author | wenzelm |
Sat, 09 Oct 2010 21:04:03 +0100 | |
changeset 39832 | 1080dee73a53 |
parent 39825 | f9066b94bf07 |
child 39833 | 6d54a48c859d |
permissions | -rw-r--r-- |
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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.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. |
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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.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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text %mlantiq {* |
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\begin{matharray}{rcl} |
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@{ML_antiquotation_def "theory"} & : & @{text ML_antiquotation} \\ |
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@{ML_antiquotation_def "theory_ref"} & : & @{text ML_antiquotation} \\ |
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\end{matharray} |
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\begin{rail} |
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('theory' | 'theory\_ref') nameref? |
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; |
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\end{rail} |
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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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\item @{text "@{theory_ref}"} is similar to @{text "@{theory}"}, but |
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produces a @{ML_type theory_ref} via @{ML "Theory.check_thy"} as |
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explained above. |
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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 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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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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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} |
|
22869 | 373 |
@{text "\<type> T"} & representing type \\ |
374 |
@{text "\<val> empty: T"} & empty default value \\ |
|
375 |
@{text "\<val> extend: T \<rightarrow> T"} & re-initialize on import \\ |
|
376 |
@{text "\<val> merge: T \<times> T \<rightarrow> T"} & join on import \\ |
|
20449 | 377 |
\end{tabular} |
378 |
\medskip |
|
379 |
||
22869 | 380 |
\noindent The @{text "empty"} value acts as initial default for |
381 |
\emph{any} theory that does not declare actual data content; @{text |
|
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
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33174
diff
changeset
|
382 |
"extend"} is acts like a unitary version of @{text "merge"}. |
20449 | 383 |
|
34921 | 384 |
Implementing @{text "merge"} can be tricky. The general idea is |
385 |
that @{text "merge (data\<^sub>1, data\<^sub>2)"} inserts those parts of @{text |
|
386 |
"data\<^sub>2"} into @{text "data\<^sub>1"} that are not yet present, while |
|
387 |
keeping the general order of things. The @{ML Library.merge} |
|
388 |
function on plain lists may serve as canonical template. |
|
389 |
||
390 |
Particularly note that shared parts of the data must not be |
|
391 |
duplicated by naive concatenation, or a theory graph that is like a |
|
392 |
chain of diamonds would cause an exponential blowup! |
|
393 |
||
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
394 |
\paragraph{Proof context data} declarations need to implement the |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
395 |
following SML signature: |
20449 | 396 |
|
397 |
\medskip |
|
398 |
\begin{tabular}{ll} |
|
22869 | 399 |
@{text "\<type> T"} & representing type \\ |
400 |
@{text "\<val> init: theory \<rightarrow> T"} & produce initial value \\ |
|
20449 | 401 |
\end{tabular} |
402 |
\medskip |
|
403 |
||
404 |
\noindent The @{text "init"} operation is supposed to produce a pure |
|
34921 | 405 |
value from the given background theory and should be somehow |
406 |
``immediate''. Whenever a proof context is initialized, which |
|
407 |
happens frequently, the the system invokes the @{text "init"} |
|
39821 | 408 |
operation of \emph{all} theory data slots ever declared. This also |
409 |
means that one needs to be economic about the total number of proof |
|
410 |
data declarations in the system, i.e.\ each ML module should declare |
|
411 |
at most one, sometimes two data slots for its internal use. |
|
412 |
Repeated data declarations to simulate a record type should be |
|
413 |
avoided! |
|
20449 | 414 |
|
20451 | 415 |
\paragraph{Generic data} provides a hybrid interface for both theory |
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
416 |
and proof data. The @{text "init"} operation for proof contexts is |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
417 |
predefined to select the current data value from the background |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
418 |
theory. |
20449 | 419 |
|
39821 | 420 |
\bigskip Any of the above data declarations over type @{text "T"} |
421 |
result in an ML structure with the following signature: |
|
20449 | 422 |
|
423 |
\medskip |
|
424 |
\begin{tabular}{ll} |
|
425 |
@{text "get: context \<rightarrow> T"} \\ |
|
426 |
@{text "put: T \<rightarrow> context \<rightarrow> context"} \\ |
|
427 |
@{text "map: (T \<rightarrow> T) \<rightarrow> context \<rightarrow> context"} \\ |
|
428 |
\end{tabular} |
|
429 |
\medskip |
|
430 |
||
34921 | 431 |
\noindent These other operations provide exclusive access for the |
432 |
particular kind of context (theory, proof, or generic context). |
|
39821 | 433 |
This interface observes the ML discipline for types and scopes: |
434 |
there is no other way to access the corresponding data slot of a |
|
435 |
context. By keeping these operations private, an Isabelle/ML module |
|
436 |
may maintain abstract values authentically. |
|
20447 | 437 |
*} |
438 |
||
20450 | 439 |
text %mlref {* |
440 |
\begin{mldecls} |
|
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
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parents:
33174
diff
changeset
|
441 |
@{index_ML_functor Theory_Data} \\ |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
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parents:
33174
diff
changeset
|
442 |
@{index_ML_functor Proof_Data} \\ |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
