--- a/doc-src/IsarImplementation/Thy/prelim.thy Thu Feb 26 08:44:44 2009 -0800
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,779 +0,0 @@
-
-(* $Id$ *)
-
-theory prelim imports base begin
-
-chapter {* Preliminaries *}
-
-section {* Contexts \label{sec:context} *}
-
-text {*
- A logical context represents the background that is required for
- formulating statements and composing proofs. It acts as a medium to
- produce formal content, depending on earlier material (declarations,
- results etc.).
-
- For example, derivations within the Isabelle/Pure logic can be
- described as a judgment @{text "\<Gamma> \<turnstile>\<^sub>\<Theta> \<phi>"}, which means that a
- proposition @{text "\<phi>"} is derivable from hypotheses @{text "\<Gamma>"}
- within the theory @{text "\<Theta>"}. There are logical reasons for
- keeping @{text "\<Theta>"} and @{text "\<Gamma>"} separate: theories can be
- liberal about supporting type constructors and schematic
- polymorphism of constants and axioms, while the inner calculus of
- @{text "\<Gamma> \<turnstile> \<phi>"} is strictly limited to Simple Type Theory (with
- fixed type variables in the assumptions).
-
- \medskip Contexts and derivations are linked by the following key
- principles:
-
- \begin{itemize}
-
- \item Transfer: monotonicity of derivations admits results to be
- transferred into a \emph{larger} context, i.e.\ @{text "\<Gamma> \<turnstile>\<^sub>\<Theta>
- \<phi>"} implies @{text "\<Gamma>' \<turnstile>\<^sub>\<Theta>\<^sub>' \<phi>"} for contexts @{text "\<Theta>'
- \<supseteq> \<Theta>"} and @{text "\<Gamma>' \<supseteq> \<Gamma>"}.
-
- \item Export: discharge of hypotheses admits results to be exported
- into a \emph{smaller} context, i.e.\ @{text "\<Gamma>' \<turnstile>\<^sub>\<Theta> \<phi>"}
- implies @{text "\<Gamma> \<turnstile>\<^sub>\<Theta> \<Delta> \<Longrightarrow> \<phi>"} where @{text "\<Gamma>' \<supseteq> \<Gamma>"} and
- @{text "\<Delta> = \<Gamma>' - \<Gamma>"}. Note that @{text "\<Theta>"} remains unchanged here,
- only the @{text "\<Gamma>"} part is affected.
-
- \end{itemize}
-
- \medskip By modeling the main characteristics of the primitive
- @{text "\<Theta>"} and @{text "\<Gamma>"} above, and abstracting over any
- particular logical content, we arrive at the fundamental notions of
- \emph{theory context} and \emph{proof context} in Isabelle/Isar.
- These implement a certain policy to manage arbitrary \emph{context
- data}. There is a strongly-typed mechanism to declare new kinds of
- data at compile time.
-
- The internal bootstrap process of Isabelle/Pure eventually reaches a
- stage where certain data slots provide the logical content of @{text
- "\<Theta>"} and @{text "\<Gamma>"} sketched above, but this does not stop there!
- Various additional data slots support all kinds of mechanisms that
- are not necessarily part of the core logic.
-
- For example, there would be data for canonical introduction and
- elimination rules for arbitrary operators (depending on the
- object-logic and application), which enables users to perform
- standard proof steps implicitly (cf.\ the @{text "rule"} method
- \cite{isabelle-isar-ref}).
-
- \medskip Thus Isabelle/Isar is able to bring forth more and more
- concepts successively. In particular, an object-logic like
- Isabelle/HOL continues the Isabelle/Pure setup by adding specific
- components for automated reasoning (classical reasoner, tableau
- prover, structured induction etc.) and derived specification
- mechanisms (inductive predicates, recursive functions etc.). All of
- this is ultimately based on the generic data management by theory
- and proof contexts introduced here.
