doc-src/IsarImplementation/Thy/Prelim.thy
author wenzelm
Sun May 01 00:01:59 2011 +0200 (2011-05-01)
changeset 42510 b9c106763325
parent 42401 9bfaf6819291
child 42616 92715b528e78
permissions -rw-r--r--
use @{rail} antiquotation (with some nested markup);
eliminated separate rail/latex phase;
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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 when
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  the next @{text "checkpoint"} is reached.
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  Derived entities may store a theory reference in order to indicate
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  the formal context from which they are derived.  This implicitly
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  assumes monotonic reasoning, because the referenced context may
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  become larger without 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.eq_thy: "theory * theory -> bool"} \\
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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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  @{index_ML Theory.parents_of: "theory -> theory list"} \\
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  @{index_ML Theory.ancestors_of: "theory -> theory list"} \\
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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 Type @{ML_type theory} represents theory contexts.  This is
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  essentially a linear type, with explicit runtime checking.
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  Primitive theory operations destroy the original version, which then
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  becomes ``stale''.  This can be prevented by explicit checkpointing,
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  which the system does at least at the boundary of toplevel command
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  transactions \secref{sec:isar-toplevel}.
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  \item @{ML "Theory.eq_thy"}~@{text "(thy\<^sub>1, thy\<^sub>2)"} check strict
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  identity of two theories.
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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 "Theory.parents_of"}~@{text "thy"} returns the direct
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  ancestors of @{text thy}.
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  \item @{ML "Theory.ancestors_of"}~@{text "thy"} returns all
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  ancestors of @{text thy} (not including @{text thy} itself).
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  \item Type @{ML_type theory_ref} represents a sliding reference to
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  an 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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text %mlantiq {*
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  \begin{matharray}{rcl}
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  @{ML_antiquotation_def "theory"} & : & @{text ML_antiquotation} \\
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  \end{matharray}
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  @{rail "
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  @@{ML_antiquotation theory} nameref?
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  "}
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  \begin{description}
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  \item @{text "@{theory}"} refers to the background theory of the
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  current context --- as abstract value.
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  \item @{text "@{theory A}"} refers to an explicitly named ancestor
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  theory @{text "A"} of the background theory of the current context
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  --- as abstract 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 from which it is derived.  The @{text
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  "init"} 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 Proof_Context.init_global: "theory -> Proof.context"} \\
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  @{index_ML Proof_Context.theory_of: "Proof.context -> theory"} \\
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  @{index_ML Proof_Context.transfer: "theory -> Proof.context -> Proof.context"} \\
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  \end{mldecls}
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  \begin{description}
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  \item Type @{ML_type Proof.context} represents proof contexts.
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  Elements of this type are essentially pure values, with a sliding
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  reference to the background theory.
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  \item @{ML Proof_Context.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 Proof_Context.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 Proof_Context.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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text %mlantiq {*
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  \begin{matharray}{rcl}
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  @{ML_antiquotation_def "context"} & : & @{text ML_antiquotation} \\
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  \end{matharray}
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  \begin{description}
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  \item @{text "@{context}"} refers to \emph{the} context at
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  compile-time --- as abstract value.  Independently of (local) theory
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  or proof mode, this always produces a meaningful result.
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  This is probably the most common antiquotation in interactive
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  experimentation with ML inside Isar.
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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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   325
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   326
text {*
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   327
  A generic context is the disjoint sum of either a theory or proof
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   328
  context.  Occasionally, this enables uniform treatment of generic
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   329
  context data, typically extra-logical information.  Operations on
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   330
  generic contexts include the usual injections, partial selections,
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   331
  and combinators for lifting operations on either component of the
wenzelm@20449
   332
  disjoint sum.
wenzelm@20449
   333
wenzelm@20449
   334
  Moreover, there are total operations @{text "theory_of"} and @{text
wenzelm@20449
   335
  "proof_of"} to convert a generic context into either kind: a theory
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   336
  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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   338
  incurs a small runtime overhead.
wenzelm@20449
   339
*}
wenzelm@20430
   340
wenzelm@20449
   341
text %mlref {*
wenzelm@20449
   342
  \begin{mldecls}
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   343
  @{index_ML_type Context.generic} \\
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   344
  @{index_ML Context.theory_of: "Context.generic -> theory"} \\
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   345
  @{index_ML Context.proof_of: "Context.generic -> Proof.context"} \\
wenzelm@20449
   346
  \end{mldecls}
wenzelm@20449
   347
wenzelm@20449
   348
  \begin{description}
wenzelm@20430
   349
wenzelm@39864
   350
  \item Type @{ML_type Context.generic} is the direct sum of @{ML_type
wenzelm@20451
   351
  "theory"} and @{ML_type "Proof.context"}, with the datatype
wenzelm@20451
   352
  constructors @{ML "Context.Theory"} and @{ML "Context.Proof"}.
wenzelm@20449
   353
wenzelm@20449
   354
  \item @{ML Context.theory_of}~@{text "context"} always produces a
wenzelm@20449
   355
  theory from the generic @{text "context"}, using @{ML
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   356
  "Proof_Context.theory_of"} as required.
wenzelm@20449
   357
wenzelm@20449
   358
  \item @{ML Context.proof_of}~@{text "context"} always produces a
wenzelm@20449
   359
  proof context from the generic @{text "context"}, using @{ML
wenzelm@42361
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  "Proof_Context.init_global"} as required (note that this re-initializes the
wenzelm@20451
   361
  context data with each invocation).
wenzelm@20449
   362
wenzelm@20449
   363
  \end{description}
wenzelm@20449
   364
*}
wenzelm@20437
   365
wenzelm@20476
   366
wenzelm@20476
   367
subsection {* Context data \label{sec:context-data} *}
wenzelm@20447
   368
wenzelm@33524
   369
text {* The main purpose of theory and proof contexts is to manage
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   370
  arbitrary (pure) data.  New data types can be declared incrementally
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   371
  at compile time.  There are separate declaration mechanisms for any
wenzelm@33524
   372
  of the three kinds of contexts: theory, proof, generic.
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   373
wenzelm@33524
   374
  \paragraph{Theory data} declarations need to implement the following
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   375
  SML signature:
wenzelm@20449
   376
wenzelm@20449
   377
  \medskip
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   378
  \begin{tabular}{ll}
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   379
  @{text "\<type> T"} & representing type \\
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   380
  @{text "\<val> empty: T"} & empty default value \\
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   381
  @{text "\<val> extend: T \<rightarrow> T"} & re-initialize on import \\
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   382
  @{text "\<val> merge: T \<times> T \<rightarrow> T"} & join on import \\
wenzelm@20449
   383
  \end{tabular}
wenzelm@20449
   384
  \medskip
wenzelm@20449
   385
wenzelm@39861
   386
  The @{text "empty"} value acts as initial default for \emph{any}
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   387
  theory that does not declare actual data content; @{text "extend"}
wenzelm@39861
   388
  is acts like a unitary version of @{text "merge"}.
wenzelm@20449
   389
wenzelm@34921
   390
  Implementing @{text "merge"} can be tricky.  The general idea is
wenzelm@34921
   391
  that @{text "merge (data\<^sub>1, data\<^sub>2)"} inserts those parts of @{text
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   392
  "data\<^sub>2"} into @{text "data\<^sub>1"} that are not yet present, while
wenzelm@34921
   393
  keeping the general order of things.  The @{ML Library.merge}
wenzelm@34921
   394
  function on plain lists may serve as canonical template.
wenzelm@34921
   395
wenzelm@34921
   396
  Particularly note that shared parts of the data must not be
wenzelm@34921
   397
  duplicated by naive concatenation, or a theory graph that is like a
wenzelm@34921
   398
  chain of diamonds would cause an exponential blowup!