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parents:
33174
diff
changeset
|
443 |
@{index_ML_functor Generic_Data} \\ |
20450 | 444 |
\end{mldecls} |
445 |
||
446 |
\begin{description} |
|
447 |
||
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
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parents:
33174
diff
changeset
|
448 |
\item @{ML_functor Theory_Data}@{text "(spec)"} declares data for |
20450 | 449 |
type @{ML_type theory} according to the specification provided as |
20451 | 450 |
argument structure. The resulting structure provides data init and |
451 |
access operations as described above. |
|
20450 | 452 |
|
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
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parents:
33174
diff
changeset
|
453 |
\item @{ML_functor Proof_Data}@{text "(spec)"} is analogous to |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
454 |
@{ML_functor Theory_Data} for type @{ML_type Proof.context}. |
20450 | 455 |
|
33524
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
456 |
\item @{ML_functor Generic_Data}@{text "(spec)"} is analogous to |
a08e6c1cbc04
updated functor Theory_Data, Proof_Data, Generic_Data;
wenzelm
parents:
33174
diff
changeset
|
457 |
@{ML_functor Theory_Data} for type @{ML_type Context.generic}. |
20450 | 458 |
|
459 |
\end{description} |
|
460 |
*} |
|
461 |
||
34928 | 462 |
text %mlex {* |
463 |
The following artificial example demonstrates theory |
|
464 |
data: we maintain a set of terms that are supposed to be wellformed |
|
465 |
wrt.\ the enclosing theory. The public interface is as follows: |
|
466 |
*} |
|
467 |
||
468 |
ML {* |
|
469 |
signature WELLFORMED_TERMS = |
|
470 |
sig |
|
471 |
val get: theory -> term list |
|
472 |
val add: term -> theory -> theory |
|
473 |
end; |
|
474 |
*} |
|
475 |
||
476 |
text {* \noindent The implementation uses private theory data |
|
477 |
internally, and only exposes an operation that involves explicit |
|
478 |
argument checking wrt.\ the given theory. *} |
|
479 |
||
480 |
ML {* |
|
481 |
structure Wellformed_Terms: WELLFORMED_TERMS = |
|
482 |
struct |
|
483 |
||
484 |
structure Terms = Theory_Data |
|
485 |
( |
|
39687 | 486 |
type T = term Ord_List.T; |
34928 | 487 |
val empty = []; |
488 |
val extend = I; |
|
489 |
fun merge (ts1, ts2) = |
|
39687 | 490 |
Ord_List.union Term_Ord.fast_term_ord ts1 ts2; |
34928 | 491 |
) |
492 |
||
493 |
val get = Terms.get; |
|
494 |
||
495 |
fun add raw_t thy = |
|
39821 | 496 |
let |
497 |
val t = Sign.cert_term thy raw_t; |
|
498 |
in |
|
499 |
Terms.map (Ord_List.insert Term_Ord.fast_term_ord t) thy |
|
500 |
end; |
|
34928 | 501 |
|
502 |
end; |
|
503 |
*} |
|
504 |
||
39821 | 505 |
text {* \noindent We use @{ML_type "term Ord_List.T"} for reasonably |
506 |
efficient representation of a set of terms: all operations are |
|
507 |
linear in the number of stored elements. Here we assume that users |
|
508 |
of this module do not care about the declaration order, since that |
|
509 |
data structure forces its own arrangement of elements. |
|
34928 | 510 |
|
511 |
Observe how the @{verbatim merge} operation joins the data slots of |
|
39687 | 512 |
the two constituents: @{ML Ord_List.union} prevents duplication of |
34928 | 513 |
common data from different branches, thus avoiding the danger of |
39821 | 514 |
exponential blowup. Plain list append etc.\ must never be used for |
515 |
theory data merges! |
|
34928 | 516 |
|
517 |
\medskip Our intended invariant is achieved as follows: |
|
518 |
\begin{enumerate} |
|
519 |
||
520 |
\item @{ML Wellformed_Terms.add} only admits terms that have passed |
|
521 |
the @{ML Sign.cert_term} check of the given theory at that point. |
|
522 |
||
523 |
\item Wellformedness in the sense of @{ML Sign.cert_term} is |
|
524 |
monotonic wrt.\ the sub-theory relation. So our data can move |
|
525 |
upwards in the hierarchy (via extension or merges), and maintain |
|
526 |
wellformedness without further checks. |
|
527 |
||
528 |
\end{enumerate} |
|
529 |
||
530 |
Note that all basic operations of the inference kernel (which |
|
531 |
includes @{ML Sign.cert_term}) observe this monotonicity principle, |
|
532 |
but other user-space tools don't. For example, fully-featured |
|
533 |
type-inference via @{ML Syntax.check_term} (cf.\ |
|
534 |
\secref{sec:term-check}) is not necessarily monotonic wrt.\ the |
|
535 |
background theory, since constraints of term constants can be |
|
39821 | 536 |
modified by later declarations, for example. |
34928 | 537 |
|
538 |
In most cases, user-space context data does not have to take such |
|
539 |
invariants too seriously. The situation is different in the |
|
540 |
implementation of the inference kernel itself, which uses the very |
|
541 |
same data mechanisms for types, constants, axioms etc. |
|
542 |
*} |
|
543 |
||
20447 | 544 |
|
26872 | 545 |
section {* Names \label{sec:names} *} |
20451 | 546 |
|
34925 | 547 |
text {* In principle, a name is just a string, but there are various |
548 |
conventions for representing additional structure. For example, |
|
34927
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
549 |
``@{text "Foo.bar.baz"}'' is considered as a long name consisting of |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
550 |
qualifier @{text "Foo.bar"} and base name @{text "baz"}. The |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
551 |
individual constituents of a name may have further substructure, |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
552 |
e.g.\ the string ``\verb,\,\verb,<alpha>,'' encodes as a single |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
553 |
symbol. |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
554 |
|
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
555 |
\medskip Subsequently, we shall introduce specific categories of |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
556 |
names. Roughly speaking these correspond to logical entities as |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
557 |
follows: |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
558 |
\begin{itemize} |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
559 |
|
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
560 |
\item Basic names (\secref{sec:basic-name}): free and bound |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
561 |
variables. |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
562 |
|
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