-*}
-
-
-subsection {* Theory context \label{sec:context-theory} *}
-
-text {*
- \glossary{Theory}{FIXME}
-
- A \emph{theory} is a data container with explicit named and unique
- identifier. Theories are related by a (nominal) sub-theory
- relation, which corresponds to the dependency graph of the original
- construction; each theory is derived from a certain sub-graph of
- ancestor theories.
-
- The @{text "merge"} operation produces the least upper bound of two
- theories, which actually degenerates into absorption of one theory
- into the other (due to the nominal sub-theory relation).
-
- The @{text "begin"} operation starts a new theory by importing
- several parent theories and entering a special @{text "draft"} mode,
- which is sustained until the final @{text "end"} operation. A draft
- theory acts like a linear type, where updates invalidate earlier
- versions. An invalidated draft is called ``stale''.
-
- The @{text "checkpoint"} operation produces an intermediate stepping
- stone that will survive the next update: both the original and the
- changed theory remain valid and are related by the sub-theory
- relation. Checkpointing essentially recovers purely functional
- theory values, at the expense of some extra internal bookkeeping.
-
- The @{text "copy"} operation produces an auxiliary version that has
- the same data content, but is unrelated to the original: updates of
- the copy do not affect the original, neither does the sub-theory
- relation hold.
-
- \medskip The example in \figref{fig:ex-theory} below shows a theory
- graph derived from @{text "Pure"}, with theory @{text "Length"}
- importing @{text "Nat"} and @{text "List"}. The body of @{text
- "Length"} consists of a sequence of updates, working mostly on
- drafts. Intermediate checkpoints may occur as well, due to the
- history mechanism provided by the Isar top-level, cf.\
- \secref{sec:isar-toplevel}.
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{rcccl}
- & & @{text "Pure"} \\
- & & @{text "\<down>"} \\
- & & @{text "FOL"} \\
- & $\swarrow$ & & $\searrow$ & \\
- @{text "Nat"} & & & & @{text "List"} \\
- & $\searrow$ & & $\swarrow$ \\
- & & @{text "Length"} \\
- & & \multicolumn{3}{l}{~~@{keyword "imports"}} \\
- & & \multicolumn{3}{l}{~~@{keyword "begin"}} \\
- & & $\vdots$~~ \\
- & & @{text "\<bullet>"}~~ \\
- & & $\vdots$~~ \\
- & & @{text "\<bullet>"}~~ \\
- & & $\vdots$~~ \\
- & & \multicolumn{3}{l}{~~@{command "end"}} \\
- \end{tabular}
- \caption{A theory definition depending on ancestors}\label{fig:ex-theory}
- \end{center}
- \end{figure}
-
- \medskip There is a separate notion of \emph{theory reference} for
- maintaining a live link to an evolving theory context: updates on
- drafts are propagated automatically. Dynamic updating stops after
- an explicit @{text "end"} only.
-
- Derived entities may store a theory reference in order to indicate
- the context they belong to. This implicitly assumes monotonic
- reasoning, because the referenced context may become larger without
- further notice.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type theory} \\
- @{index_ML Theory.subthy: "theory * theory -> bool"} \\
- @{index_ML Theory.merge: "theory * theory -> theory"} \\
- @{index_ML Theory.checkpoint: "theory -> theory"} \\
- @{index_ML Theory.copy: "theory -> theory"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML_type theory_ref} \\
- @{index_ML Theory.deref: "theory_ref -> theory"} \\
- @{index_ML Theory.check_thy: "theory -> theory_ref"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type theory} represents theory contexts. This is
- essentially a linear type! Most operations destroy the original
- version, which then becomes ``stale''.
-
- \item @{ML "Theory.subthy"}~@{text "(thy\<^sub>1, thy\<^sub>2)"}
- compares theories according to the inherent graph structure of the
- construction. This sub-theory relation is a nominal approximation
- of inclusion (@{text "\<subseteq>"}) of the corresponding content.
