3 \def\isabellecontext{prelim}%
13 \isacommand{theory}\isamarkupfalse%
14 \ prelim\ \isakeyword{imports}\ base\ \isakeyword{begin}%
22 \isamarkupchapter{Preliminaries%
26 \isamarkupsection{Contexts \label{sec:context}%
30 \begin{isamarkuptext}%
31 A logical context represents the background that is required for
32 formulating statements and composing proofs. It acts as a medium to
33 produce formal content, depending on earlier material (declarations,
36 For example, derivations within the Isabelle/Pure logic can be
37 described as a judgment \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}, which means that a
38 proposition \isa{{\isasymphi}} is derivable from hypotheses \isa{{\isasymGamma}}
39 within the theory \isa{{\isasymTheta}}. There are logical reasons for
40 keeping \isa{{\isasymTheta}} and \isa{{\isasymGamma}} separate: theories can be
41 liberal about supporting type constructors and schematic
42 polymorphism of constants and axioms, while the inner calculus of
43 \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}} is strictly limited to Simple Type Theory (with
44 fixed type variables in the assumptions).
46 \medskip Contexts and derivations are linked by the following key
51 \item Transfer: monotonicity of derivations admits results to be
52 transferred into a \emph{larger} context, i.e.\ \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}} implies \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\isactrlsub {\isacharprime}\ {\isasymphi}} for contexts \isa{{\isasymTheta}{\isacharprime}\ {\isasymsupseteq}\ {\isasymTheta}} and \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}}.
54 \item Export: discharge of hypotheses admits results to be exported
55 into a \emph{smaller} context, i.e.\ \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}
56 implies \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymDelta}\ {\isasymLongrightarrow}\ {\isasymphi}} where \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}} and
57 \isa{{\isasymDelta}\ {\isacharequal}\ {\isasymGamma}{\isacharprime}\ {\isacharminus}\ {\isasymGamma}}. Note that \isa{{\isasymTheta}} remains unchanged here,
58 only the \isa{{\isasymGamma}} part is affected.
62 \medskip By modeling the main characteristics of the primitive
63 \isa{{\isasymTheta}} and \isa{{\isasymGamma}} above, and abstracting over any
64 particular logical content, we arrive at the fundamental notions of
65 \emph{theory context} and \emph{proof context} in Isabelle/Isar.
66 These implement a certain policy to manage arbitrary \emph{context
67 data}. There is a strongly-typed mechanism to declare new kinds of
70 The internal bootstrap process of Isabelle/Pure eventually reaches a
71 stage where certain data slots provide the logical content of \isa{{\isasymTheta}} and \isa{{\isasymGamma}} sketched above, but this does not stop there!
72 Various additional data slots support all kinds of mechanisms that
73 are not necessarily part of the core logic.
75 For example, there would be data for canonical introduction and
76 elimination rules for arbitrary operators (depending on the
77 object-logic and application), which enables users to perform
78 standard proof steps implicitly (cf.\ the \isa{rule} method
79 \cite{isabelle-isar-ref}).
81 \medskip Thus Isabelle/Isar is able to bring forth more and more
82 concepts successively. In particular, an object-logic like
83 Isabelle/HOL continues the Isabelle/Pure setup by adding specific
84 components for automated reasoning (classical reasoner, tableau
85 prover, structured induction etc.) and derived specification
86 mechanisms (inductive predicates, recursive functions etc.). All of
87 this is ultimately based on the generic data management by theory
88 and proof contexts introduced here.%
92 \isamarkupsubsection{Theory context \label{sec:context-theory}%
96 \begin{isamarkuptext}%
97 \glossary{Theory}{FIXME}
99 A \emph{theory} is a data container with explicit named and unique
100 identifier. Theories are related by a (nominal) sub-theory
101 relation, which corresponds to the dependency graph of the original
102 construction; each theory is derived from a certain sub-graph of
105 The \isa{merge} operation produces the least upper bound of two
106 theories, which actually degenerates into absorption of one theory
107 into the other (due to the nominal sub-theory relation).
109 The \isa{begin} operation starts a new theory by importing
110 several parent theories and entering a special \isa{draft} mode,
111 which is sustained until the final \isa{end} operation. A draft
112 theory acts like a linear type, where updates invalidate earlier
113 versions. An invalidated draft is called ``stale''.