wenzelm@34921
   399
wenzelm@33524
   400
  \paragraph{Proof context data} declarations need to implement the
wenzelm@33524
   401
  following SML signature:
wenzelm@20449
   402
wenzelm@20449
   403
  \medskip
wenzelm@20449
   404
  \begin{tabular}{ll}
wenzelm@22869
   405
  @{text "\<type> T"} & representing type \\
wenzelm@22869
   406
  @{text "\<val> init: theory \<rightarrow> T"} & produce initial value \\
wenzelm@20449
   407
  \end{tabular}
wenzelm@20449
   408
  \medskip
wenzelm@20449
   409
wenzelm@39861
   410
  The @{text "init"} operation is supposed to produce a pure value
wenzelm@39861
   411
  from the given background theory and should be somehow
wenzelm@34921
   412
  ``immediate''.  Whenever a proof context is initialized, which
wenzelm@34921
   413
  happens frequently, the the system invokes the @{text "init"}
wenzelm@39821
   414
  operation of \emph{all} theory data slots ever declared.  This also
wenzelm@39821
   415
  means that one needs to be economic about the total number of proof
wenzelm@39821
   416
  data declarations in the system, i.e.\ each ML module should declare
wenzelm@39821
   417
  at most one, sometimes two data slots for its internal use.
wenzelm@39821
   418
  Repeated data declarations to simulate a record type should be
wenzelm@39821
   419
  avoided!
wenzelm@20449
   420
wenzelm@20451
   421
  \paragraph{Generic data} provides a hybrid interface for both theory
wenzelm@33524
   422
  and proof data.  The @{text "init"} operation for proof contexts is
wenzelm@33524
   423
  predefined to select the current data value from the background
wenzelm@33524
   424
  theory.
wenzelm@20449
   425
wenzelm@39821
   426
  \bigskip Any of the above data declarations over type @{text "T"}
wenzelm@39821
   427
  result in an ML structure with the following signature:
wenzelm@20449
   428
wenzelm@20449
   429
  \medskip
wenzelm@20449
   430
  \begin{tabular}{ll}
wenzelm@20449
   431
  @{text "get: context \<rightarrow> T"} \\
wenzelm@20449
   432
  @{text "put: T \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   433
  @{text "map: (T \<rightarrow> T) \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   434
  \end{tabular}
wenzelm@20449
   435
  \medskip
wenzelm@20449
   436
wenzelm@39861
   437
  These other operations provide exclusive access for the particular
wenzelm@39861
   438
  kind of context (theory, proof, or generic context).  This interface
wenzelm@39861
   439
  observes the ML discipline for types and scopes: there is no other
wenzelm@39861
   440
  way to access the corresponding data slot of a context.  By keeping
wenzelm@39861
   441
  these operations private, an Isabelle/ML module may maintain
wenzelm@39861
   442
  abstract values authentically.  *}
wenzelm@20447
   443
wenzelm@20450
   444
text %mlref {*
wenzelm@20450
   445
  \begin{mldecls}
wenzelm@33524
   446
  @{index_ML_functor Theory_Data} \\
wenzelm@33524
   447
  @{index_ML_functor Proof_Data} \\
wenzelm@33524
   448
  @{index_ML_functor Generic_Data} \\
wenzelm@20450
   449
  \end{mldecls}
wenzelm@20450
   450
wenzelm@20450
   451
  \begin{description}
wenzelm@20450
   452
wenzelm@33524
   453
  \item @{ML_functor Theory_Data}@{text "(spec)"} declares data for
wenzelm@20450
   454
  type @{ML_type theory} according to the specification provided as
wenzelm@20451
   455
  argument structure.  The resulting structure provides data init and
wenzelm@20451
   456
  access operations as described above.
wenzelm@20450
   457
wenzelm@33524
   458
  \item @{ML_functor Proof_Data}@{text "(spec)"} is analogous to
wenzelm@33524
   459
  @{ML_functor Theory_Data} for type @{ML_type Proof.context}.
wenzelm@20450
   460
wenzelm@33524
   461
  \item @{ML_functor Generic_Data}@{text "(spec)"} is analogous to
wenzelm@33524
   462
  @{ML_functor Theory_Data} for type @{ML_type Context.generic}.
wenzelm@20450
   463
wenzelm@20450
   464
  \end{description}
wenzelm@20450
   465
*}
wenzelm@20450
   466
wenzelm@34928
   467
text %mlex {*
wenzelm@34928
   468
  The following artificial example demonstrates theory
wenzelm@34928
   469
  data: we maintain a set of terms that are supposed to be wellformed
wenzelm@34928
   470
  wrt.\ the enclosing theory.  The public interface is as follows:
wenzelm@34928
   471
*}
wenzelm@34928
   472
wenzelm@34928
   473
ML {*
wenzelm@34928
   474
  signature WELLFORMED_TERMS =
wenzelm@34928
   475
  sig
wenzelm@34928
   476
    val get: theory -> term list
wenzelm@34928
   477
    val add: term -> theory -> theory
wenzelm@34928
   478
  end;
wenzelm@34928
   479
*}
wenzelm@34928
   480
wenzelm@39861
   481
text {* The implementation uses private theory data internally, and
wenzelm@39861
   482
  only exposes an operation that involves explicit argument checking
wenzelm@39861
   483
  wrt.\ the given theory. *}
wenzelm@34928
   484
wenzelm@34928
   485
ML {*
wenzelm@34928
   486
  structure Wellformed_Terms: WELLFORMED_TERMS =
wenzelm@34928
   487
  struct
wenzelm@34928
   488
wenzelm@34928
   489
  structure Terms = Theory_Data
wenzelm@34928
   490
  (
wenzelm@39687
   491
    type T = term Ord_List.T;
wenzelm@34928
   492
    val empty = [];
wenzelm@34928
   493
    val extend = I;
wenzelm@34928
   494
    fun merge (ts1, ts2) =
wenzelm@39687
   495
      Ord_List.union Term_Ord.fast_term_ord ts1 ts2;
wenzelm@39861
   496
  );
wenzelm@34928
   497
wenzelm@34928
   498
  val get = Terms.get;
wenzelm@34928
   499
wenzelm@34928
   500
  fun add raw_t thy =
wenzelm@39821
   501
    let
wenzelm@39821
   502
      val t = Sign.cert_term thy raw_t;
wenzelm@39821
   503
    in
wenzelm@39821
   504
      Terms.map (Ord_List.insert Term_Ord.fast_term_ord t) thy
wenzelm@39821
   505
    end;
wenzelm@34928
   506
wenzelm@34928
   507
  end;
wenzelm@34928
   508
*}
wenzelm@34928
   509
wenzelm@39864
   510
text {* Type @{ML_type "term Ord_List.T"} is used for reasonably
wenzelm@39864
   511
  efficient representation of a set of terms: all operations are
wenzelm@39864
   512
  linear in the number of stored elements.  Here we assume that users
wenzelm@39864
   513
  of this module do not care about the declaration order, since that
wenzelm@39864
   514
  data structure forces its own arrangement of elements.
wenzelm@34928
   515
wenzelm@40153
   516
  Observe how the @{ML_text merge} operation joins the data slots of
wenzelm@39687
   517
  the two constituents: @{ML Ord_List.union} prevents duplication of
wenzelm@34928
   518
  common data from different branches, thus avoiding the danger of
wenzelm@39821
   519
  exponential blowup.  Plain list append etc.\ must never be used for
wenzelm@39821
   520
  theory data merges!
wenzelm@34928
   521
wenzelm@34928
   522
  \medskip Our intended invariant is achieved as follows:
wenzelm@34928
   523
  \begin{enumerate}
wenzelm@34928
   524
wenzelm@34928
   525
  \item @{ML Wellformed_Terms.add} only admits terms that have passed
wenzelm@34928
   526
  the @{ML Sign.cert_term} check of the given theory at that point.
wenzelm@34928
   527
wenzelm@34928
   528
  \item Wellformedness in the sense of @{ML Sign.cert_term} is
wenzelm@34928
   529
  monotonic wrt.\ the sub-theory relation.  So our data can move
wenzelm@34928
   530
  upwards in the hierarchy (via extension or merges), and maintain
wenzelm@34928
   531
  wellformedness without further checks.