-
- \item @{ML "Theory.merge"}~@{text "(thy\<^sub>1, thy\<^sub>2)"}
- absorbs one theory into the other. This fails for unrelated
- theories!
-
- \item @{ML "Theory.checkpoint"}~@{text "thy"} produces a safe
- stepping stone in the linear development of @{text "thy"}. The next
- update will result in two related, valid theories.
-
- \item @{ML "Theory.copy"}~@{text "thy"} produces a variant of @{text
- "thy"} that holds a copy of the same data. The result is not
- related to the original; the original is unchanched.
-
- \item @{ML_type theory_ref} represents a sliding reference to an
- always valid theory; updates on the original are propagated
- automatically.
-
- \item @{ML "Theory.deref"}~@{text "thy_ref"} turns a @{ML_type
- "theory_ref"} into an @{ML_type "theory"} value. As the referenced
- theory evolves monotonically over time, later invocations of @{ML
- "Theory.deref"} may refer to a larger context.
-
- \item @{ML "Theory.check_thy"}~@{text "thy"} produces a @{ML_type
- "theory_ref"} from a valid @{ML_type "theory"} value.
-
- \end{description}
-*}
-
-
-subsection {* Proof context \label{sec:context-proof} *}
-
-text {*
- \glossary{Proof context}{The static context of a structured proof,
- acts like a local ``theory'' of the current portion of Isar proof
- text, generalizes the idea of local hypotheses @{text "\<Gamma>"} in
- judgments @{text "\<Gamma> \<turnstile> \<phi>"} of natural deduction calculi. There is a
- generic notion of introducing and discharging hypotheses.
- Arbritrary auxiliary context data may be adjoined.}
-
- A proof context is a container for pure data with a back-reference
- to the theory it belongs to. The @{text "init"} operation creates a
- proof context from a given theory. Modifications to draft theories
- are propagated to the proof context as usual, but there is also an
- explicit @{text "transfer"} operation to force resynchronization
- with more substantial updates to the underlying theory. The actual
- context data does not require any special bookkeeping, thanks to the
- lack of destructive features.
-
- Entities derived in a proof context need to record inherent logical
- requirements explicitly, since there is no separate context
- identification as for theories. For example, hypotheses used in
- primitive derivations (cf.\ \secref{sec:thms}) are recorded
- separately within the sequent @{text "\<Gamma> \<turnstile> \<phi>"}, just to make double
- sure. Results could still leak into an alien proof context do to
- programming errors, but Isabelle/Isar includes some extra validity
- checks in critical positions, notably at the end of a sub-proof.
-
- Proof contexts may be manipulated arbitrarily, although the common
- discipline is to follow block structure as a mental model: a given
- context is extended consecutively, and results are exported back
- into the original context. Note that the Isar proof states model
- block-structured reasoning explicitly, using a stack of proof
- contexts internally, cf.\ \secref{sec:isar-proof-state}.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type Proof.context} \\
- @{index_ML ProofContext.init: "theory -> Proof.context"} \\
- @{index_ML ProofContext.theory_of: "Proof.context -> theory"} \\
- @{index_ML ProofContext.transfer: "theory -> Proof.context -> Proof.context"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type Proof.context} represents proof contexts. Elements
- of this type are essentially pure values, with a sliding reference
- to the background theory.
-
- \item @{ML ProofContext.init}~@{text "thy"} produces a proof context
- derived from @{text "thy"}, initializing all data.
-
- \item @{ML ProofContext.theory_of}~@{text "ctxt"} selects the
- background theory from @{text "ctxt"}, dereferencing its internal
- @{ML_type theory_ref}.
-
- \item @{ML ProofContext.transfer}~@{text "thy ctxt"} promotes the
- background theory of @{text "ctxt"} to the super theory @{text
- "thy"}.
-
- \end{description}
-*}
-
-
-subsection {* Generic contexts \label{sec:generic-context} *}
-
-text {*
- A generic context is the disjoint sum of either a theory or proof
- context. Occasionally, this enables uniform treatment of generic
- context data, typically extra-logical information. Operations on
- generic contexts include the usual injections, partial selections,
- and combinators for lifting operations on either component of the
- disjoint sum.