115 The \isa{checkpoint} operation produces an intermediate stepping
116 stone that will survive the next update: both the original and the
117 changed theory remain valid and are related by the sub-theory
118 relation. Checkpointing essentially recovers purely functional
119 theory values, at the expense of some extra internal bookkeeping.
121 The \isa{copy} operation produces an auxiliary version that has
122 the same data content, but is unrelated to the original: updates of
123 the copy do not affect the original, neither does the sub-theory
126 \medskip The example in \figref{fig:ex-theory} below shows a theory
127 graph derived from \isa{Pure}, with theory \isa{Length}
128 importing \isa{Nat} and \isa{List}. The body of \isa{Length} consists of a sequence of updates, working mostly on
129 drafts. Intermediate checkpoints may occur as well, due to the
130 history mechanism provided by the Isar top-level, cf.\
131 \secref{sec:isar-toplevel}.
135 \begin{tabular}{rcccl}
137 & & \isa{{\isasymdown}} \\
139 & $\swarrow$ & & $\searrow$ & \\
140 \isa{Nat} & & & & \isa{List} \\
141 & $\searrow$ & & $\swarrow$ \\
143 & & \multicolumn{3}{l}{~~\hyperlink{keyword.imports}{\mbox{\isa{\isakeyword{imports}}}}} \\
144 & & \multicolumn{3}{l}{~~\hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}}} \\
146 & & \isa{{\isasymbullet}}~~ \\
148 & & \isa{{\isasymbullet}}~~ \\
150 & & \multicolumn{3}{l}{~~\hyperlink{command.end}{\mbox{\isa{\isacommand{end}}}}} \\
152 \caption{A theory definition depending on ancestors}\label{fig:ex-theory}
156 \medskip There is a separate notion of \emph{theory reference} for
157 maintaining a live link to an evolving theory context: updates on
158 drafts are propagated automatically. Dynamic updating stops after
159 an explicit \isa{end} only.
161 Derived entities may store a theory reference in order to indicate
162 the context they belong to. This implicitly assumes monotonic
163 reasoning, because the referenced context may become larger without
174 \begin{isamarkuptext}%
176 \indexmltype{theory}\verb|type theory| \\
177 \indexml{Theory.subthy}\verb|Theory.subthy: theory * theory -> bool| \\
178 \indexml{Theory.merge}\verb|Theory.merge: theory * theory -> theory| \\
179 \indexml{Theory.checkpoint}\verb|Theory.checkpoint: theory -> theory| \\
180 \indexml{Theory.copy}\verb|Theory.copy: theory -> theory| \\
183 \indexmltype{theory\_ref}\verb|type theory_ref| \\
184 \indexml{Theory.deref}\verb|Theory.deref: theory_ref -> theory| \\
185 \indexml{Theory.check\_thy}\verb|Theory.check_thy: theory -> theory_ref| \\
190 \item \verb|theory| represents theory contexts. This is
191 essentially a linear type! Most operations destroy the original
192 version, which then becomes ``stale''.
194 \item \verb|Theory.subthy|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}}
195 compares theories according to the inherent graph structure of the
196 construction. This sub-theory relation is a nominal approximation
197 of inclusion (\isa{{\isasymsubseteq}}) of the corresponding content.
199 \item \verb|Theory.merge|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}}
200 absorbs one theory into the other. This fails for unrelated
203 \item \verb|Theory.checkpoint|~\isa{thy} produces a safe
204 stepping stone in the linear development of \isa{thy}. The next
205 update will result in two related, valid theories.
207 \item \verb|Theory.copy|~\isa{thy} produces a variant of \isa{thy} that holds a copy of the same data. The result is not
208 related to the original; the original is unchanched.
210 \item \verb|theory_ref| represents a sliding reference to an
211 always valid theory; updates on the original are propagated
214 \item \verb|Theory.deref|~\isa{thy{\isacharunderscore}ref} turns a \verb|theory_ref| into an \verb|theory| value. As the referenced
215 theory evolves monotonically over time, later invocations of \verb|Theory.deref| may refer to a larger context.