wenzelm@34928
   532
wenzelm@34928
   533
  \end{enumerate}
wenzelm@34928
   534
wenzelm@34928
   535
  Note that all basic operations of the inference kernel (which
wenzelm@34928
   536
  includes @{ML Sign.cert_term}) observe this monotonicity principle,
wenzelm@34928
   537
  but other user-space tools don't.  For example, fully-featured
wenzelm@34928
   538
  type-inference via @{ML Syntax.check_term} (cf.\
wenzelm@34928
   539
  \secref{sec:term-check}) is not necessarily monotonic wrt.\ the
wenzelm@34928
   540
  background theory, since constraints of term constants can be
wenzelm@39821
   541
  modified by later declarations, for example.
wenzelm@34928
   542
wenzelm@34928
   543
  In most cases, user-space context data does not have to take such
wenzelm@34928
   544
  invariants too seriously.  The situation is different in the
wenzelm@34928
   545
  implementation of the inference kernel itself, which uses the very
wenzelm@34928
   546
  same data mechanisms for types, constants, axioms etc.
wenzelm@34928
   547
*}
wenzelm@34928
   548
wenzelm@20447
   549
wenzelm@39865
   550
subsection {* Configuration options \label{sec:config-options} *}
wenzelm@39865
   551
wenzelm@39865
   552
text {* A \emph{configuration option} is a named optional value of
wenzelm@39865
   553
  some basic type (Boolean, integer, string) that is stored in the
wenzelm@39865
   554
  context.  It is a simple application of general context data
wenzelm@39865
   555
  (\secref{sec:context-data}) that is sufficiently common to justify
wenzelm@39865
   556
  customized setup, which includes some concrete declarations for
wenzelm@39865
   557
  end-users using existing notation for attributes (cf.\
wenzelm@39865
   558
  \secref{sec:attributes}).
wenzelm@39865
   559
wenzelm@39865
   560
  For example, the predefined configuration option @{attribute
wenzelm@39865
   561
  show_types} controls output of explicit type constraints for
wenzelm@39876
   562
  variables in printed terms (cf.\ \secref{sec:read-print}).  Its
wenzelm@39865
   563
  value can be modified within Isar text like this:
wenzelm@39865
   564
*}
wenzelm@39865
   565
wenzelm@39865
   566
declare [[show_types = false]]
wenzelm@39865
   567
  -- {* declaration within (local) theory context *}
wenzelm@39865
   568
wenzelm@40964
   569
notepad
wenzelm@40964
   570
begin
wenzelm@39865
   571
  note [[show_types = true]]
wenzelm@39865
   572
    -- {* declaration within proof (forward mode) *}
wenzelm@39865
   573
  term x
wenzelm@39865
   574
wenzelm@39865
   575
  have "x = x"
wenzelm@39865
   576
    using [[show_types = false]]
wenzelm@39865
   577
      -- {* declaration within proof (backward mode) *}
wenzelm@39865
   578
    ..
wenzelm@40964
   579
end
wenzelm@39865
   580
wenzelm@39865
   581
text {* Configuration options that are not set explicitly hold a
wenzelm@39865
   582
  default value that can depend on the application context.  This
wenzelm@39865
   583
  allows to retrieve the value from another slot within the context,
wenzelm@39865
   584
  or fall back on a global preference mechanism, for example.
wenzelm@39865
   585
wenzelm@39865
   586
  The operations to declare configuration options and get/map their
wenzelm@39865
   587
  values are modeled as direct replacements for historic global
wenzelm@39865
   588
  references, only that the context is made explicit.  This allows
wenzelm@39865
   589
  easy configuration of tools, without relying on the execution order
wenzelm@39865
   590
  as required for old-style mutable references.  *}
wenzelm@39865
   591
wenzelm@39865
   592
text %mlref {*
wenzelm@39865
   593
  \begin{mldecls}
wenzelm@39865
   594
  @{index_ML Config.get: "Proof.context -> 'a Config.T -> 'a"} \\
wenzelm@39865
   595
  @{index_ML Config.map: "'a Config.T -> ('a -> 'a) -> Proof.context -> Proof.context"} \\
wenzelm@39865
   596
  @{index_ML Attrib.config_bool: "string -> (Context.generic -> bool) ->
wenzelm@39865
   597
  bool Config.T * (theory -> theory)"} \\
wenzelm@39865
   598
  @{index_ML Attrib.config_int: "string -> (Context.generic -> int) ->
wenzelm@39865
   599
  int Config.T * (theory -> theory)"} \\
wenzelm@40291
   600
  @{index_ML Attrib.config_real: "string -> (Context.generic -> real) ->
wenzelm@40291
   601
  real Config.T * (theory -> theory)"} \\
wenzelm@39865
   602
  @{index_ML Attrib.config_string: "string -> (Context.generic -> string) ->
wenzelm@39865
   603
  string Config.T * (theory -> theory)"} \\
wenzelm@39865
   604
  \end{mldecls}
wenzelm@39865
   605
wenzelm@39865
   606
  \begin{description}
wenzelm@39865
   607
wenzelm@39865
   608
  \item @{ML Config.get}~@{text "ctxt config"} gets the value of
wenzelm@39865
   609
  @{text "config"} in the given context.
wenzelm@39865
   610
wenzelm@39865
   611
  \item @{ML Config.map}~@{text "config f ctxt"} updates the context
wenzelm@39865
   612
  by updating the value of @{text "config"}.
wenzelm@39865
   613
wenzelm@39865
   614
  \item @{text "(config, setup) ="}~@{ML Attrib.config_bool}~@{text
wenzelm@39865
   615
  "name default"} creates a named configuration option of type
wenzelm@39865
   616
  @{ML_type bool}, with the given @{text "default"} depending on the
wenzelm@39865
   617
  application context.  The resulting @{text "config"} can be used to
wenzelm@39865
   618
  get/map its value in a given context.  The @{text "setup"} function
wenzelm@39865
   619
  needs to be applied to the theory initially, in order to make
wenzelm@39865
   620
  concrete declaration syntax available to the user.
wenzelm@39865
   621
wenzelm@40291
   622
  \item @{ML Attrib.config_int}, @{ML Attrib.config_real}, and @{ML
wenzelm@40291
   623
  Attrib.config_string} work like @{ML Attrib.config_bool}, but for
wenzelm@40291
   624
  types @{ML_type int} and @{ML_type string}, respectively.
wenzelm@39865
   625
wenzelm@39865
   626
  \end{description}
wenzelm@39865
   627
*}
wenzelm@39865
   628
wenzelm@39865
   629
text %mlex {* The following example shows how to declare and use a
wenzelm@39865
   630
  Boolean configuration option called @{text "my_flag"} with constant
wenzelm@39865
   631
  default value @{ML false}.  *}
wenzelm@39865
   632
wenzelm@39865
   633
ML {*
wenzelm@39865
   634
  val (my_flag, my_flag_setup) =
wenzelm@39865
   635
    Attrib.config_bool "my_flag" (K false)
wenzelm@39865
   636
*}
wenzelm@39865
   637
setup my_flag_setup
wenzelm@39865
   638
wenzelm@39865
   639
text {* Now the user can refer to @{attribute my_flag} in
wenzelm@40126
   640
  declarations, while ML tools can retrieve the current value from the
wenzelm@39865
   641
  context via @{ML Config.get}.  *}
wenzelm@39865
   642
wenzelm@39866
   643
ML_val {* @{assert} (Config.get @{context} my_flag = false) *}
wenzelm@39865
   644
wenzelm@39865
   645
declare [[my_flag = true]]
wenzelm@39865
   646
wenzelm@39866
   647
ML_val {* @{assert} (Config.get @{context} my_flag = true) *}
wenzelm@39865
   648
wenzelm@40964
   649
notepad
wenzelm@40964
   650
begin
wenzelm@39866
   651
  {
wenzelm@39866
   652
    note [[my_flag = false]]
wenzelm@39866
   653
    ML_val {* @{assert} (Config.get @{context} my_flag = false) *}
wenzelm@39866
   654
  }
wenzelm@39866
   655
  ML_val {* @{assert} (Config.get @{context} my_flag = true) *}
wenzelm@40964
   656
end
wenzelm@39865
   657
wenzelm@40291
   658
text {* Here is another example involving ML type @{ML_type real}
wenzelm@40291
   659
  (floating-point numbers). *}
wenzelm@40291
   660
wenzelm@40291
   661
ML {*
wenzelm@40291
   662
  val (airspeed_velocity, airspeed_velocity_setup) =
wenzelm@40291
   663
    Attrib.config_real "airspeed_velocity" (K 0.0)
wenzelm@40291
   664
*}
wenzelm@40291
   665
setup airspeed_velocity_setup
wenzelm@40291
   666
wenzelm@40296
   667
declare [[airspeed_velocity = 10]]
wenzelm@40291
   668
declare [[airspeed_velocity = 9.9]]
wenzelm@40291
   669
wenzelm@39865
   670
wenzelm@26872
   671
section {* Names \label{sec:names} *}
wenzelm@20451
   672
wenzelm@34925
   673
text {* In principle, a name is just a string, but there are various
wenzelm@34925
   674
  conventions for representing additional structure.  For example,
wenzelm@34927
   675
  ``@{text "Foo.bar.baz"}'' is considered as a long name consisting of
wenzelm@34927
   676
  qualifier @{text "Foo.bar"} and base name @{text "baz"}.  The
wenzelm@34927
   677
  individual constituents of a name may have further substructure,
wenzelm@34927
   678
  e.g.\ the string ``\verb,\,\verb,<alpha>,'' encodes as a single
wenzelm@34927
   679
  symbol.
