--- a/NEWS Wed Mar 04 10:52:47 2009 +0100
+++ b/NEWS Wed Mar 04 11:37:50 2009 +0100
@@ -500,6 +500,9 @@
Suc_Suc_eq ~> nat.inject
Suc_not_Zero Zero_not_Suc ~> nat.distinct
+* The option datatype has been moved to a new theory HOL/Option.thy.
+Renamed option_map to Option.map.
+
* Library/Nat_Infinity: added addition, numeral syntax and more
instantiations for algebraic structures. Removed some duplicate
theorems. Changes in simp rules. INCOMPATIBILITY.
--- a/doc-src/IsarImplementation/Thy/Base.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,6 +0,0 @@
-theory Base
-imports Pure
-uses "../../antiquote_setup.ML"
-begin
-
-end
--- a/doc-src/IsarImplementation/Thy/Integration.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,425 +0,0 @@
-theory Integration
-imports Base
-begin
-
-chapter {* System integration *}
-
-section {* Isar toplevel \label{sec:isar-toplevel} *}
-
-text {* The Isar toplevel may be considered the centeral hub of the
- Isabelle/Isar system, where all key components and sub-systems are
- integrated into a single read-eval-print loop of Isar commands. We
- shall even incorporate the existing {\ML} toplevel of the compiler
- and run-time system (cf.\ \secref{sec:ML-toplevel}).
-
- Isabelle/Isar departs from the original ``LCF system architecture''
- where {\ML} was really The Meta Language for defining theories and
- conducting proofs. Instead, {\ML} now only serves as the
- implementation language for the system (and user extensions), while
- the specific Isar toplevel supports the concepts of theory and proof
- development natively. This includes the graph structure of theories
- and the block structure of proofs, support for unlimited undo,
- facilities for tracing, debugging, timing, profiling etc.
-
- \medskip The toplevel maintains an implicit state, which is
- transformed by a sequence of transitions -- either interactively or
- in batch-mode. In interactive mode, Isar state transitions are
- encapsulated as safe transactions, such that both failure and undo
- are handled conveniently without destroying the underlying draft
- theory (cf.~\secref{sec:context-theory}). In batch mode,
- transitions operate in a linear (destructive) fashion, such that
- error conditions abort the present attempt to construct a theory or
- proof altogether.
-
- The toplevel state is a disjoint sum of empty @{text toplevel}, or
- @{text theory}, or @{text proof}. On entering the main Isar loop we
- start with an empty toplevel. A theory is commenced by giving a
- @{text \<THEORY>} header; within a theory we may issue theory
- commands such as @{text \<DEFINITION>}, or state a @{text
- \<THEOREM>} to be proven. Now we are within a proof state, with a
- rich collection of Isar proof commands for structured proof
- composition, or unstructured proof scripts. When the proof is
- concluded we get back to the theory, which is then updated by
- storing the resulting fact. Further theory declarations or theorem
- statements with proofs may follow, until we eventually conclude the
- theory development by issuing @{text \<END>}. The resulting theory
- is then stored within the theory database and we are back to the
- empty toplevel.
-
- In addition to these proper state transformations, there are also
- some diagnostic commands for peeking at the toplevel state without
- modifying it (e.g.\ \isakeyword{thm}, \isakeyword{term},
- \isakeyword{print-cases}).
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type Toplevel.state} \\
- @{index_ML Toplevel.UNDEF: "exn"} \\
- @{index_ML Toplevel.is_toplevel: "Toplevel.state -> bool"} \\
- @{index_ML Toplevel.theory_of: "Toplevel.state -> theory"} \\
- @{index_ML Toplevel.proof_of: "Toplevel.state -> Proof.state"} \\
- @{index_ML Toplevel.debug: "bool ref"} \\
- @{index_ML Toplevel.timing: "bool ref"} \\
- @{index_ML Toplevel.profiling: "int ref"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type Toplevel.state} represents Isar toplevel states,
- which are normally manipulated through the concept of toplevel
- transitions only (\secref{sec:toplevel-transition}). Also note that
- a raw toplevel state is subject to the same linearity restrictions
- as a theory context (cf.~\secref{sec:context-theory}).
-
- \item @{ML Toplevel.UNDEF} is raised for undefined toplevel
- operations. Many operations work only partially for certain cases,
- since @{ML_type Toplevel.state} is a sum type.
-
- \item @{ML Toplevel.is_toplevel}~@{text "state"} checks for an empty
- toplevel state.
-
- \item @{ML Toplevel.theory_of}~@{text "state"} selects the theory of
- a theory or proof (!), otherwise raises @{ML Toplevel.UNDEF}.
-
- \item @{ML Toplevel.proof_of}~@{text "state"} selects the Isar proof
- state if available, otherwise raises @{ML Toplevel.UNDEF}.
-
- \item @{ML "set Toplevel.debug"} makes the toplevel print further
- details about internal error conditions, exceptions being raised
- etc.
-
- \item @{ML "set Toplevel.timing"} makes the toplevel print timing
- information for each Isar command being executed.
-
- \item @{ML Toplevel.profiling}~@{verbatim ":="}~@{text "n"} controls
- low-level profiling of the underlying {\ML} runtime system. For
- Poly/ML, @{text "n = 1"} means time and @{text "n = 2"} space
- profiling.
-
- \end{description}
-*}
-
-
-subsection {* Toplevel transitions \label{sec:toplevel-transition} *}
-
-text {*
- An Isar toplevel transition consists of a partial function on the
- toplevel state, with additional information for diagnostics and
- error reporting: there are fields for command name, source position,
- optional source text, as well as flags for interactive-only commands
- (which issue a warning in batch-mode), printing of result state,
- etc.
-
- The operational part is represented as the sequential union of a
- list of partial functions, which are tried in turn until the first
- one succeeds. This acts like an outer case-expression for various
- alternative state transitions. For example, \isakeyword{qed} acts
- differently for a local proofs vs.\ the global ending of the main
- proof.
-
- Toplevel transitions are composed via transition transformers.
- Internally, Isar commands are put together from an empty transition
- extended by name and source position (and optional source text). It
- is then left to the individual command parser to turn the given
- concrete syntax into a suitable transition transformer that adjoins
- actual operations on a theory or proof state etc.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML Toplevel.print: "Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.no_timing: "Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.keep: "(Toplevel.state -> unit) ->
- Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.theory: "(theory -> theory) ->
- Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.theory_to_proof: "(theory -> Proof.state) ->
- Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.proof: "(Proof.state -> Proof.state) ->
- Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.proofs: "(Proof.state -> Proof.state Seq.seq) ->
- Toplevel.transition -> Toplevel.transition"} \\
- @{index_ML Toplevel.end_proof: "(bool -> Proof.state -> Proof.context) ->
- Toplevel.transition -> Toplevel.transition"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML Toplevel.print}~@{text "tr"} sets the print flag, which
- causes the toplevel loop to echo the result state (in interactive
- mode).
-
- \item @{ML Toplevel.no_timing}~@{text "tr"} indicates that the
- transition should never show timing information, e.g.\ because it is
- a diagnostic command.
-
- \item @{ML Toplevel.keep}~@{text "tr"} adjoins a diagnostic
- function.
-
- \item @{ML Toplevel.theory}~@{text "tr"} adjoins a theory
- transformer.
-
- \item @{ML Toplevel.theory_to_proof}~@{text "tr"} adjoins a global
- goal function, which turns a theory into a proof state. The theory
- may be changed before entering the proof; the generic Isar goal
- setup includes an argument that specifies how to apply the proven
- result to the theory, when the proof is finished.
-
- \item @{ML Toplevel.proof}~@{text "tr"} adjoins a deterministic
- proof command, with a singleton result.
-
- \item @{ML Toplevel.proofs}~@{text "tr"} adjoins a general proof
- command, with zero or more result states (represented as a lazy
- list).
-
- \item @{ML Toplevel.end_proof}~@{text "tr"} adjoins a concluding
- proof command, that returns the resulting theory, after storing the
- resulting facts in the context etc.
-
- \end{description}
-*}
-
-
-subsection {* Toplevel control *}
-
-text {*
- There are a few special control commands that modify the behavior
- the toplevel itself, and only make sense in interactive mode. Under
- normal circumstances, the user encounters these only implicitly as
- part of the protocol between the Isabelle/Isar system and a
- user-interface such as ProofGeneral.
-
- \begin{description}
-
- \item \isacommand{undo} follows the three-level hierarchy of empty
- toplevel vs.\ theory vs.\ proof: undo within a proof reverts to the
- previous proof context, undo after a proof reverts to the theory
- before the initial goal statement, undo of a theory command reverts
- to the previous theory value, undo of a theory header discontinues
- the current theory development and removes it from the theory
- database (\secref{sec:theory-database}).
-
- \item \isacommand{kill} aborts the current level of development:
- kill in a proof context reverts to the theory before the initial
- goal statement, kill in a theory context aborts the current theory
- development, removing it from the database.
-
- \item \isacommand{exit} drops out of the Isar toplevel into the
- underlying {\ML} toplevel (\secref{sec:ML-toplevel}). The Isar
- toplevel state is preserved and may be continued later.
-
- \item \isacommand{quit} terminates the Isabelle/Isar process without
- saving.
-
- \end{description}
-*}
-
-
-section {* ML toplevel \label{sec:ML-toplevel} *}
-
-text {*
- The {\ML} toplevel provides a read-compile-eval-print loop for {\ML}
- values, types, structures, and functors. {\ML} declarations operate
- on the global system state, which consists of the compiler
- environment plus the values of {\ML} reference variables. There is
- no clean way to undo {\ML} declarations, except for reverting to a
- previously saved state of the whole Isabelle process. {\ML} input
- is either read interactively from a TTY, or from a string (usually
- within a theory text), or from a source file (usually loaded from a
- theory).
-
- Whenever the {\ML} toplevel is active, the current Isabelle theory
- context is passed as an internal reference variable. Thus {\ML}
- code may access the theory context during compilation, it may even
- change the value of a theory being under construction --- while
- observing the usual linearity restrictions
- (cf.~\secref{sec:context-theory}).
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML the_context: "unit -> theory"} \\
- @{index_ML "Context.>> ": "(Context.generic -> Context.generic) -> unit"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML "the_context ()"} refers to the theory context of the
- {\ML} toplevel --- at compile time! {\ML} code needs to take care
- to refer to @{ML "the_context ()"} correctly. Recall that
- evaluation of a function body is delayed until actual runtime.
- Moreover, persistent {\ML} toplevel bindings to an unfinished theory
- should be avoided: code should either project out the desired
- information immediately, or produce an explicit @{ML_type
- theory_ref} (cf.\ \secref{sec:context-theory}).
-
- \item @{ML "Context.>>"}~@{text f} applies context transformation
- @{text f} to the implicit context of the {\ML} toplevel.
-
- \end{description}
-
- It is very important to note that the above functions are really
- restricted to the compile time, even though the {\ML} compiler is
- invoked at runtime! The majority of {\ML} code uses explicit
- functional arguments of a theory or proof context instead. Thus it
- may be invoked for an arbitrary context later on, without having to
- worry about any operational details.
-
- \bigskip
-
- \begin{mldecls}
- @{index_ML Isar.main: "unit -> unit"} \\
- @{index_ML Isar.loop: "unit -> unit"} \\
- @{index_ML Isar.state: "unit -> Toplevel.state"} \\
- @{index_ML Isar.exn: "unit -> (exn * string) option"} \\
- @{index_ML Isar.context: "unit -> Proof.context"} \\
- @{index_ML Isar.goal: "unit -> thm"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML "Isar.main ()"} invokes the Isar toplevel from {\ML},
- initializing an empty toplevel state.
-
- \item @{ML "Isar.loop ()"} continues the Isar toplevel with the
- current state, after having dropped out of the Isar toplevel loop.
-
- \item @{ML "Isar.state ()"} and @{ML "Isar.exn ()"} get current
- toplevel state and error condition, respectively. This only works
- after having dropped out of the Isar toplevel loop.
-
- \item @{ML "Isar.context ()"} produces the proof context from @{ML
- "Isar.state ()"}, analogous to @{ML Context.proof_of}
- (\secref{sec:generic-context}).
-
- \item @{ML "Isar.goal ()"} picks the tactical goal from @{ML
- "Isar.state ()"}, represented as a theorem according to
- \secref{sec:tactical-goals}.
-
- \end{description}
-*}
-
-
-section {* Theory database \label{sec:theory-database} *}
-
-text {*
- The theory database maintains a collection of theories, together
- with some administrative information about their original sources,
- which are held in an external store (i.e.\ some directory within the
- regular file system).
-
- The theory database is organized as a directed acyclic graph;
- entries are referenced by theory name. Although some additional
- interfaces allow to include a directory specification as well, this
- is only a hint to the underlying theory loader. The internal theory
- name space is flat!
-
- Theory @{text A} is associated with the main theory file @{text
- A}\verb,.thy,, which needs to be accessible through the theory
- loader path. Any number of additional {\ML} source files may be
- associated with each theory, by declaring these dependencies in the
- theory header as @{text \<USES>}, and loading them consecutively
- within the theory context. The system keeps track of incoming {\ML}
- sources and associates them with the current theory. The file
- @{text A}\verb,.ML, is loaded after a theory has been concluded, in
- order to support legacy proof {\ML} proof scripts.
-
- The basic internal actions of the theory database are @{text
- "update"}, @{text "outdate"}, and @{text "remove"}:
-
- \begin{itemize}
-
- \item @{text "update A"} introduces a link of @{text "A"} with a
- @{text "theory"} value of the same name; it asserts that the theory
- sources are now consistent with that value;
-
- \item @{text "outdate A"} invalidates the link of a theory database
- entry to its sources, but retains the present theory value;
-
- \item @{text "remove A"} deletes entry @{text "A"} from the theory
- database.
-
- \end{itemize}
-
- These actions are propagated to sub- or super-graphs of a theory
- entry as expected, in order to preserve global consistency of the
- state of all loaded theories with the sources of the external store.
- This implies certain causalities between actions: @{text "update"}
- or @{text "outdate"} of an entry will @{text "outdate"} all
- descendants; @{text "remove"} will @{text "remove"} all descendants.
-
- \medskip There are separate user-level interfaces to operate on the
- theory database directly or indirectly. The primitive actions then
- just happen automatically while working with the system. In
- particular, processing a theory header @{text "\<THEORY> A
- \<IMPORTS> B\<^sub>1 \<dots> B\<^sub>n \<BEGIN>"} ensures that the
- sub-graph of the collective imports @{text "B\<^sub>1 \<dots> B\<^sub>n"}
- is up-to-date, too. Earlier theories are reloaded as required, with
- @{text update} actions proceeding in topological order according to
- theory dependencies. There may be also a wave of implied @{text
- outdate} actions for derived theory nodes until a stable situation
- is achieved eventually.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML theory: "string -> theory"} \\
- @{index_ML use_thy: "string -> unit"} \\
- @{index_ML use_thys: "string list -> unit"} \\
- @{index_ML ThyInfo.touch_thy: "string -> unit"} \\
- @{index_ML ThyInfo.remove_thy: "string -> unit"} \\[1ex]
- @{index_ML ThyInfo.begin_theory}@{verbatim ": ... -> bool -> theory"} \\
- @{index_ML ThyInfo.end_theory: "theory -> unit"} \\
- @{index_ML ThyInfo.register_theory: "theory -> unit"} \\[1ex]
- @{verbatim "datatype action = Update | Outdate | Remove"} \\
- @{index_ML ThyInfo.add_hook: "(ThyInfo.action -> string -> unit) -> unit"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML theory}~@{text A} retrieves the theory value presently
- associated with name @{text A}. Note that the result might be
- outdated.
-
- \item @{ML use_thy}~@{text A} ensures that theory @{text A} is fully
- up-to-date wrt.\ the external file store, reloading outdated
- ancestors as required.
-
- \item @{ML use_thys} is similar to @{ML use_thy}, but handles
- several theories simultaneously. Thus it acts like processing the
- import header of a theory, without performing the merge of the
- result, though.
-
- \item @{ML ThyInfo.touch_thy}~@{text A} performs and @{text outdate} action
- on theory @{text A} and all descendants.
-
- \item @{ML ThyInfo.remove_thy}~@{text A} deletes theory @{text A} and all
- descendants from the theory database.
-
- \item @{ML ThyInfo.begin_theory} is the basic operation behind a
- @{text \<THEORY>} header declaration. This is {\ML} functions is
- normally not invoked directly.
-
- \item @{ML ThyInfo.end_theory} concludes the loading of a theory
- proper and stores the result in the theory database.
-
- \item @{ML ThyInfo.register_theory}~@{text "text thy"} registers an
- existing theory value with the theory loader database. There is no
- management of associated sources.
-
- \item @{ML "ThyInfo.add_hook"}~@{text f} registers function @{text
- f} as a hook for theory database actions. The function will be
- invoked with the action and theory name being involved; thus derived
- actions may be performed in associated system components, e.g.\
- maintaining the state of an editor for the theory sources.
-
- The kind and order of actions occurring in practice depends both on
- user interactions and the internal process of resolving theory
- imports. Hooks should not rely on a particular policy here! Any
- exceptions raised by the hook are ignored.
-
- \end{description}
-*}
-
-end
--- a/doc-src/IsarImplementation/Thy/Isar.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,37 +0,0 @@
-theory Isar
-imports Base
-begin
-
-chapter {* Isar language elements *}
-
-text {*
- The primary Isar language consists of three main categories of
- language elements:
-
- \begin{enumerate}
-
- \item Proof commands
-
- \item Proof methods
-
- \item Attributes
-
- \end{enumerate}
-*}
-
-
-section {* Proof commands *}
-
-text FIXME
-
-
-section {* Proof methods *}
-
-text FIXME
-
-
-section {* Attributes *}
-
-text FIXME
-
-end
--- a/doc-src/IsarImplementation/Thy/Logic.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,909 +0,0 @@
-theory Logic
-imports Base
-begin
-
-chapter {* Primitive logic \label{ch:logic} *}
-
-text {*
- The logical foundations of Isabelle/Isar are that of the Pure logic,
- which has been introduced as a Natural Deduction framework in
- \cite{paulson700}. This is essentially the same logic as ``@{text
- "\<lambda>HOL"}'' in the more abstract setting of Pure Type Systems (PTS)
- \cite{Barendregt-Geuvers:2001}, although there are some key
- differences in the specific treatment of simple types in
- Isabelle/Pure.
-
- Following type-theoretic parlance, the Pure logic consists of three
- levels of @{text "\<lambda>"}-calculus with corresponding arrows, @{text
- "\<Rightarrow>"} for syntactic function space (terms depending on terms), @{text
- "\<And>"} for universal quantification (proofs depending on terms), and
- @{text "\<Longrightarrow>"} for implication (proofs depending on proofs).
-
- Derivations are relative to a logical theory, which declares type
- constructors, constants, and axioms. Theory declarations support
- schematic polymorphism, which is strictly speaking outside the
- logic.\footnote{This is the deeper logical reason, why the theory
- context @{text "\<Theta>"} is separate from the proof context @{text "\<Gamma>"}
- of the core calculus.}
-*}
-
-
-section {* Types \label{sec:types} *}
-
-text {*
- The language of types is an uninterpreted order-sorted first-order
- algebra; types are qualified by ordered type classes.
-
- \medskip A \emph{type class} is an abstract syntactic entity
- declared in the theory context. The \emph{subclass relation} @{text
- "c\<^isub>1 \<subseteq> c\<^isub>2"} is specified by stating an acyclic
- generating relation; the transitive closure is maintained
- internally. The resulting relation is an ordering: reflexive,
- transitive, and antisymmetric.
-
- A \emph{sort} is a list of type classes written as @{text "s =
- {c\<^isub>1, \<dots>, c\<^isub>m}"}, which represents symbolic
- intersection. Notationally, the curly braces are omitted for
- singleton intersections, i.e.\ any class @{text "c"} may be read as
- a sort @{text "{c}"}. The ordering on type classes is extended to
- sorts according to the meaning of intersections: @{text
- "{c\<^isub>1, \<dots> c\<^isub>m} \<subseteq> {d\<^isub>1, \<dots>, d\<^isub>n}"} iff
- @{text "\<forall>j. \<exists>i. c\<^isub>i \<subseteq> d\<^isub>j"}. The empty intersection
- @{text "{}"} refers to the universal sort, which is the largest
- element wrt.\ the sort order. The intersections of all (finitely
- many) classes declared in the current theory are the minimal
- elements wrt.\ the sort order.
-
- \medskip A \emph{fixed type variable} is a pair of a basic name
- (starting with a @{text "'"} character) and a sort constraint, e.g.\
- @{text "('a, s)"} which is usually printed as @{text "\<alpha>\<^isub>s"}.
- A \emph{schematic type variable} is a pair of an indexname and a
- sort constraint, e.g.\ @{text "(('a, 0), s)"} which is usually
- printed as @{text "?\<alpha>\<^isub>s"}.
-
- Note that \emph{all} syntactic components contribute to the identity
- of type variables, including the sort constraint. The core logic
- handles type variables with the same name but different sorts as
- different, although some outer layers of the system make it hard to
- produce anything like this.
-
- A \emph{type constructor} @{text "\<kappa>"} is a @{text "k"}-ary operator
- on types declared in the theory. Type constructor application is
- written postfix as @{text "(\<alpha>\<^isub>1, \<dots>, \<alpha>\<^isub>k)\<kappa>"}. For
- @{text "k = 0"} the argument tuple is omitted, e.g.\ @{text "prop"}
- instead of @{text "()prop"}. For @{text "k = 1"} the parentheses
- are omitted, e.g.\ @{text "\<alpha> list"} instead of @{text "(\<alpha>)list"}.
- Further notation is provided for specific constructors, notably the
- right-associative infix @{text "\<alpha> \<Rightarrow> \<beta>"} instead of @{text "(\<alpha>,
- \<beta>)fun"}.
-
- A \emph{type} is defined inductively over type variables and type
- constructors as follows: @{text "\<tau> = \<alpha>\<^isub>s | ?\<alpha>\<^isub>s |
- (\<tau>\<^sub>1, \<dots>, \<tau>\<^sub>k)\<kappa>"}.
-
- A \emph{type abbreviation} is a syntactic definition @{text
- "(\<^vec>\<alpha>)\<kappa> = \<tau>"} of an arbitrary type expression @{text "\<tau>"} over
- variables @{text "\<^vec>\<alpha>"}. Type abbreviations appear as type
- constructors in the syntax, but are expanded before entering the
- logical core.
-
- A \emph{type arity} declares the image behavior of a type
- constructor wrt.\ the algebra of sorts: @{text "\<kappa> :: (s\<^isub>1, \<dots>,
- s\<^isub>k)s"} means that @{text "(\<tau>\<^isub>1, \<dots>, \<tau>\<^isub>k)\<kappa>"} is
- of sort @{text "s"} if every argument type @{text "\<tau>\<^isub>i"} is
- of sort @{text "s\<^isub>i"}. Arity declarations are implicitly
- completed, i.e.\ @{text "\<kappa> :: (\<^vec>s)c"} entails @{text "\<kappa> ::
- (\<^vec>s)c'"} for any @{text "c' \<supseteq> c"}.
-
- \medskip The sort algebra is always maintained as \emph{coregular},
- which means that type arities are consistent with the subclass
- relation: for any type constructor @{text "\<kappa>"}, and classes @{text
- "c\<^isub>1 \<subseteq> c\<^isub>2"}, and arities @{text "\<kappa> ::
- (\<^vec>s\<^isub>1)c\<^isub>1"} and @{text "\<kappa> ::
- (\<^vec>s\<^isub>2)c\<^isub>2"} holds @{text "\<^vec>s\<^isub>1 \<subseteq>
- \<^vec>s\<^isub>2"} component-wise.
-
- The key property of a coregular order-sorted algebra is that sort
- constraints can be solved in a most general fashion: for each type
- constructor @{text "\<kappa>"} and sort @{text "s"} there is a most general
- vector of argument sorts @{text "(s\<^isub>1, \<dots>, s\<^isub>k)"} such
- that a type scheme @{text "(\<alpha>\<^bsub>s\<^isub>1\<^esub>, \<dots>,
- \<alpha>\<^bsub>s\<^isub>k\<^esub>)\<kappa>"} is of sort @{text "s"}.
- Consequently, type unification has most general solutions (modulo
- equivalence of sorts), so type-inference produces primary types as
- expected \cite{nipkow-prehofer}.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type class} \\
- @{index_ML_type sort} \\
- @{index_ML_type arity} \\
- @{index_ML_type typ} \\
- @{index_ML map_atyps: "(typ -> typ) -> typ -> typ"} \\
- @{index_ML fold_atyps: "(typ -> 'a -> 'a) -> typ -> 'a -> 'a"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML Sign.subsort: "theory -> sort * sort -> bool"} \\
- @{index_ML Sign.of_sort: "theory -> typ * sort -> bool"} \\
- @{index_ML Sign.add_types: "(string * int * mixfix) list -> theory -> theory"} \\
- @{index_ML Sign.add_tyabbrs_i: "
- (string * string list * typ * mixfix) list -> theory -> theory"} \\
- @{index_ML Sign.primitive_class: "string * class list -> theory -> theory"} \\
- @{index_ML Sign.primitive_classrel: "class * class -> theory -> theory"} \\
- @{index_ML Sign.primitive_arity: "arity -> theory -> theory"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type class} represents type classes; this is an alias for
- @{ML_type string}.
-
- \item @{ML_type sort} represents sorts; this is an alias for
- @{ML_type "class list"}.
-
- \item @{ML_type arity} represents type arities; this is an alias for
- triples of the form @{text "(\<kappa>, \<^vec>s, s)"} for @{text "\<kappa> ::
- (\<^vec>s)s"} described above.
-
- \item @{ML_type typ} represents types; this is a datatype with
- constructors @{ML TFree}, @{ML TVar}, @{ML Type}.
-
- \item @{ML map_atyps}~@{text "f \<tau>"} applies the mapping @{text "f"}
- to all atomic types (@{ML TFree}, @{ML TVar}) occurring in @{text
- "\<tau>"}.
-
- \item @{ML fold_atyps}~@{text "f \<tau>"} iterates the operation @{text
- "f"} over all occurrences of atomic types (@{ML TFree}, @{ML TVar})
- in @{text "\<tau>"}; the type structure is traversed from left to right.
-
- \item @{ML Sign.subsort}~@{text "thy (s\<^isub>1, s\<^isub>2)"}
- tests the subsort relation @{text "s\<^isub>1 \<subseteq> s\<^isub>2"}.
-
- \item @{ML Sign.of_sort}~@{text "thy (\<tau>, s)"} tests whether type
- @{text "\<tau>"} is of sort @{text "s"}.
-
- \item @{ML Sign.add_types}~@{text "[(\<kappa>, k, mx), \<dots>]"} declares a new
- type constructors @{text "\<kappa>"} with @{text "k"} arguments and
- optional mixfix syntax.
-
- \item @{ML Sign.add_tyabbrs_i}~@{text "[(\<kappa>, \<^vec>\<alpha>, \<tau>, mx), \<dots>]"}
- defines a new type abbreviation @{text "(\<^vec>\<alpha>)\<kappa> = \<tau>"} with
- optional mixfix syntax.
-
- \item @{ML Sign.primitive_class}~@{text "(c, [c\<^isub>1, \<dots>,
- c\<^isub>n])"} declares a new class @{text "c"}, together with class
- relations @{text "c \<subseteq> c\<^isub>i"}, for @{text "i = 1, \<dots>, n"}.