217 \item \verb|Theory.check_thy|~\isa{thy} produces a \verb|theory_ref| from a valid \verb|theory| value.
230 \isamarkupsubsection{Proof context \label{sec:context-proof}%
234 \begin{isamarkuptext}%
235 \glossary{Proof context}{The static context of a structured proof,
236 acts like a local ``theory'' of the current portion of Isar proof
237 text, generalizes the idea of local hypotheses \isa{{\isasymGamma}} in
238 judgments \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}} of natural deduction calculi. There is a
239 generic notion of introducing and discharging hypotheses.
240 Arbritrary auxiliary context data may be adjoined.}
242 A proof context is a container for pure data with a back-reference
243 to the theory it belongs to. The \isa{init} operation creates a
244 proof context from a given theory. Modifications to draft theories
245 are propagated to the proof context as usual, but there is also an
246 explicit \isa{transfer} operation to force resynchronization
247 with more substantial updates to the underlying theory. The actual
248 context data does not require any special bookkeeping, thanks to the
249 lack of destructive features.
251 Entities derived in a proof context need to record inherent logical
252 requirements explicitly, since there is no separate context
253 identification as for theories. For example, hypotheses used in
254 primitive derivations (cf.\ \secref{sec:thms}) are recorded
255 separately within the sequent \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}}, just to make double
256 sure. Results could still leak into an alien proof context do to
257 programming errors, but Isabelle/Isar includes some extra validity
258 checks in critical positions, notably at the end of a sub-proof.
260 Proof contexts may be manipulated arbitrarily, although the common
261 discipline is to follow block structure as a mental model: a given
262 context is extended consecutively, and results are exported back
263 into the original context. Note that the Isar proof states model
264 block-structured reasoning explicitly, using a stack of proof
265 contexts internally, cf.\ \secref{sec:isar-proof-state}.%
275 \begin{isamarkuptext}%
277 \indexmltype{Proof.context}\verb|type Proof.context| \\
278 \indexml{ProofContext.init}\verb|ProofContext.init: theory -> Proof.context| \\
279 \indexml{ProofContext.theory\_of}\verb|ProofContext.theory_of: Proof.context -> theory| \\
280 \indexml{ProofContext.transfer}\verb|ProofContext.transfer: theory -> Proof.context -> Proof.context| \\
285 \item \verb|Proof.context| represents proof contexts. Elements
286 of this type are essentially pure values, with a sliding reference
287 to the background theory.
289 \item \verb|ProofContext.init|~\isa{thy} produces a proof context
290 derived from \isa{thy}, initializing all data.
292 \item \verb|ProofContext.theory_of|~\isa{ctxt} selects the
293 background theory from \isa{ctxt}, dereferencing its internal
296 \item \verb|ProofContext.transfer|~\isa{thy\ ctxt} promotes the
297 background theory of \isa{ctxt} to the super theory \isa{thy}.
310 \isamarkupsubsection{Generic contexts \label{sec:generic-context}%
314 \begin{isamarkuptext}%
315 A generic context is the disjoint sum of either a theory or proof
316 context. Occasionally, this enables uniform treatment of generic
317 context data, typically extra-logical information. Operations on
318 generic contexts include the usual injections, partial selections,
319 and combinators for lifting operations on either component of the
322 Moreover, there are total operations \isa{theory{\isacharunderscore}of} and \isa{proof{\isacharunderscore}of} to convert a generic context into either kind: a theory
323 can always be selected from the sum, while a proof context might
324 have to be constructed by an ad-hoc \isa{init} operation.%
334 \begin{isamarkuptext}%
336 \indexmltype{Context.generic}\verb|type Context.generic| \\
337 \indexml{Context.theory\_of}\verb|Context.theory_of: Context.generic -> theory| \\
338 \indexml{Context.proof\_of}\verb|Context.proof_of: Context.generic -> Proof.context| \\
343 \item \verb|Context.generic| is the direct sum of \verb|theory| and \verb|Proof.context|, with the datatype
344 constructors \verb|Context.Theory| and \verb|Context.Proof|.
346 \item \verb|Context.theory_of|~\isa{context} always produces a
347 theory from the generic \isa{context}, using \verb|ProofContext.theory_of| as required.