-
- Moreover, there are total operations @{text "theory_of"} and @{text
- "proof_of"} to convert a generic context into either kind: a theory
- can always be selected from the sum, while a proof context might
- have to be constructed by an ad-hoc @{text "init"} operation.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type Context.generic} \\
- @{index_ML Context.theory_of: "Context.generic -> theory"} \\
- @{index_ML Context.proof_of: "Context.generic -> Proof.context"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type Context.generic} is the direct sum of @{ML_type
- "theory"} and @{ML_type "Proof.context"}, with the datatype
- constructors @{ML "Context.Theory"} and @{ML "Context.Proof"}.
-
- \item @{ML Context.theory_of}~@{text "context"} always produces a
- theory from the generic @{text "context"}, using @{ML
- "ProofContext.theory_of"} as required.
-
- \item @{ML Context.proof_of}~@{text "context"} always produces a
- proof context from the generic @{text "context"}, using @{ML
- "ProofContext.init"} as required (note that this re-initializes the
- context data with each invocation).
-
- \end{description}
-*}
-
-
-subsection {* Context data \label{sec:context-data} *}
-
-text {*
- The main purpose of theory and proof contexts is to manage arbitrary
- data. New data types can be declared incrementally at compile time.
- There are separate declaration mechanisms for any of the three kinds
- of contexts: theory, proof, generic.
-
- \paragraph{Theory data} may refer to destructive entities, which are
- maintained in direct correspondence to the linear evolution of
- theory values, including explicit copies.\footnote{Most existing
- instances of destructive theory data are merely historical relics
- (e.g.\ the destructive theorem storage, and destructive hints for
- the Simplifier and Classical rules).} A theory data declaration
- needs to implement the following SML signature:
-
- \medskip
- \begin{tabular}{ll}
- @{text "\<type> T"} & representing type \\
- @{text "\<val> empty: T"} & empty default value \\
- @{text "\<val> copy: T \<rightarrow> T"} & refresh impure data \\
- @{text "\<val> extend: T \<rightarrow> T"} & re-initialize on import \\
- @{text "\<val> merge: T \<times> T \<rightarrow> T"} & join on import \\
- \end{tabular}
- \medskip
-
- \noindent The @{text "empty"} value acts as initial default for
- \emph{any} theory that does not declare actual data content; @{text
- "copy"} maintains persistent integrity for impure data, it is just
- the identity for pure values; @{text "extend"} is acts like a
- unitary version of @{text "merge"}, both operations should also
- include the functionality of @{text "copy"} for impure data.
-
- \paragraph{Proof context data} is purely functional. A declaration
- needs to implement the following SML signature:
-
- \medskip
- \begin{tabular}{ll}
- @{text "\<type> T"} & representing type \\
- @{text "\<val> init: theory \<rightarrow> T"} & produce initial value \\
- \end{tabular}
- \medskip
-
- \noindent The @{text "init"} operation is supposed to produce a pure
- value from the given background theory.
-
- \paragraph{Generic data} provides a hybrid interface for both theory
- and proof data. The declaration is essentially the same as for
- (pure) theory data, without @{text "copy"}. The @{text "init"}
- operation for proof contexts merely selects the current data value
- from the background theory.
-
- \bigskip A data declaration of type @{text "T"} results in the
- following interface:
-
- \medskip
- \begin{tabular}{ll}
- @{text "init: theory \<rightarrow> theory"} \\
- @{text "get: context \<rightarrow> T"} \\
- @{text "put: T \<rightarrow> context \<rightarrow> context"} \\
- @{text "map: (T \<rightarrow> T) \<rightarrow> context \<rightarrow> context"} \\
- \end{tabular}
- \medskip
-
- \noindent Here @{text "init"} is only applicable to impure theory
- data to install a fresh copy persistently (destructive update on
- uninitialized has no permanent effect). The other operations provide
- access for the particular kind of context (theory, proof, or generic
- context). Note that this is a safe interface: there is no other way
- to access the corresponding data slot of a context. By keeping
- these operations private, a component may maintain abstract values
- authentically, without other components interfering.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_functor TheoryDataFun} \\
- @{index_ML_functor ProofDataFun} \\
- @{index_ML_functor GenericDataFun} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_functor TheoryDataFun}@{text "(spec)"} declares data for
- type @{ML_type theory} according to the specification provided as
- argument structure. The resulting structure provides data init and
- access operations as described above.