-
- \item @{ML Sign.primitive_classrel}~@{text "(c\<^isub>1,
- c\<^isub>2)"} declares the class relation @{text "c\<^isub>1 \<subseteq>
- c\<^isub>2"}.
-
- \item @{ML Sign.primitive_arity}~@{text "(\<kappa>, \<^vec>s, s)"} declares
- the arity @{text "\<kappa> :: (\<^vec>s)s"}.
-
- \end{description}
-*}
-
-
-section {* Terms \label{sec:terms} *}
-
-text {*
- The language of terms is that of simply-typed @{text "\<lambda>"}-calculus
- with de-Bruijn indices for bound variables (cf.\ \cite{debruijn72}
- or \cite{paulson-ml2}), with the types being determined by the
- corresponding binders. In contrast, free variables and constants
- are have an explicit name and type in each occurrence.
-
- \medskip A \emph{bound variable} is a natural number @{text "b"},
- which accounts for the number of intermediate binders between the
- variable occurrence in the body and its binding position. For
- example, the de-Bruijn term @{text
- "\<lambda>\<^bsub>nat\<^esub>. \<lambda>\<^bsub>nat\<^esub>. 1 + 0"} would
- correspond to @{text
- "\<lambda>x\<^bsub>nat\<^esub>. \<lambda>y\<^bsub>nat\<^esub>. x + y"} in a named
- representation. Note that a bound variable may be represented by
- different de-Bruijn indices at different occurrences, depending on
- the nesting of abstractions.
-
- A \emph{loose variable} is a bound variable that is outside the
- scope of local binders. The types (and names) for loose variables
- can be managed as a separate context, that is maintained as a stack
- of hypothetical binders. The core logic operates on closed terms,
- without any loose variables.
-
- A \emph{fixed variable} is a pair of a basic name and a type, e.g.\
- @{text "(x, \<tau>)"} which is usually printed @{text "x\<^isub>\<tau>"}. A
- \emph{schematic variable} is a pair of an indexname and a type,
- e.g.\ @{text "((x, 0), \<tau>)"} which is usually printed as @{text
- "?x\<^isub>\<tau>"}.
-
- \medskip A \emph{constant} is a pair of a basic name and a type,
- e.g.\ @{text "(c, \<tau>)"} which is usually printed as @{text
- "c\<^isub>\<tau>"}. Constants are declared in the context as polymorphic
- families @{text "c :: \<sigma>"}, meaning that all substitution instances
- @{text "c\<^isub>\<tau>"} for @{text "\<tau> = \<sigma>\<vartheta>"} are valid.
-
- The vector of \emph{type arguments} of constant @{text "c\<^isub>\<tau>"}
- wrt.\ the declaration @{text "c :: \<sigma>"} is defined as the codomain of
- the matcher @{text "\<vartheta> = {?\<alpha>\<^isub>1 \<mapsto> \<tau>\<^isub>1, \<dots>,
- ?\<alpha>\<^isub>n \<mapsto> \<tau>\<^isub>n}"} presented in canonical order @{text
- "(\<tau>\<^isub>1, \<dots>, \<tau>\<^isub>n)"}. Within a given theory context,
- there is a one-to-one correspondence between any constant @{text
- "c\<^isub>\<tau>"} and the application @{text "c(\<tau>\<^isub>1, \<dots>,
- \<tau>\<^isub>n)"} of its type arguments. For example, with @{text "plus
- :: \<alpha> \<Rightarrow> \<alpha> \<Rightarrow> \<alpha>"}, the instance @{text "plus\<^bsub>nat \<Rightarrow> nat \<Rightarrow>
- nat\<^esub>"} corresponds to @{text "plus(nat)"}.
-
- Constant declarations @{text "c :: \<sigma>"} may contain sort constraints
- for type variables in @{text "\<sigma>"}. These are observed by
- type-inference as expected, but \emph{ignored} by the core logic.
- This means the primitive logic is able to reason with instances of
- polymorphic constants that the user-level type-checker would reject
- due to violation of type class restrictions.
-
- \medskip An \emph{atomic} term is either a variable or constant. A
- \emph{term} is defined inductively over atomic terms, with
- abstraction and application as follows: @{text "t = b | x\<^isub>\<tau> |
- ?x\<^isub>\<tau> | c\<^isub>\<tau> | \<lambda>\<^isub>\<tau>. t | t\<^isub>1 t\<^isub>2"}.
- Parsing and printing takes care of converting between an external
- representation with named bound variables. Subsequently, we shall
- use the latter notation instead of internal de-Bruijn
- representation.
-
- The inductive relation @{text "t :: \<tau>"} assigns a (unique) type to a
- term according to the structure of atomic terms, abstractions, and
- applicatins:
- \[
- \infer{@{text "a\<^isub>\<tau> :: \<tau>"}}{}
- \qquad
- \infer{@{text "(\<lambda>x\<^sub>\<tau>. t) :: \<tau> \<Rightarrow> \<sigma>"}}{@{text "t :: \<sigma>"}}
- \qquad
- \infer{@{text "t u :: \<sigma>"}}{@{text "t :: \<tau> \<Rightarrow> \<sigma>"} & @{text "u :: \<tau>"}}
- \]
- A \emph{well-typed term} is a term that can be typed according to these rules.
-
- Typing information can be omitted: type-inference is able to
- reconstruct the most general type of a raw term, while assigning
- most general types to all of its variables and constants.
- Type-inference depends on a context of type constraints for fixed
- variables, and declarations for polymorphic constants.
-
- The identity of atomic terms consists both of the name and the type
- component. This means that different variables @{text
- "x\<^bsub>\<tau>\<^isub>1\<^esub>"} and @{text
- "x\<^bsub>\<tau>\<^isub>2\<^esub>"} may become the same after type
- instantiation. Some outer layers of the system make it hard to
- produce variables of the same name, but different types. In
- contrast, mixed instances of polymorphic constants occur frequently.
-
- \medskip The \emph{hidden polymorphism} of a term @{text "t :: \<sigma>"}
- is the set of type variables occurring in @{text "t"}, but not in
- @{text "\<sigma>"}. This means that the term implicitly depends on type
- arguments that are not accounted in the result type, i.e.\ there are
- different type instances @{text "t\<vartheta> :: \<sigma>"} and @{text
- "t\<vartheta>' :: \<sigma>"} with the same type. This slightly
- pathological situation notoriously demands additional care.
-
- \medskip A \emph{term abbreviation} is a syntactic definition @{text
- "c\<^isub>\<sigma> \<equiv> t"} of a closed term @{text "t"} of type @{text "\<sigma>"},
- without any hidden polymorphism. A term abbreviation looks like a
- constant in the syntax, but is expanded before entering the logical
- core. Abbreviations are usually reverted when printing terms, using
- @{text "t \<rightarrow> c\<^isub>\<sigma>"} as rules for higher-order rewriting.
-
- \medskip Canonical operations on @{text "\<lambda>"}-terms include @{text
- "\<alpha>\<beta>\<eta>"}-conversion: @{text "\<alpha>"}-conversion refers to capture-free
- renaming of bound variables; @{text "\<beta>"}-conversion contracts an
- abstraction applied to an argument term, substituting the argument
- in the body: @{text "(\<lambda>x. b)a"} becomes @{text "b[a/x]"}; @{text
- "\<eta>"}-conversion contracts vacuous application-abstraction: @{text
- "\<lambda>x. f x"} becomes @{text "f"}, provided that the bound variable
- does not occur in @{text "f"}.
-
- Terms are normally treated modulo @{text "\<alpha>"}-conversion, which is
- implicit in the de-Bruijn representation. Names for bound variables
- in abstractions are maintained separately as (meaningless) comments,
- mostly for parsing and printing. Full @{text "\<alpha>\<beta>\<eta>"}-conversion is
- commonplace in various standard operations (\secref{sec:obj-rules})
- that are based on higher-order unification and matching.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type term} \\
- @{index_ML "op aconv": "term * term -> bool"} \\
- @{index_ML map_types: "(typ -> typ) -> term -> term"} \\
- @{index_ML fold_types: "(typ -> 'a -> 'a) -> term -> 'a -> 'a"} \\
- @{index_ML map_aterms: "(term -> term) -> term -> term"} \\
- @{index_ML fold_aterms: "(term -> 'a -> 'a) -> term -> 'a -> 'a"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML fastype_of: "term -> typ"} \\
- @{index_ML lambda: "term -> term -> term"} \\
- @{index_ML betapply: "term * term -> term"} \\
- @{index_ML Sign.declare_const: "Properties.T -> (binding * typ) * mixfix ->
- theory -> term * theory"} \\
- @{index_ML Sign.add_abbrev: "string -> Properties.T -> binding * term ->
- theory -> (term * term) * theory"} \\
- @{index_ML Sign.const_typargs: "theory -> string * typ -> typ list"} \\
- @{index_ML Sign.const_instance: "theory -> string * typ list -> typ"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type term} represents de-Bruijn terms, with comments in
- abstractions, and explicitly named free variables and constants;
- this is a datatype with constructors @{ML Bound}, @{ML Free}, @{ML
- Var}, @{ML Const}, @{ML Abs}, @{ML "op $"}.
-
- \item @{text "t"}~@{ML aconv}~@{text "u"} checks @{text
- "\<alpha>"}-equivalence of two terms. This is the basic equality relation
- on type @{ML_type term}; raw datatype equality should only be used
- for operations related to parsing or printing!
-
- \item @{ML map_types}~@{text "f t"} applies the mapping @{text
- "f"} to all types occurring in @{text "t"}.
-
- \item @{ML fold_types}~@{text "f t"} iterates the operation @{text
- "f"} over all occurrences of types in @{text "t"}; the term
- structure is traversed from left to right.
-
- \item @{ML map_aterms}~@{text "f t"} applies the mapping @{text "f"}
- to all atomic terms (@{ML Bound}, @{ML Free}, @{ML Var}, @{ML
- Const}) occurring in @{text "t"}.
-
- \item @{ML fold_aterms}~@{text "f t"} iterates the operation @{text
- "f"} over all occurrences of atomic terms (@{ML Bound}, @{ML Free},
- @{ML Var}, @{ML Const}) in @{text "t"}; the term structure is
- traversed from left to right.
-
- \item @{ML fastype_of}~@{text "t"} determines the type of a
- well-typed term. This operation is relatively slow, despite the
- omission of any sanity checks.
-
- \item @{ML lambda}~@{text "a b"} produces an abstraction @{text
- "\<lambda>a. b"}, where occurrences of the atomic term @{text "a"} in the
- body @{text "b"} are replaced by bound variables.
-
- \item @{ML betapply}~@{text "(t, u)"} produces an application @{text
- "t u"}, with topmost @{text "\<beta>"}-conversion if @{text "t"} is an
- abstraction.
-
- \item @{ML Sign.declare_const}~@{text "properties ((c, \<sigma>), mx)"}
- declares a new constant @{text "c :: \<sigma>"} with optional mixfix
- syntax.
-
- \item @{ML Sign.add_abbrev}~@{text "print_mode properties (c, t)"}
- introduces a new term abbreviation @{text "c \<equiv> t"}.
-
- \item @{ML Sign.const_typargs}~@{text "thy (c, \<tau>)"} and @{ML
- Sign.const_instance}~@{text "thy (c, [\<tau>\<^isub>1, \<dots>, \<tau>\<^isub>n])"}
- convert between two representations of polymorphic constants: full
- type instance vs.\ compact type arguments form.
-
- \end{description}
-*}
-
-
-section {* Theorems \label{sec:thms} *}
-
-text {*
- A \emph{proposition} is a well-typed term of type @{text "prop"}, a
- \emph{theorem} is a proven proposition (depending on a context of
- hypotheses and the background theory). Primitive inferences include
- plain Natural Deduction rules for the primary connectives @{text
- "\<And>"} and @{text "\<Longrightarrow>"} of the framework. There is also a builtin
- notion of equality/equivalence @{text "\<equiv>"}.
-*}
-
-
-subsection {* Primitive connectives and rules \label{sec:prim-rules} *}
-
-text {*
- The theory @{text "Pure"} contains constant declarations for the
- primitive connectives @{text "\<And>"}, @{text "\<Longrightarrow>"}, and @{text "\<equiv>"} of
- the logical framework, see \figref{fig:pure-connectives}. The
- derivability judgment @{text "A\<^isub>1, \<dots>, A\<^isub>n \<turnstile> B"} is
- defined inductively by the primitive inferences given in
- \figref{fig:prim-rules}, with the global restriction that the
- hypotheses must \emph{not} contain any schematic variables. The
- builtin equality is conceptually axiomatized as shown in
- \figref{fig:pure-equality}, although the implementation works
- directly with derived inferences.
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{ll}
- @{text "all :: (\<alpha> \<Rightarrow> prop) \<Rightarrow> prop"} & universal quantification (binder @{text "\<And>"}) \\
- @{text "\<Longrightarrow> :: prop \<Rightarrow> prop \<Rightarrow> prop"} & implication (right associative infix) \\
- @{text "\<equiv> :: \<alpha> \<Rightarrow> \<alpha> \<Rightarrow> prop"} & equality relation (infix) \\
- \end{tabular}
- \caption{Primitive connectives of Pure}\label{fig:pure-connectives}
- \end{center}
- \end{figure}
-
- \begin{figure}[htb]
- \begin{center}
- \[
- \infer[@{text "(axiom)"}]{@{text "\<turnstile> A"}}{@{text "A \<in> \<Theta>"}}
- \qquad
- \infer[@{text "(assume)"}]{@{text "A \<turnstile> A"}}{}
- \]
- \[
- \infer[@{text "(\<And>_intro)"}]{@{text "\<Gamma> \<turnstile> \<And>x. b[x]"}}{@{text "\<Gamma> \<turnstile> b[x]"} & @{text "x \<notin> \<Gamma>"}}
- \qquad
- \infer[@{text "(\<And>_elim)"}]{@{text "\<Gamma> \<turnstile> b[a]"}}{@{text "\<Gamma> \<turnstile> \<And>x. b[x]"}}
- \]
- \[
- \infer[@{text "(\<Longrightarrow>_intro)"}]{@{text "\<Gamma> - A \<turnstile> A \<Longrightarrow> B"}}{@{text "\<Gamma> \<turnstile> B"}}
- \qquad
- \infer[@{text "(\<Longrightarrow>_elim)"}]{@{text "\<Gamma>\<^sub>1 \<union> \<Gamma>\<^sub>2 \<turnstile> B"}}{@{text "\<Gamma>\<^sub>1 \<turnstile> A \<Longrightarrow> B"} & @{text "\<Gamma>\<^sub>2 \<turnstile> A"}}
- \]
- \caption{Primitive inferences of Pure}\label{fig:prim-rules}
- \end{center}
- \end{figure}
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{ll}
- @{text "\<turnstile> (\<lambda>x. b[x]) a \<equiv> b[a]"} & @{text "\<beta>"}-conversion \\
- @{text "\<turnstile> x \<equiv> x"} & reflexivity \\
- @{text "\<turnstile> x \<equiv> y \<Longrightarrow> P x \<Longrightarrow> P y"} & substitution \\
- @{text "\<turnstile> (\<And>x. f x \<equiv> g x) \<Longrightarrow> f \<equiv> g"} & extensionality \\
- @{text "\<turnstile> (A \<Longrightarrow> B) \<Longrightarrow> (B \<Longrightarrow> A) \<Longrightarrow> A \<equiv> B"} & logical equivalence \\
- \end{tabular}
- \caption{Conceptual axiomatization of Pure equality}\label{fig:pure-equality}
- \end{center}
- \end{figure}
-
- The introduction and elimination rules for @{text "\<And>"} and @{text
- "\<Longrightarrow>"} are analogous to formation of dependently typed @{text
- "\<lambda>"}-terms representing the underlying proof objects. Proof terms
- are irrelevant in the Pure logic, though; they cannot occur within
- propositions. The system provides a runtime option to record
- explicit proof terms for primitive inferences. Thus all three
- levels of @{text "\<lambda>"}-calculus become explicit: @{text "\<Rightarrow>"} for
- terms, and @{text "\<And>/\<Longrightarrow>"} for proofs (cf.\
- \cite{Berghofer-Nipkow:2000:TPHOL}).
-
- Observe that locally fixed parameters (as in @{text "\<And>_intro"}) need
- not be recorded in the hypotheses, because the simple syntactic
- types of Pure are always inhabitable. ``Assumptions'' @{text "x ::
- \<tau>"} for type-membership are only present as long as some @{text
- "x\<^isub>\<tau>"} occurs in the statement body.\footnote{This is the key
- difference to ``@{text "\<lambda>HOL"}'' in the PTS framework
- \cite{Barendregt-Geuvers:2001}, where hypotheses @{text "x : A"} are
- treated uniformly for propositions and types.}
-
- \medskip The axiomatization of a theory is implicitly closed by
- forming all instances of type and term variables: @{text "\<turnstile>
- A\<vartheta>"} holds for any substitution instance of an axiom
- @{text "\<turnstile> A"}. By pushing substitutions through derivations
- inductively, we also get admissible @{text "generalize"} and @{text
- "instance"} rules as shown in \figref{fig:subst-rules}.
-
- \begin{figure}[htb]
- \begin{center}
- \[
- \infer{@{text "\<Gamma> \<turnstile> B[?\<alpha>]"}}{@{text "\<Gamma> \<turnstile> B[\<alpha>]"} & @{text "\<alpha> \<notin> \<Gamma>"}}
- \quad
- \infer[\quad@{text "(generalize)"}]{@{text "\<Gamma> \<turnstile> B[?x]"}}{@{text "\<Gamma> \<turnstile> B[x]"} & @{text "x \<notin> \<Gamma>"}}
- \]
- \[
- \infer{@{text "\<Gamma> \<turnstile> B[\<tau>]"}}{@{text "\<Gamma> \<turnstile> B[?\<alpha>]"}}
- \quad
- \infer[\quad@{text "(instantiate)"}]{@{text "\<Gamma> \<turnstile> B[t]"}}{@{text "\<Gamma> \<turnstile> B[?x]"}}
- \]
- \caption{Admissible substitution rules}\label{fig:subst-rules}
- \end{center}
- \end{figure}
-
- Note that @{text "instantiate"} does not require an explicit
- side-condition, because @{text "\<Gamma>"} may never contain schematic
- variables.
-
- In principle, variables could be substituted in hypotheses as well,
- but this would disrupt the monotonicity of reasoning: deriving
- @{text "\<Gamma>\<vartheta> \<turnstile> B\<vartheta>"} from @{text "\<Gamma> \<turnstile> B"} is
- correct, but @{text "\<Gamma>\<vartheta> \<supseteq> \<Gamma>"} does not necessarily hold:
- the result belongs to a different proof context.
-
- \medskip An \emph{oracle} is a function that produces axioms on the
- fly. Logically, this is an instance of the @{text "axiom"} rule
- (\figref{fig:prim-rules}), but there is an operational difference.
- The system always records oracle invocations within derivations of
- theorems by a unique tag.
-
- Axiomatizations should be limited to the bare minimum, typically as
- part of the initial logical basis of an object-logic formalization.
- Later on, theories are usually developed in a strictly definitional
- fashion, by stating only certain equalities over new constants.
-
- A \emph{simple definition} consists of a constant declaration @{text
- "c :: \<sigma>"} together with an axiom @{text "\<turnstile> c \<equiv> t"}, where @{text "t
- :: \<sigma>"} is a closed term without any hidden polymorphism. The RHS
- may depend on further defined constants, but not @{text "c"} itself.
- Definitions of functions may be presented as @{text "c \<^vec>x \<equiv>
- t"} instead of the puristic @{text "c \<equiv> \<lambda>\<^vec>x. t"}.
-
- An \emph{overloaded definition} consists of a collection of axioms
- for the same constant, with zero or one equations @{text
- "c((\<^vec>\<alpha>)\<kappa>) \<equiv> t"} for each type constructor @{text "\<kappa>"} (for
- distinct variables @{text "\<^vec>\<alpha>"}). The RHS may mention
- previously defined constants as above, or arbitrary constants @{text
- "d(\<alpha>\<^isub>i)"} for some @{text "\<alpha>\<^isub>i"} projected from @{text
- "\<^vec>\<alpha>"}. Thus overloaded definitions essentially work by
- primitive recursion over the syntactic structure of a single type
- argument.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type ctyp} \\
- @{index_ML_type cterm} \\
- @{index_ML Thm.ctyp_of: "theory -> typ -> ctyp"} \\
- @{index_ML Thm.cterm_of: "theory -> term -> cterm"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML_type thm} \\
- @{index_ML proofs: "int ref"} \\
- @{index_ML Thm.assume: "cterm -> thm"} \\
- @{index_ML Thm.forall_intr: "cterm -> thm -> thm"} \\
- @{index_ML Thm.forall_elim: "cterm -> thm -> thm"} \\
- @{index_ML Thm.implies_intr: "cterm -> thm -> thm"} \\
- @{index_ML Thm.implies_elim: "thm -> thm -> thm"} \\
- @{index_ML Thm.generalize: "string list * string list -> int -> thm -> thm"} \\
- @{index_ML Thm.instantiate: "(ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm"} \\
- @{index_ML Thm.axiom: "theory -> string -> thm"} \\
- @{index_ML Thm.add_oracle: "bstring * ('a -> cterm) -> theory
- -> (string * ('a -> thm)) * theory"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML Theory.add_axioms_i: "(binding * term) list -> theory -> theory"} \\
- @{index_ML Theory.add_deps: "string -> string * typ -> (string * typ) list -> theory -> theory"} \\
- @{index_ML Theory.add_defs_i: "bool -> bool -> (binding * term) list -> theory -> theory"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type ctyp} and @{ML_type cterm} represent certified types
- and terms, respectively. These are abstract datatypes that
- guarantee that its values have passed the full well-formedness (and
- well-typedness) checks, relative to the declarations of type
- constructors, constants etc. in the theory.
-
- \item @{ML Thm.ctyp_of}~@{text "thy \<tau>"} and @{ML
- Thm.cterm_of}~@{text "thy t"} explicitly checks types and terms,
- respectively. This also involves some basic normalizations, such
- expansion of type and term abbreviations from the theory context.
-
- Re-certification is relatively slow and should be avoided in tight
- reasoning loops. There are separate operations to decompose
- certified entities (including actual theorems).
-
- \item @{ML_type thm} represents proven propositions. This is an
- abstract datatype that guarantees that its values have been
- constructed by basic principles of the @{ML_struct Thm} module.
- Every @{ML thm} value contains a sliding back-reference to the
- enclosing theory, cf.\ \secref{sec:context-theory}.
-
- \item @{ML proofs} determines the detail of proof recording within
- @{ML_type thm} values: @{ML 0} records only the names of oracles,
- @{ML 1} records oracle names and propositions, @{ML 2} additionally
- records full proof terms. Officially named theorems that contribute
- to a result are always recorded.
-
- \item @{ML Thm.assume}, @{ML Thm.forall_intr}, @{ML
- Thm.forall_elim}, @{ML Thm.implies_intr}, and @{ML Thm.implies_elim}
- correspond to the primitive inferences of \figref{fig:prim-rules}.
-
- \item @{ML Thm.generalize}~@{text "(\<^vec>\<alpha>, \<^vec>x)"}
- corresponds to the @{text "generalize"} rules of
- \figref{fig:subst-rules}. Here collections of type and term
- variables are generalized simultaneously, specified by the given
- basic names.
-
- \item @{ML Thm.instantiate}~@{text "(\<^vec>\<alpha>\<^isub>s,
- \<^vec>x\<^isub>\<tau>)"} corresponds to the @{text "instantiate"} rules
- of \figref{fig:subst-rules}. Type variables are substituted before
- term variables. Note that the types in @{text "\<^vec>x\<^isub>\<tau>"}
- refer to the instantiated versions.
-
- \item @{ML Thm.axiom}~@{text "thy name"} retrieves a named
- axiom, cf.\ @{text "axiom"} in \figref{fig:prim-rules}.
-
- \item @{ML Thm.add_oracle}~@{text "(name, oracle)"} produces a named
- oracle rule, essentially generating arbitrary axioms on the fly,
- cf.\ @{text "axiom"} in \figref{fig:prim-rules}.
-
- \item @{ML Theory.add_axioms_i}~@{text "[(name, A), \<dots>]"} declares
- arbitrary propositions as axioms.
-
- \item @{ML Theory.add_deps}~@{text "name c\<^isub>\<tau>
- \<^vec>d\<^isub>\<sigma>"} declares dependencies of a named specification
- for constant @{text "c\<^isub>\<tau>"}, relative to existing
- specifications for constants @{text "\<^vec>d\<^isub>\<sigma>"}.
-
- \item @{ML Theory.add_defs_i}~@{text "unchecked overloaded [(name, c
- \<^vec>x \<equiv> t), \<dots>]"} states a definitional axiom for an existing
- constant @{text "c"}. Dependencies are recorded (cf.\ @{ML
- Theory.add_deps}), unless the @{text "unchecked"} option is set.
-
- \end{description}
-*}
-
-
-subsection {* Auxiliary definitions *}
-
-text {*
- Theory @{text "Pure"} provides a few auxiliary definitions, see
- \figref{fig:pure-aux}. These special constants are normally not
- exposed to the user, but appear in internal encodings.
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{ll}
- @{text "conjunction :: prop \<Rightarrow> prop \<Rightarrow> prop"} & (infix @{text "&"}) \\
- @{text "\<turnstile> A & B \<equiv> (\<And>C. (A \<Longrightarrow> B \<Longrightarrow> C) \<Longrightarrow> C)"} \\[1ex]
- @{text "prop :: prop \<Rightarrow> prop"} & (prefix @{text "#"}, suppressed) \\
- @{text "#A \<equiv> A"} \\[1ex]
- @{text "term :: \<alpha> \<Rightarrow> prop"} & (prefix @{text "TERM"}) \\
- @{text "term x \<equiv> (\<And>A. A \<Longrightarrow> A)"} \\[1ex]
- @{text "TYPE :: \<alpha> itself"} & (prefix @{text "TYPE"}) \\
- @{text "(unspecified)"} \\
- \end{tabular}
- \caption{Definitions of auxiliary connectives}\label{fig:pure-aux}
- \end{center}
- \end{figure}
-
- Derived conjunction rules include introduction @{text "A \<Longrightarrow> B \<Longrightarrow> A &
- B"}, and destructions @{text "A & B \<Longrightarrow> A"} and @{text "A & B \<Longrightarrow> B"}.
- Conjunction allows to treat simultaneous assumptions and conclusions
- uniformly. For example, multiple claims are intermediately
- represented as explicit conjunction, but this is refined into
- separate sub-goals before the user continues the proof; the final
- result is projected into a list of theorems (cf.\
- \secref{sec:tactical-goals}).
-
- The @{text "prop"} marker (@{text "#"}) makes arbitrarily complex
- propositions appear as atomic, without changing the meaning: @{text
- "\<Gamma> \<turnstile> A"} and @{text "\<Gamma> \<turnstile> #A"} are interchangeable. See
- \secref{sec:tactical-goals} for specific operations.
-
- The @{text "term"} marker turns any well-typed term into a derivable
- proposition: @{text "\<turnstile> TERM t"} holds unconditionally. Although
- this is logically vacuous, it allows to treat terms and proofs
- uniformly, similar to a type-theoretic framework.
-
- The @{text "TYPE"} constructor is the canonical representative of
- the unspecified type @{text "\<alpha> itself"}; it essentially injects the
- language of types into that of terms. There is specific notation
- @{text "TYPE(\<tau>)"} for @{text "TYPE\<^bsub>\<tau>
- itself\<^esub>"}.