349 \item \verb|Context.proof_of|~\isa{context} always produces a
350 proof context from the generic \isa{context}, using \verb|ProofContext.init| as required (note that this re-initializes the
351 context data with each invocation).
364 \isamarkupsubsection{Context data \label{sec:context-data}%
368 \begin{isamarkuptext}%
369 The main purpose of theory and proof contexts is to manage arbitrary
370 data. New data types can be declared incrementally at compile time.
371 There are separate declaration mechanisms for any of the three kinds
372 of contexts: theory, proof, generic.
374 \paragraph{Theory data} may refer to destructive entities, which are
375 maintained in direct correspondence to the linear evolution of
376 theory values, including explicit copies.\footnote{Most existing
377 instances of destructive theory data are merely historical relics
378 (e.g.\ the destructive theorem storage, and destructive hints for
379 the Simplifier and Classical rules).} A theory data declaration
380 needs to implement the following SML signature:
384 \isa{{\isasymtype}\ T} & representing type \\
385 \isa{{\isasymval}\ empty{\isacharcolon}\ T} & empty default value \\
386 \isa{{\isasymval}\ copy{\isacharcolon}\ T\ {\isasymrightarrow}\ T} & refresh impure data \\
387 \isa{{\isasymval}\ extend{\isacharcolon}\ T\ {\isasymrightarrow}\ T} & re-initialize on import \\
388 \isa{{\isasymval}\ merge{\isacharcolon}\ T\ {\isasymtimes}\ T\ {\isasymrightarrow}\ T} & join on import \\
392 \noindent The \isa{empty} value acts as initial default for
393 \emph{any} theory that does not declare actual data content; \isa{copy} maintains persistent integrity for impure data, it is just
394 the identity for pure values; \isa{extend} is acts like a
395 unitary version of \isa{merge}, both operations should also
396 include the functionality of \isa{copy} for impure data.
398 \paragraph{Proof context data} is purely functional. A declaration
399 needs to implement the following SML signature:
403 \isa{{\isasymtype}\ T} & representing type \\
404 \isa{{\isasymval}\ init{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} & produce initial value \\
408 \noindent The \isa{init} operation is supposed to produce a pure
409 value from the given background theory.
411 \paragraph{Generic data} provides a hybrid interface for both theory
412 and proof data. The declaration is essentially the same as for
413 (pure) theory data, without \isa{copy}. The \isa{init}
414 operation for proof contexts merely selects the current data value
415 from the background theory.
417 \bigskip A data declaration of type \isa{T} results in the
422 \isa{init{\isacharcolon}\ theory\ {\isasymrightarrow}\ theory} \\
423 \isa{get{\isacharcolon}\ context\ {\isasymrightarrow}\ T} \\
424 \isa{put{\isacharcolon}\ T\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
425 \isa{map{\isacharcolon}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
429 \noindent Here \isa{init} is only applicable to impure theory
430 data to install a fresh copy persistently (destructive update on
431 uninitialized has no permanent effect). The other operations provide
432 access for the particular kind of context (theory, proof, or generic
433 context). Note that this is a safe interface: there is no other way
434 to access the corresponding data slot of a context. By keeping
435 these operations private, a component may maintain abstract values
436 authentically, without other components interfering.%
446 \begin{isamarkuptext}%
448 \indexmlfunctor{TheoryDataFun}\verb|functor TheoryDataFun| \\
449 \indexmlfunctor{ProofDataFun}\verb|functor ProofDataFun| \\
450 \indexmlfunctor{GenericDataFun}\verb|functor GenericDataFun| \\
455 \item \verb|TheoryDataFun|\isa{{\isacharparenleft}spec{\isacharparenright}} declares data for
456 type \verb|theory| according to the specification provided as
457 argument structure. The resulting structure provides data init and
458 access operations as described above.
460 \item \verb|ProofDataFun|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
461 \verb|TheoryDataFun| for type \verb|Proof.context|.
463 \item \verb|GenericDataFun|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
464 \verb|TheoryDataFun| for type \verb|Context.generic|.