-
- \item @{ML_functor ProofDataFun}@{text "(spec)"} is analogous to
- @{ML_functor TheoryDataFun} for type @{ML_type Proof.context}.
-
- \item @{ML_functor GenericDataFun}@{text "(spec)"} is analogous to
- @{ML_functor TheoryDataFun} for type @{ML_type Context.generic}.
-
- \end{description}
-*}
-
-
-section {* Names \label{sec:names} *}
-
-text {*
- In principle, a name is just a string, but there are various
- convention for encoding additional structure. For example, ``@{text
- "Foo.bar.baz"}'' is considered as a qualified name consisting of
- three basic name components. The individual constituents of a name
- may have further substructure, e.g.\ the string
- ``\verb,\,\verb,<alpha>,'' encodes as a single symbol.
-*}
-
-
-subsection {* Strings of symbols *}
-
-text {*
- \glossary{Symbol}{The smallest unit of text in Isabelle, subsumes
- plain ASCII characters as well as an infinite collection of named
- symbols (for greek, math etc.).}
-
- A \emph{symbol} constitutes the smallest textual unit in Isabelle
- --- raw characters are normally not encountered at all. Isabelle
- strings consist of a sequence of symbols, represented as a packed
- string or a list of strings. Each symbol is in itself a small
- string, which has either one of the following forms:
-
- \begin{enumerate}
-
- \item a single ASCII character ``@{text "c"}'', for example
- ``\verb,a,'',
-
- \item a regular symbol ``\verb,\,\verb,<,@{text "ident"}\verb,>,'',
- for example ``\verb,\,\verb,<alpha>,'',
-
- \item a control symbol ``\verb,\,\verb,<^,@{text "ident"}\verb,>,'',
- for example ``\verb,\,\verb,<^bold>,'',
-
- \item a raw symbol ``\verb,\,\verb,<^raw:,@{text text}\verb,>,''
- where @{text text} constists of printable characters excluding
- ``\verb,.,'' and ``\verb,>,'', for example
- ``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
-
- \item a numbered raw control symbol ``\verb,\,\verb,<^raw,@{text
- n}\verb,>, where @{text n} consists of digits, for example
- ``\verb,\,\verb,<^raw42>,''.
-
- \end{enumerate}
-
- \noindent The @{text "ident"} syntax for symbol names is @{text
- "letter (letter | digit)\<^sup>*"}, where @{text "letter =
- A..Za..z"} and @{text "digit = 0..9"}. There are infinitely many
- regular symbols and control symbols, but a fixed collection of
- standard symbols is treated specifically. For example,
- ``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it
- may occur within regular Isabelle identifiers.
-
- Since the character set underlying Isabelle symbols is 7-bit ASCII
- and 8-bit characters are passed through transparently, Isabelle may
- also process Unicode/UCS data in UTF-8 encoding. Unicode provides
- its own collection of mathematical symbols, but there is no built-in
- link to the standard collection of Isabelle.