563 |
\item Indexed names (\secref{sec:indexname}): schematic variables. |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
564 |
|
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
565 |
\item Long names (\secref{sec:long-name}): constants of any kind |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
566 |
(type constructors, term constants, other concepts defined in user |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
567 |
space). Such entities are typically managed via name spaces |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
568 |
(\secref{sec:name-space}). |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
569 |
|
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
34926
diff
changeset
|
570 |
\end{itemize} |
20451 | 571 |
*} |
20437 | 572 |
|
573 |
||
574 |
subsection {* Strings of symbols *} |
|
575 |
||
34925 | 576 |
text {* A \emph{symbol} constitutes the smallest textual unit in |
577 |
Isabelle --- raw ML characters are normally not encountered at all! |
|
578 |
Isabelle strings consist of a sequence of symbols, represented as a |
|
579 |
packed string or an exploded list of strings. Each symbol is in |
|
580 |
itself a small string, which has either one of the following forms: |
|
20437 | 581 |
|
20451 | 582 |
\begin{enumerate} |
20437 | 583 |
|
37533
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
584 |
\item a single ASCII character ``@{text "c"}'', for example |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
585 |
``\verb,a,'', |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
586 |
|
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
587 |
\item a codepoint according to UTF8 (non-ASCII byte sequence), |
20437 | 588 |
|
20488 | 589 |
\item a regular symbol ``\verb,\,\verb,<,@{text "ident"}\verb,>,'', |
20476 | 590 |
for example ``\verb,\,\verb,<alpha>,'', |
20437 | 591 |
|
20488 | 592 |
\item a control symbol ``\verb,\,\verb,<^,@{text "ident"}\verb,>,'', |
20476 | 593 |
for example ``\verb,\,\verb,<^bold>,'', |
20437 | 594 |
|
20488 | 595 |
\item a raw symbol ``\verb,\,\verb,<^raw:,@{text text}\verb,>,'' |
34925 | 596 |
where @{text text} consists of printable characters excluding |
20476 | 597 |
``\verb,.,'' and ``\verb,>,'', for example |
598 |
``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'', |
|
20437 | 599 |
|
20488 | 600 |
\item a numbered raw control symbol ``\verb,\,\verb,<^raw,@{text |
20476 | 601 |
n}\verb,>, where @{text n} consists of digits, for example |
20451 | 602 |
``\verb,\,\verb,<^raw42>,''. |
20437 | 603 |
|
20451 | 604 |
\end{enumerate} |
20437 | 605 |
|
20476 | 606 |
\noindent The @{text "ident"} syntax for symbol names is @{text |
607 |
"letter (letter | digit)\<^sup>*"}, where @{text "letter = |
|
608 |
A..Za..z"} and @{text "digit = 0..9"}. There are infinitely many |
|
609 |
regular symbols and control symbols, but a fixed collection of |
|
610 |
standard symbols is treated specifically. For example, |
|
20488 | 611 |
``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it |
612 |
may occur within regular Isabelle identifiers. |
|
20437 | 613 |
|
37533
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
614 |
The character set underlying Isabelle symbols is 7-bit ASCII, but |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
615 |
8-bit character sequences are passed-through unchanged. Unicode/UCS |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
616 |
data in UTF-8 encoding is processed in a non-strict fashion, such |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
617 |
that well-formed code sequences are recognized |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
618 |
accordingly.\footnote{Note that ISO-Latin-1 differs from UTF-8 only |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
619 |
in some special punctuation characters that even have replacements |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
620 |
within the standard collection of Isabelle symbols. Text consisting |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
621 |
of ASCII plus accented letters can be processed in either encoding.} |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
622 |
Unicode provides its own collection of mathematical symbols, but |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
623 |
within the core Isabelle/ML world there is no link to the standard |
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
624 |
collection of Isabelle regular symbols. |
20476 | 625 |
|
626 |
\medskip Output of Isabelle symbols depends on the print mode |
|
29758 | 627 |
(\secref{print-mode}). For example, the standard {\LaTeX} setup of |
628 |
the Isabelle document preparation system would present |
|
20451 | 629 |
``\verb,\,\verb,<alpha>,'' as @{text "\<alpha>"}, and |
630 |
``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as @{text |
|
34925 | 631 |
"\<^bold>\<alpha>"}. On-screen rendering usually works by mapping a finite |
632 |
subset of Isabelle symbols to suitable Unicode characters. |
|
20451 | 633 |
*} |
20437 | 634 |
|
635 |
text %mlref {* |
|
636 |
\begin{mldecls} |
|
34921 | 637 |
@{index_ML_type "Symbol.symbol": string} \\ |
20437 | 638 |
@{index_ML Symbol.explode: "string -> Symbol.symbol list"} \\ |
639 |
@{index_ML Symbol.is_letter: "Symbol.symbol -> bool"} \\ |
|
640 |
@{index_ML Symbol.is_digit: "Symbol.symbol -> bool"} \\ |
|
641 |
@{index_ML Symbol.is_quasi: "Symbol.symbol -> bool"} \\ |
|
20547 | 642 |
@{index_ML Symbol.is_blank: "Symbol.symbol -> bool"} \\ |
643 |
\end{mldecls} |
|
644 |
\begin{mldecls} |
|
20437 | 645 |
@{index_ML_type "Symbol.sym"} \\ |
646 |
@{index_ML Symbol.decode: "Symbol.symbol -> Symbol.sym"} \\ |
|
647 |
\end{mldecls} |
|
648 |
||
649 |
\begin{description} |
|
650 |
||
20488 | 651 |
\item @{ML_type "Symbol.symbol"} represents individual Isabelle |
34921 | 652 |
symbols. |
20437 | 653 |
|
20476 | 654 |
\item @{ML "Symbol.explode"}~@{text "str"} produces a symbol list |
39821 | 655 |
from the packed form. This function supersedes @{ML |
20476 | 656 |
"String.explode"} for virtually all purposes of manipulating text in |
34925 | 657 |
Isabelle!\footnote{The runtime overhead for exploded strings is |
658 |
mainly that of the list structure: individual symbols that happen to |
|
39821 | 659 |
be a singleton string do not require extra memory in Poly/ML.} |
20437 | 660 |
|
661 |
\item @{ML "Symbol.is_letter"}, @{ML "Symbol.is_digit"}, @{ML |
|
20476 | 662 |