wenzelm@34927
   680
wenzelm@34927
   681
  \medskip Subsequently, we shall introduce specific categories of
wenzelm@34927
   682
  names.  Roughly speaking these correspond to logical entities as
wenzelm@34927
   683
  follows:
wenzelm@34927
   684
  \begin{itemize}
wenzelm@34927
   685
wenzelm@34927
   686
  \item Basic names (\secref{sec:basic-name}): free and bound
wenzelm@34927
   687
  variables.
wenzelm@34927
   688
wenzelm@34927
   689
  \item Indexed names (\secref{sec:indexname}): schematic variables.
wenzelm@34927
   690
wenzelm@34927
   691
  \item Long names (\secref{sec:long-name}): constants of any kind
wenzelm@34927
   692
  (type constructors, term constants, other concepts defined in user
wenzelm@34927
   693
  space).  Such entities are typically managed via name spaces
wenzelm@34927
   694
  (\secref{sec:name-space}).
wenzelm@34927
   695
wenzelm@34927
   696
  \end{itemize}
wenzelm@20451
   697
*}
wenzelm@20437
   698
wenzelm@20437
   699
wenzelm@39863
   700
subsection {* Strings of symbols \label{sec:symbols} *}
wenzelm@20437
   701
wenzelm@34925
   702
text {* A \emph{symbol} constitutes the smallest textual unit in
wenzelm@34925
   703
  Isabelle --- raw ML characters are normally not encountered at all!
wenzelm@34925
   704
  Isabelle strings consist of a sequence of symbols, represented as a
wenzelm@34925
   705
  packed string or an exploded list of strings.  Each symbol is in
wenzelm@34925
   706
  itself a small string, which has either one of the following forms:
wenzelm@20437
   707
wenzelm@20451
   708
  \begin{enumerate}
wenzelm@20437
   709
wenzelm@37533
   710
  \item a single ASCII character ``@{text "c"}'', for example
wenzelm@37533
   711
  ``\verb,a,'',
wenzelm@37533
   712
wenzelm@37533
   713
  \item a codepoint according to UTF8 (non-ASCII byte sequence),
wenzelm@20437
   714
wenzelm@20488
   715
  \item a regular symbol ``\verb,\,\verb,<,@{text "ident"}\verb,>,'',
wenzelm@20476
   716
  for example ``\verb,\,\verb,<alpha>,'',
wenzelm@20437
   717
wenzelm@20488
   718
  \item a control symbol ``\verb,\,\verb,<^,@{text "ident"}\verb,>,'',
wenzelm@20476
   719
  for example ``\verb,\,\verb,<^bold>,'',
wenzelm@20437
   720
wenzelm@20488
   721
  \item a raw symbol ``\verb,\,\verb,<^raw:,@{text text}\verb,>,''
wenzelm@34925
   722
  where @{text text} consists of printable characters excluding
wenzelm@20476
   723
  ``\verb,.,'' and ``\verb,>,'', for example
wenzelm@20476
   724
  ``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
wenzelm@20437
   725
wenzelm@20488
   726
  \item a numbered raw control symbol ``\verb,\,\verb,<^raw,@{text
wenzelm@20476
   727
  n}\verb,>, where @{text n} consists of digits, for example
wenzelm@20451
   728
  ``\verb,\,\verb,<^raw42>,''.
wenzelm@20437
   729
wenzelm@20451
   730
  \end{enumerate}
wenzelm@20437
   731
wenzelm@39861
   732
  The @{text "ident"} syntax for symbol names is @{text "letter
wenzelm@39861
   733
  (letter | digit)\<^sup>*"}, where @{text "letter = A..Za..z"} and @{text
wenzelm@39861
   734
  "digit = 0..9"}.  There are infinitely many regular symbols and
wenzelm@39861
   735
  control symbols, but a fixed collection of standard symbols is
wenzelm@39861
   736
  treated specifically.  For example, ``\verb,\,\verb,<alpha>,'' is
wenzelm@39861
   737
  classified as a letter, which means it may occur within regular
wenzelm@39861
   738
  Isabelle identifiers.
wenzelm@20437
   739
wenzelm@37533
   740
  The character set underlying Isabelle symbols is 7-bit ASCII, but
wenzelm@37533
   741
  8-bit character sequences are passed-through unchanged.  Unicode/UCS
wenzelm@37533
   742
  data in UTF-8 encoding is processed in a non-strict fashion, such
wenzelm@37533
   743
  that well-formed code sequences are recognized
wenzelm@37533
   744
  accordingly.\footnote{Note that ISO-Latin-1 differs from UTF-8 only
wenzelm@37533
   745
  in some special punctuation characters that even have replacements
wenzelm@37533
   746
  within the standard collection of Isabelle symbols.  Text consisting
wenzelm@37533
   747
  of ASCII plus accented letters can be processed in either encoding.}
wenzelm@37533
   748
  Unicode provides its own collection of mathematical symbols, but
wenzelm@37533
   749
  within the core Isabelle/ML world there is no link to the standard
wenzelm@37533
   750
  collection of Isabelle regular symbols.
wenzelm@20476
   751
wenzelm@20476
   752
  \medskip Output of Isabelle symbols depends on the print mode
wenzelm@29758
   753
  (\secref{print-mode}).  For example, the standard {\LaTeX} setup of
wenzelm@29758
   754
  the Isabelle document preparation system would present
wenzelm@20451
   755
  ``\verb,\,\verb,<alpha>,'' as @{text "\<alpha>"}, and
wenzelm@20451
   756
  ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as @{text
wenzelm@34925
   757
  "\<^bold>\<alpha>"}.  On-screen rendering usually works by mapping a finite
wenzelm@34925
   758
  subset of Isabelle symbols to suitable Unicode characters.
wenzelm@20451
   759
*}
wenzelm@20437
   760
wenzelm@20437
   761
text %mlref {*
wenzelm@20437
   762
  \begin{mldecls}
wenzelm@34921
   763
  @{index_ML_type "Symbol.symbol": string} \\
wenzelm@20437
   764
  @{index_ML Symbol.explode: "string -> Symbol.symbol list"} \\
wenzelm@20437
   765
  @{index_ML Symbol.is_letter: "Symbol.symbol -> bool"} \\
wenzelm@20437
   766
  @{index_ML Symbol.is_digit: "Symbol.symbol -> bool"} \\
wenzelm@20437
   767
  @{index_ML Symbol.is_quasi: "Symbol.symbol -> bool"} \\
wenzelm@20547
   768
  @{index_ML Symbol.is_blank: "Symbol.symbol -> bool"} \\
wenzelm@20547
   769
  \end{mldecls}
wenzelm@20547
   770
  \begin{mldecls}
wenzelm@20437
   771
  @{index_ML_type "Symbol.sym"} \\
wenzelm@20437
   772
  @{index_ML Symbol.decode: "Symbol.symbol -> Symbol.sym"} \\
wenzelm@20437
   773
  \end{mldecls}
wenzelm@20437
   774
wenzelm@20437
   775
  \begin{description}
wenzelm@20437
   776
wenzelm@39864
   777
  \item Type @{ML_type "Symbol.symbol"} represents individual Isabelle
wenzelm@34921
   778
  symbols.
