--- a/doc-src/IsarImplementation/Thy/Local_Theory.thy Mon Aug 27 16:48:41 2012 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,167 +0,0 @@
-theory Local_Theory
-imports Base
-begin
-
-chapter {* Local theory specifications \label{ch:local-theory} *}
-
-text {*
- A \emph{local theory} combines aspects of both theory and proof
- context (cf.\ \secref{sec:context}), such that definitional
- specifications may be given relatively to parameters and
- assumptions. A local theory is represented as a regular proof
- context, augmented by administrative data about the \emph{target
- context}.
-
- The target is usually derived from the background theory by adding
- local @{text "\<FIX>"} and @{text "\<ASSUME>"} elements, plus
- suitable modifications of non-logical context data (e.g.\ a special
- type-checking discipline). Once initialized, the target is ready to
- absorb definitional primitives: @{text "\<DEFINE>"} for terms and
- @{text "\<NOTE>"} for theorems. Such definitions may get
- transformed in a target-specific way, but the programming interface
- hides such details.
-
- Isabelle/Pure provides target mechanisms for locales, type-classes,
- type-class instantiations, and general overloading. In principle,
- users can implement new targets as well, but this rather arcane
- discipline is beyond the scope of this manual. In contrast,
- implementing derived definitional packages to be used within a local
- theory context is quite easy: the interfaces are even simpler and
- more abstract than the underlying primitives for raw theories.
-
- Many definitional packages for local theories are available in
- Isabelle. Although a few old packages only work for global
- theories, the standard way of implementing definitional packages in
- Isabelle is via the local theory interface.
-*}
-
-
-section {* Definitional elements *}
-
-text {*
- There are separate elements @{text "\<DEFINE> c \<equiv> t"} for terms, and
- @{text "\<NOTE> b = thm"} for theorems. Types are treated
- implicitly, according to Hindley-Milner discipline (cf.\
- \secref{sec:variables}). These definitional primitives essentially
- act like @{text "let"}-bindings within a local context that may
- already contain earlier @{text "let"}-bindings and some initial
- @{text "\<lambda>"}-bindings. Thus we gain \emph{dependent definitions}
- that are relative to an initial axiomatic context. The following
- diagram illustrates this idea of axiomatic elements versus
- definitional elements:
-
- \begin{center}
- \begin{tabular}{|l|l|l|}
- \hline
- & @{text "\<lambda>"}-binding & @{text "let"}-binding \\
- \hline
- types & fixed @{text "\<alpha>"} & arbitrary @{text "\<beta>"} \\
- terms & @{text "\<FIX> x :: \<tau>"} & @{text "\<DEFINE> c \<equiv> t"} \\
- theorems & @{text "\<ASSUME> a: A"} & @{text "\<NOTE> b = \<^BG>B\<^EN>"} \\
- \hline
- \end{tabular}
- \end{center}
-
- A user package merely needs to produce suitable @{text "\<DEFINE>"}
- and @{text "\<NOTE>"} elements according to the application. For
- example, a package for inductive definitions might first @{text
- "\<DEFINE>"} a certain predicate as some fixed-point construction,
- then @{text "\<NOTE>"} a proven result about monotonicity of the
- functor involved here, and then produce further derived concepts via
- additional @{text "\<DEFINE>"} and @{text "\<NOTE>"} elements.
-
- The cumulative sequence of @{text "\<DEFINE>"} and @{text "\<NOTE>"}
- produced at package runtime is managed by the local theory
- infrastructure by means of an \emph{auxiliary context}. Thus the
- system holds up the impression of working within a fully abstract
- situation with hypothetical entities: @{text "\<DEFINE> c \<equiv> t"}
- always results in a literal fact @{text "\<^BG>c \<equiv> t\<^EN>"}, where
- @{text "c"} is a fixed variable @{text "c"}. The details about
- global constants, name spaces etc. are handled internally.
-
- So the general structure of a local theory is a sandwich of three
- layers:
-
- \begin{center}
- \framebox{\quad auxiliary context \quad\framebox{\quad target context \quad\framebox{\quad background theory\quad}}}
- \end{center}
-
- When a definitional package is finished, the auxiliary context is
- reset to the target context. The target now holds definitions for
- terms and theorems that stem from the hypothetical @{text
- "\<DEFINE>"} and @{text "\<NOTE>"} elements, transformed by the
- particular target policy (see \cite[\S4--5]{Haftmann-Wenzel:2009}
- for details). *}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type local_theory: Proof.context} \\
- @{index_ML Named_Target.init: "(local_theory -> local_theory) ->
- string -> theory -> local_theory"} \\[1ex]
- @{index_ML Local_Theory.define: "(binding * mixfix) * (Attrib.binding * term) ->
- local_theory -> (term * (string * thm)) * local_theory"} \\
- @{index_ML Local_Theory.note: "Attrib.binding * thm list ->
- local_theory -> (string * thm list) * local_theory"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item Type @{ML_type local_theory} represents local theories.
- Although this is merely an alias for @{ML_type Proof.context}, it is
- semantically a subtype of the same: a @{ML_type local_theory} holds
- target information as special context data. Subtyping means that
- any value @{text "lthy:"}~@{ML_type local_theory} can be also used
- with operations on expecting a regular @{text "ctxt:"}~@{ML_type
- Proof.context}.
-
- \item @{ML Named_Target.init}~@{text "before_exit name thy"}
- initializes a local theory derived from the given background theory.
- An empty name refers to a \emph{global theory} context, and a
- non-empty name refers to a @{command locale} or @{command class}
- context (a fully-qualified internal name is expected here). This is
- useful for experimentation --- normally the Isar toplevel already
- takes care to initialize the local theory context. The given @{text
- "before_exit"} function is invoked before leaving the context; in
- most situations plain identity @{ML I} is sufficient.
-
- \item @{ML Local_Theory.define}~@{text "((b, mx), (a, rhs))
- lthy"} defines a local entity according to the specification that is
- given relatively to the current @{text "lthy"} context. In
- particular the term of the RHS may refer to earlier local entities
- from the auxiliary context, or hypothetical parameters from the
- target context. The result is the newly defined term (which is
- always a fixed variable with exactly the same name as specified for
- the LHS), together with an equational theorem that states the
- definition as a hypothetical fact.
-
- Unless an explicit name binding is given for the RHS, the resulting
- fact will be called @{text "b_def"}. Any given attributes are
- applied to that same fact --- immediately in the auxiliary context
- \emph{and} in any transformed versions stemming from target-specific
- policies or any later interpretations of results from the target
- context (think of @{command locale} and @{command interpretation},
- for example). This means that attributes should be usually plain
- declarations such as @{attribute simp}, while non-trivial rules like
- @{attribute simplified} are better avoided.
-
- \item @{ML Local_Theory.note}~@{text "(a, ths) lthy"} is
- analogous to @{ML Local_Theory.define}, but defines facts instead of
- terms. There is also a slightly more general variant @{ML
- Local_Theory.notes} that defines several facts (with attribute
- expressions) simultaneously.
-
- This is essentially the internal version of the @{command lemmas}
- command, or @{command declare} if an empty name binding is given.
-
- \end{description}
-*}
-
-
-section {* Morphisms and declarations \label{sec:morphisms} *}
-
-text {* FIXME
-
- \medskip See also \cite{Chaieb-Wenzel:2007}.
-*}
-
-end