"Symbol.is_quasi"}, @{ML "Symbol.is_blank"} classify standard |
663 |
symbols according to fixed syntactic conventions of Isabelle, cf.\ |
|
664 |
\cite{isabelle-isar-ref}. |
|
20437 | 665 |
|
666 |
\item @{ML_type "Symbol.sym"} is a concrete datatype that represents |
|
20488 | 667 |
the different kinds of symbols explicitly, with constructors @{ML |
37533
d775bd70f571
explicit treatment of UTF8 character sequences as Isabelle symbols;
wenzelm
parents:
36611
diff
changeset
|
668 |
"Symbol.Char"}, @{ML "Symbol.Sym"}, @{ML "Symbol.UTF8"}, @{ML |
d775bd70f571
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|
669 |
"Symbol.Ctrl"}, @{ML "Symbol.Raw"}. |
20437 | 670 |
|
671 |
\item @{ML "Symbol.decode"} converts the string representation of a |
|
20451 | 672 |
symbol into the datatype version. |
20437 | 673 |
|
674 |
\end{description} |
|
34925 | 675 |
|
676 |
\paragraph{Historical note.} In the original SML90 standard the |
|
677 |
primitive ML type @{ML_type char} did not exists, and the basic @{ML |
|
678 |
"explode: string -> string list"} operation would produce a list of |
|
679 |
singleton strings as in Isabelle/ML today. When SML97 came out, |
|
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|
680 |
Isabelle did not adopt its slightly anachronistic 8-bit characters, |
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|
681 |
but the idea of exploding a string into a list of small strings was |
34925 | 682 |
extended to ``symbols'' as explained above. Thus Isabelle sources |
683 |
can refer to an infinite store of user-defined symbols, without |
|
684 |
having to worry about the multitude of Unicode encodings. |
|
20437 | 685 |
*} |
686 |
||
687 |
||
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|
688 |
subsection {* Basic names \label{sec:basic-name} *} |
20476 | 689 |
|
690 |
text {* |
|
691 |
A \emph{basic name} essentially consists of a single Isabelle |
|
692 |
identifier. There are conventions to mark separate classes of basic |
|
29761 | 693 |
names, by attaching a suffix of underscores: one underscore means |
694 |
\emph{internal name}, two underscores means \emph{Skolem name}, |
|
695 |
three underscores means \emph{internal Skolem name}. |
|
20476 | 696 |
|
697 |
For example, the basic name @{text "foo"} has the internal version |
|
698 |
@{text "foo_"}, with Skolem versions @{text "foo__"} and @{text |
|
699 |
"foo___"}, respectively. |
|
700 |
||
20488 | 701 |
These special versions provide copies of the basic name space, apart |
702 |
from anything that normally appears in the user text. For example, |
|
703 |
system generated variables in Isar proof contexts are usually marked |
|
34926 | 704 |
as internal, which prevents mysterious names like @{text "xaa"} to |
705 |
appear in human-readable text. |
|
20476 | 706 |
|
20488 | 707 |
\medskip Manipulating binding scopes often requires on-the-fly |
708 |
renamings. A \emph{name context} contains a collection of already |
|
709 |
used names. The @{text "declare"} operation adds names to the |
|
710 |
context. |
|
20476 | 711 |
|
20488 | 712 |
The @{text "invents"} operation derives a number of fresh names from |
713 |
a given starting point. For example, the first three names derived |
|
714 |
from @{text "a"} are @{text "a"}, @{text "b"}, @{text "c"}. |
|
20476 | 715 |
|
716 |
The @{text "variants"} operation produces fresh names by |
|
20488 | 717 |
incrementing tentative names as base-26 numbers (with digits @{text |
718 |
"a..z"}) until all clashes are resolved. For example, name @{text |
|
719 |
"foo"} results in variants @{text "fooa"}, @{text "foob"}, @{text |
|
720 |
"fooc"}, \dots, @{text "fooaa"}, @{text "fooab"} etc.; each renaming |
|
721 |
step picks the next unused variant from this sequence. |
|
20476 | 722 |
*} |
723 |
||
724 |
text %mlref {* |
|
725 |
\begin{mldecls} |
|
726 |
@{index_ML Name.internal: "string -> string"} \\ |
|
20547 | 727 |
@{index_ML Name.skolem: "string -> string"} \\ |
728 |
\end{mldecls} |
|
729 |
\begin{mldecls} |
|
20476 | 730 |
@{index_ML_type Name.context} \\ |
731 |
@{index_ML Name.context: Name.context} \\ |
|
732 |
@{index_ML Name.declare: "string -> Name.context -> Name.context"} \\ |
|
733 |
@{index_ML Name.invents: "Name.context -> string -> int -> string list"} \\ |
|
734 |
@{index_ML Name.variants: "string list -> Name.context -> string list * Name.context"} \\ |
|
735 |
\end{mldecls} |
|
34926 | 736 |
\begin{mldecls} |
737 |
@{index_ML Variable.names_of: "Proof.context -> Name.context"} \\ |
|
738 |
\end{mldecls} |
|
20476 | 739 |
|
740 |
\begin{description} |
|
741 |
||
742 |
\item @{ML Name.internal}~@{text "name"} produces an internal name |
|
743 |
by adding one underscore. |
|
744 |
||
745 |
\item @{ML Name.skolem}~@{text "name"} produces a Skolem name by |
|
746 |
adding two underscores. |
|
747 |
||
748 |
\item @{ML_type Name.context} represents the context of already used |
|
749 |
names; the initial value is @{ML "Name.context"}. |
|
750 |
||
20488 | 751 |
\item @{ML Name.declare}~@{text "name"} enters a used name into the |
752 |
context. |
|
20437 | 753 |
|
20488 | 754 |
\item @{ML Name.invents}~@{text "context name n"} produces @{text |
755 |
"n"} fresh names derived from @{text "name"}. |
|
756 |
||
757 |
\item @{ML Name.variants}~@{text "names context"} produces fresh |
|
29761 | 758 |
variants of @{text "names"}; the result is entered into the context. |
20476 | 759 |
|
34926 | 760 |
\item @{ML Variable.names_of}~@{text "ctxt"} retrieves the context |
761 |
of declared type and term variable names. Projecting a proof |
|
762 |
context down to a primitive name context is occasionally useful when |
|
763 |
invoking lower-level operations. Regular management of ``fresh |
|
764 |
variables'' is done by suitable operations of structure @{ML_struct |
|
765 |
Variable}, which is also able to provide an official status of |
|
766 |
``locally fixed variable'' within the logical environment (cf.\ |
|
767 |
\secref{sec:variables}). |
|
768 |
||
20476 | 769 |
\end{description} |
770 |
*} |
|
771 |
||
772 |
||
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|
773 |
subsection {* Indexed names \label{sec:indexname} *} |
20476 | 774 |
|
775 |
text {* |
|
776 |
An \emph{indexed name} (or @{text "indexname"}) is a pair of a basic |
|
20488 | 777 |
name and a natural number. This representation allows efficient |
778 |
renaming by incrementing the second component only. The canonical |
|
779 |
