  @{index_ML Binding.prefix: "bool -> string -> binding -> binding"} \\
wenzelm@34927
   882
  @{index_ML Binding.conceal: "binding -> binding"} \\
wenzelm@34927
   883
  @{index_ML Binding.str_of: "binding -> string"} \\
wenzelm@34927
   884
  \end{mldecls}
wenzelm@20547
   885
  \begin{mldecls}
haftmann@33174
   886
  @{index_ML_type Name_Space.naming} \\
haftmann@33174
   887
  @{index_ML Name_Space.default_naming: Name_Space.naming} \\
haftmann@33174
   888
  @{index_ML Name_Space.add_path: "string -> Name_Space.naming -> Name_Space.naming"} \\
haftmann@33174
   889
  @{index_ML Name_Space.full_name: "Name_Space.naming -> binding -> string"} \\
wenzelm@20547
   890
  \end{mldecls}
wenzelm@20547
   891
  \begin{mldecls}
haftmann@33174
   892
  @{index_ML_type Name_Space.T} \\
haftmann@33174
   893
  @{index_ML Name_Space.empty: "string -> Name_Space.T"} \\
haftmann@33174
   894
  @{index_ML Name_Space.merge: "Name_Space.T * Name_Space.T -> Name_Space.T"} \\
haftmann@33174
   895
  @{index_ML Name_Space.declare: "bool -> Name_Space.naming -> binding -> Name_Space.T ->
haftmann@33174
   896
  string * Name_Space.T"} \\
haftmann@33174
   897
  @{index_ML Name_Space.intern: "Name_Space.T -> string -> string"} \\
haftmann@33174
   898
  @{index_ML Name_Space.extern: "Name_Space.T -> string -> string"} \\
wenzelm@34927
   899
  @{index_ML Name_Space.is_concealed: "Name_Space.T -> string -> bool"}
wenzelm@20476
   900
  \end{mldecls}
wenzelm@20437
   901
wenzelm@20476
   902
  \begin{description}
wenzelm@20476
   903
wenzelm@34927
   904
  \item @{ML_type binding} represents the abstract concept of name
wenzelm@34927
   905
  bindings.
wenzelm@34927
   906
wenzelm@34927
   907
  \item @{ML Binding.empty} is the empty binding.
wenzelm@20476
   908
wenzelm@34927
   909
  \item @{ML Binding.name}~@{text "name"} produces a binding with base
wenzelm@34927
   910
  name @{text "name"}.
wenzelm@34927
   911
wenzelm@34927
   912
  \item @{ML Binding.qualify}~@{text "mandatory name binding"}
wenzelm@34927
   913
  prefixes qualifier @{text "name"} to @{text "binding"}.  The @{text
wenzelm@34927
   914
  "mandatory"} flag tells if this name component always needs to be
wenzelm@34927
   915
  given in name space accesses --- this is mostly @{text "false"} in
wenzelm@34927
   916
  practice.  Note that this part of qualification is typically used in
wenzelm@34927
   917
  derived specification mechanisms.
wenzelm@20437
   918
wenzelm@34927
   919
  \item @{ML Binding.prefix} is similar to @{ML Binding.qualify}, but
wenzelm@34927
   920
  affects the system prefix.  This part of extra qualification is
wenzelm@34927
   921
  typically used in the infrastructure for modular specifications,
wenzelm@34927
   922
  notably ``local theory targets'' (see also \chref{ch:local-theory}).
wenzelm@20437
   923
wenzelm@34927
   924
  \item @{ML Binding.conceal}~@{text "binding"} indicates that the
wenzelm@34927
   925
  binding shall refer to an entity that serves foundational purposes
wenzelm@34927
   926
  only.  This flag helps to mark implementation details of
wenzelm@34927
   927
  specification mechanism etc.  Other tools should not depend on the
wenzelm@34927
   928
  particulars of concealed entities (cf.\ @{ML
wenzelm@34927
   929
  Name_Space.is_concealed}).
wenzelm@34927
   930
wenzelm@34927
   931
  \item @{ML Binding.str_of}~@{text "binding"} produces a string
wenzelm@34927
   932
  representation for human-readable output, together with some formal
wenzelm@34927
   933
  markup that might get used in GUI front-ends, for example.
wenzelm@20476
   934
haftmann@33174
   935
  \item @{ML_type Name_Space.naming} represents the abstract concept of
wenzelm@20476
   936
  a naming policy.
wenzelm@20437
   937
haftmann@33174
   938
  \item @{ML Name_Space.default_naming} is the default naming policy.
wenzelm@20476
   939
  In a theory context, this is usually augmented by a path prefix
wenzelm@20476
   940
  consisting of the theory name.
wenzelm@20476
   941
haftmann@33174
   942
  \item @{ML Name_Space.add_path}~@{text "path naming"} augments the
wenzelm@20488
   943
  naming policy by extending its path component.
wenzelm@20437
   944
haftmann@33174
   945
  \item @{ML Name_Space.full_name}~@{text "naming binding"} turns a
wenzelm@30281
   946
  name binding (usually a basic name) into the fully qualified
haftmann@29008
   947
  internal name, according to the given naming policy.
wenzelm@20476
   948
haftmann@33174
   949
  \item @{ML_type Name_Space.T} represents name spaces.
wenzelm@20476
   950
haftmann@33174
   951
  \item @{ML Name_Space.empty}~@{text "kind"} and @{ML Name_Space.merge}~@{text
wenzelm@20488
   952
  "(space\<^isub>1, space\<^isub>2)"} are the canonical operations for
wenzelm@20488
   953
  maintaining name spaces according to theory data management
haftmann@33174
   954
  (\secref{sec:context-data}); @{text "kind"} is a formal comment
haftmann@33174
   955
  to characterize the purpose of a name space.
wenzelm@20437
   956
haftmann@33174
   957
  \item @{ML Name_Space.declare}~@{text "strict naming bindings
haftmann@33174
   958
  space"} enters a name binding as fully qualified internal name into
haftmann@33174
   959
  the name space, with external accesses determined by the naming
haftmann@33174
   960
  policy.
wenzelm@20476
   961
haftmann@33174
   962
  \item @{ML Name_Space.intern}~@{text "space name"} internalizes a
wenzelm@20476
   963
  (partially qualified) external name.
wenzelm@20437
   964
wenzelm@20488
   965
  This operation is mostly for parsing!  Note that fully qualified
wenzelm@20476
   966
  names stemming from declarations are produced via @{ML
haftmann@33174
   967
  "Name_Space.full_name"} and @{ML "Name_Space.declare"}
haftmann@29008
   968
  (or their derivatives for @{ML_type theory} and
wenzelm@20488
   969
  @{ML_type Proof.context}).
wenzelm@20437
   970
haftmann@33174
   971
  \item @{ML Name_Space.extern}~@{text "space name"} externalizes a
wenzelm@20476
   972
  (fully qualified) internal name.
wenzelm@20476
   973
wenzelm@30281
   974
  This operation is mostly for printing!  User code should not rely on
wenzelm@30281
   975
  the precise result too much.
wenzelm@20476
   976
wenzelm@34927
   977
  \item @{ML Name_Space.is_concealed}~@{text "space name"} indicates
wenzelm@34927
   978
  whether @{text "name"} refers to a strictly private entity that
wenzelm@34927
   979
  other tools are supposed to ignore!
wenzelm@34927
   980
wenzelm@20476
   981
  \end{description}
wenzelm@20476
   982
*}
wenzelm@30272
   983
wenzelm@18537
   984
end