477 \isamarkupsection{Names \label{sec:names}%
481 \begin{isamarkuptext}%
482 In principle, a name is just a string, but there are various
483 convention for encoding additional structure. For example, ``\isa{Foo{\isachardot}bar{\isachardot}baz}'' is considered as a qualified name consisting of
484 three basic name components. The individual constituents of a name
485 may have further substructure, e.g.\ the string
486 ``\verb,\,\verb,<alpha>,'' encodes as a single symbol.%
490 \isamarkupsubsection{Strings of symbols%
494 \begin{isamarkuptext}%
495 \glossary{Symbol}{The smallest unit of text in Isabelle, subsumes
496 plain ASCII characters as well as an infinite collection of named
497 symbols (for greek, math etc.).}
499 A \emph{symbol} constitutes the smallest textual unit in Isabelle
500 --- raw characters are normally not encountered at all. Isabelle
501 strings consist of a sequence of symbols, represented as a packed
502 string or a list of strings. Each symbol is in itself a small
503 string, which has either one of the following forms:
507 \item a single ASCII character ``\isa{c}'', for example
510 \item a regular symbol ``\verb,\,\verb,<,\isa{ident}\verb,>,'',
511 for example ``\verb,\,\verb,<alpha>,'',
513 \item a control symbol ``\verb,\,\verb,<^,\isa{ident}\verb,>,'',
514 for example ``\verb,\,\verb,<^bold>,'',
516 \item a raw symbol ``\verb,\,\verb,<^raw:,\isa{text}\verb,>,''
517 where \isa{text} constists of printable characters excluding
518 ``\verb,.,'' and ``\verb,>,'', for example
519 ``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
521 \item a numbered raw control symbol ``\verb,\,\verb,<^raw,\isa{n}\verb,>, where \isa{n} consists of digits, for example
522 ``\verb,\,\verb,<^raw42>,''.
526 \noindent The \isa{ident} syntax for symbol names is \isa{letter\ {\isacharparenleft}letter\ {\isacharbar}\ digit{\isacharparenright}\isactrlsup {\isacharasterisk}}, where \isa{letter\ {\isacharequal}\ A{\isachardot}{\isachardot}Za{\isachardot}{\isachardot}z} and \isa{digit\ {\isacharequal}\ {\isadigit{0}}{\isachardot}{\isachardot}{\isadigit{9}}}. There are infinitely many
527 regular symbols and control symbols, but a fixed collection of
528 standard symbols is treated specifically. For example,
529 ``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it
530 may occur within regular Isabelle identifiers.
532 Since the character set underlying Isabelle symbols is 7-bit ASCII
533 and 8-bit characters are passed through transparently, Isabelle may
534 also process Unicode/UCS data in UTF-8 encoding. Unicode provides
535 its own collection of mathematical symbols, but there is no built-in
536 link to the standard collection of Isabelle.
538 \medskip Output of Isabelle symbols depends on the print mode
539 (\secref{FIXME}). For example, the standard {\LaTeX} setup of the
540 Isabelle document preparation system would present
541 ``\verb,\,\verb,<alpha>,'' as \isa{{\isasymalpha}}, and
542 ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as \isa{\isactrlbold {\isasymalpha}}.%
552 \begin{isamarkuptext}%
554 \indexmltype{Symbol.symbol}\verb|type Symbol.symbol| \\
555 \indexml{Symbol.explode}\verb|Symbol.explode: string -> Symbol.symbol list| \\
556 \indexml{Symbol.is\_letter}\verb|Symbol.is_letter: Symbol.symbol -> bool| \\
557 \indexml{Symbol.is\_digit}\verb|Symbol.is_digit: Symbol.symbol -> bool| \\
558 \indexml{Symbol.is\_quasi}\verb|Symbol.is_quasi: Symbol.symbol -> bool| \\
559 \indexml{Symbol.is\_blank}\verb|Symbol.is_blank: Symbol.symbol -> bool| \\
562 \indexmltype{Symbol.sym}\verb|type Symbol.sym| \\
563 \indexml{Symbol.decode}\verb|Symbol.decode: Symbol.symbol -> Symbol.sym| \\
568 \item \verb|Symbol.symbol| represents individual Isabelle
569 symbols; this is an alias for \verb|string|.