-
- \medskip Output of Isabelle symbols depends on the print mode
- (\secref{FIXME}). For example, the standard {\LaTeX} setup of the
- Isabelle document preparation system would present
- ``\verb,\,\verb,<alpha>,'' as @{text "\<alpha>"}, and
- ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as @{text
- "\<^bold>\<alpha>"}.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type "Symbol.symbol"} \\
- @{index_ML Symbol.explode: "string -> Symbol.symbol list"} \\
- @{index_ML Symbol.is_letter: "Symbol.symbol -> bool"} \\
- @{index_ML Symbol.is_digit: "Symbol.symbol -> bool"} \\
- @{index_ML Symbol.is_quasi: "Symbol.symbol -> bool"} \\
- @{index_ML Symbol.is_blank: "Symbol.symbol -> bool"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML_type "Symbol.sym"} \\
- @{index_ML Symbol.decode: "Symbol.symbol -> Symbol.sym"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type "Symbol.symbol"} represents individual Isabelle
- symbols; this is an alias for @{ML_type "string"}.
-
- \item @{ML "Symbol.explode"}~@{text "str"} produces a symbol list
- from the packed form. This function supercedes @{ML
- "String.explode"} for virtually all purposes of manipulating text in
- Isabelle!
-
- \item @{ML "Symbol.is_letter"}, @{ML "Symbol.is_digit"}, @{ML
- "Symbol.is_quasi"}, @{ML "Symbol.is_blank"} classify standard
- symbols according to fixed syntactic conventions of Isabelle, cf.\
- \cite{isabelle-isar-ref}.
-
- \item @{ML_type "Symbol.sym"} is a concrete datatype that represents
- the different kinds of symbols explicitly, with constructors @{ML
- "Symbol.Char"}, @{ML "Symbol.Sym"}, @{ML "Symbol.Ctrl"}, @{ML
- "Symbol.Raw"}.
-
- \item @{ML "Symbol.decode"} converts the string representation of a
- symbol into the datatype version.
-
- \end{description}
-*}
-
-
-subsection {* Basic names \label{sec:basic-names} *}
-
-text {*
- A \emph{basic name} essentially consists of a single Isabelle
- identifier. There are conventions to mark separate classes of basic
- names, by attaching a suffix of underscores (@{text "_"}): one
- underscore means \emph{internal name}, two underscores means
- \emph{Skolem name}, three underscores means \emph{internal Skolem
- name}.
-
- For example, the basic name @{text "foo"} has the internal version
- @{text "foo_"}, with Skolem versions @{text "foo__"} and @{text
- "foo___"}, respectively.
-
- These special versions provide copies of the basic name space, apart
- from anything that normally appears in the user text. For example,
- system generated variables in Isar proof contexts are usually marked
- as internal, which prevents mysterious name references like @{text
- "xaa"} to appear in the text.
-
- \medskip Manipulating binding scopes often requires on-the-fly
- renamings. A \emph{name context} contains a collection of already
- used names. The @{text "declare"} operation adds names to the
- context.
-
- The @{text "invents"} operation derives a number of fresh names from
- a given starting point. For example, the first three names derived
- from @{text "a"} are @{text "a"}, @{text "b"}, @{text "c"}.
-
- The @{text "variants"} operation produces fresh names by
- incrementing tentative names as base-26 numbers (with digits @{text
- "a..z"}) until all clashes are resolved. For example, name @{text
- "foo"} results in variants @{text "fooa"}, @{text "foob"}, @{text
- "fooc"}, \dots, @{text "fooaa"}, @{text "fooab"} etc.; each renaming
- step picks the next unused variant from this sequence.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML Name.internal: "string -> string"} \\
- @{index_ML Name.skolem: "string -> string"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML_type Name.context} \\
- @{index_ML Name.context: Name.context} \\
- @{index_ML Name.declare: "string -> Name.context -> Name.context"} \\
- @{index_ML Name.invents: "Name.context -> string -> int -> string list"} \\
- @{index_ML Name.variants: "string list -> Name.context -> string list * Name.context"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML Name.internal}~@{text "name"} produces an internal name
- by adding one underscore.
-
- \item @{ML Name.skolem}~@{text "name"} produces a Skolem name by
- adding two underscores.
-
- \item @{ML_type Name.context} represents the context of already used
- names; the initial value is @{ML "Name.context"}.