- Although being devoid of any particular meaning, the @{text
- "TYPE(\<tau>)"} accounts for the type @{text "\<tau>"} within the term
- language. In particular, @{text "TYPE(\<alpha>)"} may be used as formal
- argument in primitive definitions, in order to circumvent hidden
- polymorphism (cf.\ \secref{sec:terms}). For example, @{text "c
- TYPE(\<alpha>) \<equiv> A[\<alpha>]"} defines @{text "c :: \<alpha> itself \<Rightarrow> prop"} in terms of
- a proposition @{text "A"} that depends on an additional type
- argument, which is essentially a predicate on types.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML Conjunction.intr: "thm -> thm -> thm"} \\
- @{index_ML Conjunction.elim: "thm -> thm * thm"} \\
- @{index_ML Drule.mk_term: "cterm -> thm"} \\
- @{index_ML Drule.dest_term: "thm -> cterm"} \\
- @{index_ML Logic.mk_type: "typ -> term"} \\
- @{index_ML Logic.dest_type: "term -> typ"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML Conjunction.intr} derives @{text "A & B"} from @{text
- "A"} and @{text "B"}.
-
- \item @{ML Conjunction.elim} derives @{text "A"} and @{text "B"}
- from @{text "A & B"}.
-
- \item @{ML Drule.mk_term} derives @{text "TERM t"}.
-
- \item @{ML Drule.dest_term} recovers term @{text "t"} from @{text
- "TERM t"}.
-
- \item @{ML Logic.mk_type}~@{text "\<tau>"} produces the term @{text
- "TYPE(\<tau>)"}.
-
- \item @{ML Logic.dest_type}~@{text "TYPE(\<tau>)"} recovers the type
- @{text "\<tau>"}.
-
- \end{description}
-*}
-
-
-section {* Object-level rules \label{sec:obj-rules} *}
-
-text {*
- The primitive inferences covered so far mostly serve foundational
- purposes. User-level reasoning usually works via object-level rules
- that are represented as theorems of Pure. Composition of rules
- involves \emph{backchaining}, \emph{higher-order unification} modulo
- @{text "\<alpha>\<beta>\<eta>"}-conversion of @{text "\<lambda>"}-terms, and so-called
- \emph{lifting} of rules into a context of @{text "\<And>"} and @{text
- "\<Longrightarrow>"} connectives. Thus the full power of higher-order Natural
- Deduction in Isabelle/Pure becomes readily available.
-*}
-
-
-subsection {* Hereditary Harrop Formulae *}
-
-text {*
- The idea of object-level rules is to model Natural Deduction
- inferences in the style of Gentzen \cite{Gentzen:1935}, but we allow
- arbitrary nesting similar to \cite{extensions91}. The most basic
- rule format is that of a \emph{Horn Clause}:
- \[
- \infer{@{text "A"}}{@{text "A\<^sub>1"} & @{text "\<dots>"} & @{text "A\<^sub>n"}}
- \]
- where @{text "A, A\<^sub>1, \<dots>, A\<^sub>n"} are atomic propositions
- of the framework, usually of the form @{text "Trueprop B"}, where
- @{text "B"} is a (compound) object-level statement. This
- object-level inference corresponds to an iterated implication in
- Pure like this:
- \[
- @{text "A\<^sub>1 \<Longrightarrow> \<dots> A\<^sub>n \<Longrightarrow> A"}
- \]
- As an example consider conjunction introduction: @{text "A \<Longrightarrow> B \<Longrightarrow> A \<and>
- B"}. Any parameters occurring in such rule statements are
- conceptionally treated as arbitrary:
- \[
- @{text "\<And>x\<^sub>1 \<dots> x\<^sub>m. A\<^sub>1 x\<^sub>1 \<dots> x\<^sub>m \<Longrightarrow> \<dots> A\<^sub>n x\<^sub>1 \<dots> x\<^sub>m \<Longrightarrow> A x\<^sub>1 \<dots> x\<^sub>m"}
- \]
-
- Nesting of rules means that the positions of @{text "A\<^sub>i"} may
- again hold compound rules, not just atomic propositions.
- Propositions of this format are called \emph{Hereditary Harrop
- Formulae} in the literature \cite{Miller:1991}. Here we give an
- inductive characterization as follows:
-
- \medskip
- \begin{tabular}{ll}
- @{text "\<^bold>x"} & set of variables \\
- @{text "\<^bold>A"} & set of atomic propositions \\
- @{text "\<^bold>H = \<And>\<^bold>x\<^sup>*. \<^bold>H\<^sup>* \<Longrightarrow> \<^bold>A"} & set of Hereditary Harrop Formulas \\
- \end{tabular}
- \medskip
-
- \noindent Thus we essentially impose nesting levels on propositions
- formed from @{text "\<And>"} and @{text "\<Longrightarrow>"}. At each level there is a
- prefix of parameters and compound premises, concluding an atomic
- proposition. Typical examples are @{text "\<longrightarrow>"}-introduction @{text
- "(A \<Longrightarrow> B) \<Longrightarrow> A \<longrightarrow> B"} or mathematical induction @{text "P 0 \<Longrightarrow> (\<And>n. P n
- \<Longrightarrow> P (Suc n)) \<Longrightarrow> P n"}. Even deeper nesting occurs in well-founded
- induction @{text "(\<And>x. (\<And>y. y \<prec> x \<Longrightarrow> P y) \<Longrightarrow> P x) \<Longrightarrow> P x"}, but this
- already marks the limit of rule complexity seen in practice.
-
- \medskip Regular user-level inferences in Isabelle/Pure always
- maintain the following canonical form of results:
-
- \begin{itemize}
-
- \item Normalization by @{text "(A \<Longrightarrow> (\<And>x. B x)) \<equiv> (\<And>x. A \<Longrightarrow> B x)"},
- which is a theorem of Pure, means that quantifiers are pushed in
- front of implication at each level of nesting. The normal form is a
- Hereditary Harrop Formula.
-
- \item The outermost prefix of parameters is represented via
- schematic variables: instead of @{text "\<And>\<^vec>x. \<^vec>H \<^vec>x
- \<Longrightarrow> A \<^vec>x"} we have @{text "\<^vec>H ?\<^vec>x \<Longrightarrow> A ?\<^vec>x"}.
- Note that this representation looses information about the order of
- parameters, and vacuous quantifiers vanish automatically.
-
- \end{itemize}
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML MetaSimplifier.norm_hhf: "thm -> thm"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML MetaSimplifier.norm_hhf}~@{text thm} normalizes the given
- theorem according to the canonical form specified above. This is
- occasionally helpful to repair some low-level tools that do not
- handle Hereditary Harrop Formulae properly.
-
- \end{description}
-*}
-
-
-subsection {* Rule composition *}
-
-text {*
- The rule calculus of Isabelle/Pure provides two main inferences:
- @{inference resolution} (i.e.\ back-chaining of rules) and
- @{inference assumption} (i.e.\ closing a branch), both modulo
- higher-order unification. There are also combined variants, notably
- @{inference elim_resolution} and @{inference dest_resolution}.
-
- To understand the all-important @{inference resolution} principle,
- we first consider raw @{inference_def composition} (modulo
- higher-order unification with substitution @{text "\<vartheta>"}):
- \[
- \infer[(@{inference_def composition})]{@{text "\<^vec>A\<vartheta> \<Longrightarrow> C\<vartheta>"}}
- {@{text "\<^vec>A \<Longrightarrow> B"} & @{text "B' \<Longrightarrow> C"} & @{text "B\<vartheta> = B'\<vartheta>"}}
- \]
- Here the conclusion of the first rule is unified with the premise of
- the second; the resulting rule instance inherits the premises of the
- first and conclusion of the second. Note that @{text "C"} can again
- consist of iterated implications. We can also permute the premises
- of the second rule back-and-forth in order to compose with @{text
- "B'"} in any position (subsequently we shall always refer to
- position 1 w.l.o.g.).
-
- In @{inference composition} the internal structure of the common
- part @{text "B"} and @{text "B'"} is not taken into account. For
- proper @{inference resolution} we require @{text "B"} to be atomic,
- and explicitly observe the structure @{text "\<And>\<^vec>x. \<^vec>H
- \<^vec>x \<Longrightarrow> B' \<^vec>x"} of the premise of the second rule. The
- idea is to adapt the first rule by ``lifting'' it into this context,
- by means of iterated application of the following inferences:
- \[
- \infer[(@{inference_def imp_lift})]{@{text "(\<^vec>H \<Longrightarrow> \<^vec>A) \<Longrightarrow> (\<^vec>H \<Longrightarrow> B)"}}{@{text "\<^vec>A \<Longrightarrow> B"}}
- \]
- \[
- \infer[(@{inference_def all_lift})]{@{text "(\<And>\<^vec>x. \<^vec>A (?\<^vec>a \<^vec>x)) \<Longrightarrow> (\<And>\<^vec>x. B (?\<^vec>a \<^vec>x))"}}{@{text "\<^vec>A ?\<^vec>a \<Longrightarrow> B ?\<^vec>a"}}
- \]
- By combining raw composition with lifting, we get full @{inference
- resolution} as follows:
- \[
- \infer[(@{inference_def resolution})]
- {@{text "(\<And>\<^vec>x. \<^vec>H \<^vec>x \<Longrightarrow> \<^vec>A (?\<^vec>a \<^vec>x))\<vartheta> \<Longrightarrow> C\<vartheta>"}}
- {\begin{tabular}{l}
- @{text "\<^vec>A ?\<^vec>a \<Longrightarrow> B ?\<^vec>a"} \\
- @{text "(\<And>\<^vec>x. \<^vec>H \<^vec>x \<Longrightarrow> B' \<^vec>x) \<Longrightarrow> C"} \\
- @{text "(\<lambda>\<^vec>x. B (?\<^vec>a \<^vec>x))\<vartheta> = B'\<vartheta>"} \\
- \end{tabular}}
- \]
-
- Continued resolution of rules allows to back-chain a problem towards
- more and sub-problems. Branches are closed either by resolving with
- a rule of 0 premises, or by producing a ``short-circuit'' within a
- solved situation (again modulo unification):
- \[
- \infer[(@{inference_def assumption})]{@{text "C\<vartheta>"}}
- {@{text "(\<And>\<^vec>x. \<^vec>H \<^vec>x \<Longrightarrow> A \<^vec>x) \<Longrightarrow> C"} & @{text "A\<vartheta> = H\<^sub>i\<vartheta>"}~~\text{(for some~@{text i})}}
- \]
-
- FIXME @{inference_def elim_resolution}, @{inference_def dest_resolution}
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML "op RS": "thm * thm -> thm"} \\
- @{index_ML "op OF": "thm * thm list -> thm"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{text "rule\<^sub>1 RS rule\<^sub>2"} resolves @{text
- "rule\<^sub>1"} with @{text "rule\<^sub>2"} according to the
- @{inference resolution} principle explained above. Note that the
- corresponding attribute in the Isar language is called @{attribute
- THEN}.
-
- \item @{text "rule OF rules"} resolves a list of rules with the
- first rule, addressing its premises @{text "1, \<dots>, length rules"}
- (operating from last to first). This means the newly emerging
- premises are all concatenated, without interfering. Also note that
- compared to @{text "RS"}, the rule argument order is swapped: @{text
- "rule\<^sub>1 RS rule\<^sub>2 = rule\<^sub>2 OF [rule\<^sub>1]"}.
-
- \end{description}
-*}
-
-end
--- a/doc-src/IsarImplementation/Thy/Prelim.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,764 +0,0 @@
-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 {*
- A \emph{theory} is a data container with explicit name 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 unchanged.
-
- \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 {*
- 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 due 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.
-*}
-
-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> T"} \\
- @{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 {*
- 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{print-mode}). 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: 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
- variants 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
--- a/doc-src/IsarImplementation/Thy/Proof.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,330 +0,0 @@
-theory Proof
-imports Base
-begin
-
-chapter {* Structured proofs *}
-
-section {* Variables \label{sec:variables} *}
-
-text {*
- Any variable that is not explicitly bound by @{text "\<lambda>"}-abstraction
- is considered as ``free''. Logically, free variables act like
- outermost universal quantification at the sequent level: @{text
- "A\<^isub>1(x), \<dots>, A\<^isub>n(x) \<turnstile> B(x)"} means that the result
- holds \emph{for all} values of @{text "x"}. Free variables for
- terms (not types) can be fully internalized into the logic: @{text
- "\<turnstile> B(x)"} and @{text "\<turnstile> \<And>x. B(x)"} are interchangeable, provided
- that @{text "x"} does not occur elsewhere in the context.
- Inspecting @{text "\<turnstile> \<And>x. B(x)"} more closely, we see that inside the
- quantifier, @{text "x"} is essentially ``arbitrary, but fixed'',
- while from outside it appears as a place-holder for instantiation
- (thanks to @{text "\<And>"} elimination).
-
- The Pure logic represents the idea of variables being either inside
- or outside the current scope by providing separate syntactic
- categories for \emph{fixed variables} (e.g.\ @{text "x"}) vs.\
- \emph{schematic variables} (e.g.\ @{text "?x"}). Incidently, a
- universal result @{text "\<turnstile> \<And>x. B(x)"} has the HHF normal form @{text
- "\<turnstile> B(?x)"}, which represents its generality nicely without requiring
- an explicit quantifier. The same principle works for type
- variables: @{text "\<turnstile> B(?\<alpha>)"} represents the idea of ``@{text "\<turnstile>
- \<forall>\<alpha>. B(\<alpha>)"}'' without demanding a truly polymorphic framework.
-
- \medskip Additional care is required to treat type variables in a
- way that facilitates type-inference. In principle, term variables
- depend on type variables, which means that type variables would have
- to be declared first. For example, a raw type-theoretic framework
- would demand the context to be constructed in stages as follows:
- @{text "\<Gamma> = \<alpha>: type, x: \<alpha>, a: A(x\<^isub>\<alpha>)"}.
-
- We allow a slightly less formalistic mode of operation: term
- variables @{text "x"} are fixed without specifying a type yet
- (essentially \emph{all} potential occurrences of some instance
- @{text "x\<^isub>\<tau>"} are fixed); the first occurrence of @{text "x"}
- within a specific term assigns its most general type, which is then
- maintained consistently in the context. The above example becomes
- @{text "\<Gamma> = x: term, \<alpha>: type, A(x\<^isub>\<alpha>)"}, where type @{text
- "\<alpha>"} is fixed \emph{after} term @{text "x"}, and the constraint
- @{text "x :: \<alpha>"} is an implicit consequence of the occurrence of
- @{text "x\<^isub>\<alpha>"} in the subsequent proposition.
-
- This twist of dependencies is also accommodated by the reverse
- operation of exporting results from a context: a type variable
- @{text "\<alpha>"} is considered fixed as long as it occurs in some fixed
- term variable of the context. For example, exporting @{text "x:
- term, \<alpha>: type \<turnstile> x\<^isub>\<alpha> = x\<^isub>\<alpha>"} produces in the first step
- @{text "x: term \<turnstile> x\<^isub>\<alpha> = x\<^isub>\<alpha>"} for fixed @{text "\<alpha>"},
- and only in the second step @{text "\<turnstile> ?x\<^isub>?\<^isub>\<alpha> =
- ?x\<^isub>?\<^isub>\<alpha>"} for schematic @{text "?x"} and @{text "?\<alpha>"}.
-
- \medskip The Isabelle/Isar proof context manages the gory details of
- term vs.\ type variables, with high-level principles for moving the
- frontier between fixed and schematic variables.
-
- The @{text "add_fixes"} operation explictly declares fixed
- variables; the @{text "declare_term"} operation absorbs a term into
- a context by fixing new type variables and adding syntactic
- constraints.
-
- The @{text "export"} operation is able to perform the main work of
- generalizing term and type variables as sketched above, assuming
- that fixing variables and terms have been declared properly.
-
- There @{text "import"} operation makes a generalized fact a genuine
- part of the context, by inventing fixed variables for the schematic
- ones. The effect can be reversed by using @{text "export"} later,
- potentially with an extended context; the result is equivalent to
- the original modulo renaming of schematic variables.
-
- The @{text "focus"} operation provides a variant of @{text "import"}
- for nested propositions (with explicit quantification): @{text
- "\<And>x\<^isub>1 \<dots> x\<^isub>n. B(x\<^isub>1, \<dots>, x\<^isub>n)"} is
- decomposed by inventing fixed variables @{text "x\<^isub>1, \<dots>,
- x\<^isub>n"} for the body.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML Variable.add_fixes: "
- string list -> Proof.context -> string list * Proof.context"} \\
- @{index_ML Variable.variant_fixes: "
- string list -> Proof.context -> string list * Proof.context"} \\
- @{index_ML Variable.declare_term: "term -> Proof.context -> Proof.context"} \\
- @{index_ML Variable.declare_constraints: "term -> Proof.context -> Proof.context"} \\
- @{index_ML Variable.export: "Proof.context -> Proof.context -> thm list -> thm list"} \\
- @{index_ML Variable.polymorphic: "Proof.context -> term list -> term list"} \\
- @{index_ML Variable.import_thms: "bool -> thm list -> Proof.context ->
- ((ctyp list * cterm list) * thm list) * Proof.context"} \\
- @{index_ML Variable.focus: "cterm -> Proof.context -> (cterm list * cterm) * Proof.context"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML Variable.add_fixes}~@{text "xs ctxt"} fixes term
- variables @{text "xs"}, returning the resulting internal names. By
- default, the internal representation coincides with the external
- one, which also means that the given variables must not be fixed
- already. There is a different policy within a local proof body: the
- given names are just hints for newly invented Skolem variables.
-
- \item @{ML Variable.variant_fixes} is similar to @{ML
- Variable.add_fixes}, but always produces fresh variants of the given
- names.
-
- \item @{ML Variable.declare_term}~@{text "t ctxt"} declares term
- @{text "t"} to belong to the context. This automatically fixes new
- type variables, but not term variables. Syntactic constraints for
- type and term variables are declared uniformly, though.
-
- \item @{ML Variable.declare_constraints}~@{text "t ctxt"} declares
- syntactic constraints from term @{text "t"}, without making it part
- of the context yet.
-
- \item @{ML Variable.export}~@{text "inner outer thms"} generalizes
- fixed type and term variables in @{text "thms"} according to the
- difference of the @{text "inner"} and @{text "outer"} context,
- following the principles sketched above.
-
- \item @{ML Variable.polymorphic}~@{text "ctxt ts"} generalizes type
- variables in @{text "ts"} as far as possible, even those occurring
- in fixed term variables. The default policy of type-inference is to
- fix newly introduced type variables, which is essentially reversed
- with @{ML Variable.polymorphic}: here the given terms are detached
- from the context as far as possible.
-
- \item @{ML Variable.import_thms}~@{text "open thms ctxt"} invents fixed
- type and term variables for the schematic ones occurring in @{text
- "thms"}. The @{text "open"} flag indicates whether the fixed names
- should be accessible to the user, otherwise newly introduced names
- are marked as ``internal'' (\secref{sec:names}).
-
- \item @{ML Variable.focus}~@{text B} decomposes the outermost @{text
- "\<And>"} prefix of proposition @{text "B"}.
-
- \end{description}
-*}
-
-
-section {* Assumptions \label{sec:assumptions} *}
-
-text {*
- An \emph{assumption} is a proposition that it is postulated in the
- current context. Local conclusions may use assumptions as
- additional facts, but this imposes implicit hypotheses that weaken
- the overall statement.
-
- Assumptions are restricted to fixed non-schematic statements, i.e.\
- all generality needs to be expressed by explicit quantifiers.
- Nevertheless, the result will be in HHF normal form with outermost
- quantifiers stripped. For example, by assuming @{text "\<And>x :: \<alpha>. P
- x"} we get @{text "\<And>x :: \<alpha>. P x \<turnstile> P ?x"} for schematic @{text "?x"}
- of fixed type @{text "\<alpha>"}. Local derivations accumulate more and
- more explicit references to hypotheses: @{text "A\<^isub>1, \<dots>,
- A\<^isub>n \<turnstile> B"} where @{text "A\<^isub>1, \<dots>, A\<^isub>n"} needs to
- be covered by the assumptions of the current context.
-
- \medskip The @{text "add_assms"} operation augments the context by
- local assumptions, which are parameterized by an arbitrary @{text
- "export"} rule (see below).
-
- The @{text "export"} operation moves facts from a (larger) inner
- context into a (smaller) outer context, by discharging the
- difference of the assumptions as specified by the associated export
- rules. Note that the discharged portion is determined by the
- difference contexts, not the facts being exported! There is a
- separate flag to indicate a goal context, where the result is meant
- to refine an enclosing sub-goal of a structured proof state.
-
- \medskip The most basic export rule discharges assumptions directly
- by means of the @{text "\<Longrightarrow>"} introduction rule:
- \[
- \infer[(@{text "\<Longrightarrow>_intro"})]{@{text "\<Gamma> \\ A \<turnstile> A \<Longrightarrow> B"}}{@{text "\<Gamma> \<turnstile> B"}}
- \]
-
- The variant for goal refinements marks the newly introduced
- premises, which causes the canonical Isar goal refinement scheme to
- enforce unification with local premises within the goal:
- \[
- \infer[(@{text "#\<Longrightarrow>_intro"})]{@{text "\<Gamma> \\ A \<turnstile> #A \<Longrightarrow> B"}}{@{text "\<Gamma> \<turnstile> B"}}
- \]
-
- \medskip Alternative versions of assumptions may perform arbitrary
- transformations on export, as long as the corresponding portion of
- hypotheses is removed from the given facts. For example, a local
- definition works by fixing @{text "x"} and assuming @{text "x \<equiv> t"},
- with the following export rule to reverse the effect:
- \[
- \infer[(@{text "\<equiv>-expand"})]{@{text "\<Gamma> \\ x \<equiv> t \<turnstile> B t"}}{@{text "\<Gamma> \<turnstile> B x"}}
- \]
- This works, because the assumption @{text "x \<equiv> t"} was introduced in
- a context with @{text "x"} being fresh, so @{text "x"} does not
- occur in @{text "\<Gamma>"} here.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type Assumption.export} \\
- @{index_ML Assumption.assume: "cterm -> thm"} \\
- @{index_ML Assumption.add_assms:
- "Assumption.export ->
- cterm list -> Proof.context -> thm list * Proof.context"} \\
- @{index_ML Assumption.add_assumes: "
- cterm list -> Proof.context -> thm list * Proof.context"} \\
- @{index_ML Assumption.export: "bool -> Proof.context -> Proof.context -> thm -> thm"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type Assumption.export} represents arbitrary export
- rules, which is any function of type @{ML_type "bool -> cterm list -> thm -> thm"},
- where the @{ML_type "bool"} indicates goal mode, and the @{ML_type
- "cterm list"} the collection of assumptions to be discharged
- simultaneously.
-
- \item @{ML Assumption.assume}~@{text "A"} turns proposition @{text
- "A"} into a raw assumption @{text "A \<turnstile> A'"}, where the conclusion
- @{text "A'"} is in HHF normal form.
-
- \item @{ML Assumption.add_assms}~@{text "r As"} augments the context
- by assumptions @{text "As"} with export rule @{text "r"}. The
- resulting facts are hypothetical theorems as produced by the raw
- @{ML Assumption.assume}.
-
- \item @{ML Assumption.add_assumes}~@{text "As"} is a special case of
- @{ML Assumption.add_assms} where the export rule performs @{text
- "\<Longrightarrow>_intro"} or @{text "#\<Longrightarrow>_intro"}, depending on goal mode.
-
- \item @{ML Assumption.export}~@{text "is_goal inner outer thm"}
- exports result @{text "thm"} from the the @{text "inner"} context
- back into the @{text "outer"} one; @{text "is_goal = true"} means
- this is a goal context. The result is in HHF normal form. Note
- that @{ML "ProofContext.export"} combines @{ML "Variable.export"}
- and @{ML "Assumption.export"} in the canonical way.
-
- \end{description}
-*}
-
-
-section {* Results \label{sec:results} *}
-
-text {*
- Local results are established by monotonic reasoning from facts
- within a context. This allows common combinations of theorems,
- e.g.\ via @{text "\<And>/\<Longrightarrow>"} elimination, resolution rules, or equational
- reasoning, see \secref{sec:thms}. Unaccounted context manipulations
- should be avoided, notably raw @{text "\<And>/\<Longrightarrow>"} introduction or ad-hoc
- references to free variables or assumptions not present in the proof
- context.
-
- \medskip The @{text "SUBPROOF"} combinator allows to structure a
- tactical proof recursively by decomposing a selected sub-goal:
- @{text "(\<And>x. A(x) \<Longrightarrow> B(x)) \<Longrightarrow> \<dots>"} is turned into @{text "B(x) \<Longrightarrow> \<dots>"}
- after fixing @{text "x"} and assuming @{text "A(x)"}. This means
- the tactic needs to solve the conclusion, but may use the premise as
- a local fact, for locally fixed variables.
-
- The @{text "prove"} operation provides an interface for structured
- backwards reasoning under program control, with some explicit sanity
- checks of the result. The goal context can be augmented by
- additional fixed variables (cf.\ \secref{sec:variables}) and
- assumptions (cf.\ \secref{sec:assumptions}), which will be available
- as local facts during the proof and discharged into implications in
- the result. Type and term variables are generalized as usual,
- according to the context.
-
- The @{text "obtain"} operation produces results by eliminating
- existing facts by means of a given tactic. This acts like a dual
- conclusion: the proof demonstrates that the context may be augmented
- by certain fixed variables and assumptions. See also
- \cite{isabelle-isar-ref} for the user-level @{text "\<OBTAIN>"} and
- @{text "\<GUESS>"} elements. Final results, which may not refer to
- the parameters in the conclusion, need to exported explicitly into
- the original context.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML SUBPROOF:
- "({context: Proof.context, schematics: ctyp list * cterm list,
- params: cterm list, asms: cterm list, concl: cterm,
- prems: thm list} -> tactic) -> Proof.context -> int -> tactic"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML Goal.prove: "Proof.context -> string list -> term list -> term ->
- ({prems: thm list, context: Proof.context} -> tactic) -> thm"} \\
- @{index_ML Goal.prove_multi: "Proof.context -> string list -> term list -> term list ->
- ({prems: thm list, context: Proof.context} -> tactic) -> thm list"} \\
- \end{mldecls}
- \begin{mldecls}
- @{index_ML Obtain.result: "(Proof.context -> tactic) ->
- thm list -> Proof.context -> (cterm list * thm list) * Proof.context"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML SUBPROOF}~@{text "tac ctxt i"} decomposes the structure
- of the specified sub-goal, producing an extended context and a
- reduced goal, which needs to be solved by the given tactic. All
- schematic parameters of the goal are imported into the context as
- fixed ones, which may not be instantiated in the sub-proof.
-
- \item @{ML Goal.prove}~@{text "ctxt xs As C tac"} states goal @{text
- "C"} in the context augmented by fixed variables @{text "xs"} and
- assumptions @{text "As"}, and applies tactic @{text "tac"} to solve
- it. The latter may depend on the local assumptions being presented
- as facts. The result is in HHF normal form.
-
- \item @{ML Goal.prove_multi} is simular to @{ML Goal.prove}, but
- states several conclusions simultaneously. The goal is encoded by
- means of Pure conjunction; @{ML Goal.conjunction_tac} will turn this
- into a collection of individual subgoals.
-
- \item @{ML Obtain.result}~@{text "tac thms ctxt"} eliminates the
- given facts using a tactic, which results in additional fixed
- variables and assumptions in the context. Final results need to be
- exported explicitly.