way to rename two collections of indexnames apart from each other is |
|
780 |
this: determine the maximum index @{text "maxidx"} of the first |
|
781 |
collection, then increment all indexes of the second collection by |
|
782 |
@{text "maxidx + 1"}; the maximum index of an empty collection is |
|
783 |
@{text "-1"}. |
|
20476 | 784 |
|
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|
785 |
Occasionally, basic names are injected into the same pair type of |
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|
786 |
indexed names: then @{text "(x, -1)"} is used to encode the basic |
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|
787 |
name @{text "x"}. |
20488 | 788 |
|
789 |
\medskip Isabelle syntax observes the following rules for |
|
790 |
representing an indexname @{text "(x, i)"} as a packed string: |
|
20476 | 791 |
|
792 |
\begin{itemize} |
|
793 |
||
20479 | 794 |
\item @{text "?x"} if @{text "x"} does not end with a digit and @{text "i = 0"}, |
20476 | 795 |
|
796 |
\item @{text "?xi"} if @{text "x"} does not end with a digit, |
|
797 |
||
20488 | 798 |
\item @{text "?x.i"} otherwise. |
20476 | 799 |
|
800 |
\end{itemize} |
|
20470 | 801 |
|
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|
802 |
Indexnames may acquire large index numbers after several maxidx |
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|
803 |
shifts have been applied. Results are usually normalized towards |
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|
804 |
@{text "0"} at certain checkpoints, notably at the end of a proof. |
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|
805 |
This works by producing variants of the corresponding basic name |
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|
806 |
components. For example, the collection @{text "?x1, ?x7, ?x42"} |
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|
807 |
becomes @{text "?x, ?xa, ?xb"}. |
20476 | 808 |
*} |
809 |
||
810 |
text %mlref {* |
|
811 |
\begin{mldecls} |
|
812 |
@{index_ML_type indexname} \\ |
|
813 |
\end{mldecls} |
|
814 |
||
815 |
\begin{description} |
|
816 |
||
817 |
\item @{ML_type indexname} represents indexed names. This is an |
|
818 |
abbreviation for @{ML_type "string * int"}. The second component is |
|
819 |
usually non-negative, except for situations where @{text "(x, -1)"} |
|
34926 | 820 |
is used to inject basic names into this type. Other negative |
821 |
indexes should not be used. |
|
20476 | 822 |
|
823 |
\end{description} |
|
824 |
*} |
|
825 |
||
826 |
||
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|
827 |
subsection {* Long names \label{sec:long-name} *} |
20476 | 828 |
|
34927
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|
829 |
text {* A \emph{long name} consists of a sequence of non-empty name |
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|
830 |
components. The packed representation uses a dot as separator, as |
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|
831 |
in ``@{text "A.b.c"}''. The last component is called \emph{base |
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|
832 |
name}, the remaining prefix is called \emph{qualifier} (which may be |
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|
833 |
empty). The qualifier can be understood as the access path to the |
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changeset
|
834 |
named entity while passing through some nested block-structure, |
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changeset
|
835 |
although our free-form long names do not really enforce any strict |
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changeset
|
836 |
discipline. |
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changeset
|
837 |
|
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|
838 |
For example, an item named ``@{text "A.b.c"}'' may be understood as |
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|
839 |
a local entity @{text "c"}, within a local structure @{text "b"}, |
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|
840 |
within a global structure @{text "A"}. In practice, long names |
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|
841 |
usually represent 1--3 levels of qualification. User ML code should |
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changeset
|
842 |
not make any assumptions about the particular structure of long |
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changeset
|
843 |
names! |
20437 | 844 |
|
20476 | 845 |
The empty name is commonly used as an indication of unnamed |
34927
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changeset
|
846 |
entities, or entities that are not entered into the corresponding |
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changeset
|
847 |
name space, whenever this makes any sense. The basic operations on |
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changeset
|
848 |
long names map empty names again to empty names. |
20437 | 849 |
*} |
850 |
||
20476 | 851 |
text %mlref {* |
852 |
\begin{mldecls} |
|
30365 | 853 |
@{index_ML Long_Name.base_name: "string -> string"} \\ |
854 |
@{index_ML Long_Name.qualifier: "string -> string"} \\ |
|
855 |
@{index_ML Long_Name.append: "string -> string -> string"} \\ |
|
856 |
@{index_ML Long_Name.implode: "string list -> string"} \\ |
|
857 |
@{index_ML Long_Name.explode: "string -> string list"} \\ |
|
20547 | 858 |
\end{mldecls} |
34927
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changeset
|
859 |
|
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changeset
|
860 |
\begin{description} |
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changeset
|
861 |
|
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|
862 |
\item @{ML Long_Name.base_name}~@{text "name"} returns the base name |
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changeset
|
863 |
of a long name. |
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changeset
|
864 |
|
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|
865 |
\item @{ML Long_Name.qualifier}~@{text "name"} returns the qualifier |
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changeset
|
866 |
of a long name. |
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changeset
|
867 |
|
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|
868 |
\item @{ML Long_Name.append}~@{text "name\<^isub>1 name\<^isub>2"} appends two long |
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changeset