571 \item \verb|Symbol.explode|~\isa{str} produces a symbol list
572 from the packed form. This function supercedes \verb|String.explode| for virtually all purposes of manipulating text in
575 \item \verb|Symbol.is_letter|, \verb|Symbol.is_digit|, \verb|Symbol.is_quasi|, \verb|Symbol.is_blank| classify standard
576 symbols according to fixed syntactic conventions of Isabelle, cf.\
577 \cite{isabelle-isar-ref}.
579 \item \verb|Symbol.sym| is a concrete datatype that represents
580 the different kinds of symbols explicitly, with constructors \verb|Symbol.Char|, \verb|Symbol.Sym|, \verb|Symbol.Ctrl|, \verb|Symbol.Raw|.
582 \item \verb|Symbol.decode| converts the string representation of a
583 symbol into the datatype version.
596 \isamarkupsubsection{Basic names \label{sec:basic-names}%
600 \begin{isamarkuptext}%
601 A \emph{basic name} essentially consists of a single Isabelle
602 identifier. There are conventions to mark separate classes of basic
603 names, by attaching a suffix of underscores (\isa{{\isacharunderscore}}): one
604 underscore means \emph{internal name}, two underscores means
605 \emph{Skolem name}, three underscores means \emph{internal Skolem
608 For example, the basic name \isa{foo} has the internal version
609 \isa{foo{\isacharunderscore}}, with Skolem versions \isa{foo{\isacharunderscore}{\isacharunderscore}} and \isa{foo{\isacharunderscore}{\isacharunderscore}{\isacharunderscore}}, respectively.
611 These special versions provide copies of the basic name space, apart
612 from anything that normally appears in the user text. For example,
613 system generated variables in Isar proof contexts are usually marked
614 as internal, which prevents mysterious name references like \isa{xaa} to appear in the text.
616 \medskip Manipulating binding scopes often requires on-the-fly
617 renamings. A \emph{name context} contains a collection of already
618 used names. The \isa{declare} operation adds names to the
621 The \isa{invents} operation derives a number of fresh names from
622 a given starting point. For example, the first three names derived
623 from \isa{a} are \isa{a}, \isa{b}, \isa{c}.
625 The \isa{variants} operation produces fresh names by
626 incrementing tentative names as base-26 numbers (with digits \isa{a{\isachardot}{\isachardot}z}) until all clashes are resolved. For example, name \isa{foo} results in variants \isa{fooa}, \isa{foob}, \isa{fooc}, \dots, \isa{fooaa}, \isa{fooab} etc.; each renaming
627 step picks the next unused variant from this sequence.%
637 \begin{isamarkuptext}%
639 \indexml{Name.internal}\verb|Name.internal: string -> string| \\
640 \indexml{Name.skolem}\verb|Name.skolem: string -> string| \\
643 \indexmltype{Name.context}\verb|type Name.context| \\
644 \indexml{Name.context}\verb|Name.context: Name.context| \\
645 \indexml{Name.declare}\verb|Name.declare: string -> Name.context -> Name.context| \\
646 \indexml{Name.invents}\verb|Name.invents: Name.context -> string -> int -> string list| \\
647 \indexml{Name.variants}\verb|Name.variants: string list -> Name.context -> string list * Name.context| \\
652 \item \verb|Name.internal|~\isa{name} produces an internal name
653 by adding one underscore.
655 \item \verb|Name.skolem|~\isa{name} produces a Skolem name by
656 adding two underscores.
658 \item \verb|Name.context| represents the context of already used
659 names; the initial value is \verb|Name.context|.
661 \item \verb|Name.declare|~\isa{name} enters a used name into the
664 \item \verb|Name.invents|~\isa{context\ name\ n} produces \isa{n} fresh names derived from \isa{name}.
666 \item \verb|Name.variants|~\isa{names\ context} produces fresh
667 varians of \isa{names}; the result is entered into the context.
680 \isamarkupsubsection{Indexed names%
684 \begin{isamarkuptext}%
685 An \emph{indexed name} (or \isa{indexname}) is a pair of a basic
686 name and a natural number. This representation allows efficient
687 renaming by incrementing the second component only. The canonical
688 way to rename two collections of indexnames apart from each other is
689 this: determine the maximum index \isa{maxidx} of the first
690 collection, then increment all indexes of the second collection by
691 \isa{maxidx\ {\isacharplus}\ {\isadigit{1}}}; the maximum index of an empty collection is
692 \isa{{\isacharminus}{\isadigit{1}}}.