-
- \end{description}
-*}
-
-end
--- a/doc-src/IsarImplementation/Thy/Tactic.thy Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,405 +0,0 @@
-theory Tactic
-imports Base
-begin
-
-chapter {* Tactical reasoning *}
-
-text {*
- Tactical reasoning works by refining the initial claim in a
- backwards fashion, until a solved form is reached. A @{text "goal"}
- consists of several subgoals that need to be solved in order to
- achieve the main statement; zero subgoals means that the proof may
- be finished. A @{text "tactic"} is a refinement operation that maps
- a goal to a lazy sequence of potential successors. A @{text
- "tactical"} is a combinator for composing tactics.
-*}
-
-
-section {* Goals \label{sec:tactical-goals} *}
-
-text {*
- Isabelle/Pure represents a goal as a theorem stating that the
- subgoals imply the main goal: @{text "A\<^sub>1 \<Longrightarrow> \<dots> \<Longrightarrow> A\<^sub>n \<Longrightarrow>
- C"}. The outermost goal structure is that of a Horn Clause: i.e.\
- an iterated implication without any quantifiers\footnote{Recall that
- outermost @{text "\<And>x. \<phi>[x]"} is always represented via schematic
- variables in the body: @{text "\<phi>[?x]"}. These variables may get
- instantiated during the course of reasoning.}. For @{text "n = 0"}
- a goal is called ``solved''.
-
- The structure of each subgoal @{text "A\<^sub>i"} is that of a
- general Hereditary Harrop Formula @{text "\<And>x\<^sub>1 \<dots>
- \<And>x\<^sub>k. H\<^sub>1 \<Longrightarrow> \<dots> \<Longrightarrow> H\<^sub>m \<Longrightarrow> B"}. Here @{text
- "x\<^sub>1, \<dots>, x\<^sub>k"} are goal parameters, i.e.\
- arbitrary-but-fixed entities of certain types, and @{text
- "H\<^sub>1, \<dots>, H\<^sub>m"} are goal hypotheses, i.e.\ facts that may
- be assumed locally. Together, this forms the goal context of the
- conclusion @{text B} to be established. The goal hypotheses may be
- again arbitrary Hereditary Harrop Formulas, although the level of
- nesting rarely exceeds 1--2 in practice.
-
- The main conclusion @{text C} is internally marked as a protected
- proposition, which is represented explicitly by the notation @{text
- "#C"}. This ensures that the decomposition into subgoals and main
- conclusion is well-defined for arbitrarily structured claims.
-
- \medskip Basic goal management is performed via the following
- Isabelle/Pure rules:
-
- \[
- \infer[@{text "(init)"}]{@{text "C \<Longrightarrow> #C"}}{} \qquad
- \infer[@{text "(finish)"}]{@{text "C"}}{@{text "#C"}}
- \]
-
- \medskip The following low-level variants admit general reasoning
- with protected propositions:
-
- \[
- \infer[@{text "(protect)"}]{@{text "#C"}}{@{text "C"}} \qquad
- \infer[@{text "(conclude)"}]{@{text "A\<^sub>1 \<Longrightarrow> \<dots> \<Longrightarrow> A\<^sub>n \<Longrightarrow> C"}}{@{text "A\<^sub>1 \<Longrightarrow> \<dots> \<Longrightarrow> A\<^sub>n \<Longrightarrow> #C"}}
- \]
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML Goal.init: "cterm -> thm"} \\
- @{index_ML Goal.finish: "thm -> thm"} \\
- @{index_ML Goal.protect: "thm -> thm"} \\
- @{index_ML Goal.conclude: "thm -> thm"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML "Goal.init"}~@{text C} initializes a tactical goal from
- the well-formed proposition @{text C}.
-
- \item @{ML "Goal.finish"}~@{text "thm"} checks whether theorem
- @{text "thm"} is a solved goal (no subgoals), and concludes the
- result by removing the goal protection.
-
- \item @{ML "Goal.protect"}~@{text "thm"} protects the full statement
- of theorem @{text "thm"}.
-
- \item @{ML "Goal.conclude"}~@{text "thm"} removes the goal
- protection, even if there are pending subgoals.
-
- \end{description}
-*}
-
-
-section {* Tactics *}
-
-text {* A @{text "tactic"} is a function @{text "goal \<rightarrow> goal\<^sup>*\<^sup>*"} that
- maps a given goal state (represented as a theorem, cf.\
- \secref{sec:tactical-goals}) to a lazy sequence of potential
- successor states. The underlying sequence implementation is lazy
- both in head and tail, and is purely functional in \emph{not}
- supporting memoing.\footnote{The lack of memoing and the strict
- nature of SML requires some care when working with low-level
- sequence operations, to avoid duplicate or premature evaluation of
- results.}
-
- An \emph{empty result sequence} means that the tactic has failed: in
- a compound tactic expressions other tactics might be tried instead,
- or the whole refinement step might fail outright, producing a
- toplevel error message. When implementing tactics from scratch, one
- should take care to observe the basic protocol of mapping regular
- error conditions to an empty result; only serious faults should
- emerge as exceptions.
-
- By enumerating \emph{multiple results}, a tactic can easily express
- the potential outcome of an internal search process. There are also
- combinators for building proof tools that involve search
- systematically, see also \secref{sec:tacticals}.
-
- \medskip As explained in \secref{sec:tactical-goals}, a goal state
- essentially consists of a list of subgoals that imply the main goal
- (conclusion). Tactics may operate on all subgoals or on a
- particularly specified subgoal, but must not change the main
- conclusion (apart from instantiating schematic goal variables).
-
- Tactics with explicit \emph{subgoal addressing} are of the form
- @{text "int \<rightarrow> tactic"} and may be applied to a particular subgoal
- (counting from 1). If the subgoal number is out of range, the
- tactic should fail with an empty result sequence, but must not raise
- an exception!
-
- Operating on a particular subgoal means to replace it by an interval
- of zero or more subgoals in the same place; other subgoals must not
- be affected, apart from instantiating schematic variables ranging
- over the whole goal state.
-
- A common pattern of composing tactics with subgoal addressing is to
- try the first one, and then the second one only if the subgoal has
- not been solved yet. Special care is required here to avoid bumping
- into unrelated subgoals that happen to come after the original
- subgoal. Assuming that there is only a single initial subgoal is a
- very common error when implementing tactics!
-
- Tactics with internal subgoal addressing should expose the subgoal
- index as @{text "int"} argument in full generality; a hardwired
- subgoal 1 inappropriate.
-
- \medskip The main well-formedness conditions for proper tactics are
- summarized as follows.
-
- \begin{itemize}
-
- \item General tactic failure is indicated by an empty result, only
- serious faults may produce an exception.
-
- \item The main conclusion must not be changed, apart from
- instantiating schematic variables.
-
- \item A tactic operates either uniformly on all subgoals, or
- specifically on a selected subgoal (without bumping into unrelated
- subgoals).
-
- \item Range errors in subgoal addressing produce an empty result.
-
- \end{itemize}
-
- Some of these conditions are checked by higher-level goal
- infrastructure (\secref{sec:results}); others are not checked
- explicitly, and violating them merely results in ill-behaved tactics
- experienced by the user (e.g.\ tactics that insist in being
- applicable only to singleton goals, or disallow composition with
- basic tacticals).
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML_type tactic: "thm -> thm Seq.seq"} \\
- @{index_ML no_tac: tactic} \\
- @{index_ML all_tac: tactic} \\
- @{index_ML print_tac: "string -> tactic"} \\[1ex]
- @{index_ML PRIMITIVE: "(thm -> thm) -> tactic"} \\[1ex]
- @{index_ML SUBGOAL: "(term * int -> tactic) -> int -> tactic"} \\
- @{index_ML CSUBGOAL: "(cterm * int -> tactic) -> int -> tactic"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML_type tactic} represents tactics. The well-formedness
- conditions described above need to be observed. See also @{"file"
- "~~/src/Pure/General/seq.ML"} for the underlying implementation of
- lazy sequences.
-
- \item @{ML_type "int -> tactic"} represents tactics with explicit
- subgoal addressing, with well-formedness conditions as described
- above.
-
- \item @{ML no_tac} is a tactic that always fails, returning the
- empty sequence.
-
- \item @{ML all_tac} is a tactic that always succeeds, returning a
- singleton sequence with unchanged goal state.
-
- \item @{ML print_tac}~@{text "message"} is like @{ML all_tac}, but
- prints a message together with the goal state on the tracing
- channel.
-
- \item @{ML PRIMITIVE}~@{text rule} turns a primitive inference rule
- into a tactic with unique result. Exception @{ML THM} is considered
- a regular tactic failure and produces an empty result; other
- exceptions are passed through.
-
- \item @{ML SUBGOAL}~@{text "(fn (subgoal, i) => tactic)"} is the
- most basic form to produce a tactic with subgoal addressing. The
- given abstraction over the subgoal term and subgoal number allows to
- peek at the relevant information of the full goal state. The
- subgoal range is checked as required above.
-
- \item @{ML CSUBGOAL} is similar to @{ML SUBGOAL}, but passes the
- subgoal as @{ML_type cterm} instead of raw @{ML_type term}. This
- avoids expensive re-certification in situations where the subgoal is
- used directly for primitive inferences.
-
- \end{description}
-*}
-
-
-subsection {* Resolution and assumption tactics \label{sec:resolve-assume-tac} *}
-
-text {* \emph{Resolution} is the most basic mechanism for refining a
- subgoal using a theorem as object-level rule.
- \emph{Elim-resolution} is particularly suited for elimination rules:
- it resolves with a rule, proves its first premise by assumption, and
- finally deletes that assumption from any new subgoals.
- \emph{Destruct-resolution} is like elim-resolution, but the given
- destruction rules are first turned into canonical elimination
- format. \emph{Forward-resolution} is like destruct-resolution, but
- without deleting the selected assumption. The @{text "r/e/d/f"}
- naming convention is maintained for several different kinds of
- resolution rules and tactics.
-
- Assumption tactics close a subgoal by unifying some of its premises
- against its conclusion.
-
- \medskip All the tactics in this section operate on a subgoal
- designated by a positive integer. Other subgoals might be affected
- indirectly, due to instantiation of schematic variables.
-
- There are various sources of non-determinism, the tactic result
- sequence enumerates all possibilities of the following choices (if
- applicable):
-
- \begin{enumerate}
-
- \item selecting one of the rules given as argument to the tactic;
-
- \item selecting a subgoal premise to eliminate, unifying it against
- the first premise of the rule;
-
- \item unifying the conclusion of the subgoal to the conclusion of
- the rule.
-
- \end{enumerate}
-
- Recall that higher-order unification may produce multiple results
- that are enumerated here.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML resolve_tac: "thm list -> int -> tactic"} \\
- @{index_ML eresolve_tac: "thm list -> int -> tactic"} \\
- @{index_ML dresolve_tac: "thm list -> int -> tactic"} \\
- @{index_ML forward_tac: "thm list -> int -> tactic"} \\[1ex]
- @{index_ML assume_tac: "int -> tactic"} \\
- @{index_ML eq_assume_tac: "int -> tactic"} \\[1ex]
- @{index_ML match_tac: "thm list -> int -> tactic"} \\
- @{index_ML ematch_tac: "thm list -> int -> tactic"} \\
- @{index_ML dmatch_tac: "thm list -> int -> tactic"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML resolve_tac}~@{text "thms i"} refines the goal state
- using the given theorems, which should normally be introduction
- rules. The tactic resolves a rule's conclusion with subgoal @{text
- i}, replacing it by the corresponding versions of the rule's
- premises.
-
- \item @{ML eresolve_tac}~@{text "thms i"} performs elim-resolution
- with the given theorems, which should normally be elimination rules.
-
- \item @{ML dresolve_tac}~@{text "thms i"} performs
- destruct-resolution with the given theorems, which should normally
- be destruction rules. This replaces an assumption by the result of
- applying one of the rules.
-
- \item @{ML forward_tac} is like @{ML dresolve_tac} except that the
- selected assumption is not deleted. It applies a rule to an
- assumption, adding the result as a new assumption.
-
- \item @{ML assume_tac}~@{text i} attempts to solve subgoal @{text i}
- by assumption (modulo higher-order unification).
-
- \item @{ML eq_assume_tac} is similar to @{ML assume_tac}, but checks
- only for immediate @{text "\<alpha>"}-convertibility instead of using
- unification. It succeeds (with a unique next state) if one of the
- assumptions is equal to the subgoal's conclusion. Since it does not
- instantiate variables, it cannot make other subgoals unprovable.
-
- \item @{ML match_tac}, @{ML ematch_tac}, and @{ML dmatch_tac} are
- similar to @{ML resolve_tac}, @{ML eresolve_tac}, and @{ML
- dresolve_tac}, respectively, but do not instantiate schematic
- variables in the goal state.
-
- Flexible subgoals are not updated at will, but are left alone.
- Strictly speaking, matching means to treat the unknowns in the goal
- state as constants; these tactics merely discard unifiers that would
- update the goal state.
-
- \end{description}
-*}
-
-
-subsection {* Explicit instantiation within a subgoal context *}
-
-text {* The main resolution tactics (\secref{sec:resolve-assume-tac})
- use higher-order unification, which works well in many practical
- situations despite its daunting theoretical properties.
- Nonetheless, there are important problem classes where unguided
- higher-order unification is not so useful. This typically involves
- rules like universal elimination, existential introduction, or
- equational substitution. Here the unification problem involves
- fully flexible @{text "?P ?x"} schemes, which are hard to manage
- without further hints.
-
- By providing a (small) rigid term for @{text "?x"} explicitly, the
- remaining unification problem is to assign a (large) term to @{text
- "?P"}, according to the shape of the given subgoal. This is
- sufficiently well-behaved in most practical situations.
-
- \medskip Isabelle provides separate versions of the standard @{text
- "r/e/d/f"} resolution tactics that allow to provide explicit
- instantiations of unknowns of the given rule, wrt.\ terms that refer
- to the implicit context of the selected subgoal.
-
- An instantiation consists of a list of pairs of the form @{text
- "(?x, t)"}, where @{text ?x} is a schematic variable occurring in
- the given rule, and @{text t} is a term from the current proof
- context, augmented by the local goal parameters of the selected
- subgoal; cf.\ the @{text "focus"} operation described in
- \secref{sec:variables}.
-
- Entering the syntactic context of a subgoal is a brittle operation,
- because its exact form is somewhat accidental, and the choice of
- bound variable names depends on the presence of other local and
- global names. Explicit renaming of subgoal parameters prior to
- explicit instantiation might help to achieve a bit more robustness.
-
- Type instantiations may be given as well, via pairs like @{text
- "(?'a, \<tau>)"}. Type instantiations are distinguished from term
- instantiations by the syntactic form of the schematic variable.
- Types are instantiated before terms are. Since term instantiation
- already performs type-inference as expected, explicit type
- instantiations are seldom necessary.
-*}
-
-text %mlref {*
- \begin{mldecls}
- @{index_ML res_inst_tac: "Proof.context -> (indexname * string) list -> thm -> int -> tactic"} \\
- @{index_ML eres_inst_tac: "Proof.context -> (indexname * string) list -> thm -> int -> tactic"} \\
- @{index_ML dres_inst_tac: "Proof.context -> (indexname * string) list -> thm -> int -> tactic"} \\
- @{index_ML forw_inst_tac: "Proof.context -> (indexname * string) list -> thm -> int -> tactic"} \\[1ex]
- @{index_ML rename_tac: "string list -> int -> tactic"} \\
- \end{mldecls}
-
- \begin{description}
-
- \item @{ML res_inst_tac}~@{text "ctxt insts thm i"} instantiates the
- rule @{text thm} with the instantiations @{text insts}, as described
- above, and then performs resolution on subgoal @{text i}.
-
- \item @{ML eres_inst_tac} is like @{ML res_inst_tac}, but performs
- elim-resolution.
-
- \item @{ML dres_inst_tac} is like @{ML res_inst_tac}, but performs
- destruct-resolution.
-
- \item @{ML forw_inst_tac} is like @{ML dres_inst_tac} except that
- the selected assumption is not deleted.
-
- \item @{ML rename_tac}~@{text "names i"} renames the innermost
- parameters of subgoal @{text i} according to the provided @{text
- names} (which need to be distinct indentifiers).
-
- \end{description}
-*}
-
-
-section {* Tacticals \label{sec:tacticals} *}
-
-text {*
- A \emph{tactical} is a functional combinator for building up complex
- tactics from simpler ones. Typical tactical perform sequential
- composition, disjunction (choice), iteration, or goal addressing.
- Various search strategies may be expressed via tacticals.
-
- \medskip FIXME
-*}
-
-end
--- a/doc-src/IsarImplementation/Thy/document/Base.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
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-%
-\begin{isabellebody}%
-\def\isabellecontext{Base}%
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-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
-\isacommand{theory}\isamarkupfalse%
-\ Base\isanewline
-\isakeyword{imports}\ Pure\isanewline
-\isakeyword{uses}\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isacharslash}{\isachardot}{\isachardot}{\isacharslash}antiquote{\isacharunderscore}setup{\isachardot}ML{\isachardoublequoteclose}\isanewline
-\isakeyword{begin}\isanewline
-\isanewline
-\isacommand{end}\isamarkupfalse%
-%
-\endisatagtheory
-{\isafoldtheory}%
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-\isadelimtheory
-\isanewline
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-\endisadelimtheory
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:
--- a/doc-src/IsarImplementation/Thy/document/Integration.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,520 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Integration}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\isatagtheory
-\isacommand{theory}\isamarkupfalse%
-\ Integration\isanewline
-\isakeyword{imports}\ Base\isanewline
-\isakeyword{begin}%
-\endisatagtheory
-{\isafoldtheory}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\isamarkupchapter{System integration%
-}
-\isamarkuptrue%
-%
-\isamarkupsection{Isar toplevel \label{sec:isar-toplevel}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The Isar toplevel may be considered the centeral hub of the
- Isabelle/Isar system, where all key components and sub-systems are
- integrated into a single read-eval-print loop of Isar commands. We
- shall even incorporate the existing {\ML} toplevel of the compiler
- and run-time system (cf.\ \secref{sec:ML-toplevel}).
-
- Isabelle/Isar departs from the original ``LCF system architecture''
- where {\ML} was really The Meta Language for defining theories and
- conducting proofs. Instead, {\ML} now only serves as the
- implementation language for the system (and user extensions), while
- the specific Isar toplevel supports the concepts of theory and proof
- development natively. This includes the graph structure of theories
- and the block structure of proofs, support for unlimited undo,
- facilities for tracing, debugging, timing, profiling etc.
-
- \medskip The toplevel maintains an implicit state, which is
- transformed by a sequence of transitions -- either interactively or
- in batch-mode. In interactive mode, Isar state transitions are
- encapsulated as safe transactions, such that both failure and undo
- are handled conveniently without destroying the underlying draft
- theory (cf.~\secref{sec:context-theory}). In batch mode,
- transitions operate in a linear (destructive) fashion, such that
- error conditions abort the present attempt to construct a theory or
- proof altogether.
-
- The toplevel state is a disjoint sum of empty \isa{toplevel}, or
- \isa{theory}, or \isa{proof}. On entering the main Isar loop we
- start with an empty toplevel. A theory is commenced by giving a
- \isa{{\isasymTHEORY}} header; within a theory we may issue theory
- commands such as \isa{{\isasymDEFINITION}}, or state a \isa{{\isasymTHEOREM}} to be proven. Now we are within a proof state, with a
- rich collection of Isar proof commands for structured proof
- composition, or unstructured proof scripts. When the proof is
- concluded we get back to the theory, which is then updated by
- storing the resulting fact. Further theory declarations or theorem
- statements with proofs may follow, until we eventually conclude the
- theory development by issuing \isa{{\isasymEND}}. The resulting theory
- is then stored within the theory database and we are back to the
- empty toplevel.
-
- In addition to these proper state transformations, there are also
- some diagnostic commands for peeking at the toplevel state without
- modifying it (e.g.\ \isakeyword{thm}, \isakeyword{term},
- \isakeyword{print-cases}).%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{Toplevel.state}\verb|type Toplevel.state| \\
- \indexdef{}{ML}{Toplevel.UNDEF}\verb|Toplevel.UNDEF: exn| \\
- \indexdef{}{ML}{Toplevel.is\_toplevel}\verb|Toplevel.is_toplevel: Toplevel.state -> bool| \\
- \indexdef{}{ML}{Toplevel.theory\_of}\verb|Toplevel.theory_of: Toplevel.state -> theory| \\
- \indexdef{}{ML}{Toplevel.proof\_of}\verb|Toplevel.proof_of: Toplevel.state -> Proof.state| \\
- \indexdef{}{ML}{Toplevel.debug}\verb|Toplevel.debug: bool ref| \\
- \indexdef{}{ML}{Toplevel.timing}\verb|Toplevel.timing: bool ref| \\
- \indexdef{}{ML}{Toplevel.profiling}\verb|Toplevel.profiling: int ref| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Toplevel.state| represents Isar toplevel states,
- which are normally manipulated through the concept of toplevel
- transitions only (\secref{sec:toplevel-transition}). Also note that
- a raw toplevel state is subject to the same linearity restrictions
- as a theory context (cf.~\secref{sec:context-theory}).
-
- \item \verb|Toplevel.UNDEF| is raised for undefined toplevel
- operations. Many operations work only partially for certain cases,
- since \verb|Toplevel.state| is a sum type.
-
- \item \verb|Toplevel.is_toplevel|~\isa{state} checks for an empty
- toplevel state.
-
- \item \verb|Toplevel.theory_of|~\isa{state} selects the theory of
- a theory or proof (!), otherwise raises \verb|Toplevel.UNDEF|.
-
- \item \verb|Toplevel.proof_of|~\isa{state} selects the Isar proof
- state if available, otherwise raises \verb|Toplevel.UNDEF|.
-
- \item \verb|set Toplevel.debug| makes the toplevel print further
- details about internal error conditions, exceptions being raised
- etc.
-
- \item \verb|set Toplevel.timing| makes the toplevel print timing
- information for each Isar command being executed.
-
- \item \verb|Toplevel.profiling|~\verb|:=|~\isa{n} controls
- low-level profiling of the underlying {\ML} runtime system. For
- Poly/ML, \isa{n\ {\isacharequal}\ {\isadigit{1}}} means time and \isa{n\ {\isacharequal}\ {\isadigit{2}}} space
- profiling.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsubsection{Toplevel transitions \label{sec:toplevel-transition}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-An Isar toplevel transition consists of a partial function on the
- toplevel state, with additional information for diagnostics and
- error reporting: there are fields for command name, source position,
- optional source text, as well as flags for interactive-only commands
- (which issue a warning in batch-mode), printing of result state,
- etc.
-
- The operational part is represented as the sequential union of a
- list of partial functions, which are tried in turn until the first
- one succeeds. This acts like an outer case-expression for various
- alternative state transitions. For example, \isakeyword{qed} acts
- differently for a local proofs vs.\ the global ending of the main
- proof.
-
- Toplevel transitions are composed via transition transformers.
- Internally, Isar commands are put together from an empty transition
- extended by name and source position (and optional source text). It
- is then left to the individual command parser to turn the given
- concrete syntax into a suitable transition transformer that adjoins
- actual operations on a theory or proof state etc.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{Toplevel.print}\verb|Toplevel.print: Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.no\_timing}\verb|Toplevel.no_timing: Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.keep}\verb|Toplevel.keep: (Toplevel.state -> unit) ->|\isasep\isanewline%
-\verb| Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.theory}\verb|Toplevel.theory: (theory -> theory) ->|\isasep\isanewline%
-\verb| Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.theory\_to\_proof}\verb|Toplevel.theory_to_proof: (theory -> Proof.state) ->|\isasep\isanewline%
-\verb| Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.proof}\verb|Toplevel.proof: (Proof.state -> Proof.state) ->|\isasep\isanewline%
-\verb| Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.proofs}\verb|Toplevel.proofs: (Proof.state -> Proof.state Seq.seq) ->|\isasep\isanewline%
-\verb| Toplevel.transition -> Toplevel.transition| \\
- \indexdef{}{ML}{Toplevel.end\_proof}\verb|Toplevel.end_proof: (bool -> Proof.state -> Proof.context) ->|\isasep\isanewline%
-\verb| Toplevel.transition -> Toplevel.transition| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Toplevel.print|~\isa{tr} sets the print flag, which
- causes the toplevel loop to echo the result state (in interactive
- mode).
-
- \item \verb|Toplevel.no_timing|~\isa{tr} indicates that the
- transition should never show timing information, e.g.\ because it is
- a diagnostic command.
-
- \item \verb|Toplevel.keep|~\isa{tr} adjoins a diagnostic
- function.
-
- \item \verb|Toplevel.theory|~\isa{tr} adjoins a theory
- transformer.
-
- \item \verb|Toplevel.theory_to_proof|~\isa{tr} adjoins a global
- goal function, which turns a theory into a proof state. The theory
- may be changed before entering the proof; the generic Isar goal
- setup includes an argument that specifies how to apply the proven
- result to the theory, when the proof is finished.
-
- \item \verb|Toplevel.proof|~\isa{tr} adjoins a deterministic
- proof command, with a singleton result.
-
- \item \verb|Toplevel.proofs|~\isa{tr} adjoins a general proof
- command, with zero or more result states (represented as a lazy
- list).
-
- \item \verb|Toplevel.end_proof|~\isa{tr} adjoins a concluding
- proof command, that returns the resulting theory, after storing the
- resulting facts in the context etc.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsubsection{Toplevel control%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-There are a few special control commands that modify the behavior
- the toplevel itself, and only make sense in interactive mode. Under
- normal circumstances, the user encounters these only implicitly as
- part of the protocol between the Isabelle/Isar system and a
- user-interface such as ProofGeneral.
-
- \begin{description}
-
- \item \isacommand{undo} follows the three-level hierarchy of empty
- toplevel vs.\ theory vs.\ proof: undo within a proof reverts to the
- previous proof context, undo after a proof reverts to the theory
- before the initial goal statement, undo of a theory command reverts
- to the previous theory value, undo of a theory header discontinues
- the current theory development and removes it from the theory
- database (\secref{sec:theory-database}).
-
- \item \isacommand{kill} aborts the current level of development:
- kill in a proof context reverts to the theory before the initial
- goal statement, kill in a theory context aborts the current theory
- development, removing it from the database.
-
- \item \isacommand{exit} drops out of the Isar toplevel into the
- underlying {\ML} toplevel (\secref{sec:ML-toplevel}). The Isar
- toplevel state is preserved and may be continued later.
-
- \item \isacommand{quit} terminates the Isabelle/Isar process without
- saving.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{ML toplevel \label{sec:ML-toplevel}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The {\ML} toplevel provides a read-compile-eval-print loop for {\ML}
- values, types, structures, and functors. {\ML} declarations operate
- on the global system state, which consists of the compiler
- environment plus the values of {\ML} reference variables. There is
- no clean way to undo {\ML} declarations, except for reverting to a
- previously saved state of the whole Isabelle process. {\ML} input
- is either read interactively from a TTY, or from a string (usually
- within a theory text), or from a source file (usually loaded from a
- theory).
-
- Whenever the {\ML} toplevel is active, the current Isabelle theory
- context is passed as an internal reference variable. Thus {\ML}
- code may access the theory context during compilation, it may even
- change the value of a theory being under construction --- while
- observing the usual linearity restrictions
- (cf.~\secref{sec:context-theory}).%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{the\_context}\verb|the_context: unit -> theory| \\
- \indexdef{}{ML}{Context.$>$$>$ }\verb|Context.>> : (Context.generic -> Context.generic) -> unit| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|the_context ()| refers to the theory context of the
- {\ML} toplevel --- at compile time! {\ML} code needs to take care
- to refer to \verb|the_context ()| correctly. Recall that
- evaluation of a function body is delayed until actual runtime.