|
869 |
names. |
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changeset
|
870 |
|
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|
871 |
\item @{ML Long_Name.implode}~@{text "names"} and @{ML |
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|
872 |
Long_Name.explode}~@{text "name"} convert between the packed string |
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|
873 |
representation and the explicit list form of long names. |
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changeset
|
874 |
|
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|
875 |
\end{description} |
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changeset
|
876 |
*} |
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changeset
|
877 |
|
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changeset
|
878 |
|
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|
879 |
subsection {* Name spaces \label{sec:name-space} *} |
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changeset
|
880 |
|
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|
881 |
text {* A @{text "name space"} manages a collection of long names, |
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|
882 |
together with a mapping between partially qualified external names |
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|
883 |
and fully qualified internal names (in both directions). Note that |
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changeset
|
884 |
the corresponding @{text "intern"} and @{text "extern"} operations |
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|
885 |
are mostly used for parsing and printing only! The @{text |
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|
886 |
"declare"} operation augments a name space according to the accesses |
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changeset
|
887 |
determined by a given binding, and a naming policy from the context. |
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changeset
|
888 |
|
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|
889 |
\medskip A @{text "binding"} specifies details about the prospective |
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changeset
|
890 |
long name of a newly introduced formal entity. It consists of a |
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changeset
|
891 |
base name, prefixes for qualification (separate ones for system |
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changeset
|
892 |
infrastructure and user-space mechanisms), a slot for the original |
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changeset
|
893 |
source position, and some additional flags. |
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changeset
|
894 |
|
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changeset
|
895 |
\medskip A @{text "naming"} provides some additional details for |
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changeset
|
896 |
producing a long name from a binding. Normally, the naming is |
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changeset
|
897 |
implicit in the theory or proof context. The @{text "full"} |
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changeset
|
898 |
operation (and its variants for different context types) produces a |
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changeset
|
899 |
fully qualified internal name to be entered into a name space. The |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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changeset
|
900 |
main equation of this ``chemical reaction'' when binding new |
c4c02ac736a6
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changeset
|
901 |
entities in a context is as follows: |
c4c02ac736a6
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parents:
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diff
changeset
|
902 |
|
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parents:
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diff
changeset
|
903 |
\smallskip |
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diff
changeset
|
904 |
\begin{tabular}{l} |
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changeset
|
905 |
@{text "binding + naming \<longrightarrow> long name + name space accesses"} |
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parents:
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diff
changeset
|
906 |
\end{tabular} |
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parents:
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diff
changeset
|
907 |
\smallskip |
c4c02ac736a6
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parents:
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diff
changeset
|
908 |
|
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|
909 |
\medskip As a general principle, there is a separate name space for |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
910 |
each kind of formal entity, e.g.\ fact, logical constant, type |
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parents:
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diff
changeset
|
911 |
constructor, type class. It is usually clear from the occurrence in |
c4c02ac736a6
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parents:
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diff
changeset
|
912 |
concrete syntax (or from the scope) which kind of entity a name |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
913 |
refers to. For example, the very same name @{text "c"} may be used |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
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diff
changeset
|
914 |
uniformly for a constant, type constructor, and type class. |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
915 |
|
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parents:
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changeset
|
916 |
There are common schemes to name derived entities systematically |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
917 |
according to the name of the main logical entity involved, e.g.\ |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
918 |
fact @{text "c.intro"} for a canonical introduction rule related to |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
919 |
constant @{text "c"}. This technique of mapping names from one |
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more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