-
- \item @{ML Name.declare}~@{text "name"} enters a used name into the
- context.
-
- \item @{ML Name.invents}~@{text "context name n"} produces @{text
- "n"} fresh names derived from @{text "name"}.
-
- \item @{ML Name.variants}~@{text "names context"} produces fresh
- varians of @{text "names"}; the result is entered into the context.
-
- \end{description}
-*}
-
-
-subsection {* Indexed names *}
-
-text {*
- An \emph{indexed name} (or @{text "indexname"}) is a pair of a basic
- name and a natural number. This representation allows efficient
- renaming by incrementing the second component only. The canonical
- way to rename two collections of indexnames apart from each other is
- this: determine the maximum index @{text "maxidx"} of the first
- collection, then increment all indexes of the second collection by
- @{text "maxidx + 1"}; the maximum index of an empty collection is
- @{text "-1"}.
-
- Occasionally, basic names and indexed names are injected into the
- same pair type: the (improper) indexname @{text "(x, -1)"} is used
- to encode basic names.
-
- \medskip Isabelle syntax observes the following rules for
- representing an indexname @{text "(x, i)"} as a packed string:
-
- \begin{itemize}
-
- \item @{text "?x"} if @{text "x"} does not end with a digit and @{text "i = 0"},
-
- \item @{text "?xi"} if @{text "x"} does not end with a digit,
-
- \item @{text "?x.i"} otherwise.
-
- \end{itemize}
-
- Indexnames may acquire large index numbers over time. Results are
- normalized towards @{text "0"} at certain checkpoints, notably at
- the end of a proof. This works by producing variants of the
- corresponding basic name components. For example, the collection
- @{text "?x1, ?x7, ?x42"} becomes @{text "?x, ?xa, ?xb"}.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type indexname} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type indexname} represents indexed names. This is an
- abbreviation for @{ML_type "string * int"}. The second component is
- usually non-negative, except for situations where @{text "(x, -1)"}
- is used to embed basic names into this type.
-
- \end{description}
-*}
-
-
-subsection {* Qualified names and name spaces *}
-
-text {*
- A \emph{qualified name} consists of a non-empty sequence of basic
- name components. The packed representation uses a dot as separator,
- as in ``@{text "A.b.c"}''. The last component is called \emph{base}
- name, the remaining prefix \emph{qualifier} (which may be empty).
- The idea of qualified names is to encode nested structures by
- recording the access paths as qualifiers. For example, an item
- named ``@{text "A.b.c"}'' may be understood as a local entity @{text
- "c"}, within a local structure @{text "b"}, within a global
- structure @{text "A"}. Typically, name space hierarchies consist of
- 1--2 levels of qualification, but this need not be always so.
-
- The empty name is commonly used as an indication of unnamed
- entities, whenever this makes any sense. The basic operations on
- qualified names are smart enough to pass through such improper names
- unchanged.
-
- \medskip A @{text "naming"} policy tells how to turn a name
- specification into a fully qualified internal name (by the @{text
- "full"} operation), and how fully qualified names may be accessed
- externally. For example, the default naming policy is to prefix an
- implicit path: @{text "full x"} produces @{text "path.x"}, and the
- standard accesses for @{text "path.x"} include both @{text "x"} and
- @{text "path.x"}. Normally, the naming is implicit in the theory or
- proof context; there are separate versions of the corresponding.
-
- \medskip A @{text "name space"} manages a collection of fully
- internalized names, together with a mapping between external names
- and internal names (in both directions). The corresponding @{text
- "intern"} and @{text "extern"} operations are mostly used for
- parsing and printing only! The @{text "declare"} operation augments
- a name space according to the accesses determined by the naming
- policy.
-
- \medskip As a general principle, there is a separate name space for
- each kind of formal entity, e.g.\ logical constant, type
- constructor, type class, theorem. It is usually clear from the
- occurrence in concrete syntax (or from the scope) which kind of
- entity a name refers to. For example, the very same name @{text
- "c"} may be used uniformly for a constant, type constructor, and
- type class.