wenzelm@20437
   779
wenzelm@20476
   780
  \item @{ML "Symbol.explode"}~@{text "str"} produces a symbol list
wenzelm@39821
   781
  from the packed form.  This function supersedes @{ML
wenzelm@20476
   782
  "String.explode"} for virtually all purposes of manipulating text in
wenzelm@34925
   783
  Isabelle!\footnote{The runtime overhead for exploded strings is
wenzelm@34925
   784
  mainly that of the list structure: individual symbols that happen to
wenzelm@39821
   785
  be a singleton string do not require extra memory in Poly/ML.}
wenzelm@20437
   786
wenzelm@20437
   787
  \item @{ML "Symbol.is_letter"}, @{ML "Symbol.is_digit"}, @{ML
wenzelm@20476
   788
  "Symbol.is_quasi"}, @{ML "Symbol.is_blank"} classify standard
wenzelm@20476
   789
  symbols according to fixed syntactic conventions of Isabelle, cf.\
wenzelm@20476
   790
  \cite{isabelle-isar-ref}.
wenzelm@20437
   791
wenzelm@39864
   792
  \item Type @{ML_type "Symbol.sym"} is a concrete datatype that
wenzelm@39864
   793
  represents the different kinds of symbols explicitly, with
wenzelm@39864
   794
  constructors @{ML "Symbol.Char"}, @{ML "Symbol.Sym"}, @{ML
wenzelm@39864
   795
  "Symbol.UTF8"}, @{ML "Symbol.Ctrl"}, @{ML "Symbol.Raw"}.
wenzelm@20437
   796
wenzelm@20437
   797
  \item @{ML "Symbol.decode"} converts the string representation of a
wenzelm@20451
   798
  symbol into the datatype version.
wenzelm@20437
   799
wenzelm@20437
   800
  \end{description}
wenzelm@34925
   801
wenzelm@34925
   802
  \paragraph{Historical note.} In the original SML90 standard the
wenzelm@40628
   803
  primitive ML type @{ML_type char} did not exists, and the @{ML_text
wenzelm@34925
   804
  "explode: string -> string list"} operation would produce a list of
wenzelm@40628
   805
  singleton strings as does @{ML "raw_explode: string -> string list"}
wenzelm@40628
   806
  in Isabelle/ML today.  When SML97 came out, Isabelle did not adopt
wenzelm@40628
   807
  its slightly anachronistic 8-bit characters, but the idea of
wenzelm@40628
   808
  exploding a string into a list of small strings was extended to
wenzelm@40628
   809
  ``symbols'' as explained above.  Thus Isabelle sources can refer to
wenzelm@40628
   810
  an infinite store of user-defined symbols, without having to worry
wenzelm@40628
   811
  about the multitude of Unicode encodings.  *}
wenzelm@20437
   812
wenzelm@20437
   813
wenzelm@34927
   814
subsection {* Basic names \label{sec:basic-name} *}
wenzelm@20476
   815
wenzelm@20476
   816
text {*
wenzelm@20476
   817
  A \emph{basic name} essentially consists of a single Isabelle
wenzelm@20476
   818
  identifier.  There are conventions to mark separate classes of basic
wenzelm@29761
   819
  names, by attaching a suffix of underscores: one underscore means
wenzelm@29761
   820
  \emph{internal name}, two underscores means \emph{Skolem name},
wenzelm@29761
   821
  three underscores means \emph{internal Skolem name}.
wenzelm@20476
   822
wenzelm@20476
   823
  For example, the basic name @{text "foo"} has the internal version
wenzelm@20476
   824
  @{text "foo_"}, with Skolem versions @{text "foo__"} and @{text
wenzelm@20476
   825
  "foo___"}, respectively.
wenzelm@20476
   826
wenzelm@20488
   827
  These special versions provide copies of the basic name space, apart
wenzelm@20488
   828
  from anything that normally appears in the user text.  For example,
wenzelm@20488
   829
  system generated variables in Isar proof contexts are usually marked
wenzelm@34926
   830
  as internal, which prevents mysterious names like @{text "xaa"} to
wenzelm@34926
   831
  appear in human-readable text.
wenzelm@20476
   832
wenzelm@20488
   833
  \medskip Manipulating binding scopes often requires on-the-fly
wenzelm@20488
   834
  renamings.  A \emph{name context} contains a collection of already
wenzelm@20488
   835
  used names.  The @{text "declare"} operation adds names to the
wenzelm@20488
   836
  context.
wenzelm@20476
   837
wenzelm@20488
   838
  The @{text "invents"} operation derives a number of fresh names from
wenzelm@20488
   839
  a given starting point.  For example, the first three names derived
wenzelm@20488
   840
  from @{text "a"} are @{text "a"}, @{text "b"}, @{text "c"}.
wenzelm@20476
   841
wenzelm@20476
   842
  The @{text "variants"} operation produces fresh names by
wenzelm@20488
   843
  incrementing tentative names as base-26 numbers (with digits @{text
wenzelm@20488
   844
  "a..z"}) until all clashes are resolved.  For example, name @{text
wenzelm@20488
   845
  "foo"} results in variants @{text "fooa"}, @{text "foob"}, @{text
wenzelm@20488
   846
  "fooc"}, \dots, @{text "fooaa"}, @{text "fooab"} etc.; each renaming
wenzelm@20488
   847
  step picks the next unused variant from this sequence.
wenzelm@20476
   848
*}
wenzelm@20476
   849
wenzelm@20476
   850
text %mlref {*
wenzelm@20476
   851
  \begin{mldecls}
wenzelm@20476
   852
  @{index_ML Name.internal: "string -> string"} \\
wenzelm@20547
   853
  @{index_ML Name.skolem: "string -> string"} \\
wenzelm@20547
   854
  \end{mldecls}
wenzelm@20547
   855
  \begin{mldecls}
wenzelm@20476
   856
  @{index_ML_type Name.context} \\
wenzelm@20476
   857
  @{index_ML Name.context: Name.context} \\
wenzelm@20476
   858
  @{index_ML Name.declare: "string -> Name.context -> Name.context"} \\
wenzelm@20476
   859
  @{index_ML Name.invents: "Name.context -> string -> int -> string list"} \\
wenzelm@20476
   860
  @{index_ML Name.variants: "string list -> Name.context -> string list * Name.context"} \\
wenzelm@20476
   861
  \end{mldecls}
wenzelm@34926
   862
  \begin{mldecls}
wenzelm@34926
   863
  @{index_ML Variable.names_of: "Proof.context -> Name.context"} \\
wenzelm@34926
   864
  \end{mldecls}
wenzelm@20476
   865
wenzelm@20476
   866
  \begin{description}
wenzelm@20476
   867
wenzelm@20476
   868
  \item @{ML Name.internal}~@{text "name"} produces an internal name
wenzelm@20476
   869
  by adding one underscore.
wenzelm@20476
   870
wenzelm@20476
   871
  \item @{ML Name.skolem}~@{text "name"} produces a Skolem name by
wenzelm@20476
   872
  adding two underscores.
wenzelm@20476
   873
wenzelm@39864
   874
  \item Type @{ML_type Name.context} represents the context of already
wenzelm@39864
   875
  used names; the initial value is @{ML "Name.context"}.
wenzelm@20476
   876
wenzelm@20488
   877
  \item @{ML Name.declare}~@{text "name"} enters a used name into the
wenzelm@20488
   878
  context.
wenzelm@20437
   879
wenzelm@20488
   880
  \item @{ML Name.invents}~@{text "context name n"} produces @{text
wenzelm@20488
   881
  "n"} fresh names derived from @{text "name"}.
wenzelm@20488
   882
wenzelm@20488
   883
  \item @{ML Name.variants}~@{text "names context"} produces fresh
wenzelm@29761
   884
  variants of @{text "names"}; the result is entered into the context.