920 |
space into another requires some care in order to avoid conflicts. |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
921 |
In particular, theorem names derived from a type constructor or type |
c4c02ac736a6
more details on long names, binding/naming, name space;
wenzelm
parents:
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diff
changeset
|
922 |
class are better suffixed in addition to the usual qualification, |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
923 |
e.g.\ @{text "c_type.intro"} and @{text "c_class.intro"} for |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
924 |
theorems related to type @{text "c"} and class @{text "c"}, |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
925 |
respectively. |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
926 |
*} |
c4c02ac736a6
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parents:
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diff
changeset
|
927 |
|
c4c02ac736a6
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parents:
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diff
changeset
|
928 |
text %mlref {* |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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diff
changeset
|
929 |
\begin{mldecls} |
c4c02ac736a6
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parents:
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diff
changeset
|
930 |
@{index_ML_type binding} \\ |
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parents:
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diff
changeset
|
931 |
@{index_ML Binding.empty: binding} \\ |
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parents:
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changeset
|
932 |
@{index_ML Binding.name: "string -> binding"} \\ |
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more details on long names, binding/naming, name space;
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parents:
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changeset
|
933 |
@{index_ML Binding.qualify: "bool -> string -> binding -> binding"} \\ |
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parents:
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diff
changeset
|
934 |
@{index_ML Binding.prefix: "bool -> string -> binding -> binding"} \\ |
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changeset
|
935 |
@{index_ML Binding.conceal: "binding -> binding"} \\ |
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diff
changeset
|
936 |
@{index_ML Binding.str_of: "binding -> string"} \\ |
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changeset
|
937 |
\end{mldecls} |
20547 | 938 |
\begin{mldecls} |
33174 | 939 |
@{index_ML_type Name_Space.naming} \\ |
940 |
@{index_ML Name_Space.default_naming: Name_Space.naming} \\ |
|
941 |
@{index_ML Name_Space.add_path: "string -> Name_Space.naming -> Name_Space.naming"} \\ |
|
942 |
@{index_ML Name_Space.full_name: "Name_Space.naming -> binding -> string"} \\ |
|
20547 | 943 |
\end{mldecls} |
944 |
\begin{mldecls} |
|
33174 | 945 |
@{index_ML_type Name_Space.T} \\ |
946 |
@{index_ML Name_Space.empty: "string -> Name_Space.T"} \\ |
|
947 |
@{index_ML Name_Space.merge: "Name_Space.T * Name_Space.T -> Name_Space.T"} \\ |
|
948 |
@{index_ML Name_Space.declare: "bool -> Name_Space.naming -> binding -> Name_Space.T -> |
|
949 |
string * Name_Space.T"} \\ |
|
950 |
@{index_ML Name_Space.intern: "Name_Space.T -> string -> string"} \\ |
|
951 |
@{index_ML Name_Space.extern: "Name_Space.T -> string -> string"} \\ |
|
34927
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changeset
|
952 |
@{index_ML Name_Space.is_concealed: "Name_Space.T -> string -> bool"} |
20476 | 953 |
\end{mldecls} |
20437 | 954 |
|
20476 | 955 |
\begin{description} |
956 |
||
34927
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|
957 |
\item @{ML_type binding} represents the abstract concept of name |
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parents:
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changeset
|
958 |
bindings. |
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parents:
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diff
changeset
|
959 |
|
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changeset
|
960 |
\item @{ML Binding.empty} is the empty binding. |
20476 | 961 |
|
34927
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changeset
|
962 |
\item @{ML Binding.name}~@{text "name"} produces a binding with base |
39832 | 963 |
name @{text "name"}. Note that this lacks proper source position |
964 |
information; see also the ML antiquotation @{ML_antiquotation |
|
965 |
binding}. |
|
34927
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parents:
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changeset
|
966 |
|
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changeset
|
967 |
\item @{ML Binding.qualify}~@{text "mandatory name binding"} |
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changeset
|
968 |
prefixes qualifier @{text "name"} to @{text "binding"}. The @{text |
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parents:
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changeset
|
969 |
"mandatory"} flag tells if this name component always needs to be |
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changeset
|
970 |
given in name space accesses --- this is mostly @{text "false"} in |
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changeset
|
971 |
practice. Note that this part of qualification is typically used in |
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parents:
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changeset
|
972 |
derived specification mechanisms. |
20437 | 973 |
|
34927
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parents:
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changeset
|
974 |
\item @{ML Binding.prefix} is similar to @{ML Binding.qualify}, but |
c4c02ac736a6
more details on long names, binding/naming, name space;
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changeset
|
975 |
affects the system prefix. This part of extra qualification is |
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parents:
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changeset
|
976 |
typically used in the infrastructure for modular specifications, |
c4c02ac736a6