- Moreover, persistent {\ML} toplevel bindings to an unfinished theory
- should be avoided: code should either project out the desired
- information immediately, or produce an explicit \verb|theory_ref| (cf.\ \secref{sec:context-theory}).
-
- \item \verb|Context.>>|~\isa{f} applies context transformation
- \isa{f} to the implicit context of the {\ML} toplevel.
-
- \end{description}
-
- It is very important to note that the above functions are really
- restricted to the compile time, even though the {\ML} compiler is
- invoked at runtime! The majority of {\ML} code uses explicit
- functional arguments of a theory or proof context instead. Thus it
- may be invoked for an arbitrary context later on, without having to
- worry about any operational details.
-
- \bigskip
-
- \begin{mldecls}
- \indexdef{}{ML}{Isar.main}\verb|Isar.main: unit -> unit| \\
- \indexdef{}{ML}{Isar.loop}\verb|Isar.loop: unit -> unit| \\
- \indexdef{}{ML}{Isar.state}\verb|Isar.state: unit -> Toplevel.state| \\
- \indexdef{}{ML}{Isar.exn}\verb|Isar.exn: unit -> (exn * string) option| \\
- \indexdef{}{ML}{Isar.context}\verb|Isar.context: unit -> Proof.context| \\
- \indexdef{}{ML}{Isar.goal}\verb|Isar.goal: unit -> thm| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Isar.main ()| invokes the Isar toplevel from {\ML},
- initializing an empty toplevel state.
-
- \item \verb|Isar.loop ()| continues the Isar toplevel with the
- current state, after having dropped out of the Isar toplevel loop.
-
- \item \verb|Isar.state ()| and \verb|Isar.exn ()| get current
- toplevel state and error condition, respectively. This only works
- after having dropped out of the Isar toplevel loop.
-
- \item \verb|Isar.context ()| produces the proof context from \verb|Isar.state ()|, analogous to \verb|Context.proof_of|
- (\secref{sec:generic-context}).
-
- \item \verb|Isar.goal ()| picks the tactical goal from \verb|Isar.state ()|, represented as a theorem according to
- \secref{sec:tactical-goals}.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsection{Theory database \label{sec:theory-database}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The theory database maintains a collection of theories, together
- with some administrative information about their original sources,
- which are held in an external store (i.e.\ some directory within the
- regular file system).
-
- The theory database is organized as a directed acyclic graph;
- entries are referenced by theory name. Although some additional
- interfaces allow to include a directory specification as well, this
- is only a hint to the underlying theory loader. The internal theory
- name space is flat!
-
- Theory \isa{A} is associated with the main theory file \isa{A}\verb,.thy,, which needs to be accessible through the theory
- loader path. Any number of additional {\ML} source files may be
- associated with each theory, by declaring these dependencies in the
- theory header as \isa{{\isasymUSES}}, and loading them consecutively
- within the theory context. The system keeps track of incoming {\ML}
- sources and associates them with the current theory. The file
- \isa{A}\verb,.ML, is loaded after a theory has been concluded, in
- order to support legacy proof {\ML} proof scripts.
-
- The basic internal actions of the theory database are \isa{update}, \isa{outdate}, and \isa{remove}:
-
- \begin{itemize}
-
- \item \isa{update\ A} introduces a link of \isa{A} with a
- \isa{theory} value of the same name; it asserts that the theory
- sources are now consistent with that value;
-
- \item \isa{outdate\ A} invalidates the link of a theory database
- entry to its sources, but retains the present theory value;
-
- \item \isa{remove\ A} deletes entry \isa{A} from the theory
- database.
-
- \end{itemize}
-
- These actions are propagated to sub- or super-graphs of a theory
- entry as expected, in order to preserve global consistency of the
- state of all loaded theories with the sources of the external store.
- This implies certain causalities between actions: \isa{update}
- or \isa{outdate} of an entry will \isa{outdate} all
- descendants; \isa{remove} will \isa{remove} all descendants.
-
- \medskip There are separate user-level interfaces to operate on the
- theory database directly or indirectly. The primitive actions then
- just happen automatically while working with the system. In
- particular, processing a theory header \isa{{\isasymTHEORY}\ A\ {\isasymIMPORTS}\ B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n\ {\isasymBEGIN}} ensures that the
- sub-graph of the collective imports \isa{B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n}
- is up-to-date, too. Earlier theories are reloaded as required, with
- \isa{update} actions proceeding in topological order according to
- theory dependencies. There may be also a wave of implied \isa{outdate} actions for derived theory nodes until a stable situation
- is achieved eventually.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{theory}\verb|theory: string -> theory| \\
- \indexdef{}{ML}{use\_thy}\verb|use_thy: string -> unit| \\
- \indexdef{}{ML}{use\_thys}\verb|use_thys: string list -> unit| \\
- \indexdef{}{ML}{ThyInfo.touch\_thy}\verb|ThyInfo.touch_thy: string -> unit| \\
- \indexdef{}{ML}{ThyInfo.remove\_thy}\verb|ThyInfo.remove_thy: string -> unit| \\[1ex]
- \indexdef{}{ML}{ThyInfo.begin\_theory}\verb|ThyInfo.begin_theory|\verb|: ... -> bool -> theory| \\
- \indexdef{}{ML}{ThyInfo.end\_theory}\verb|ThyInfo.end_theory: theory -> unit| \\
- \indexdef{}{ML}{ThyInfo.register\_theory}\verb|ThyInfo.register_theory: theory -> unit| \\[1ex]
- \verb|datatype action = Update |\verb,|,\verb| Outdate |\verb,|,\verb| Remove| \\
- \indexdef{}{ML}{ThyInfo.add\_hook}\verb|ThyInfo.add_hook: (ThyInfo.action -> string -> unit) -> unit| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|theory|~\isa{A} retrieves the theory value presently
- associated with name \isa{A}. Note that the result might be
- outdated.
-
- \item \verb|use_thy|~\isa{A} ensures that theory \isa{A} is fully
- up-to-date wrt.\ the external file store, reloading outdated
- ancestors as required.
-
- \item \verb|use_thys| is similar to \verb|use_thy|, but handles
- several theories simultaneously. Thus it acts like processing the
- import header of a theory, without performing the merge of the
- result, though.
-
- \item \verb|ThyInfo.touch_thy|~\isa{A} performs and \isa{outdate} action
- on theory \isa{A} and all descendants.
-
- \item \verb|ThyInfo.remove_thy|~\isa{A} deletes theory \isa{A} and all
- descendants from the theory database.
-
- \item \verb|ThyInfo.begin_theory| is the basic operation behind a
- \isa{{\isasymTHEORY}} header declaration. This is {\ML} functions is
- normally not invoked directly.
-
- \item \verb|ThyInfo.end_theory| concludes the loading of a theory
- proper and stores the result in the theory database.
-
- \item \verb|ThyInfo.register_theory|~\isa{text\ thy} registers an
- existing theory value with the theory loader database. There is no
- management of associated sources.
-
- \item \verb|ThyInfo.add_hook|~\isa{f} registers function \isa{f} as a hook for theory database actions. The function will be
- invoked with the action and theory name being involved; thus derived
- actions may be performed in associated system components, e.g.\
- maintaining the state of an editor for the theory sources.
-
- The kind and order of actions occurring in practice depends both on
- user interactions and the internal process of resolving theory
- imports. Hooks should not rely on a particular policy here! Any
- exceptions raised by the hook are ignored.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
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-\isanewline
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:
--- a/doc-src/IsarImplementation/Thy/document/Isar.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,86 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Isar}%
-%
-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
-\isacommand{theory}\isamarkupfalse%
-\ Isar\isanewline
-\isakeyword{imports}\ Base\isanewline
-\isakeyword{begin}%
-\endisatagtheory
-{\isafoldtheory}%
-%
-\isadelimtheory
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-\endisadelimtheory
-%
-\isamarkupchapter{Isar language elements%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The primary Isar language consists of three main categories of
- language elements:
-
- \begin{enumerate}
-
- \item Proof commands
-
- \item Proof methods
-
- \item Attributes
-
- \end{enumerate}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Proof commands%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-FIXME%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Proof methods%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-FIXME%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Attributes%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-FIXME%
-\end{isamarkuptext}%
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-\endisadelimtheory
-\isanewline
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:
--- a/doc-src/IsarImplementation/Thy/document/Logic.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,959 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Logic}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
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-\isatagtheory
-\isacommand{theory}\isamarkupfalse%
-\ Logic\isanewline
-\isakeyword{imports}\ Base\isanewline
-\isakeyword{begin}%
-\endisatagtheory
-{\isafoldtheory}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\isamarkupchapter{Primitive logic \label{ch:logic}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The logical foundations of Isabelle/Isar are that of the Pure logic,
- which has been introduced as a Natural Deduction framework in
- \cite{paulson700}. This is essentially the same logic as ``\isa{{\isasymlambda}HOL}'' in the more abstract setting of Pure Type Systems (PTS)
- \cite{Barendregt-Geuvers:2001}, although there are some key
- differences in the specific treatment of simple types in
- Isabelle/Pure.
-
- Following type-theoretic parlance, the Pure logic consists of three
- levels of \isa{{\isasymlambda}}-calculus with corresponding arrows, \isa{{\isasymRightarrow}} for syntactic function space (terms depending on terms), \isa{{\isasymAnd}} for universal quantification (proofs depending on terms), and
- \isa{{\isasymLongrightarrow}} for implication (proofs depending on proofs).
-
- Derivations are relative to a logical theory, which declares type
- constructors, constants, and axioms. Theory declarations support
- schematic polymorphism, which is strictly speaking outside the
- logic.\footnote{This is the deeper logical reason, why the theory
- context \isa{{\isasymTheta}} is separate from the proof context \isa{{\isasymGamma}}
- of the core calculus.}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Types \label{sec:types}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The language of types is an uninterpreted order-sorted first-order
- algebra; types are qualified by ordered type classes.
-
- \medskip A \emph{type class} is an abstract syntactic entity
- declared in the theory context. The \emph{subclass relation} \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}} is specified by stating an acyclic
- generating relation; the transitive closure is maintained
- internally. The resulting relation is an ordering: reflexive,
- transitive, and antisymmetric.
-
- A \emph{sort} is a list of type classes written as \isa{s\ {\isacharequal}\ {\isacharbraceleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlisub m{\isacharbraceright}}, which represents symbolic
- intersection. Notationally, the curly braces are omitted for
- singleton intersections, i.e.\ any class \isa{c} may be read as
- a sort \isa{{\isacharbraceleft}c{\isacharbraceright}}. The ordering on type classes is extended to
- sorts according to the meaning of intersections: \isa{{\isacharbraceleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ c\isactrlisub m{\isacharbraceright}\ {\isasymsubseteq}\ {\isacharbraceleft}d\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ d\isactrlisub n{\isacharbraceright}} iff
- \isa{{\isasymforall}j{\isachardot}\ {\isasymexists}i{\isachardot}\ c\isactrlisub i\ {\isasymsubseteq}\ d\isactrlisub j}. The empty intersection
- \isa{{\isacharbraceleft}{\isacharbraceright}} refers to the universal sort, which is the largest
- element wrt.\ the sort order. The intersections of all (finitely
- many) classes declared in the current theory are the minimal
- elements wrt.\ the sort order.
-
- \medskip A \emph{fixed type variable} is a pair of a basic name
- (starting with a \isa{{\isacharprime}} character) and a sort constraint, e.g.\
- \isa{{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ s{\isacharparenright}} which is usually printed as \isa{{\isasymalpha}\isactrlisub s}.
- A \emph{schematic type variable} is a pair of an indexname and a
- sort constraint, e.g.\ \isa{{\isacharparenleft}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ s{\isacharparenright}} which is usually
- printed as \isa{{\isacharquery}{\isasymalpha}\isactrlisub s}.
-
- Note that \emph{all} syntactic components contribute to the identity
- of type variables, including the sort constraint. The core logic
- handles type variables with the same name but different sorts as
- different, although some outer layers of the system make it hard to
- produce anything like this.
-
- A \emph{type constructor} \isa{{\isasymkappa}} is a \isa{k}-ary operator
- on types declared in the theory. Type constructor application is
- written postfix as \isa{{\isacharparenleft}{\isasymalpha}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlisub k{\isacharparenright}{\isasymkappa}}. For
- \isa{k\ {\isacharequal}\ {\isadigit{0}}} the argument tuple is omitted, e.g.\ \isa{prop}
- instead of \isa{{\isacharparenleft}{\isacharparenright}prop}. For \isa{k\ {\isacharequal}\ {\isadigit{1}}} the parentheses
- are omitted, e.g.\ \isa{{\isasymalpha}\ list} instead of \isa{{\isacharparenleft}{\isasymalpha}{\isacharparenright}list}.
- Further notation is provided for specific constructors, notably the
- right-associative infix \isa{{\isasymalpha}\ {\isasymRightarrow}\ {\isasymbeta}} instead of \isa{{\isacharparenleft}{\isasymalpha}{\isacharcomma}\ {\isasymbeta}{\isacharparenright}fun}.
-
- A \emph{type} is defined inductively over type variables and type
- constructors as follows: \isa{{\isasymtau}\ {\isacharequal}\ {\isasymalpha}\isactrlisub s\ {\isacharbar}\ {\isacharquery}{\isasymalpha}\isactrlisub s\ {\isacharbar}\ {\isacharparenleft}{\isasymtau}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlsub k{\isacharparenright}{\isasymkappa}}.
-
- A \emph{type abbreviation} is a syntactic definition \isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}{\isasymkappa}\ {\isacharequal}\ {\isasymtau}} of an arbitrary type expression \isa{{\isasymtau}} over
- variables \isa{\isactrlvec {\isasymalpha}}. Type abbreviations appear as type
- constructors in the syntax, but are expanded before entering the
- logical core.
-
- A \emph{type arity} declares the image behavior of a type
- constructor wrt.\ the algebra of sorts: \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlisub k{\isacharparenright}s} means that \isa{{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub k{\isacharparenright}{\isasymkappa}} is
- of sort \isa{s} if every argument type \isa{{\isasymtau}\isactrlisub i} is
- of sort \isa{s\isactrlisub i}. Arity declarations are implicitly
- completed, i.e.\ \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c} entails \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isacharprime}} for any \isa{c{\isacharprime}\ {\isasymsupseteq}\ c}.
-
- \medskip The sort algebra is always maintained as \emph{coregular},
- which means that type arities are consistent with the subclass
- relation: for any type constructor \isa{{\isasymkappa}}, and classes \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}, and arities \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{1}}{\isacharparenright}c\isactrlisub {\isadigit{1}}} and \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{2}}{\isacharparenright}c\isactrlisub {\isadigit{2}}} holds \isa{\isactrlvec s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ \isactrlvec s\isactrlisub {\isadigit{2}}} component-wise.
-
- The key property of a coregular order-sorted algebra is that sort
- constraints can be solved in a most general fashion: for each type
- constructor \isa{{\isasymkappa}} and sort \isa{s} there is a most general
- vector of argument sorts \isa{{\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlisub k{\isacharparenright}} such
- that a type scheme \isa{{\isacharparenleft}{\isasymalpha}\isactrlbsub s\isactrlisub {\isadigit{1}}\isactrlesub {\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlbsub s\isactrlisub k\isactrlesub {\isacharparenright}{\isasymkappa}} is of sort \isa{s}.
- Consequently, type unification has most general solutions (modulo
- equivalence of sorts), so type-inference produces primary types as
- expected \cite{nipkow-prehofer}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{class}\verb|type class| \\
- \indexdef{}{ML type}{sort}\verb|type sort| \\
- \indexdef{}{ML type}{arity}\verb|type arity| \\
- \indexdef{}{ML type}{typ}\verb|type typ| \\
- \indexdef{}{ML}{map\_atyps}\verb|map_atyps: (typ -> typ) -> typ -> typ| \\
- \indexdef{}{ML}{fold\_atyps}\verb|fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML}{Sign.subsort}\verb|Sign.subsort: theory -> sort * sort -> bool| \\
- \indexdef{}{ML}{Sign.of\_sort}\verb|Sign.of_sort: theory -> typ * sort -> bool| \\
- \indexdef{}{ML}{Sign.add\_types}\verb|Sign.add_types: (string * int * mixfix) list -> theory -> theory| \\
- \indexdef{}{ML}{Sign.add\_tyabbrs\_i}\verb|Sign.add_tyabbrs_i: |\isasep\isanewline%
-\verb| (string * string list * typ * mixfix) list -> theory -> theory| \\
- \indexdef{}{ML}{Sign.primitive\_class}\verb|Sign.primitive_class: string * class list -> theory -> theory| \\
- \indexdef{}{ML}{Sign.primitive\_classrel}\verb|Sign.primitive_classrel: class * class -> theory -> theory| \\
- \indexdef{}{ML}{Sign.primitive\_arity}\verb|Sign.primitive_arity: arity -> theory -> theory| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|class| represents type classes; this is an alias for
- \verb|string|.
-
- \item \verb|sort| represents sorts; this is an alias for
- \verb|class list|.
-
- \item \verb|arity| represents type arities; this is an alias for
- triples of the form \isa{{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ \isactrlvec s{\isacharcomma}\ s{\isacharparenright}} for \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}s} described above.
-
- \item \verb|typ| represents types; this is a datatype with
- constructors \verb|TFree|, \verb|TVar|, \verb|Type|.
-
- \item \verb|map_atyps|~\isa{f\ {\isasymtau}} applies the mapping \isa{f}
- to all atomic types (\verb|TFree|, \verb|TVar|) occurring in \isa{{\isasymtau}}.
-
- \item \verb|fold_atyps|~\isa{f\ {\isasymtau}} iterates the operation \isa{f} over all occurrences of atomic types (\verb|TFree|, \verb|TVar|)
- in \isa{{\isasymtau}}; the type structure is traversed from left to right.
-
- \item \verb|Sign.subsort|~\isa{thy\ {\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ s\isactrlisub {\isadigit{2}}{\isacharparenright}}
- tests the subsort relation \isa{s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ s\isactrlisub {\isadigit{2}}}.
-
- \item \verb|Sign.of_sort|~\isa{thy\ {\isacharparenleft}{\isasymtau}{\isacharcomma}\ s{\isacharparenright}} tests whether type
- \isa{{\isasymtau}} is of sort \isa{s}.
-
- \item \verb|Sign.add_types|~\isa{{\isacharbrackleft}{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ k{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}} declares a new
- type constructors \isa{{\isasymkappa}} with \isa{k} arguments and
- optional mixfix syntax.
-
- \item \verb|Sign.add_tyabbrs_i|~\isa{{\isacharbrackleft}{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ \isactrlvec {\isasymalpha}{\isacharcomma}\ {\isasymtau}{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}}
- defines a new type abbreviation \isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}{\isasymkappa}\ {\isacharequal}\ {\isasymtau}} with
- optional mixfix syntax.
-
- \item \verb|Sign.primitive_class|~\isa{{\isacharparenleft}c{\isacharcomma}\ {\isacharbrackleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlisub n{\isacharbrackright}{\isacharparenright}} declares a new class \isa{c}, together with class
- relations \isa{c\ {\isasymsubseteq}\ c\isactrlisub i}, for \isa{i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n}.
-
- \item \verb|Sign.primitive_classrel|~\isa{{\isacharparenleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ c\isactrlisub {\isadigit{2}}{\isacharparenright}} declares the class relation \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}.
-
- \item \verb|Sign.primitive_arity|~\isa{{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ \isactrlvec s{\isacharcomma}\ s{\isacharparenright}} declares
- the arity \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}s}.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsection{Terms \label{sec:terms}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The language of terms is that of simply-typed \isa{{\isasymlambda}}-calculus
- with de-Bruijn indices for bound variables (cf.\ \cite{debruijn72}
- or \cite{paulson-ml2}), with the types being determined by the
- corresponding binders. In contrast, free variables and constants
- are have an explicit name and type in each occurrence.
-
- \medskip A \emph{bound variable} is a natural number \isa{b},
- which accounts for the number of intermediate binders between the
- variable occurrence in the body and its binding position. For
- example, the de-Bruijn term \isa{{\isasymlambda}\isactrlbsub nat\isactrlesub {\isachardot}\ {\isasymlambda}\isactrlbsub nat\isactrlesub {\isachardot}\ {\isadigit{1}}\ {\isacharplus}\ {\isadigit{0}}} would
- correspond to \isa{{\isasymlambda}x\isactrlbsub nat\isactrlesub {\isachardot}\ {\isasymlambda}y\isactrlbsub nat\isactrlesub {\isachardot}\ x\ {\isacharplus}\ y} in a named
- representation. Note that a bound variable may be represented by
- different de-Bruijn indices at different occurrences, depending on
- the nesting of abstractions.
-
- A \emph{loose variable} is a bound variable that is outside the
- scope of local binders. The types (and names) for loose variables
- can be managed as a separate context, that is maintained as a stack
- of hypothetical binders. The core logic operates on closed terms,
- without any loose variables.
-
- A \emph{fixed variable} is a pair of a basic name and a type, e.g.\
- \isa{{\isacharparenleft}x{\isacharcomma}\ {\isasymtau}{\isacharparenright}} which is usually printed \isa{x\isactrlisub {\isasymtau}}. A
- \emph{schematic variable} is a pair of an indexname and a type,
- e.g.\ \isa{{\isacharparenleft}{\isacharparenleft}x{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ {\isasymtau}{\isacharparenright}} which is usually printed as \isa{{\isacharquery}x\isactrlisub {\isasymtau}}.
-
- \medskip A \emph{constant} is a pair of a basic name and a type,
- e.g.\ \isa{{\isacharparenleft}c{\isacharcomma}\ {\isasymtau}{\isacharparenright}} which is usually printed as \isa{c\isactrlisub {\isasymtau}}. Constants are declared in the context as polymorphic
- families \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}, meaning that all substitution instances
- \isa{c\isactrlisub {\isasymtau}} for \isa{{\isasymtau}\ {\isacharequal}\ {\isasymsigma}{\isasymvartheta}} are valid.
-
- The vector of \emph{type arguments} of constant \isa{c\isactrlisub {\isasymtau}}
- wrt.\ the declaration \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} is defined as the codomain of
- the matcher \isa{{\isasymvartheta}\ {\isacharequal}\ {\isacharbraceleft}{\isacharquery}{\isasymalpha}\isactrlisub {\isadigit{1}}\ {\isasymmapsto}\ {\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isacharquery}{\isasymalpha}\isactrlisub n\ {\isasymmapsto}\ {\isasymtau}\isactrlisub n{\isacharbraceright}} presented in canonical order \isa{{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharparenright}}. Within a given theory context,
- there is a one-to-one correspondence between any constant \isa{c\isactrlisub {\isasymtau}} and the application \isa{c{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharparenright}} of its type arguments. For example, with \isa{plus\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}}, the instance \isa{plus\isactrlbsub nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat\isactrlesub } corresponds to \isa{plus{\isacharparenleft}nat{\isacharparenright}}.
-
- Constant declarations \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} may contain sort constraints
- for type variables in \isa{{\isasymsigma}}. These are observed by
- type-inference as expected, but \emph{ignored} by the core logic.
- This means the primitive logic is able to reason with instances of
- polymorphic constants that the user-level type-checker would reject
- due to violation of type class restrictions.
-
- \medskip An \emph{atomic} term is either a variable or constant. A
- \emph{term} is defined inductively over atomic terms, with
- abstraction and application as follows: \isa{t\ {\isacharequal}\ b\ {\isacharbar}\ x\isactrlisub {\isasymtau}\ {\isacharbar}\ {\isacharquery}x\isactrlisub {\isasymtau}\ {\isacharbar}\ c\isactrlisub {\isasymtau}\ {\isacharbar}\ {\isasymlambda}\isactrlisub {\isasymtau}{\isachardot}\ t\ {\isacharbar}\ t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}}.
- Parsing and printing takes care of converting between an external
- representation with named bound variables. Subsequently, we shall
- use the latter notation instead of internal de-Bruijn
- representation.
-
- The inductive relation \isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}} assigns a (unique) type to a
- term according to the structure of atomic terms, abstractions, and
- applicatins:
- \[
- \infer{\isa{a\isactrlisub {\isasymtau}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}}{}
- \qquad
- \infer{\isa{{\isacharparenleft}{\isasymlambda}x\isactrlsub {\isasymtau}{\isachardot}\ t{\isacharparenright}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isasymRightarrow}\ {\isasymsigma}}}{\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}}
- \qquad
- \infer{\isa{t\ u\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}}{\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isasymRightarrow}\ {\isasymsigma}} & \isa{u\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}}
- \]
- A \emph{well-typed term} is a term that can be typed according to these rules.
-
- Typing information can be omitted: type-inference is able to
- reconstruct the most general type of a raw term, while assigning
- most general types to all of its variables and constants.
- Type-inference depends on a context of type constraints for fixed
- variables, and declarations for polymorphic constants.
-
- The identity of atomic terms consists both of the name and the type
- component. This means that different variables \isa{x\isactrlbsub {\isasymtau}\isactrlisub {\isadigit{1}}\isactrlesub } and \isa{x\isactrlbsub {\isasymtau}\isactrlisub {\isadigit{2}}\isactrlesub } may become the same after type
- instantiation. Some outer layers of the system make it hard to
- produce variables of the same name, but different types. In
- contrast, mixed instances of polymorphic constants occur frequently.
-
- \medskip The \emph{hidden polymorphism} of a term \isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}
- is the set of type variables occurring in \isa{t}, but not in
- \isa{{\isasymsigma}}. This means that the term implicitly depends on type
- arguments that are not accounted in the result type, i.e.\ there are
- different type instances \isa{t{\isasymvartheta}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} and \isa{t{\isasymvartheta}{\isacharprime}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} with the same type. This slightly
- pathological situation notoriously demands additional care.
-
- \medskip A \emph{term abbreviation} is a syntactic definition \isa{c\isactrlisub {\isasymsigma}\ {\isasymequiv}\ t} of a closed term \isa{t} of type \isa{{\isasymsigma}},
- without any hidden polymorphism. A term abbreviation looks like a
- constant in the syntax, but is expanded before entering the logical
- core. Abbreviations are usually reverted when printing terms, using
- \isa{t\ {\isasymrightarrow}\ c\isactrlisub {\isasymsigma}} as rules for higher-order rewriting.
-
- \medskip Canonical operations on \isa{{\isasymlambda}}-terms include \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion: \isa{{\isasymalpha}}-conversion refers to capture-free
- renaming of bound variables; \isa{{\isasymbeta}}-conversion contracts an
- abstraction applied to an argument term, substituting the argument
- in the body: \isa{{\isacharparenleft}{\isasymlambda}x{\isachardot}\ b{\isacharparenright}a} becomes \isa{b{\isacharbrackleft}a{\isacharslash}x{\isacharbrackright}}; \isa{{\isasymeta}}-conversion contracts vacuous application-abstraction: \isa{{\isasymlambda}x{\isachardot}\ f\ x} becomes \isa{f}, provided that the bound variable
- does not occur in \isa{f}.