-
- There are common schemes to name theorems systematically, according
- to the name of the main logical entity involved, e.g.\ @{text
- "c.intro"} for a canonical theorem related to constant @{text "c"}.
- This technique of mapping names from one space into another requires
- some care in order to avoid conflicts. In particular, theorem names
- derived from a type constructor or type class are better suffixed in
- addition to the usual qualification, e.g.\ @{text "c_type.intro"}
- and @{text "c_class.intro"} for theorems related to type @{text "c"}
- and class @{text "c"}, respectively.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML NameSpace.base: "string -> string"} \\
- @{index_ML NameSpace.qualifier: "string -> string"} \\
- @{index_ML NameSpace.append: "string -> string -> string"} \\
- @{index_ML NameSpace.implode: "string list -> string"} \\
- @{index_ML NameSpace.explode: "string -> string list"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML_type NameSpace.naming} \\
- @{index_ML NameSpace.default_naming: NameSpace.naming} \\
- @{index_ML NameSpace.add_path: "string -> NameSpace.naming -> NameSpace.naming"} \\
- @{index_ML NameSpace.full_name: "NameSpace.naming -> binding -> string"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML_type NameSpace.T} \\
- @{index_ML NameSpace.empty: NameSpace.T} \\
- @{index_ML NameSpace.merge: "NameSpace.T * NameSpace.T -> NameSpace.T"} \\
- @{index_ML NameSpace.declare: "NameSpace.naming -> binding -> NameSpace.T -> string * NameSpace.T"} \\
- @{index_ML NameSpace.intern: "NameSpace.T -> string -> string"} \\
- @{index_ML NameSpace.extern: "NameSpace.T -> string -> string"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML NameSpace.base}~@{text "name"} returns the base name of a
- qualified name.
-
- \item @{ML NameSpace.qualifier}~@{text "name"} returns the qualifier
- of a qualified name.
-
- \item @{ML NameSpace.append}~@{text "name\<^isub>1 name\<^isub>2"}
- appends two qualified names.
-
- \item @{ML NameSpace.implode}~@{text "name"} and @{ML
- NameSpace.explode}~@{text "names"} convert between the packed string
- representation and the explicit list form of qualified names.
-
- \item @{ML_type NameSpace.naming} represents the abstract concept of
- a naming policy.
-
- \item @{ML NameSpace.default_naming} is the default naming policy.
- In a theory context, this is usually augmented by a path prefix
- consisting of the theory name.
-
- \item @{ML NameSpace.add_path}~@{text "path naming"} augments the
- naming policy by extending its path component.
-
- \item @{ML NameSpace.full_name}@{text "naming binding"} turns a name
- binding (usually a basic name) into the fully qualified
- internal name, according to the given naming policy.
-
- \item @{ML_type NameSpace.T} represents name spaces.
-
- \item @{ML NameSpace.empty} and @{ML NameSpace.merge}~@{text
- "(space\<^isub>1, space\<^isub>2)"} are the canonical operations for
- maintaining name spaces according to theory data management
- (\secref{sec:context-data}).
-
- \item @{ML NameSpace.declare}~@{text "naming bindings space"} enters a
- name binding as fully qualified internal name into the name space,
- with external accesses determined by the naming policy.
-
- \item @{ML NameSpace.intern}~@{text "space name"} internalizes a
- (partially qualified) external name.
-
- This operation is mostly for parsing! Note that fully qualified
- names stemming from declarations are produced via @{ML
- "NameSpace.full_name"} and @{ML "NameSpace.declare"}
- (or their derivatives for @{ML_type theory} and
- @{ML_type Proof.context}).
-
- \item @{ML NameSpace.extern}~@{text "space name"} externalizes a
- (fully qualified) internal name.
-
- This operation is mostly for printing! Note unqualified names are
- produced via @{ML NameSpace.base}.
-
- \end{description}
-*}
-
-end