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parents:
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diff
changeset
|
977 |
notably ``local theory targets'' (see also \chref{ch:local-theory}). |
20437 | 978 |
|
34927
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changeset
|
979 |
\item @{ML Binding.conceal}~@{text "binding"} indicates that the |
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changeset
|
980 |
binding shall refer to an entity that serves foundational purposes |
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more details on long names, binding/naming, name space;
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changeset
|
981 |
only. This flag helps to mark implementation details of |
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changeset
|
982 |
specification mechanism etc. Other tools should not depend on the |
c4c02ac736a6
more details on long names, binding/naming, name space;
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parents:
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changeset
|
983 |
particulars of concealed entities (cf.\ @{ML |
c4c02ac736a6
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parents:
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changeset
|
984 |
Name_Space.is_concealed}). |
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parents:
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diff
changeset
|
985 |
|
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parents:
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changeset
|
986 |
\item @{ML Binding.str_of}~@{text "binding"} produces a string |
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changeset
|
987 |
representation for human-readable output, together with some formal |
c4c02ac736a6
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parents:
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changeset
|
988 |
markup that might get used in GUI front-ends, for example. |
20476 | 989 |
|
33174 | 990 |
\item @{ML_type Name_Space.naming} represents the abstract concept of |
20476 | 991 |
a naming policy. |
20437 | 992 |
|
33174 | 993 |
\item @{ML Name_Space.default_naming} is the default naming policy. |
20476 | 994 |
In a theory context, this is usually augmented by a path prefix |
995 |
consisting of the theory name. |
|
996 |
||
33174 | 997 |
\item @{ML Name_Space.add_path}~@{text "path naming"} augments the |
20488 | 998 |
naming policy by extending its path component. |
20437 | 999 |
|
33174 | 1000 |
\item @{ML Name_Space.full_name}~@{text "naming binding"} turns a |
30281
9ad15d8ed311
renamed NameSpace.base to NameSpace.base_name (in accordance with "full_name");
wenzelm
parents:
30272
diff
changeset
|
1001 |
name binding (usually a basic name) into the fully qualified |
29008 | 1002 |
internal name, according to the given naming policy. |
20476 | 1003 |
|
33174 | 1004 |
\item @{ML_type Name_Space.T} represents name spaces. |
20476 | 1005 |
|
33174 | 1006 |
\item @{ML Name_Space.empty}~@{text "kind"} and @{ML Name_Space.merge}~@{text |
20488 | 1007 |
"(space\<^isub>1, space\<^isub>2)"} are the canonical operations for |
1008 |
maintaining name spaces according to theory data management |
|
33174 | 1009 |
(\secref{sec:context-data}); @{text "kind"} is a formal comment |
1010 |
to characterize the purpose of a name space. |
|
20437 | 1011 |
|
33174 | 1012 |
\item @{ML Name_Space.declare}~@{text "strict naming bindings |
1013 |
space"} enters a name binding as fully qualified internal name into |
|
1014 |
the name space, with external accesses determined by the naming |
|
1015 |
policy. |
|
20476 | 1016 |
|
33174 | 1017 |
\item @{ML Name_Space.intern}~@{text "space name"} internalizes a |
20476 | 1018 |
(partially qualified) external name. |
20437 | 1019 |
|
20488 | 1020 |
This operation is mostly for parsing! Note that fully qualified |
20476 | 1021 |
names stemming from declarations are produced via @{ML |
33174 | 1022 |
"Name_Space.full_name"} and @{ML "Name_Space.declare"} |
29008 | 1023 |
(or their derivatives for @{ML_type theory} and |
20488 | 1024 |
@{ML_type Proof.context}). |
20437 | 1025 |
|
33174 | 1026 |
\item @{ML Name_Space.extern}~@{text "space name"} externalizes a |
20476 | 1027 |
(fully qualified) internal name. |
1028 |
||
30281
9ad15d8ed311
renamed NameSpace.base to NameSpace.base_name (in accordance with "full_name");
wenzelm
parents:
30272
diff
changeset
|
1029 |
This operation is mostly for printing! User code should not rely on |
9ad15d8ed311
renamed NameSpace.base to NameSpace.base_name (in accordance with "full_name");
wenzelm
parents:
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diff
changeset
|
1030 |
the precise result too much. |
20476 | 1031 |
|
34927
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more details on long names, binding/naming, name space;
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parents:
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changeset
|
1032 |
\item @{ML Name_Space.is_concealed}~@{text "space name"} indicates |
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parents:
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changeset
|
1033 |
whether @{text "name"} refers to a strictly private entity that |
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more details on long names, binding/naming, name space;
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parents:
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changeset
|
1034 |
other tools are supposed to ignore! |
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parents:
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changeset
|
1035 |
|
20476 | 1036 |
\end{description} |
1037 |
*} |
|
30272 | 1038 |
|
39832 | 1039 |
text %mlantiq {* |
1040 |
\begin{matharray}{rcl} |
|
1041 |
@{ML_antiquotation_def "binding"} & : & @{text ML_antiquotation} \\ |
|
1042 |
\end{matharray} |
|
1043 |
||
1044 |
\begin{rail} |
|
1045 |
'binding' name |
|
1046 |
; |
|
1047 |
\end{rail} |
|
1048 |
||
1049 |
\begin{description} |
|
1050 |
||
1051 |
\item @{text "@{binding name}"} produces a binding with base name |
|
1052 |
@{text "name"} and the source position taken from the concrete |
|
1053 |
syntax of this antiquotation. In many situations this is more |
|
1054 |
appropriate than the more basic @{ML Binding.name} function. |
|
1055 |
||
1056 |
\end{description} |
|
1057 |
*} |
|
1058 |
||
18537 | 1059 |
end |