wenzelm@20476
   885
wenzelm@34926
   886
  \item @{ML Variable.names_of}~@{text "ctxt"} retrieves the context
wenzelm@34926
   887
  of declared type and term variable names.  Projecting a proof
wenzelm@34926
   888
  context down to a primitive name context is occasionally useful when
wenzelm@34926
   889
  invoking lower-level operations.  Regular management of ``fresh
wenzelm@34926
   890
  variables'' is done by suitable operations of structure @{ML_struct
wenzelm@34926
   891
  Variable}, which is also able to provide an official status of
wenzelm@34926
   892
  ``locally fixed variable'' within the logical environment (cf.\
wenzelm@34926
   893
  \secref{sec:variables}).
wenzelm@34926
   894
wenzelm@20476
   895
  \end{description}
wenzelm@20476
   896
*}
wenzelm@20476
   897
wenzelm@39857
   898
text %mlex {* The following simple examples demonstrate how to produce
wenzelm@39857
   899
  fresh names from the initial @{ML Name.context}. *}
wenzelm@39857
   900
wenzelm@39857
   901
ML {*
wenzelm@39866
   902
  val list1 = Name.invents Name.context "a" 5;
wenzelm@39866
   903
  @{assert} (list1 = ["a", "b", "c", "d", "e"]);
wenzelm@39866
   904
wenzelm@39866
   905
  val list2 =
wenzelm@39866
   906
    #1 (Name.variants ["x", "x", "a", "a", "'a", "'a"] Name.context);
wenzelm@39866
   907
  @{assert} (list2 = ["x", "xa", "a", "aa", "'a", "'aa"]);
wenzelm@39857
   908
*}
wenzelm@39857
   909
wenzelm@40126
   910
text {* \medskip The same works relatively to the formal context as
wenzelm@39861
   911
  follows. *}
wenzelm@39857
   912
wenzelm@39857
   913
locale ex = fixes a b c :: 'a
wenzelm@39857
   914
begin
wenzelm@39857
   915
wenzelm@39857
   916
ML {*
wenzelm@39857
   917
  val names = Variable.names_of @{context};
wenzelm@39866
   918
wenzelm@39866
   919
  val list1 = Name.invents names "a" 5;
wenzelm@39866
   920
  @{assert} (list1 = ["d", "e", "f", "g", "h"]);
wenzelm@39866
   921
wenzelm@39866
   922
  val list2 =
wenzelm@39866
   923
    #1 (Name.variants ["x", "x", "a", "a", "'a", "'a"] names);
wenzelm@39866
   924
  @{assert} (list2 = ["x", "xa", "aa", "ab", "'aa", "'ab"]);
wenzelm@39857
   925
*}
wenzelm@39857
   926
wenzelm@39857
   927
end
wenzelm@39857
   928
wenzelm@20476
   929
wenzelm@34927
   930
subsection {* Indexed names \label{sec:indexname} *}
wenzelm@20476
   931
wenzelm@20476
   932
text {*
wenzelm@20476
   933
  An \emph{indexed name} (or @{text "indexname"}) is a pair of a basic
wenzelm@20488
   934
  name and a natural number.  This representation allows efficient
wenzelm@20488
   935
  renaming by incrementing the second component only.  The canonical
wenzelm@20488
   936
  way to rename two collections of indexnames apart from each other is
wenzelm@20488
   937
  this: determine the maximum index @{text "maxidx"} of the first
wenzelm@20488
   938
  collection, then increment all indexes of the second collection by
wenzelm@20488
   939
  @{text "maxidx + 1"}; the maximum index of an empty collection is
wenzelm@20488
   940
  @{text "-1"}.
wenzelm@20476
   941
wenzelm@34927
   942
  Occasionally, basic names are injected into the same pair type of
wenzelm@34927
   943
  indexed names: then @{text "(x, -1)"} is used to encode the basic
wenzelm@34927
   944
  name @{text "x"}.
wenzelm@20488
   945
wenzelm@20488
   946
  \medskip Isabelle syntax observes the following rules for
wenzelm@20488
   947
  representing an indexname @{text "(x, i)"} as a packed string:
wenzelm@20476
   948
wenzelm@20476
   949
  \begin{itemize}
wenzelm@20476
   950
wenzelm@20479
   951
  \item @{text "?x"} if @{text "x"} does not end with a digit and @{text "i = 0"},
wenzelm@20476
   952
wenzelm@20476
   953
  \item @{text "?xi"} if @{text "x"} does not end with a digit,
wenzelm@20476
   954
wenzelm@20488
   955
  \item @{text "?x.i"} otherwise.
wenzelm@20476
   956
wenzelm@20476
   957
  \end{itemize}
wenzelm@20470
   958
wenzelm@34927
   959
  Indexnames may acquire large index numbers after several maxidx
wenzelm@34927
   960
  shifts have been applied.  Results are usually normalized towards
wenzelm@34927
   961
  @{text "0"} at certain checkpoints, notably at the end of a proof.
wenzelm@34927
   962
  This works by producing variants of the corresponding basic name
wenzelm@34927
   963
  components.  For example, the collection @{text "?x1, ?x7, ?x42"}
wenzelm@34927
   964
  becomes @{text "?x, ?xa, ?xb"}.
wenzelm@20476
   965
*}
wenzelm@20476
   966
wenzelm@20476
   967
text %mlref {*
wenzelm@20476
   968
  \begin{mldecls}
wenzelm@39861
   969
  @{index_ML_type indexname: "string * int"} \\
wenzelm@20476
   970
  \end{mldecls}
wenzelm@20476
   971
wenzelm@20476
   972
  \begin{description}
wenzelm@20476
   973
wenzelm@39864
   974
  \item Type @{ML_type indexname} represents indexed names.  This is
wenzelm@39864
   975
  an abbreviation for @{ML_type "string * int"}.  The second component
wenzelm@39864
   976
  is usually non-negative, except for situations where @{text "(x,
wenzelm@39864
   977
  -1)"} is used to inject basic names into this type.  Other negative
wenzelm@34926
   978
  indexes should not be used.
wenzelm@20476
   979
wenzelm@20476
   980
  \end{description}
wenzelm@20476
   981
*}
wenzelm@20476
   982
wenzelm@20476
   983
wenzelm@34927
   984
subsection {* Long names \label{sec:long-name} *}
wenzelm@20476
   985
wenzelm@34927
   986
text {* A \emph{long name} consists of a sequence of non-empty name
wenzelm@34927
   987
  components.  The packed representation uses a dot as separator, as
wenzelm@34927
   988
  in ``@{text "A.b.c"}''.  The last component is called \emph{base
wenzelm@34927
   989
  name}, the remaining prefix is called \emph{qualifier} (which may be
wenzelm@34927
   990
  empty).  The qualifier can be understood as the access path to the
wenzelm@34927
   991
  named entity while passing through some nested block-structure,
wenzelm@34927
   992
  although our free-form long names do not really enforce any strict
wenzelm@34927
   993
  discipline.
wenzelm@34927
   994
wenzelm@34927
   995
  For example, an item named ``@{text "A.b.c"}'' may be understood as
wenzelm@34927
   996
  a local entity @{text "c"}, within a local structure @{text "b"},
wenzelm@34927
   997
  within a global structure @{text "A"}.  In practice, long names
wenzelm@34927
   998
  usually represent 1--3 levels of qualification.  User ML code should
wenzelm@34927
   999
  not make any assumptions about the particular structure of long
wenzelm@34927
  1000
  names!
wenzelm@20437
  1001
wenzelm@20476
  1002
  The empty name is commonly used as an indication of unnamed
wenzelm@34927
  1003
  entities, or entities that are not entered into the corresponding
wenzelm@34927
  1004
  name space, whenever this makes any sense.  The basic operations on
wenzelm@34927
  1005
  long names map empty names again to empty names.