694 Occasionally, basic names and indexed names are injected into the
695 same pair type: the (improper) indexname \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}} is used
696 to encode basic names.
698 \medskip Isabelle syntax observes the following rules for
699 representing an indexname \isa{{\isacharparenleft}x{\isacharcomma}\ i{\isacharparenright}} as a packed string:
703 \item \isa{{\isacharquery}x} if \isa{x} does not end with a digit and \isa{i\ {\isacharequal}\ {\isadigit{0}}},
705 \item \isa{{\isacharquery}xi} if \isa{x} does not end with a digit,
707 \item \isa{{\isacharquery}x{\isachardot}i} otherwise.
711 Indexnames may acquire large index numbers over time. Results are
712 normalized towards \isa{{\isadigit{0}}} at certain checkpoints, notably at
713 the end of a proof. This works by producing variants of the
714 corresponding basic name components. For example, the collection
715 \isa{{\isacharquery}x{\isadigit{1}}{\isacharcomma}\ {\isacharquery}x{\isadigit{7}}{\isacharcomma}\ {\isacharquery}x{\isadigit{4}}{\isadigit{2}}} becomes \isa{{\isacharquery}x{\isacharcomma}\ {\isacharquery}xa{\isacharcomma}\ {\isacharquery}xb}.%
725 \begin{isamarkuptext}%
727 \indexmltype{indexname}\verb|type indexname| \\
732 \item \verb|indexname| represents indexed names. This is an
733 abbreviation for \verb|string * int|. The second component is
734 usually non-negative, except for situations where \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}}
735 is used to embed basic names into this type.
748 \isamarkupsubsection{Qualified names and name spaces%
752 \begin{isamarkuptext}%
753 A \emph{qualified name} consists of a non-empty sequence of basic
754 name components. The packed representation uses a dot as separator,
755 as in ``\isa{A{\isachardot}b{\isachardot}c}''. The last component is called \emph{base}
756 name, the remaining prefix \emph{qualifier} (which may be empty).
757 The idea of qualified names is to encode nested structures by
758 recording the access paths as qualifiers. For example, an item
759 named ``\isa{A{\isachardot}b{\isachardot}c}'' may be understood as a local entity \isa{c}, within a local structure \isa{b}, within a global
760 structure \isa{A}. Typically, name space hierarchies consist of
761 1--2 levels of qualification, but this need not be always so.
763 The empty name is commonly used as an indication of unnamed
764 entities, whenever this makes any sense. The basic operations on
765 qualified names are smart enough to pass through such improper names
768 \medskip A \isa{naming} policy tells how to turn a name
769 specification into a fully qualified internal name (by the \isa{full} operation), and how fully qualified names may be accessed
770 externally. For example, the default naming policy is to prefix an
771 implicit path: \isa{full\ x} produces \isa{path{\isachardot}x}, and the
772 standard accesses for \isa{path{\isachardot}x} include both \isa{x} and
773 \isa{path{\isachardot}x}. Normally, the naming is implicit in the theory or
774 proof context; there are separate versions of the corresponding.
776 \medskip A \isa{name\ space} manages a collection of fully
777 internalized names, together with a mapping between external names
778 and internal names (in both directions). The corresponding \isa{intern} and \isa{extern} operations are mostly used for
779 parsing and printing only! The \isa{declare} operation augments
780 a name space according to the accesses determined by the naming
783 \medskip As a general principle, there is a separate name space for
784 each kind of formal entity, e.g.\ logical constant, type
785 constructor, type class, theorem. It is usually clear from the
786 occurrence in concrete syntax (or from the scope) which kind of
787 entity a name refers to. For example, the very same name \isa{c} may be used uniformly for a constant, type constructor, and
790 There are common schemes to name theorems systematically, according
791 to the name of the main logical entity involved, e.g.\ \isa{c{\isachardot}intro} for a canonical theorem related to constant \isa{c}.