-
- Terms are normally treated modulo \isa{{\isasymalpha}}-conversion, which is
- implicit in the de-Bruijn representation. Names for bound variables
- in abstractions are maintained separately as (meaningless) comments,
- mostly for parsing and printing. Full \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion is
- commonplace in various standard operations (\secref{sec:obj-rules})
- that are based on higher-order unification and matching.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{term}\verb|type term| \\
- \indexdef{}{ML}{op aconv}\verb|op aconv: term * term -> bool| \\
- \indexdef{}{ML}{map\_types}\verb|map_types: (typ -> typ) -> term -> term| \\
- \indexdef{}{ML}{fold\_types}\verb|fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a| \\
- \indexdef{}{ML}{map\_aterms}\verb|map_aterms: (term -> term) -> term -> term| \\
- \indexdef{}{ML}{fold\_aterms}\verb|fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML}{fastype\_of}\verb|fastype_of: term -> typ| \\
- \indexdef{}{ML}{lambda}\verb|lambda: term -> term -> term| \\
- \indexdef{}{ML}{betapply}\verb|betapply: term * term -> term| \\
- \indexdef{}{ML}{Sign.declare\_const}\verb|Sign.declare_const: Properties.T -> (binding * typ) * mixfix ->|\isasep\isanewline%
-\verb| theory -> term * theory| \\
- \indexdef{}{ML}{Sign.add\_abbrev}\verb|Sign.add_abbrev: string -> Properties.T -> binding * term ->|\isasep\isanewline%
-\verb| theory -> (term * term) * theory| \\
- \indexdef{}{ML}{Sign.const\_typargs}\verb|Sign.const_typargs: theory -> string * typ -> typ list| \\
- \indexdef{}{ML}{Sign.const\_instance}\verb|Sign.const_instance: theory -> string * typ list -> typ| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|term| represents de-Bruijn terms, with comments in
- abstractions, and explicitly named free variables and constants;
- this is a datatype with constructors \verb|Bound|, \verb|Free|, \verb|Var|, \verb|Const|, \verb|Abs|, \verb|op $|.
-
- \item \isa{t}~\verb|aconv|~\isa{u} checks \isa{{\isasymalpha}}-equivalence of two terms. This is the basic equality relation
- on type \verb|term|; raw datatype equality should only be used
- for operations related to parsing or printing!
-
- \item \verb|map_types|~\isa{f\ t} applies the mapping \isa{f} to all types occurring in \isa{t}.
-
- \item \verb|fold_types|~\isa{f\ t} iterates the operation \isa{f} over all occurrences of types in \isa{t}; the term
- structure is traversed from left to right.
-
- \item \verb|map_aterms|~\isa{f\ t} applies the mapping \isa{f}
- to all atomic terms (\verb|Bound|, \verb|Free|, \verb|Var|, \verb|Const|) occurring in \isa{t}.
-
- \item \verb|fold_aterms|~\isa{f\ t} iterates the operation \isa{f} over all occurrences of atomic terms (\verb|Bound|, \verb|Free|,
- \verb|Var|, \verb|Const|) in \isa{t}; the term structure is
- traversed from left to right.
-
- \item \verb|fastype_of|~\isa{t} determines the type of a
- well-typed term. This operation is relatively slow, despite the
- omission of any sanity checks.
-
- \item \verb|lambda|~\isa{a\ b} produces an abstraction \isa{{\isasymlambda}a{\isachardot}\ b}, where occurrences of the atomic term \isa{a} in the
- body \isa{b} are replaced by bound variables.
-
- \item \verb|betapply|~\isa{{\isacharparenleft}t{\isacharcomma}\ u{\isacharparenright}} produces an application \isa{t\ u}, with topmost \isa{{\isasymbeta}}-conversion if \isa{t} is an
- abstraction.
-
- \item \verb|Sign.declare_const|~\isa{properties\ {\isacharparenleft}{\isacharparenleft}c{\isacharcomma}\ {\isasymsigma}{\isacharparenright}{\isacharcomma}\ mx{\isacharparenright}}
- declares a new constant \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} with optional mixfix
- syntax.
-
- \item \verb|Sign.add_abbrev|~\isa{print{\isacharunderscore}mode\ properties\ {\isacharparenleft}c{\isacharcomma}\ t{\isacharparenright}}
- introduces a new term abbreviation \isa{c\ {\isasymequiv}\ t}.
-
- \item \verb|Sign.const_typargs|~\isa{thy\ {\isacharparenleft}c{\isacharcomma}\ {\isasymtau}{\isacharparenright}} and \verb|Sign.const_instance|~\isa{thy\ {\isacharparenleft}c{\isacharcomma}\ {\isacharbrackleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharbrackright}{\isacharparenright}}
- convert between two representations of polymorphic constants: full
- type instance vs.\ compact type arguments form.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsection{Theorems \label{sec:thms}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-A \emph{proposition} is a well-typed term of type \isa{prop}, a
- \emph{theorem} is a proven proposition (depending on a context of
- hypotheses and the background theory). Primitive inferences include
- plain Natural Deduction rules for the primary connectives \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} of the framework. There is also a builtin
- notion of equality/equivalence \isa{{\isasymequiv}}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Primitive connectives and rules \label{sec:prim-rules}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The theory \isa{Pure} contains constant declarations for the
- primitive connectives \isa{{\isasymAnd}}, \isa{{\isasymLongrightarrow}}, and \isa{{\isasymequiv}} of
- the logical framework, see \figref{fig:pure-connectives}. The
- derivability judgment \isa{A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n\ {\isasymturnstile}\ B} is
- defined inductively by the primitive inferences given in
- \figref{fig:prim-rules}, with the global restriction that the
- hypotheses must \emph{not} contain any schematic variables. The
- builtin equality is conceptually axiomatized as shown in
- \figref{fig:pure-equality}, although the implementation works
- directly with derived inferences.
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{ll}
- \isa{all\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isasymalpha}\ {\isasymRightarrow}\ prop{\isacharparenright}\ {\isasymRightarrow}\ prop} & universal quantification (binder \isa{{\isasymAnd}}) \\
- \isa{{\isasymLongrightarrow}\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop\ {\isasymRightarrow}\ prop} & implication (right associative infix) \\
- \isa{{\isasymequiv}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ prop} & equality relation (infix) \\
- \end{tabular}
- \caption{Primitive connectives of Pure}\label{fig:pure-connectives}
- \end{center}
- \end{figure}
-
- \begin{figure}[htb]
- \begin{center}
- \[
- \infer[\isa{{\isacharparenleft}axiom{\isacharparenright}}]{\isa{{\isasymturnstile}\ A}}{\isa{A\ {\isasymin}\ {\isasymTheta}}}
- \qquad
- \infer[\isa{{\isacharparenleft}assume{\isacharparenright}}]{\isa{A\ {\isasymturnstile}\ A}}{}
- \]
- \[
- \infer[\isa{{\isacharparenleft}{\isasymAnd}{\isacharunderscore}intro{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ b{\isacharbrackleft}x{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ b{\isacharbrackleft}x{\isacharbrackright}} & \isa{x\ {\isasymnotin}\ {\isasymGamma}}}
- \qquad
- \infer[\isa{{\isacharparenleft}{\isasymAnd}{\isacharunderscore}elim{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ b{\isacharbrackleft}a{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ b{\isacharbrackleft}x{\isacharbrackright}}}
- \]
- \[
- \infer[\isa{{\isacharparenleft}{\isasymLongrightarrow}{\isacharunderscore}intro{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B}}
- \qquad
- \infer[\isa{{\isacharparenleft}{\isasymLongrightarrow}{\isacharunderscore}elim{\isacharparenright}}]{\isa{{\isasymGamma}\isactrlsub {\isadigit{1}}\ {\isasymunion}\ {\isasymGamma}\isactrlsub {\isadigit{2}}\ {\isasymturnstile}\ B}}{\isa{{\isasymGamma}\isactrlsub {\isadigit{1}}\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B} & \isa{{\isasymGamma}\isactrlsub {\isadigit{2}}\ {\isasymturnstile}\ A}}
- \]
- \caption{Primitive inferences of Pure}\label{fig:prim-rules}
- \end{center}
- \end{figure}
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{ll}
- \isa{{\isasymturnstile}\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ b{\isacharbrackleft}x{\isacharbrackright}{\isacharparenright}\ a\ {\isasymequiv}\ b{\isacharbrackleft}a{\isacharbrackright}} & \isa{{\isasymbeta}}-conversion \\
- \isa{{\isasymturnstile}\ x\ {\isasymequiv}\ x} & reflexivity \\
- \isa{{\isasymturnstile}\ x\ {\isasymequiv}\ y\ {\isasymLongrightarrow}\ P\ x\ {\isasymLongrightarrow}\ P\ y} & substitution \\
- \isa{{\isasymturnstile}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ f\ x\ {\isasymequiv}\ g\ x{\isacharparenright}\ {\isasymLongrightarrow}\ f\ {\isasymequiv}\ g} & extensionality \\
- \isa{{\isasymturnstile}\ {\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymequiv}\ B} & logical equivalence \\
- \end{tabular}
- \caption{Conceptual axiomatization of Pure equality}\label{fig:pure-equality}
- \end{center}
- \end{figure}
-
- The introduction and elimination rules for \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} are analogous to formation of dependently typed \isa{{\isasymlambda}}-terms representing the underlying proof objects. Proof terms
- are irrelevant in the Pure logic, though; they cannot occur within
- propositions. The system provides a runtime option to record
- explicit proof terms for primitive inferences. Thus all three
- levels of \isa{{\isasymlambda}}-calculus become explicit: \isa{{\isasymRightarrow}} for
- terms, and \isa{{\isasymAnd}{\isacharslash}{\isasymLongrightarrow}} for proofs (cf.\
- \cite{Berghofer-Nipkow:2000:TPHOL}).
-
- Observe that locally fixed parameters (as in \isa{{\isasymAnd}{\isacharunderscore}intro}) need
- not be recorded in the hypotheses, because the simple syntactic
- types of Pure are always inhabitable. ``Assumptions'' \isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}} for type-membership are only present as long as some \isa{x\isactrlisub {\isasymtau}} occurs in the statement body.\footnote{This is the key
- difference to ``\isa{{\isasymlambda}HOL}'' in the PTS framework
- \cite{Barendregt-Geuvers:2001}, where hypotheses \isa{x\ {\isacharcolon}\ A} are
- treated uniformly for propositions and types.}
-
- \medskip The axiomatization of a theory is implicitly closed by
- forming all instances of type and term variables: \isa{{\isasymturnstile}\ A{\isasymvartheta}} holds for any substitution instance of an axiom
- \isa{{\isasymturnstile}\ A}. By pushing substitutions through derivations
- inductively, we also get admissible \isa{generalize} and \isa{instance} rules as shown in \figref{fig:subst-rules}.
-
- \begin{figure}[htb]
- \begin{center}
- \[
- \infer{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}{\isasymalpha}{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} & \isa{{\isasymalpha}\ {\isasymnotin}\ {\isasymGamma}}}
- \quad
- \infer[\quad\isa{{\isacharparenleft}generalize{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}x{\isacharbrackright}} & \isa{x\ {\isasymnotin}\ {\isasymGamma}}}
- \]
- \[
- \infer{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isasymtau}{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}{\isasymalpha}{\isacharbrackright}}}
- \quad
- \infer[\quad\isa{{\isacharparenleft}instantiate{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}t{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}}
- \]
- \caption{Admissible substitution rules}\label{fig:subst-rules}
- \end{center}
- \end{figure}
-
- Note that \isa{instantiate} does not require an explicit
- side-condition, because \isa{{\isasymGamma}} may never contain schematic
- variables.
-
- In principle, variables could be substituted in hypotheses as well,
- but this would disrupt the monotonicity of reasoning: deriving
- \isa{{\isasymGamma}{\isasymvartheta}\ {\isasymturnstile}\ B{\isasymvartheta}} from \isa{{\isasymGamma}\ {\isasymturnstile}\ B} is
- correct, but \isa{{\isasymGamma}{\isasymvartheta}\ {\isasymsupseteq}\ {\isasymGamma}} does not necessarily hold:
- the result belongs to a different proof context.
-
- \medskip An \emph{oracle} is a function that produces axioms on the
- fly. Logically, this is an instance of the \isa{axiom} rule
- (\figref{fig:prim-rules}), but there is an operational difference.
- The system always records oracle invocations within derivations of
- theorems by a unique tag.
-
- Axiomatizations should be limited to the bare minimum, typically as
- part of the initial logical basis of an object-logic formalization.
- Later on, theories are usually developed in a strictly definitional
- fashion, by stating only certain equalities over new constants.
-
- A \emph{simple definition} consists of a constant declaration \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} together with an axiom \isa{{\isasymturnstile}\ c\ {\isasymequiv}\ t}, where \isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} is a closed term without any hidden polymorphism. The RHS
- may depend on further defined constants, but not \isa{c} itself.
- Definitions of functions may be presented as \isa{c\ \isactrlvec x\ {\isasymequiv}\ t} instead of the puristic \isa{c\ {\isasymequiv}\ {\isasymlambda}\isactrlvec x{\isachardot}\ t}.
-
- An \emph{overloaded definition} consists of a collection of axioms
- for the same constant, with zero or one equations \isa{c{\isacharparenleft}{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}{\isasymkappa}{\isacharparenright}\ {\isasymequiv}\ t} for each type constructor \isa{{\isasymkappa}} (for
- distinct variables \isa{\isactrlvec {\isasymalpha}}). The RHS may mention
- previously defined constants as above, or arbitrary constants \isa{d{\isacharparenleft}{\isasymalpha}\isactrlisub i{\isacharparenright}} for some \isa{{\isasymalpha}\isactrlisub i} projected from \isa{\isactrlvec {\isasymalpha}}. Thus overloaded definitions essentially work by
- primitive recursion over the syntactic structure of a single type
- argument.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{ctyp}\verb|type ctyp| \\
- \indexdef{}{ML type}{cterm}\verb|type cterm| \\
- \indexdef{}{ML}{Thm.ctyp\_of}\verb|Thm.ctyp_of: theory -> typ -> ctyp| \\
- \indexdef{}{ML}{Thm.cterm\_of}\verb|Thm.cterm_of: theory -> term -> cterm| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML type}{thm}\verb|type thm| \\
- \indexdef{}{ML}{proofs}\verb|proofs: int ref| \\
- \indexdef{}{ML}{Thm.assume}\verb|Thm.assume: cterm -> thm| \\
- \indexdef{}{ML}{Thm.forall\_intr}\verb|Thm.forall_intr: cterm -> thm -> thm| \\
- \indexdef{}{ML}{Thm.forall\_elim}\verb|Thm.forall_elim: cterm -> thm -> thm| \\
- \indexdef{}{ML}{Thm.implies\_intr}\verb|Thm.implies_intr: cterm -> thm -> thm| \\
- \indexdef{}{ML}{Thm.implies\_elim}\verb|Thm.implies_elim: thm -> thm -> thm| \\
- \indexdef{}{ML}{Thm.generalize}\verb|Thm.generalize: string list * string list -> int -> thm -> thm| \\
- \indexdef{}{ML}{Thm.instantiate}\verb|Thm.instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm| \\
- \indexdef{}{ML}{Thm.axiom}\verb|Thm.axiom: theory -> string -> thm| \\
- \indexdef{}{ML}{Thm.add\_oracle}\verb|Thm.add_oracle: bstring * ('a -> cterm) -> theory|\isasep\isanewline%
-\verb| -> (string * ('a -> thm)) * theory| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML}{Theory.add\_axioms\_i}\verb|Theory.add_axioms_i: (binding * term) list -> theory -> theory| \\
- \indexdef{}{ML}{Theory.add\_deps}\verb|Theory.add_deps: string -> string * typ -> (string * typ) list -> theory -> theory| \\
- \indexdef{}{ML}{Theory.add\_defs\_i}\verb|Theory.add_defs_i: bool -> bool -> (binding * term) list -> theory -> theory| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|ctyp| and \verb|cterm| represent certified types
- and terms, respectively. These are abstract datatypes that
- guarantee that its values have passed the full well-formedness (and
- well-typedness) checks, relative to the declarations of type
- constructors, constants etc. in the theory.
-
- \item \verb|Thm.ctyp_of|~\isa{thy\ {\isasymtau}} and \verb|Thm.cterm_of|~\isa{thy\ t} explicitly checks types and terms,
- respectively. This also involves some basic normalizations, such
- expansion of type and term abbreviations from the theory context.
-
- Re-certification is relatively slow and should be avoided in tight
- reasoning loops. There are separate operations to decompose
- certified entities (including actual theorems).
-
- \item \verb|thm| represents proven propositions. This is an
- abstract datatype that guarantees that its values have been
- constructed by basic principles of the \verb|Thm| module.
- Every \verb|thm| value contains a sliding back-reference to the
- enclosing theory, cf.\ \secref{sec:context-theory}.
-
- \item \verb|proofs| determines the detail of proof recording within
- \verb|thm| values: \verb|0| records only the names of oracles,
- \verb|1| records oracle names and propositions, \verb|2| additionally
- records full proof terms. Officially named theorems that contribute
- to a result are always recorded.
-
- \item \verb|Thm.assume|, \verb|Thm.forall_intr|, \verb|Thm.forall_elim|, \verb|Thm.implies_intr|, and \verb|Thm.implies_elim|
- correspond to the primitive inferences of \figref{fig:prim-rules}.
-
- \item \verb|Thm.generalize|~\isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharcomma}\ \isactrlvec x{\isacharparenright}}
- corresponds to the \isa{generalize} rules of
- \figref{fig:subst-rules}. Here collections of type and term
- variables are generalized simultaneously, specified by the given
- basic names.
-
- \item \verb|Thm.instantiate|~\isa{{\isacharparenleft}\isactrlvec {\isasymalpha}\isactrlisub s{\isacharcomma}\ \isactrlvec x\isactrlisub {\isasymtau}{\isacharparenright}} corresponds to the \isa{instantiate} rules
- of \figref{fig:subst-rules}. Type variables are substituted before
- term variables. Note that the types in \isa{\isactrlvec x\isactrlisub {\isasymtau}}
- refer to the instantiated versions.
-
- \item \verb|Thm.axiom|~\isa{thy\ name} retrieves a named
- axiom, cf.\ \isa{axiom} in \figref{fig:prim-rules}.
-
- \item \verb|Thm.add_oracle|~\isa{{\isacharparenleft}name{\isacharcomma}\ oracle{\isacharparenright}} produces a named
- oracle rule, essentially generating arbitrary axioms on the fly,
- cf.\ \isa{axiom} in \figref{fig:prim-rules}.
-
- \item \verb|Theory.add_axioms_i|~\isa{{\isacharbrackleft}{\isacharparenleft}name{\isacharcomma}\ A{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}} declares
- arbitrary propositions as axioms.
-
- \item \verb|Theory.add_deps|~\isa{name\ c\isactrlisub {\isasymtau}\ \isactrlvec d\isactrlisub {\isasymsigma}} declares dependencies of a named specification
- for constant \isa{c\isactrlisub {\isasymtau}}, relative to existing
- specifications for constants \isa{\isactrlvec d\isactrlisub {\isasymsigma}}.
-
- \item \verb|Theory.add_defs_i|~\isa{unchecked\ overloaded\ {\isacharbrackleft}{\isacharparenleft}name{\isacharcomma}\ c\ \isactrlvec x\ {\isasymequiv}\ t{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}} states a definitional axiom for an existing
- constant \isa{c}. Dependencies are recorded (cf.\ \verb|Theory.add_deps|), unless the \isa{unchecked} option is set.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
-{\isafoldmlref}%
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-\endisadelimmlref
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-\isamarkupsubsection{Auxiliary definitions%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Theory \isa{Pure} provides a few auxiliary definitions, see
- \figref{fig:pure-aux}. These special constants are normally not
- exposed to the user, but appear in internal encodings.
-
- \begin{figure}[htb]
- \begin{center}
- \begin{tabular}{ll}
- \isa{conjunction\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop\ {\isasymRightarrow}\ prop} & (infix \isa{{\isacharampersand}}) \\
- \isa{{\isasymturnstile}\ A\ {\isacharampersand}\ B\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}C{\isachardot}\ {\isacharparenleft}A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isacharparenright}} \\[1ex]
- \isa{prop\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop} & (prefix \isa{{\isacharhash}}, suppressed) \\
- \isa{{\isacharhash}A\ {\isasymequiv}\ A} \\[1ex]
- \isa{term\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ prop} & (prefix \isa{TERM}) \\
- \isa{term\ x\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}A{\isachardot}\ A\ {\isasymLongrightarrow}\ A{\isacharparenright}} \\[1ex]
- \isa{TYPE\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ itself} & (prefix \isa{TYPE}) \\
- \isa{{\isacharparenleft}unspecified{\isacharparenright}} \\
- \end{tabular}
- \caption{Definitions of auxiliary connectives}\label{fig:pure-aux}
- \end{center}
- \end{figure}
-
- Derived conjunction rules include introduction \isa{A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ A\ {\isacharampersand}\ B}, and destructions \isa{A\ {\isacharampersand}\ B\ {\isasymLongrightarrow}\ A} and \isa{A\ {\isacharampersand}\ B\ {\isasymLongrightarrow}\ B}.
- Conjunction allows to treat simultaneous assumptions and conclusions
- uniformly. For example, multiple claims are intermediately
- represented as explicit conjunction, but this is refined into
- separate sub-goals before the user continues the proof; the final
- result is projected into a list of theorems (cf.\
- \secref{sec:tactical-goals}).
-
- The \isa{prop} marker (\isa{{\isacharhash}}) makes arbitrarily complex
- propositions appear as atomic, without changing the meaning: \isa{{\isasymGamma}\ {\isasymturnstile}\ A} and \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isacharhash}A} are interchangeable. See
- \secref{sec:tactical-goals} for specific operations.
-
- The \isa{term} marker turns any well-typed term into a derivable
- proposition: \isa{{\isasymturnstile}\ TERM\ t} holds unconditionally. Although
- this is logically vacuous, it allows to treat terms and proofs
- uniformly, similar to a type-theoretic framework.
-
- The \isa{TYPE} constructor is the canonical representative of
- the unspecified type \isa{{\isasymalpha}\ itself}; it essentially injects the
- language of types into that of terms. There is specific notation
- \isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}} for \isa{TYPE\isactrlbsub {\isasymtau}\ itself\isactrlesub }.
- Although being devoid of any particular meaning, the \isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}} accounts for the type \isa{{\isasymtau}} within the term
- language. In particular, \isa{TYPE{\isacharparenleft}{\isasymalpha}{\isacharparenright}} may be used as formal
- argument in primitive definitions, in order to circumvent hidden
- polymorphism (cf.\ \secref{sec:terms}). For example, \isa{c\ TYPE{\isacharparenleft}{\isasymalpha}{\isacharparenright}\ {\isasymequiv}\ A{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} defines \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ itself\ {\isasymRightarrow}\ prop} in terms of
- a proposition \isa{A} that depends on an additional type
- argument, which is essentially a predicate on types.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isadelimmlref
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-\endisadelimmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{Conjunction.intr}\verb|Conjunction.intr: thm -> thm -> thm| \\
- \indexdef{}{ML}{Conjunction.elim}\verb|Conjunction.elim: thm -> thm * thm| \\
- \indexdef{}{ML}{Drule.mk\_term}\verb|Drule.mk_term: cterm -> thm| \\
- \indexdef{}{ML}{Drule.dest\_term}\verb|Drule.dest_term: thm -> cterm| \\
- \indexdef{}{ML}{Logic.mk\_type}\verb|Logic.mk_type: typ -> term| \\
- \indexdef{}{ML}{Logic.dest\_type}\verb|Logic.dest_type: term -> typ| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Conjunction.intr| derives \isa{A\ {\isacharampersand}\ B} from \isa{A} and \isa{B}.
-
- \item \verb|Conjunction.elim| derives \isa{A} and \isa{B}
- from \isa{A\ {\isacharampersand}\ B}.
-
- \item \verb|Drule.mk_term| derives \isa{TERM\ t}.
-
- \item \verb|Drule.dest_term| recovers term \isa{t} from \isa{TERM\ t}.
-
- \item \verb|Logic.mk_type|~\isa{{\isasymtau}} produces the term \isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}}.
-
- \item \verb|Logic.dest_type|~\isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}} recovers the type
- \isa{{\isasymtau}}.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
-{\isafoldmlref}%
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-\isadelimmlref
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-\endisadelimmlref
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-\isamarkupsection{Object-level rules \label{sec:obj-rules}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The primitive inferences covered so far mostly serve foundational
- purposes. User-level reasoning usually works via object-level rules
- that are represented as theorems of Pure. Composition of rules
- involves \emph{backchaining}, \emph{higher-order unification} modulo
- \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion of \isa{{\isasymlambda}}-terms, and so-called
- \emph{lifting} of rules into a context of \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} connectives. Thus the full power of higher-order Natural
- Deduction in Isabelle/Pure becomes readily available.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Hereditary Harrop Formulae%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The idea of object-level rules is to model Natural Deduction
- inferences in the style of Gentzen \cite{Gentzen:1935}, but we allow
- arbitrary nesting similar to \cite{extensions91}. The most basic
- rule format is that of a \emph{Horn Clause}:
- \[
- \infer{\isa{A}}{\isa{A\isactrlsub {\isadigit{1}}} & \isa{{\isasymdots}} & \isa{A\isactrlsub n}}
- \]
- where \isa{A{\isacharcomma}\ A\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlsub n} are atomic propositions
- of the framework, usually of the form \isa{Trueprop\ B}, where
- \isa{B} is a (compound) object-level statement. This
- object-level inference corresponds to an iterated implication in
- Pure like this:
- \[
- \isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ A}
- \]
- As an example consider conjunction introduction: \isa{A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ A\ {\isasymand}\ B}. Any parameters occurring in such rule statements are
- conceptionally treated as arbitrary:
- \[
- \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ A\isactrlsub {\isadigit{1}}\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymLongrightarrow}\ A\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m}
- \]
-
- Nesting of rules means that the positions of \isa{A\isactrlsub i} may
- again hold compound rules, not just atomic propositions.
- Propositions of this format are called \emph{Hereditary Harrop
- Formulae} in the literature \cite{Miller:1991}. Here we give an
- inductive characterization as follows:
-
- \medskip
- \begin{tabular}{ll}
- \isa{\isactrlbold x} & set of variables \\
- \isa{\isactrlbold A} & set of atomic propositions \\
- \isa{\isactrlbold H\ \ {\isacharequal}\ \ {\isasymAnd}\isactrlbold x\isactrlsup {\isacharasterisk}{\isachardot}\ \isactrlbold H\isactrlsup {\isacharasterisk}\ {\isasymLongrightarrow}\ \isactrlbold A} & set of Hereditary Harrop Formulas \\
- \end{tabular}
- \medskip
-
- \noindent Thus we essentially impose nesting levels on propositions
- formed from \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}}. At each level there is a
- prefix of parameters and compound premises, concluding an atomic
- proposition. Typical examples are \isa{{\isasymlongrightarrow}}-introduction \isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymlongrightarrow}\ B} or mathematical induction \isa{P\ {\isadigit{0}}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}n{\isachardot}\ P\ n\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ P\ n}. Even deeper nesting occurs in well-founded
- induction \isa{{\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isacharparenleft}{\isasymAnd}y{\isachardot}\ y\ {\isasymprec}\ x\ {\isasymLongrightarrow}\ P\ y{\isacharparenright}\ {\isasymLongrightarrow}\ P\ x{\isacharparenright}\ {\isasymLongrightarrow}\ P\ x}, but this
- already marks the limit of rule complexity seen in practice.
-
- \medskip Regular user-level inferences in Isabelle/Pure always
- maintain the following canonical form of results:
-
- \begin{itemize}
-
- \item Normalization by \isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x{\isacharparenright}{\isacharparenright}\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ A\ {\isasymLongrightarrow}\ B\ x{\isacharparenright}},
- which is a theorem of Pure, means that quantifiers are pushed in
- front of implication at each level of nesting. The normal form is a
- Hereditary Harrop Formula.