wenzelm@20437
  1006
*}
wenzelm@20437
  1007
wenzelm@20476
  1008
text %mlref {*
wenzelm@20476
  1009
  \begin{mldecls}
wenzelm@30365
  1010
  @{index_ML Long_Name.base_name: "string -> string"} \\
wenzelm@30365
  1011
  @{index_ML Long_Name.qualifier: "string -> string"} \\
wenzelm@30365
  1012
  @{index_ML Long_Name.append: "string -> string -> string"} \\
wenzelm@30365
  1013
  @{index_ML Long_Name.implode: "string list -> string"} \\
wenzelm@30365
  1014
  @{index_ML Long_Name.explode: "string -> string list"} \\
wenzelm@20547
  1015
  \end{mldecls}
wenzelm@34927
  1016
wenzelm@34927
  1017
  \begin{description}
wenzelm@34927
  1018
wenzelm@34927
  1019
  \item @{ML Long_Name.base_name}~@{text "name"} returns the base name
wenzelm@34927
  1020
  of a long name.
wenzelm@34927
  1021
wenzelm@34927
  1022
  \item @{ML Long_Name.qualifier}~@{text "name"} returns the qualifier
wenzelm@34927
  1023
  of a long name.
wenzelm@34927
  1024
wenzelm@34927
  1025
  \item @{ML Long_Name.append}~@{text "name\<^isub>1 name\<^isub>2"} appends two long
wenzelm@34927
  1026
  names.
wenzelm@34927
  1027
wenzelm@34927
  1028
  \item @{ML Long_Name.implode}~@{text "names"} and @{ML
wenzelm@34927
  1029
  Long_Name.explode}~@{text "name"} convert between the packed string
wenzelm@34927
  1030
  representation and the explicit list form of long names.
wenzelm@34927
  1031
wenzelm@34927
  1032
  \end{description}
wenzelm@34927
  1033
*}
wenzelm@34927
  1034
wenzelm@34927
  1035
wenzelm@34927
  1036
subsection {* Name spaces \label{sec:name-space} *}
wenzelm@34927
  1037
wenzelm@34927
  1038
text {* A @{text "name space"} manages a collection of long names,
wenzelm@34927
  1039
  together with a mapping between partially qualified external names
wenzelm@34927
  1040
  and fully qualified internal names (in both directions).  Note that
wenzelm@34927
  1041
  the corresponding @{text "intern"} and @{text "extern"} operations
wenzelm@34927
  1042
  are mostly used for parsing and printing only!  The @{text
wenzelm@34927
  1043
  "declare"} operation augments a name space according to the accesses
wenzelm@34927
  1044
  determined by a given binding, and a naming policy from the context.
wenzelm@34927
  1045
wenzelm@34927
  1046
  \medskip A @{text "binding"} specifies details about the prospective
wenzelm@34927
  1047
  long name of a newly introduced formal entity.  It consists of a
wenzelm@34927
  1048
  base name, prefixes for qualification (separate ones for system
wenzelm@34927
  1049
  infrastructure and user-space mechanisms), a slot for the original
wenzelm@34927
  1050
  source position, and some additional flags.
wenzelm@34927
  1051
wenzelm@34927
  1052
  \medskip A @{text "naming"} provides some additional details for
wenzelm@34927
  1053
  producing a long name from a binding.  Normally, the naming is
wenzelm@34927
  1054
  implicit in the theory or proof context.  The @{text "full"}
wenzelm@34927
  1055
  operation (and its variants for different context types) produces a
wenzelm@34927
  1056
  fully qualified internal name to be entered into a name space.  The
wenzelm@34927
  1057
  main equation of this ``chemical reaction'' when binding new
wenzelm@34927
  1058
  entities in a context is as follows:
wenzelm@34927
  1059
wenzelm@39861
  1060
  \medskip
wenzelm@34927
  1061
  \begin{tabular}{l}
wenzelm@34927
  1062
  @{text "binding + naming \<longrightarrow> long name + name space accesses"}
wenzelm@34927
  1063
  \end{tabular}
wenzelm@34927
  1064
wenzelm@39861
  1065
  \bigskip As a general principle, there is a separate name space for
wenzelm@34927
  1066
  each kind of formal entity, e.g.\ fact, logical constant, type
wenzelm@34927
  1067
  constructor, type class.  It is usually clear from the occurrence in
wenzelm@34927
  1068
  concrete syntax (or from the scope) which kind of entity a name
wenzelm@34927
  1069
  refers to.  For example, the very same name @{text "c"} may be used
wenzelm@34927
  1070
  uniformly for a constant, type constructor, and type class.
wenzelm@34927
  1071
wenzelm@34927
  1072
  There are common schemes to name derived entities systematically
wenzelm@34927
  1073
  according to the name of the main logical entity involved, e.g.\
wenzelm@34927
  1074
  fact @{text "c.intro"} for a canonical introduction rule related to
wenzelm@34927
  1075
  constant @{text "c"}.  This technique of mapping names from one
wenzelm@34927
  1076
  space into another requires some care in order to avoid conflicts.
wenzelm@34927
  1077
  In particular, theorem names derived from a type constructor or type
wenzelm@39839
  1078
  class should get an additional suffix in addition to the usual
wenzelm@39839
  1079
  qualification.  This leads to the following conventions for derived
wenzelm@39839
  1080
  names:
wenzelm@39839
  1081
wenzelm@39839
  1082
  \medskip
wenzelm@39839
  1083
  \begin{tabular}{ll}
wenzelm@39839
  1084
  logical entity & fact name \\\hline
wenzelm@39839
  1085
  constant @{text "c"} & @{text "c.intro"} \\
wenzelm@39839
  1086
  type @{text "c"} & @{text "c_type.intro"} \\
wenzelm@39839
  1087
  class @{text "c"} & @{text "c_class.intro"} \\
wenzelm@39839
  1088
  \end{tabular}
wenzelm@34927
  1089
*}
wenzelm@34927
  1090
wenzelm@34927
  1091
text %mlref {*
wenzelm@34927
  1092
  \begin{mldecls}
wenzelm@34927
  1093
  @{index_ML_type binding} \\
wenzelm@34927
  1094
  @{index_ML Binding.empty: binding} \\
wenzelm@34927
  1095
  @{index_ML Binding.name: "string -> binding"} \\
wenzelm@34927
  1096
  @{index_ML Binding.qualify: "bool -> string -> binding -> binding"} \\
wenzelm@34927
  1097
  @{index_ML Binding.prefix: "bool -> string -> binding -> binding"} \\
wenzelm@34927
  1098
  @{index_ML Binding.conceal: "binding -> binding"} \\
wenzelm@34927
  1099
  @{index_ML Binding.str_of: "binding -> string"} \\
wenzelm@34927
  1100
  \end{mldecls}
wenzelm@20547
  1101
  \begin{mldecls}
haftmann@33174
  1102
  @{index_ML_type Name_Space.naming} \\
haftmann@33174
  1103
  @{index_ML Name_Space.default_naming: Name_Space.naming} \\
haftmann@33174
  1104
  @{index_ML Name_Space.add_path: "string -> Name_Space.naming -> Name_Space.naming"} \\
haftmann@33174
  1105
  @{index_ML Name_Space.full_name: "Name_Space.naming -> binding -> string"} \\
wenzelm@20547
  1106
  \end{mldecls}
wenzelm@20547
  1107
  \begin{mldecls}
haftmann@33174
  1108
  @{index_ML_type Name_Space.T} \\
haftmann@33174
  1109
  @{index_ML Name_Space.empty: "string -> Name_Space.T"} \\
haftmann@33174
  1110
  @{index_ML Name_Space.merge: "Name_Space.T * Name_Space.T -> Name_Space.T"} \\
wenzelm@42401
  1111
  @{index_ML Name_Space.declare: "Proof.context -> bool ->
wenzelm@42401
  1112
  Name_Space.naming -> binding -> Name_Space.T -> string * Name_Space.T"} \\
haftmann@33174
  1113
  @{index_ML Name_Space.intern: "Name_Space.T -> string -> string"} \\
wenzelm@42358
  1114
  @{index_ML Name_Space.extern: "Proof.context -> Name_Space.T -> string -> string"} \\
wenzelm@34927
  1115
  @{index_ML Name_Space.is_concealed: "Name_Space.T -> string -> bool"}
wenzelm@20476
  1116
  \end{mldecls}
wenzelm@20437
  1117
wenzelm@20476
  1118
  \begin{description}
wenzelm@20476
  1119
wenzelm@39864
  1120
  \item Type @{ML_type binding} represents the abstract concept of
wenzelm@39864
  1121
  name bindings.