792 This technique of mapping names from one space into another requires
793 some care in order to avoid conflicts. In particular, theorem names
794 derived from a type constructor or type class are better suffixed in
795 addition to the usual qualification, e.g.\ \isa{c{\isacharunderscore}type{\isachardot}intro}
796 and \isa{c{\isacharunderscore}class{\isachardot}intro} for theorems related to type \isa{c}
797 and class \isa{c}, respectively.%
807 \begin{isamarkuptext}%
809 \indexml{NameSpace.base}\verb|NameSpace.base: string -> string| \\
810 \indexml{NameSpace.qualifier}\verb|NameSpace.qualifier: string -> string| \\
811 \indexml{NameSpace.append}\verb|NameSpace.append: string -> string -> string| \\
812 \indexml{NameSpace.implode}\verb|NameSpace.implode: string list -> string| \\
813 \indexml{NameSpace.explode}\verb|NameSpace.explode: string -> string list| \\
816 \indexmltype{NameSpace.naming}\verb|type NameSpace.naming| \\
817 \indexml{NameSpace.default\_naming}\verb|NameSpace.default_naming: NameSpace.naming| \\
818 \indexml{NameSpace.add\_path}\verb|NameSpace.add_path: string -> NameSpace.naming -> NameSpace.naming| \\
819 \indexml{NameSpace.full\_name}\verb|NameSpace.full_name: NameSpace.naming -> binding -> string| \\
822 \indexmltype{NameSpace.T}\verb|type NameSpace.T| \\
823 \indexml{NameSpace.empty}\verb|NameSpace.empty: NameSpace.T| \\
824 \indexml{NameSpace.merge}\verb|NameSpace.merge: NameSpace.T * NameSpace.T -> NameSpace.T| \\
825 \indexml{NameSpace.declare}\verb|NameSpace.declare: NameSpace.naming -> binding -> NameSpace.T -> string * NameSpace.T| \\
826 \indexml{NameSpace.intern}\verb|NameSpace.intern: NameSpace.T -> string -> string| \\
827 \indexml{NameSpace.extern}\verb|NameSpace.extern: NameSpace.T -> string -> string| \\
832 \item \verb|NameSpace.base|~\isa{name} returns the base name of a
835 \item \verb|NameSpace.qualifier|~\isa{name} returns the qualifier
838 \item \verb|NameSpace.append|~\isa{name\isactrlisub {\isadigit{1}}\ name\isactrlisub {\isadigit{2}}}
839 appends two qualified names.
841 \item \verb|NameSpace.implode|~\isa{name} and \verb|NameSpace.explode|~\isa{names} convert between the packed string
842 representation and the explicit list form of qualified names.
844 \item \verb|NameSpace.naming| represents the abstract concept of
847 \item \verb|NameSpace.default_naming| is the default naming policy.
848 In a theory context, this is usually augmented by a path prefix
849 consisting of the theory name.
851 \item \verb|NameSpace.add_path|~\isa{path\ naming} augments the
852 naming policy by extending its path component.
854 \item \verb|NameSpace.full_name|\isa{naming\ binding} turns a name
855 binding (usually a basic name) into the fully qualified
856 internal name, according to the given naming policy.
858 \item \verb|NameSpace.T| represents name spaces.
860 \item \verb|NameSpace.empty| and \verb|NameSpace.merge|~\isa{{\isacharparenleft}space\isactrlisub {\isadigit{1}}{\isacharcomma}\ space\isactrlisub {\isadigit{2}}{\isacharparenright}} are the canonical operations for
861 maintaining name spaces according to theory data management
862 (\secref{sec:context-data}).
864 \item \verb|NameSpace.declare|~\isa{naming\ bindings\ space} enters a
865 name binding as fully qualified internal name into the name space,
866 with external accesses determined by the naming policy.
868 \item \verb|NameSpace.intern|~\isa{space\ name} internalizes a
869 (partially qualified) external name.
871 This operation is mostly for parsing! Note that fully qualified
872 names stemming from declarations are produced via \verb|NameSpace.full_name| and \verb|NameSpace.declare|
873 (or their derivatives for \verb|theory| and
874 \verb|Proof.context|).
876 \item \verb|NameSpace.extern|~\isa{space\ name} externalizes a
877 (fully qualified) internal name.
879 This operation is mostly for printing! Note unqualified names are
880 produced via \verb|NameSpace.base|.
898 \isacommand{end}\isamarkupfalse%
910 %%% TeX-master: "root"