-
- \item The outermost prefix of parameters is represented via
- schematic variables: instead of \isa{{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ A\ \isactrlvec x} we have \isa{\isactrlvec H\ {\isacharquery}\isactrlvec x\ {\isasymLongrightarrow}\ A\ {\isacharquery}\isactrlvec x}.
- Note that this representation looses information about the order of
- parameters, and vacuous quantifiers vanish automatically.
-
- \end{itemize}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
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-\endisadelimmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{MetaSimplifier.norm\_hhf}\verb|MetaSimplifier.norm_hhf: thm -> thm| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|MetaSimplifier.norm_hhf|~\isa{thm} normalizes the given
- theorem according to the canonical form specified above. This is
- occasionally helpful to repair some low-level tools that do not
- handle Hereditary Harrop Formulae properly.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
-{\isafoldmlref}%
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-\endisadelimmlref
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-\isamarkupsubsection{Rule composition%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The rule calculus of Isabelle/Pure provides two main inferences:
- \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} (i.e.\ back-chaining of rules) and
- \hyperlink{inference.assumption}{\mbox{\isa{assumption}}} (i.e.\ closing a branch), both modulo
- higher-order unification. There are also combined variants, notably
- \hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isacharunderscore}resolution}}} and \hyperlink{inference.dest-resolution}{\mbox{\isa{dest{\isacharunderscore}resolution}}}.
-
- To understand the all-important \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} principle,
- we first consider raw \indexdef{}{inference}{composition}\hypertarget{inference.composition}{\hyperlink{inference.composition}{\mbox{\isa{composition}}}} (modulo
- higher-order unification with substitution \isa{{\isasymvartheta}}):
- \[
- \infer[(\indexdef{}{inference}{composition}\hypertarget{inference.composition}{\hyperlink{inference.composition}{\mbox{\isa{composition}}}})]{\isa{\isactrlvec A{\isasymvartheta}\ {\isasymLongrightarrow}\ C{\isasymvartheta}}}
- {\isa{\isactrlvec A\ {\isasymLongrightarrow}\ B} & \isa{B{\isacharprime}\ {\isasymLongrightarrow}\ C} & \isa{B{\isasymvartheta}\ {\isacharequal}\ B{\isacharprime}{\isasymvartheta}}}
- \]
- Here the conclusion of the first rule is unified with the premise of
- the second; the resulting rule instance inherits the premises of the
- first and conclusion of the second. Note that \isa{C} can again
- consist of iterated implications. We can also permute the premises
- of the second rule back-and-forth in order to compose with \isa{B{\isacharprime}} in any position (subsequently we shall always refer to
- position 1 w.l.o.g.).
-
- In \hyperlink{inference.composition}{\mbox{\isa{composition}}} the internal structure of the common
- part \isa{B} and \isa{B{\isacharprime}} is not taken into account. For
- proper \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} we require \isa{B} to be atomic,
- and explicitly observe the structure \isa{{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ B{\isacharprime}\ \isactrlvec x} of the premise of the second rule. The
- idea is to adapt the first rule by ``lifting'' it into this context,
- by means of iterated application of the following inferences:
- \[
- \infer[(\indexdef{}{inference}{imp\_lift}\hypertarget{inference.imp-lift}{\hyperlink{inference.imp-lift}{\mbox{\isa{imp{\isacharunderscore}lift}}}})]{\isa{{\isacharparenleft}\isactrlvec H\ {\isasymLongrightarrow}\ \isactrlvec A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}\isactrlvec H\ {\isasymLongrightarrow}\ B{\isacharparenright}}}{\isa{\isactrlvec A\ {\isasymLongrightarrow}\ B}}
- \]
- \[
- \infer[(\indexdef{}{inference}{all\_lift}\hypertarget{inference.all-lift}{\hyperlink{inference.all-lift}{\mbox{\isa{all{\isacharunderscore}lift}}}})]{\isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec A\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ B\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}}}{\isa{\isactrlvec A\ {\isacharquery}\isactrlvec a\ {\isasymLongrightarrow}\ B\ {\isacharquery}\isactrlvec a}}
- \]
- By combining raw composition with lifting, we get full \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} as follows:
- \[
- \infer[(\indexdef{}{inference}{resolution}\hypertarget{inference.resolution}{\hyperlink{inference.resolution}{\mbox{\isa{resolution}}}})]
- {\isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ \isactrlvec A\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isasymLongrightarrow}\ C{\isasymvartheta}}}
- {\begin{tabular}{l}
- \isa{\isactrlvec A\ {\isacharquery}\isactrlvec a\ {\isasymLongrightarrow}\ B\ {\isacharquery}\isactrlvec a} \\
- \isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ B{\isacharprime}\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C} \\
- \isa{{\isacharparenleft}{\isasymlambda}\isactrlvec x{\isachardot}\ B\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isacharequal}\ B{\isacharprime}{\isasymvartheta}} \\
- \end{tabular}}
- \]
-
- Continued resolution of rules allows to back-chain a problem towards
- more and sub-problems. Branches are closed either by resolving with
- a rule of 0 premises, or by producing a ``short-circuit'' within a
- solved situation (again modulo unification):
- \[
- \infer[(\indexdef{}{inference}{assumption}\hypertarget{inference.assumption}{\hyperlink{inference.assumption}{\mbox{\isa{assumption}}}})]{\isa{C{\isasymvartheta}}}
- {\isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ A\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C} & \isa{A{\isasymvartheta}\ {\isacharequal}\ H\isactrlsub i{\isasymvartheta}}~~\text{(for some~\isa{i})}}
- \]
-
- FIXME \indexdef{}{inference}{elim\_resolution}\hypertarget{inference.elim-resolution}{\hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isacharunderscore}resolution}}}}, \indexdef{}{inference}{dest\_resolution}\hypertarget{inference.dest-resolution}{\hyperlink{inference.dest-resolution}{\mbox{\isa{dest{\isacharunderscore}resolution}}}}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{op RS}\verb|op RS: thm * thm -> thm| \\
- \indexdef{}{ML}{op OF}\verb|op OF: thm * thm list -> thm| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \isa{rule\isactrlsub {\isadigit{1}}\ RS\ rule\isactrlsub {\isadigit{2}}} resolves \isa{rule\isactrlsub {\isadigit{1}}} with \isa{rule\isactrlsub {\isadigit{2}}} according to the
- \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} principle explained above. Note that the
- corresponding attribute in the Isar language is called \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}.
-
- \item \isa{rule\ OF\ rules} resolves a list of rules with the
- first rule, addressing its premises \isa{{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ length\ rules}
- (operating from last to first). This means the newly emerging
- premises are all concatenated, without interfering. Also note that
- compared to \isa{RS}, the rule argument order is swapped: \isa{rule\isactrlsub {\isadigit{1}}\ RS\ rule\isactrlsub {\isadigit{2}}\ {\isacharequal}\ rule\isactrlsub {\isadigit{2}}\ OF\ {\isacharbrackleft}rule\isactrlsub {\isadigit{1}}{\isacharbrackright}}.
-
- \end{description}%
-\end{isamarkuptext}%
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--- a/doc-src/IsarImplementation/Thy/document/Prelim.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,896 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Prelim}%
-%
-\isadelimtheory
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-\endisadelimtheory
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-\ Prelim\isanewline
-\isakeyword{imports}\ Base\isanewline
-\isakeyword{begin}%
-\endisatagtheory
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-\endisadelimtheory
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-\isamarkupchapter{Preliminaries%
-}
-\isamarkuptrue%
-%
-\isamarkupsection{Contexts \label{sec:context}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-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 \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}, which means that a
- proposition \isa{{\isasymphi}} is derivable from hypotheses \isa{{\isasymGamma}}
- within the theory \isa{{\isasymTheta}}. There are logical reasons for
- keeping \isa{{\isasymTheta}} and \isa{{\isasymGamma}} separate: theories can be
- liberal about supporting type constructors and schematic
- polymorphism of constants and axioms, while the inner calculus of
- \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}} 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.\ \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}}.
-
- \item Export: discharge of hypotheses admits results to be exported
- into a \emph{smaller} context, i.e.\ \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}
- implies \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymDelta}\ {\isasymLongrightarrow}\ {\isasymphi}} where \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}} and
- \isa{{\isasymDelta}\ {\isacharequal}\ {\isasymGamma}{\isacharprime}\ {\isacharminus}\ {\isasymGamma}}. Note that \isa{{\isasymTheta}} remains unchanged here,
- only the \isa{{\isasymGamma}} part is affected.
-
- \end{itemize}
-
- \medskip By modeling the main characteristics of the primitive
- \isa{{\isasymTheta}} and \isa{{\isasymGamma}} 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 \isa{{\isasymTheta}} and \isa{{\isasymGamma}} 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 \isa{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.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Theory context \label{sec:context-theory}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-A \emph{theory} is a data container with explicit name 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 \isa{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 \isa{begin} operation starts a new theory by importing
- several parent theories and entering a special \isa{draft} mode,
- which is sustained until the final \isa{end} operation. A draft
- theory acts like a linear type, where updates invalidate earlier
- versions. An invalidated draft is called ``stale''.
-
- The \isa{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 \isa{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 \isa{Pure}, with theory \isa{Length}
- importing \isa{Nat} and \isa{List}. The body of \isa{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}
- & & \isa{Pure} \\
- & & \isa{{\isasymdown}} \\
- & & \isa{FOL} \\
- & $\swarrow$ & & $\searrow$ & \\
- \isa{Nat} & & & & \isa{List} \\
- & $\searrow$ & & $\swarrow$ \\
- & & \isa{Length} \\
- & & \multicolumn{3}{l}{~~\hyperlink{keyword.imports}{\mbox{\isa{\isakeyword{imports}}}}} \\
- & & \multicolumn{3}{l}{~~\hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}}} \\
- & & $\vdots$~~ \\
- & & \isa{{\isasymbullet}}~~ \\
- & & $\vdots$~~ \\
- & & \isa{{\isasymbullet}}~~ \\
- & & $\vdots$~~ \\
- & & \multicolumn{3}{l}{~~\hyperlink{command.end}{\mbox{\isa{\isacommand{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 \isa{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.%
-\end{isamarkuptext}%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{theory}\verb|type theory| \\
- \indexdef{}{ML}{Theory.subthy}\verb|Theory.subthy: theory * theory -> bool| \\
- \indexdef{}{ML}{Theory.merge}\verb|Theory.merge: theory * theory -> theory| \\
- \indexdef{}{ML}{Theory.checkpoint}\verb|Theory.checkpoint: theory -> theory| \\
- \indexdef{}{ML}{Theory.copy}\verb|Theory.copy: theory -> theory| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML type}{theory\_ref}\verb|type theory_ref| \\
- \indexdef{}{ML}{Theory.deref}\verb|Theory.deref: theory_ref -> theory| \\
- \indexdef{}{ML}{Theory.check\_thy}\verb|Theory.check_thy: theory -> theory_ref| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|theory| represents theory contexts. This is
- essentially a linear type! Most operations destroy the original
- version, which then becomes ``stale''.
-
- \item \verb|Theory.subthy|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}}
- compares theories according to the inherent graph structure of the
- construction. This sub-theory relation is a nominal approximation
- of inclusion (\isa{{\isasymsubseteq}}) of the corresponding content.
-
- \item \verb|Theory.merge|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}}
- absorbs one theory into the other. This fails for unrelated
- theories!
-
- \item \verb|Theory.checkpoint|~\isa{thy} produces a safe
- stepping stone in the linear development of \isa{thy}. The next
- update will result in two related, valid theories.
-
- \item \verb|Theory.copy|~\isa{thy} produces a variant of \isa{thy} that holds a copy of the same data. The result is not
- related to the original; the original is unchanged.
-
- \item \verb|theory_ref| represents a sliding reference to an
- always valid theory; updates on the original are propagated
- automatically.
-
- \item \verb|Theory.deref|~\isa{thy{\isacharunderscore}ref} turns a \verb|theory_ref| into an \verb|theory| value. As the referenced
- theory evolves monotonically over time, later invocations of \verb|Theory.deref| may refer to a larger context.
-
- \item \verb|Theory.check_thy|~\isa{thy} produces a \verb|theory_ref| from a valid \verb|theory| value.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsubsection{Proof context \label{sec:context-proof}%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-A proof context is a container for pure data with a back-reference
- to the theory it belongs to. The \isa{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 \isa{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 \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}}, just to make double
- sure. Results could still leak into an alien proof context due 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.%
-\end{isamarkuptext}%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{Proof.context}\verb|type Proof.context| \\
- \indexdef{}{ML}{ProofContext.init}\verb|ProofContext.init: theory -> Proof.context| \\
- \indexdef{}{ML}{ProofContext.theory\_of}\verb|ProofContext.theory_of: Proof.context -> theory| \\
- \indexdef{}{ML}{ProofContext.transfer}\verb|ProofContext.transfer: theory -> Proof.context -> Proof.context| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Proof.context| represents proof contexts. Elements
- of this type are essentially pure values, with a sliding reference
- to the background theory.
-
- \item \verb|ProofContext.init|~\isa{thy} produces a proof context
- derived from \isa{thy}, initializing all data.
-
- \item \verb|ProofContext.theory_of|~\isa{ctxt} selects the
- background theory from \isa{ctxt}, dereferencing its internal
- \verb|theory_ref|.
-
- \item \verb|ProofContext.transfer|~\isa{thy\ ctxt} promotes the
- background theory of \isa{ctxt} to the super theory \isa{thy}.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsubsection{Generic contexts \label{sec:generic-context}%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-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 \isa{theory{\isacharunderscore}of} and \isa{proof{\isacharunderscore}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 \isa{init} operation.%
-\end{isamarkuptext}%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{Context.generic}\verb|type Context.generic| \\
- \indexdef{}{ML}{Context.theory\_of}\verb|Context.theory_of: Context.generic -> theory| \\
- \indexdef{}{ML}{Context.proof\_of}\verb|Context.proof_of: Context.generic -> Proof.context| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Context.generic| is the direct sum of \verb|theory| and \verb|Proof.context|, with the datatype
- constructors \verb|Context.Theory| and \verb|Context.Proof|.
-
- \item \verb|Context.theory_of|~\isa{context} always produces a
- theory from the generic \isa{context}, using \verb|ProofContext.theory_of| as required.
-
- \item \verb|Context.proof_of|~\isa{context} always produces a
- proof context from the generic \isa{context}, using \verb|ProofContext.init| as required (note that this re-initializes the
- context data with each invocation).
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsubsection{Context data \label{sec:context-data}%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-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}
- \isa{{\isasymtype}\ T} & representing type \\
- \isa{{\isasymval}\ empty{\isacharcolon}\ T} & empty default value \\
- \isa{{\isasymval}\ copy{\isacharcolon}\ T\ {\isasymrightarrow}\ T} & refresh impure data \\
- \isa{{\isasymval}\ extend{\isacharcolon}\ T\ {\isasymrightarrow}\ T} & re-initialize on import \\
- \isa{{\isasymval}\ merge{\isacharcolon}\ T\ {\isasymtimes}\ T\ {\isasymrightarrow}\ T} & join on import \\
- \end{tabular}
- \medskip
-
- \noindent The \isa{empty} value acts as initial default for
- \emph{any} theory that does not declare actual data content; \isa{copy} maintains persistent integrity for impure data, it is just
- the identity for pure values; \isa{extend} is acts like a
- unitary version of \isa{merge}, both operations should also
- include the functionality of \isa{copy} for impure data.
-
- \paragraph{Proof context data} is purely functional. A declaration
- needs to implement the following SML signature:
-
- \medskip
- \begin{tabular}{ll}
- \isa{{\isasymtype}\ T} & representing type \\
- \isa{{\isasymval}\ init{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} & produce initial value \\
- \end{tabular}
- \medskip
-
- \noindent The \isa{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 \isa{copy}. The \isa{init}
- operation for proof contexts merely selects the current data value
- from the background theory.
-
- \bigskip A data declaration of type \isa{T} results in the
- following interface:
-
- \medskip
- \begin{tabular}{ll}
- \isa{init{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} \\
- \isa{get{\isacharcolon}\ context\ {\isasymrightarrow}\ T} \\
- \isa{put{\isacharcolon}\ T\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
- \isa{map{\isacharcolon}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
- \end{tabular}
- \medskip
-
- \noindent Here \isa{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.%
-\end{isamarkuptext}%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML functor}{TheoryDataFun}\verb|functor TheoryDataFun| \\
- \indexdef{}{ML functor}{ProofDataFun}\verb|functor ProofDataFun| \\
- \indexdef{}{ML functor}{GenericDataFun}\verb|functor GenericDataFun| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|TheoryDataFun|\isa{{\isacharparenleft}spec{\isacharparenright}} declares data for
- type \verb|theory| according to the specification provided as
- argument structure. The resulting structure provides data init and
- access operations as described above.
-
- \item \verb|ProofDataFun|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
- \verb|TheoryDataFun| for type \verb|Proof.context|.
-
- \item \verb|GenericDataFun|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
- \verb|TheoryDataFun| for type \verb|Context.generic|.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsection{Names \label{sec:names}%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-In principle, a name is just a string, but there are various
- convention for encoding additional structure. For example, ``\isa{Foo{\isachardot}bar{\isachardot}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.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isamarkupsubsection{Strings of symbols%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-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 ``\isa{c}'', for example
- ``\verb,a,'',
-
- \item a regular symbol ``\verb,\,\verb,<,\isa{ident}\verb,>,'',
- for example ``\verb,\,\verb,<alpha>,'',
-
- \item a control symbol ``\verb,\,\verb,<^,\isa{ident}\verb,>,'',
- for example ``\verb,\,\verb,<^bold>,'',
-
- \item a raw symbol ``\verb,\,\verb,<^raw:,\isa{text}\verb,>,''
- where \isa{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,\isa{n}\verb,>, where \isa{n} consists of digits, for example
- ``\verb,\,\verb,<^raw42>,''.
-
- \end{enumerate}
-
- \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
- 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{print-mode}). For example, the standard {\LaTeX} setup of
- the Isabelle document preparation system would present
- ``\verb,\,\verb,<alpha>,'' as \isa{{\isasymalpha}}, and
- ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as \isa{\isactrlbold {\isasymalpha}}.%
-\end{isamarkuptext}%
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-\begin{mldecls}
- \indexdef{}{ML type}{Symbol.symbol}\verb|type Symbol.symbol| \\
- \indexdef{}{ML}{Symbol.explode}\verb|Symbol.explode: string -> Symbol.symbol list| \\
- \indexdef{}{ML}{Symbol.is\_letter}\verb|Symbol.is_letter: Symbol.symbol -> bool| \\
- \indexdef{}{ML}{Symbol.is\_digit}\verb|Symbol.is_digit: Symbol.symbol -> bool| \\
- \indexdef{}{ML}{Symbol.is\_quasi}\verb|Symbol.is_quasi: Symbol.symbol -> bool| \\
- \indexdef{}{ML}{Symbol.is\_blank}\verb|Symbol.is_blank: Symbol.symbol -> bool| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML type}{Symbol.sym}\verb|type Symbol.sym| \\
- \indexdef{}{ML}{Symbol.decode}\verb|Symbol.decode: Symbol.symbol -> Symbol.sym| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Symbol.symbol| represents individual Isabelle
- symbols; this is an alias for \verb|string|.
-
- \item \verb|Symbol.explode|~\isa{str} produces a symbol list
- from the packed form. This function supercedes \verb|String.explode| for virtually all purposes of manipulating text in
- Isabelle!
-
- \item \verb|Symbol.is_letter|, \verb|Symbol.is_digit|, \verb|Symbol.is_quasi|, \verb|Symbol.is_blank| classify standard
- symbols according to fixed syntactic conventions of Isabelle, cf.\
- \cite{isabelle-isar-ref}.
-
- \item \verb|Symbol.sym| is a concrete datatype that represents
- the different kinds of symbols explicitly, with constructors \verb|Symbol.Char|, \verb|Symbol.Sym|, \verb|Symbol.Ctrl|, \verb|Symbol.Raw|.
-
- \item \verb|Symbol.decode| converts the string representation of a
- symbol into the datatype version.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsubsection{Basic names \label{sec:basic-names}%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-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: one underscore means
- \emph{internal name}, two underscores means \emph{Skolem name},
- three underscores means \emph{internal Skolem name}.
-
- For example, the basic name \isa{foo} has the internal version
- \isa{foo{\isacharunderscore}}, with Skolem versions \isa{foo{\isacharunderscore}{\isacharunderscore}} and \isa{foo{\isacharunderscore}{\isacharunderscore}{\isacharunderscore}}, 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 \isa{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 \isa{declare} operation adds names to the
- context.
-
- The \isa{invents} operation derives a number of fresh names from
- a given starting point. For example, the first three names derived
- from \isa{a} are \isa{a}, \isa{b}, \isa{c}.
-
- The \isa{variants} operation produces fresh names by
- 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
- step picks the next unused variant from this sequence.%
-\end{isamarkuptext}%
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-\begin{mldecls}
- \indexdef{}{ML}{Name.internal}\verb|Name.internal: string -> string| \\
- \indexdef{}{ML}{Name.skolem}\verb|Name.skolem: string -> string| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML type}{Name.context}\verb|type Name.context| \\
- \indexdef{}{ML}{Name.context}\verb|Name.context: Name.context| \\
- \indexdef{}{ML}{Name.declare}\verb|Name.declare: string -> Name.context -> Name.context| \\
- \indexdef{}{ML}{Name.invents}\verb|Name.invents: Name.context -> string -> int -> string list| \\
- \indexdef{}{ML}{Name.variants}\verb|Name.variants: string list -> Name.context -> string list * Name.context| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Name.internal|~\isa{name} produces an internal name
- by adding one underscore.
-
- \item \verb|Name.skolem|~\isa{name} produces a Skolem name by
- adding two underscores.
-
- \item \verb|Name.context| represents the context of already used
- names; the initial value is \verb|Name.context|.
-
- \item \verb|Name.declare|~\isa{name} enters a used name into the
- context.
-
- \item \verb|Name.invents|~\isa{context\ name\ n} produces \isa{n} fresh names derived from \isa{name}.
-
- \item \verb|Name.variants|~\isa{names\ context} produces fresh
- variants of \isa{names}; the result is entered into the context.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsubsection{Indexed names%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-An \emph{indexed name} (or \isa{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 \isa{maxidx} of the first
- collection, then increment all indexes of the second collection by
- \isa{maxidx\ {\isacharplus}\ {\isadigit{1}}}; the maximum index of an empty collection is
- \isa{{\isacharminus}{\isadigit{1}}}.
-
- Occasionally, basic names and indexed names are injected into the
- same pair type: the (improper) indexname \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}} is used
- to encode basic names.
-
- \medskip Isabelle syntax observes the following rules for
- representing an indexname \isa{{\isacharparenleft}x{\isacharcomma}\ i{\isacharparenright}} as a packed string:
-
- \begin{itemize}
-
- \item \isa{{\isacharquery}x} if \isa{x} does not end with a digit and \isa{i\ {\isacharequal}\ {\isadigit{0}}},
-
- \item \isa{{\isacharquery}xi} if \isa{x} does not end with a digit,
-
- \item \isa{{\isacharquery}x{\isachardot}i} otherwise.
-
- \end{itemize}
-
- Indexnames may acquire large index numbers over time. Results are
- normalized towards \isa{{\isadigit{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
- \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}.%
-\end{isamarkuptext}%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{indexname}\verb|type indexname| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|indexname| represents indexed names. This is an
- abbreviation for \verb|string * int|. The second component is
- usually non-negative, except for situations where \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}}
- is used to embed basic names into this type.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isamarkupsubsection{Qualified names and name spaces%
-}
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-A \emph{qualified name} consists of a non-empty sequence of basic
- name components. The packed representation uses a dot as separator,
- as in ``\isa{A{\isachardot}b{\isachardot}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 ``\isa{A{\isachardot}b{\isachardot}c}'' may be understood as a local entity \isa{c}, within a local structure \isa{b}, within a global
- structure \isa{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 \isa{naming} policy tells how to turn a name
- specification into a fully qualified internal name (by the \isa{full} operation), and how fully qualified names may be accessed
- externally. For example, the default naming policy is to prefix an
- implicit path: \isa{full\ x} produces \isa{path{\isachardot}x}, and the
- standard accesses for \isa{path{\isachardot}x} include both \isa{x} and
- \isa{path{\isachardot}x}. Normally, the naming is implicit in the theory or
- proof context; there are separate versions of the corresponding.
-
- \medskip A \isa{name\ space} manages a collection of fully
- internalized names, together with a mapping between external names
- and internal names (in both directions). The corresponding \isa{intern} and \isa{extern} operations are mostly used for
- parsing and printing only! The \isa{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 \isa{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.\ \isa{c{\isachardot}intro} for a canonical theorem related to constant \isa{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.\ \isa{c{\isacharunderscore}type{\isachardot}intro}
- and \isa{c{\isacharunderscore}class{\isachardot}intro} for theorems related to type \isa{c}
- and class \isa{c}, respectively.%
-\end{isamarkuptext}%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{NameSpace.base}\verb|NameSpace.base: string -> string| \\
- \indexdef{}{ML}{NameSpace.qualifier}\verb|NameSpace.qualifier: string -> string| \\
- \indexdef{}{ML}{NameSpace.append}\verb|NameSpace.append: string -> string -> string| \\
- \indexdef{}{ML}{NameSpace.implode}\verb|NameSpace.implode: string list -> string| \\
- \indexdef{}{ML}{NameSpace.explode}\verb|NameSpace.explode: string -> string list| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML type}{NameSpace.naming}\verb|type NameSpace.naming| \\
- \indexdef{}{ML}{NameSpace.default\_naming}\verb|NameSpace.default_naming: NameSpace.naming| \\
- \indexdef{}{ML}{NameSpace.add\_path}\verb|NameSpace.add_path: string -> NameSpace.naming -> NameSpace.naming| \\
- \indexdef{}{ML}{NameSpace.full\_name}\verb|NameSpace.full_name: NameSpace.naming -> binding -> string| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML type}{NameSpace.T}\verb|type NameSpace.T| \\
- \indexdef{}{ML}{NameSpace.empty}\verb|NameSpace.empty: NameSpace.T| \\
- \indexdef{}{ML}{NameSpace.merge}\verb|NameSpace.merge: NameSpace.T * NameSpace.T -> NameSpace.T| \\
- \indexdef{}{ML}{NameSpace.declare}\verb|NameSpace.declare: NameSpace.naming -> binding -> NameSpace.T -> string * NameSpace.T| \\
- \indexdef{}{ML}{NameSpace.intern}\verb|NameSpace.intern: NameSpace.T -> string -> string| \\
- \indexdef{}{ML}{NameSpace.extern}\verb|NameSpace.extern: NameSpace.T -> string -> string| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|NameSpace.base|~\isa{name} returns the base name of a
- qualified name.
-
- \item \verb|NameSpace.qualifier|~\isa{name} returns the qualifier
- of a qualified name.
-
- \item \verb|NameSpace.append|~\isa{name\isactrlisub {\isadigit{1}}\ name\isactrlisub {\isadigit{2}}}
- appends two qualified names.
-
- \item \verb|NameSpace.implode|~\isa{name} and \verb|NameSpace.explode|~\isa{names} convert between the packed string
- representation and the explicit list form of qualified names.
-
- \item \verb|NameSpace.naming| represents the abstract concept of
- a naming policy.
-
- \item \verb|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 \verb|NameSpace.add_path|~\isa{path\ naming} augments the
- naming policy by extending its path component.