wenzelm@34927
  1122
wenzelm@34927
  1123
  \item @{ML Binding.empty} is the empty binding.
wenzelm@20476
  1124
wenzelm@34927
  1125
  \item @{ML Binding.name}~@{text "name"} produces a binding with base
wenzelm@39832
  1126
  name @{text "name"}.  Note that this lacks proper source position
wenzelm@39832
  1127
  information; see also the ML antiquotation @{ML_antiquotation
wenzelm@39832
  1128
  binding}.
wenzelm@34927
  1129
wenzelm@34927
  1130
  \item @{ML Binding.qualify}~@{text "mandatory name binding"}
wenzelm@34927
  1131
  prefixes qualifier @{text "name"} to @{text "binding"}.  The @{text
wenzelm@34927
  1132
  "mandatory"} flag tells if this name component always needs to be
wenzelm@34927
  1133
  given in name space accesses --- this is mostly @{text "false"} in
wenzelm@34927
  1134
  practice.  Note that this part of qualification is typically used in
wenzelm@34927
  1135
  derived specification mechanisms.
wenzelm@20437
  1136
wenzelm@34927
  1137
  \item @{ML Binding.prefix} is similar to @{ML Binding.qualify}, but
wenzelm@34927
  1138
  affects the system prefix.  This part of extra qualification is
wenzelm@34927
  1139
  typically used in the infrastructure for modular specifications,
wenzelm@34927
  1140
  notably ``local theory targets'' (see also \chref{ch:local-theory}).
wenzelm@20437
  1141
wenzelm@34927
  1142
  \item @{ML Binding.conceal}~@{text "binding"} indicates that the
wenzelm@34927
  1143
  binding shall refer to an entity that serves foundational purposes
wenzelm@34927
  1144
  only.  This flag helps to mark implementation details of
wenzelm@34927
  1145
  specification mechanism etc.  Other tools should not depend on the
wenzelm@34927
  1146
  particulars of concealed entities (cf.\ @{ML
wenzelm@34927
  1147
  Name_Space.is_concealed}).
wenzelm@34927
  1148
wenzelm@34927
  1149
  \item @{ML Binding.str_of}~@{text "binding"} produces a string
wenzelm@34927
  1150
  representation for human-readable output, together with some formal
wenzelm@34927
  1151
  markup that might get used in GUI front-ends, for example.
wenzelm@20476
  1152
wenzelm@39864
  1153
  \item Type @{ML_type Name_Space.naming} represents the abstract
wenzelm@39864
  1154
  concept of a naming policy.
wenzelm@20437
  1155
haftmann@33174
  1156
  \item @{ML Name_Space.default_naming} is the default naming policy.
wenzelm@20476
  1157
  In a theory context, this is usually augmented by a path prefix
wenzelm@20476
  1158
  consisting of the theory name.
wenzelm@20476
  1159
haftmann@33174
  1160
  \item @{ML Name_Space.add_path}~@{text "path naming"} augments the
wenzelm@20488
  1161
  naming policy by extending its path component.
wenzelm@20437
  1162
haftmann@33174
  1163
  \item @{ML Name_Space.full_name}~@{text "naming binding"} turns a
wenzelm@30281
  1164
  name binding (usually a basic name) into the fully qualified
haftmann@29008
  1165
  internal name, according to the given naming policy.
wenzelm@20476
  1166
wenzelm@39864
  1167
  \item Type @{ML_type Name_Space.T} represents name spaces.
wenzelm@20476
  1168
haftmann@33174
  1169
  \item @{ML Name_Space.empty}~@{text "kind"} and @{ML Name_Space.merge}~@{text
wenzelm@20488
  1170
  "(space\<^isub>1, space\<^isub>2)"} are the canonical operations for
wenzelm@20488
  1171
  maintaining name spaces according to theory data management
haftmann@33174
  1172
  (\secref{sec:context-data}); @{text "kind"} is a formal comment
haftmann@33174
  1173
  to characterize the purpose of a name space.
wenzelm@20437
  1174
wenzelm@42401
  1175
  \item @{ML Name_Space.declare}~@{text "ctxt strict naming bindings
haftmann@33174
  1176
  space"} enters a name binding as fully qualified internal name into
haftmann@33174
  1177
  the name space, with external accesses determined by the naming
haftmann@33174
  1178
  policy.
wenzelm@20476
  1179
haftmann@33174
  1180
  \item @{ML Name_Space.intern}~@{text "space name"} internalizes a
wenzelm@20476
  1181
  (partially qualified) external name.
wenzelm@20437
  1182
wenzelm@20488
  1183
  This operation is mostly for parsing!  Note that fully qualified
wenzelm@20476
  1184
  names stemming from declarations are produced via @{ML
haftmann@33174
  1185
  "Name_Space.full_name"} and @{ML "Name_Space.declare"}
haftmann@29008
  1186
  (or their derivatives for @{ML_type theory} and
wenzelm@20488
  1187
  @{ML_type Proof.context}).
wenzelm@20437
  1188
wenzelm@42358
  1189
  \item @{ML Name_Space.extern}~@{text "ctxt space name"} externalizes a
wenzelm@20476
  1190
  (fully qualified) internal name.
wenzelm@20476
  1191
wenzelm@30281
  1192
  This operation is mostly for printing!  User code should not rely on
wenzelm@30281
  1193
  the precise result too much.
wenzelm@20476
  1194
wenzelm@34927
  1195
  \item @{ML Name_Space.is_concealed}~@{text "space name"} indicates
wenzelm@34927
  1196
  whether @{text "name"} refers to a strictly private entity that
wenzelm@34927
  1197
  other tools are supposed to ignore!
wenzelm@34927
  1198
wenzelm@20476
  1199
  \end{description}
wenzelm@20476
  1200
*}
wenzelm@30272
  1201
wenzelm@39832
  1202
text %mlantiq {*
wenzelm@39832
  1203
  \begin{matharray}{rcl}
wenzelm@39832
  1204
  @{ML_antiquotation_def "binding"} & : & @{text ML_antiquotation} \\
wenzelm@39832
  1205
  \end{matharray}
wenzelm@39832
  1206
wenzelm@42510
  1207
  @{rail "
wenzelm@42510
  1208
  @@{ML_antiquotation binding} name
wenzelm@42510
  1209
  "}
wenzelm@39832
  1210
wenzelm@39832
  1211
  \begin{description}
wenzelm@39832
  1212
wenzelm@39832
  1213
  \item @{text "@{binding name}"} produces a binding with base name
wenzelm@39832
  1214
  @{text "name"} and the source position taken from the concrete
wenzelm@39832
  1215
  syntax of this antiquotation.  In many situations this is more
wenzelm@39832
  1216
  appropriate than the more basic @{ML Binding.name} function.
wenzelm@39832
  1217
wenzelm@39832
  1218
  \end{description}
wenzelm@39832
  1219
*}
wenzelm@39832
  1220
wenzelm@39833
  1221
text %mlex {* The following example yields the source position of some
wenzelm@40126
  1222
  concrete binding inlined into the text:
wenzelm@39833
  1223
*}
wenzelm@39833
  1224
wenzelm@39833
  1225
ML {* Binding.pos_of @{binding here} *}
wenzelm@39833
  1226
wenzelm@39861
  1227
text {* \medskip That position can be also printed in a message as
wenzelm@40126
  1228
  follows: *}
wenzelm@39833
  1229
wenzelm@39833
  1230
ML_command {*
wenzelm@39833
  1231
  writeln
wenzelm@39833
  1232
    ("Look here" ^ Position.str_of (Binding.pos_of @{binding here}))
wenzelm@39833
  1233
*}
wenzelm@39833
  1234
wenzelm@39861
  1235
text {* This illustrates a key virtue of formalized bindings as
wenzelm@39861
  1236
  opposed to raw specifications of base names: the system can use this
wenzelm@40126
  1237
  additional information for feedback given to the user (error
wenzelm@40126
  1238
  messages etc.). *}
wenzelm@39833
  1239
wenzelm@18537
  1240
end