-
- \item \verb|NameSpace.full_name|\isa{naming\ binding} turns a name
- binding (usually a basic name) into the fully qualified
- internal name, according to the given naming policy.
-
- \item \verb|NameSpace.T| represents name spaces.
-
- \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
- maintaining name spaces according to theory data management
- (\secref{sec:context-data}).
-
- \item \verb|NameSpace.declare|~\isa{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 \verb|NameSpace.intern|~\isa{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 \verb|NameSpace.full_name| and \verb|NameSpace.declare|
- (or their derivatives for \verb|theory| and
- \verb|Proof.context|).
-
- \item \verb|NameSpace.extern|~\isa{space\ name} externalizes a
- (fully qualified) internal name.
-
- This operation is mostly for printing! Note unqualified names are
- produced via \verb|NameSpace.base|.
-
- \end{description}%
-\end{isamarkuptext}%
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-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:
--- a/doc-src/IsarImplementation/Thy/document/Proof.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,394 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Proof}%
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-\isadelimtheory
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-\endisadelimtheory
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-\ Proof\isanewline
-\isakeyword{imports}\ Base\isanewline
-\isakeyword{begin}%
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-\endisadelimtheory
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-\isamarkupchapter{Structured proofs%
-}
-\isamarkuptrue%
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-\isamarkupsection{Variables \label{sec:variables}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Any variable that is not explicitly bound by \isa{{\isasymlambda}}-abstraction
- is considered as ``free''. Logically, free variables act like
- outermost universal quantification at the sequent level: \isa{A\isactrlisub {\isadigit{1}}{\isacharparenleft}x{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n{\isacharparenleft}x{\isacharparenright}\ {\isasymturnstile}\ B{\isacharparenleft}x{\isacharparenright}} means that the result
- holds \emph{for all} values of \isa{x}. Free variables for
- terms (not types) can be fully internalized into the logic: \isa{{\isasymturnstile}\ B{\isacharparenleft}x{\isacharparenright}} and \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}} are interchangeable, provided
- that \isa{x} does not occur elsewhere in the context.
- Inspecting \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}} more closely, we see that inside the
- quantifier, \isa{x} is essentially ``arbitrary, but fixed'',
- while from outside it appears as a place-holder for instantiation
- (thanks to \isa{{\isasymAnd}} elimination).
-
- The Pure logic represents the idea of variables being either inside
- or outside the current scope by providing separate syntactic
- categories for \emph{fixed variables} (e.g.\ \isa{x}) vs.\
- \emph{schematic variables} (e.g.\ \isa{{\isacharquery}x}). Incidently, a
- universal result \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}} has the HHF normal form \isa{{\isasymturnstile}\ B{\isacharparenleft}{\isacharquery}x{\isacharparenright}}, which represents its generality nicely without requiring
- an explicit quantifier. The same principle works for type
- variables: \isa{{\isasymturnstile}\ B{\isacharparenleft}{\isacharquery}{\isasymalpha}{\isacharparenright}} represents the idea of ``\isa{{\isasymturnstile}\ {\isasymforall}{\isasymalpha}{\isachardot}\ B{\isacharparenleft}{\isasymalpha}{\isacharparenright}}'' without demanding a truly polymorphic framework.
-
- \medskip Additional care is required to treat type variables in a
- way that facilitates type-inference. In principle, term variables
- depend on type variables, which means that type variables would have
- to be declared first. For example, a raw type-theoretic framework
- would demand the context to be constructed in stages as follows:
- \isa{{\isasymGamma}\ {\isacharequal}\ {\isasymalpha}{\isacharcolon}\ type{\isacharcomma}\ x{\isacharcolon}\ {\isasymalpha}{\isacharcomma}\ a{\isacharcolon}\ A{\isacharparenleft}x\isactrlisub {\isasymalpha}{\isacharparenright}}.
-
- We allow a slightly less formalistic mode of operation: term
- variables \isa{x} are fixed without specifying a type yet
- (essentially \emph{all} potential occurrences of some instance
- \isa{x\isactrlisub {\isasymtau}} are fixed); the first occurrence of \isa{x}
- within a specific term assigns its most general type, which is then
- maintained consistently in the context. The above example becomes
- \isa{{\isasymGamma}\ {\isacharequal}\ x{\isacharcolon}\ term{\isacharcomma}\ {\isasymalpha}{\isacharcolon}\ type{\isacharcomma}\ A{\isacharparenleft}x\isactrlisub {\isasymalpha}{\isacharparenright}}, where type \isa{{\isasymalpha}} is fixed \emph{after} term \isa{x}, and the constraint
- \isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}} is an implicit consequence of the occurrence of
- \isa{x\isactrlisub {\isasymalpha}} in the subsequent proposition.
-
- This twist of dependencies is also accommodated by the reverse
- operation of exporting results from a context: a type variable
- \isa{{\isasymalpha}} is considered fixed as long as it occurs in some fixed
- term variable of the context. For example, exporting \isa{x{\isacharcolon}\ term{\isacharcomma}\ {\isasymalpha}{\isacharcolon}\ type\ {\isasymturnstile}\ x\isactrlisub {\isasymalpha}\ {\isacharequal}\ x\isactrlisub {\isasymalpha}} produces in the first step
- \isa{x{\isacharcolon}\ term\ {\isasymturnstile}\ x\isactrlisub {\isasymalpha}\ {\isacharequal}\ x\isactrlisub {\isasymalpha}} for fixed \isa{{\isasymalpha}},
- and only in the second step \isa{{\isasymturnstile}\ {\isacharquery}x\isactrlisub {\isacharquery}\isactrlisub {\isasymalpha}\ {\isacharequal}\ {\isacharquery}x\isactrlisub {\isacharquery}\isactrlisub {\isasymalpha}} for schematic \isa{{\isacharquery}x} and \isa{{\isacharquery}{\isasymalpha}}.
-
- \medskip The Isabelle/Isar proof context manages the gory details of
- term vs.\ type variables, with high-level principles for moving the
- frontier between fixed and schematic variables.
-
- The \isa{add{\isacharunderscore}fixes} operation explictly declares fixed
- variables; the \isa{declare{\isacharunderscore}term} operation absorbs a term into
- a context by fixing new type variables and adding syntactic
- constraints.
-
- The \isa{export} operation is able to perform the main work of
- generalizing term and type variables as sketched above, assuming
- that fixing variables and terms have been declared properly.
-
- There \isa{import} operation makes a generalized fact a genuine
- part of the context, by inventing fixed variables for the schematic
- ones. The effect can be reversed by using \isa{export} later,
- potentially with an extended context; the result is equivalent to
- the original modulo renaming of schematic variables.
-
- The \isa{focus} operation provides a variant of \isa{import}
- for nested propositions (with explicit quantification): \isa{{\isasymAnd}x\isactrlisub {\isadigit{1}}\ {\isasymdots}\ x\isactrlisub n{\isachardot}\ B{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlisub n{\isacharparenright}} is
- decomposed by inventing fixed variables \isa{x\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlisub n} for the body.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisadelimmlref
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-\isatagmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{Variable.add\_fixes}\verb|Variable.add_fixes: |\isasep\isanewline%
-\verb| string list -> Proof.context -> string list * Proof.context| \\
- \indexdef{}{ML}{Variable.variant\_fixes}\verb|Variable.variant_fixes: |\isasep\isanewline%
-\verb| string list -> Proof.context -> string list * Proof.context| \\
- \indexdef{}{ML}{Variable.declare\_term}\verb|Variable.declare_term: term -> Proof.context -> Proof.context| \\
- \indexdef{}{ML}{Variable.declare\_constraints}\verb|Variable.declare_constraints: term -> Proof.context -> Proof.context| \\
- \indexdef{}{ML}{Variable.export}\verb|Variable.export: Proof.context -> Proof.context -> thm list -> thm list| \\
- \indexdef{}{ML}{Variable.polymorphic}\verb|Variable.polymorphic: Proof.context -> term list -> term list| \\
- \indexdef{}{ML}{Variable.import\_thms}\verb|Variable.import_thms: bool -> thm list -> Proof.context ->|\isasep\isanewline%
-\verb| ((ctyp list * cterm list) * thm list) * Proof.context| \\
- \indexdef{}{ML}{Variable.focus}\verb|Variable.focus: cterm -> Proof.context -> (cterm list * cterm) * Proof.context| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Variable.add_fixes|~\isa{xs\ ctxt} fixes term
- variables \isa{xs}, returning the resulting internal names. By
- default, the internal representation coincides with the external
- one, which also means that the given variables must not be fixed
- already. There is a different policy within a local proof body: the
- given names are just hints for newly invented Skolem variables.
-
- \item \verb|Variable.variant_fixes| is similar to \verb|Variable.add_fixes|, but always produces fresh variants of the given
- names.
-
- \item \verb|Variable.declare_term|~\isa{t\ ctxt} declares term
- \isa{t} to belong to the context. This automatically fixes new
- type variables, but not term variables. Syntactic constraints for
- type and term variables are declared uniformly, though.
-
- \item \verb|Variable.declare_constraints|~\isa{t\ ctxt} declares
- syntactic constraints from term \isa{t}, without making it part
- of the context yet.
-
- \item \verb|Variable.export|~\isa{inner\ outer\ thms} generalizes
- fixed type and term variables in \isa{thms} according to the
- difference of the \isa{inner} and \isa{outer} context,
- following the principles sketched above.
-
- \item \verb|Variable.polymorphic|~\isa{ctxt\ ts} generalizes type
- variables in \isa{ts} as far as possible, even those occurring
- in fixed term variables. The default policy of type-inference is to
- fix newly introduced type variables, which is essentially reversed
- with \verb|Variable.polymorphic|: here the given terms are detached
- from the context as far as possible.
-
- \item \verb|Variable.import_thms|~\isa{open\ thms\ ctxt} invents fixed
- type and term variables for the schematic ones occurring in \isa{thms}. The \isa{open} flag indicates whether the fixed names
- should be accessible to the user, otherwise newly introduced names
- are marked as ``internal'' (\secref{sec:names}).
-
- \item \verb|Variable.focus|~\isa{B} decomposes the outermost \isa{{\isasymAnd}} prefix of proposition \isa{B}.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isamarkupsection{Assumptions \label{sec:assumptions}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-An \emph{assumption} is a proposition that it is postulated in the
- current context. Local conclusions may use assumptions as
- additional facts, but this imposes implicit hypotheses that weaken
- the overall statement.
-
- Assumptions are restricted to fixed non-schematic statements, i.e.\
- all generality needs to be expressed by explicit quantifiers.
- Nevertheless, the result will be in HHF normal form with outermost
- quantifiers stripped. For example, by assuming \isa{{\isasymAnd}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ P\ x} we get \isa{{\isasymAnd}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ P\ x\ {\isasymturnstile}\ P\ {\isacharquery}x} for schematic \isa{{\isacharquery}x}
- of fixed type \isa{{\isasymalpha}}. Local derivations accumulate more and
- more explicit references to hypotheses: \isa{A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n\ {\isasymturnstile}\ B} where \isa{A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n} needs to
- be covered by the assumptions of the current context.
-
- \medskip The \isa{add{\isacharunderscore}assms} operation augments the context by
- local assumptions, which are parameterized by an arbitrary \isa{export} rule (see below).
-
- The \isa{export} operation moves facts from a (larger) inner
- context into a (smaller) outer context, by discharging the
- difference of the assumptions as specified by the associated export
- rules. Note that the discharged portion is determined by the
- difference contexts, not the facts being exported! There is a
- separate flag to indicate a goal context, where the result is meant
- to refine an enclosing sub-goal of a structured proof state.
-
- \medskip The most basic export rule discharges assumptions directly
- by means of the \isa{{\isasymLongrightarrow}} introduction rule:
- \[
- \infer[(\isa{{\isasymLongrightarrow}{\isacharunderscore}intro})]{\isa{{\isasymGamma}\ {\isacharbackslash}\ A\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B}}
- \]
-
- The variant for goal refinements marks the newly introduced
- premises, which causes the canonical Isar goal refinement scheme to
- enforce unification with local premises within the goal:
- \[
- \infer[(\isa{{\isacharhash}{\isasymLongrightarrow}{\isacharunderscore}intro})]{\isa{{\isasymGamma}\ {\isacharbackslash}\ A\ {\isasymturnstile}\ {\isacharhash}A\ {\isasymLongrightarrow}\ B}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B}}
- \]
-
- \medskip Alternative versions of assumptions may perform arbitrary
- transformations on export, as long as the corresponding portion of
- hypotheses is removed from the given facts. For example, a local
- definition works by fixing \isa{x} and assuming \isa{x\ {\isasymequiv}\ t},
- with the following export rule to reverse the effect:
- \[
- \infer[(\isa{{\isasymequiv}{\isacharminus}expand})]{\isa{{\isasymGamma}\ {\isacharbackslash}\ x\ {\isasymequiv}\ t\ {\isasymturnstile}\ B\ t}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B\ x}}
- \]
- This works, because the assumption \isa{x\ {\isasymequiv}\ t} was introduced in
- a context with \isa{x} being fresh, so \isa{x} does not
- occur in \isa{{\isasymGamma}} here.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{Assumption.export}\verb|type Assumption.export| \\
- \indexdef{}{ML}{Assumption.assume}\verb|Assumption.assume: cterm -> thm| \\
- \indexdef{}{ML}{Assumption.add\_assms}\verb|Assumption.add_assms: Assumption.export ->|\isasep\isanewline%
-\verb| cterm list -> Proof.context -> thm list * Proof.context| \\
- \indexdef{}{ML}{Assumption.add\_assumes}\verb|Assumption.add_assumes: |\isasep\isanewline%
-\verb| cterm list -> Proof.context -> thm list * Proof.context| \\
- \indexdef{}{ML}{Assumption.export}\verb|Assumption.export: bool -> Proof.context -> Proof.context -> thm -> thm| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Assumption.export| represents arbitrary export
- rules, which is any function of type \verb|bool -> cterm list -> thm -> thm|,
- where the \verb|bool| indicates goal mode, and the \verb|cterm list| the collection of assumptions to be discharged
- simultaneously.
-
- \item \verb|Assumption.assume|~\isa{A} turns proposition \isa{A} into a raw assumption \isa{A\ {\isasymturnstile}\ A{\isacharprime}}, where the conclusion
- \isa{A{\isacharprime}} is in HHF normal form.
-
- \item \verb|Assumption.add_assms|~\isa{r\ As} augments the context
- by assumptions \isa{As} with export rule \isa{r}. The
- resulting facts are hypothetical theorems as produced by the raw
- \verb|Assumption.assume|.
-
- \item \verb|Assumption.add_assumes|~\isa{As} is a special case of
- \verb|Assumption.add_assms| where the export rule performs \isa{{\isasymLongrightarrow}{\isacharunderscore}intro} or \isa{{\isacharhash}{\isasymLongrightarrow}{\isacharunderscore}intro}, depending on goal mode.
-
- \item \verb|Assumption.export|~\isa{is{\isacharunderscore}goal\ inner\ outer\ thm}
- exports result \isa{thm} from the the \isa{inner} context
- back into the \isa{outer} one; \isa{is{\isacharunderscore}goal\ {\isacharequal}\ true} means
- this is a goal context. The result is in HHF normal form. Note
- that \verb|ProofContext.export| combines \verb|Variable.export|
- and \verb|Assumption.export| in the canonical way.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
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-\isadelimmlref
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-\endisadelimmlref
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-\isamarkupsection{Results \label{sec:results}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Local results are established by monotonic reasoning from facts
- within a context. This allows common combinations of theorems,
- e.g.\ via \isa{{\isasymAnd}{\isacharslash}{\isasymLongrightarrow}} elimination, resolution rules, or equational
- reasoning, see \secref{sec:thms}. Unaccounted context manipulations
- should be avoided, notably raw \isa{{\isasymAnd}{\isacharslash}{\isasymLongrightarrow}} introduction or ad-hoc
- references to free variables or assumptions not present in the proof
- context.
-
- \medskip The \isa{SUBPROOF} combinator allows to structure a
- tactical proof recursively by decomposing a selected sub-goal:
- \isa{{\isacharparenleft}{\isasymAnd}x{\isachardot}\ A{\isacharparenleft}x{\isacharparenright}\ {\isasymLongrightarrow}\ B{\isacharparenleft}x{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}} is turned into \isa{B{\isacharparenleft}x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}}
- after fixing \isa{x} and assuming \isa{A{\isacharparenleft}x{\isacharparenright}}. This means
- the tactic needs to solve the conclusion, but may use the premise as
- a local fact, for locally fixed variables.
-
- The \isa{prove} operation provides an interface for structured
- backwards reasoning under program control, with some explicit sanity
- checks of the result. The goal context can be augmented by
- additional fixed variables (cf.\ \secref{sec:variables}) and
- assumptions (cf.\ \secref{sec:assumptions}), which will be available
- as local facts during the proof and discharged into implications in
- the result. Type and term variables are generalized as usual,
- according to the context.
-
- The \isa{obtain} operation produces results by eliminating
- existing facts by means of a given tactic. This acts like a dual
- conclusion: the proof demonstrates that the context may be augmented
- by certain fixed variables and assumptions. See also
- \cite{isabelle-isar-ref} for the user-level \isa{{\isasymOBTAIN}} and
- \isa{{\isasymGUESS}} elements. Final results, which may not refer to
- the parameters in the conclusion, need to exported explicitly into
- the original context.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isadelimmlref
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-\endisadelimmlref
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-\isatagmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{SUBPROOF}\verb|SUBPROOF: ({context: Proof.context, schematics: ctyp list * cterm list,|\isasep\isanewline%
-\verb| params: cterm list, asms: cterm list, concl: cterm,|\isasep\isanewline%
-\verb| prems: thm list} -> tactic) -> Proof.context -> int -> tactic| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML}{Goal.prove}\verb|Goal.prove: Proof.context -> string list -> term list -> term ->|\isasep\isanewline%
-\verb| ({prems: thm list, context: Proof.context} -> tactic) -> thm| \\
- \indexdef{}{ML}{Goal.prove\_multi}\verb|Goal.prove_multi: Proof.context -> string list -> term list -> term list ->|\isasep\isanewline%
-\verb| ({prems: thm list, context: Proof.context} -> tactic) -> thm list| \\
- \end{mldecls}
- \begin{mldecls}
- \indexdef{}{ML}{Obtain.result}\verb|Obtain.result: (Proof.context -> tactic) ->|\isasep\isanewline%
-\verb| thm list -> Proof.context -> (cterm list * thm list) * Proof.context| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|SUBPROOF|~\isa{tac\ ctxt\ i} decomposes the structure
- of the specified sub-goal, producing an extended context and a
- reduced goal, which needs to be solved by the given tactic. All
- schematic parameters of the goal are imported into the context as
- fixed ones, which may not be instantiated in the sub-proof.
-
- \item \verb|Goal.prove|~\isa{ctxt\ xs\ As\ C\ tac} states goal \isa{C} in the context augmented by fixed variables \isa{xs} and
- assumptions \isa{As}, and applies tactic \isa{tac} to solve
- it. The latter may depend on the local assumptions being presented
- as facts. The result is in HHF normal form.
-
- \item \verb|Goal.prove_multi| is simular to \verb|Goal.prove|, but
- states several conclusions simultaneously. The goal is encoded by
- means of Pure conjunction; \verb|Goal.conjunction_tac| will turn this
- into a collection of individual subgoals.
-
- \item \verb|Obtain.result|~\isa{tac\ thms\ ctxt} eliminates the
- given facts using a tactic, which results in additional fixed
- variables and assumptions in the context. Final results need to be
- exported explicitly.
-
- \end{description}%
-\end{isamarkuptext}%
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-\isanewline
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:
--- a/doc-src/IsarImplementation/Thy/document/Tactic.tex Wed Mar 04 10:52:47 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,497 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Tactic}%
-%
-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
-\isacommand{theory}\isamarkupfalse%
-\ Tactic\isanewline
-\isakeyword{imports}\ Base\isanewline
-\isakeyword{begin}%
-\endisatagtheory
-{\isafoldtheory}%
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-\isadelimtheory
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-\endisadelimtheory
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-\isamarkupchapter{Tactical reasoning%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Tactical reasoning works by refining the initial claim in a
- backwards fashion, until a solved form is reached. A \isa{goal}
- consists of several subgoals that need to be solved in order to
- achieve the main statement; zero subgoals means that the proof may
- be finished. A \isa{tactic} is a refinement operation that maps
- a goal to a lazy sequence of potential successors. A \isa{tactical} is a combinator for composing tactics.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Goals \label{sec:tactical-goals}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Isabelle/Pure represents a goal as a theorem stating that the
- subgoals imply the main goal: \isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C}. The outermost goal structure is that of a Horn Clause: i.e.\
- an iterated implication without any quantifiers\footnote{Recall that
- outermost \isa{{\isasymAnd}x{\isachardot}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}} is always represented via schematic
- variables in the body: \isa{{\isasymphi}{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}. These variables may get
- instantiated during the course of reasoning.}. For \isa{n\ {\isacharequal}\ {\isadigit{0}}}
- a goal is called ``solved''.
-
- The structure of each subgoal \isa{A\isactrlsub i} is that of a
- general Hereditary Harrop Formula \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymAnd}x\isactrlsub k{\isachardot}\ H\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ H\isactrlsub m\ {\isasymLongrightarrow}\ B}. Here \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub k} are goal parameters, i.e.\
- arbitrary-but-fixed entities of certain types, and \isa{H\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ H\isactrlsub m} are goal hypotheses, i.e.\ facts that may
- be assumed locally. Together, this forms the goal context of the
- conclusion \isa{B} to be established. The goal hypotheses may be
- again arbitrary Hereditary Harrop Formulas, although the level of
- nesting rarely exceeds 1--2 in practice.
-
- The main conclusion \isa{C} is internally marked as a protected
- proposition, which is represented explicitly by the notation \isa{{\isacharhash}C}. This ensures that the decomposition into subgoals and main
- conclusion is well-defined for arbitrarily structured claims.
-
- \medskip Basic goal management is performed via the following
- Isabelle/Pure rules:
-
- \[
- \infer[\isa{{\isacharparenleft}init{\isacharparenright}}]{\isa{C\ {\isasymLongrightarrow}\ {\isacharhash}C}}{} \qquad
- \infer[\isa{{\isacharparenleft}finish{\isacharparenright}}]{\isa{C}}{\isa{{\isacharhash}C}}
- \]
-
- \medskip The following low-level variants admit general reasoning
- with protected propositions:
-
- \[
- \infer[\isa{{\isacharparenleft}protect{\isacharparenright}}]{\isa{{\isacharhash}C}}{\isa{C}} \qquad
- \infer[\isa{{\isacharparenleft}conclude{\isacharparenright}}]{\isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C}}{\isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ A\isactrlsub n\ {\isasymLongrightarrow}\ {\isacharhash}C}}
- \]%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
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-\endisadelimmlref
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-\isatagmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{Goal.init}\verb|Goal.init: cterm -> thm| \\
- \indexdef{}{ML}{Goal.finish}\verb|Goal.finish: thm -> thm| \\
- \indexdef{}{ML}{Goal.protect}\verb|Goal.protect: thm -> thm| \\
- \indexdef{}{ML}{Goal.conclude}\verb|Goal.conclude: thm -> thm| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|Goal.init|~\isa{C} initializes a tactical goal from
- the well-formed proposition \isa{C}.
-
- \item \verb|Goal.finish|~\isa{thm} checks whether theorem
- \isa{thm} is a solved goal (no subgoals), and concludes the
- result by removing the goal protection.
-
- \item \verb|Goal.protect|~\isa{thm} protects the full statement
- of theorem \isa{thm}.
-
- \item \verb|Goal.conclude|~\isa{thm} removes the goal
- protection, even if there are pending subgoals.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
-{\isafoldmlref}%
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-\isadelimmlref
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-\endisadelimmlref
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-\isamarkupsection{Tactics%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-A \isa{tactic} is a function \isa{goal\ {\isasymrightarrow}\ goal\isactrlsup {\isacharasterisk}\isactrlsup {\isacharasterisk}} that
- maps a given goal state (represented as a theorem, cf.\
- \secref{sec:tactical-goals}) to a lazy sequence of potential
- successor states. The underlying sequence implementation is lazy
- both in head and tail, and is purely functional in \emph{not}
- supporting memoing.\footnote{The lack of memoing and the strict
- nature of SML requires some care when working with low-level
- sequence operations, to avoid duplicate or premature evaluation of
- results.}
-
- An \emph{empty result sequence} means that the tactic has failed: in
- a compound tactic expressions other tactics might be tried instead,
- or the whole refinement step might fail outright, producing a
- toplevel error message. When implementing tactics from scratch, one
- should take care to observe the basic protocol of mapping regular
- error conditions to an empty result; only serious faults should
- emerge as exceptions.
-
- By enumerating \emph{multiple results}, a tactic can easily express
- the potential outcome of an internal search process. There are also
- combinators for building proof tools that involve search
- systematically, see also \secref{sec:tacticals}.
-
- \medskip As explained in \secref{sec:tactical-goals}, a goal state
- essentially consists of a list of subgoals that imply the main goal
- (conclusion). Tactics may operate on all subgoals or on a
- particularly specified subgoal, but must not change the main
- conclusion (apart from instantiating schematic goal variables).
-
- Tactics with explicit \emph{subgoal addressing} are of the form
- \isa{int\ {\isasymrightarrow}\ tactic} and may be applied to a particular subgoal
- (counting from 1). If the subgoal number is out of range, the
- tactic should fail with an empty result sequence, but must not raise
- an exception!
-
- Operating on a particular subgoal means to replace it by an interval
- of zero or more subgoals in the same place; other subgoals must not
- be affected, apart from instantiating schematic variables ranging
- over the whole goal state.
-
- A common pattern of composing tactics with subgoal addressing is to
- try the first one, and then the second one only if the subgoal has
- not been solved yet. Special care is required here to avoid bumping
- into unrelated subgoals that happen to come after the original
- subgoal. Assuming that there is only a single initial subgoal is a
- very common error when implementing tactics!
-
- Tactics with internal subgoal addressing should expose the subgoal
- index as \isa{int} argument in full generality; a hardwired
- subgoal 1 inappropriate.
-
- \medskip The main well-formedness conditions for proper tactics are
- summarized as follows.
-
- \begin{itemize}
-
- \item General tactic failure is indicated by an empty result, only
- serious faults may produce an exception.
-
- \item The main conclusion must not be changed, apart from
- instantiating schematic variables.
-
- \item A tactic operates either uniformly on all subgoals, or
- specifically on a selected subgoal (without bumping into unrelated
- subgoals).
-
- \item Range errors in subgoal addressing produce an empty result.
-
- \end{itemize}
-
- Some of these conditions are checked by higher-level goal
- infrastructure (\secref{sec:results}); others are not checked
- explicitly, and violating them merely results in ill-behaved tactics
- experienced by the user (e.g.\ tactics that insist in being
- applicable only to singleton goals, or disallow composition with
- basic tacticals).%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isadelimmlref
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-\endisadelimmlref
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-\isatagmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML type}{tactic}\verb|type tactic = thm -> thm Seq.seq| \\
- \indexdef{}{ML}{no\_tac}\verb|no_tac: tactic| \\
- \indexdef{}{ML}{all\_tac}\verb|all_tac: tactic| \\
- \indexdef{}{ML}{print\_tac}\verb|print_tac: string -> tactic| \\[1ex]
- \indexdef{}{ML}{PRIMITIVE}\verb|PRIMITIVE: (thm -> thm) -> tactic| \\[1ex]
- \indexdef{}{ML}{SUBGOAL}\verb|SUBGOAL: (term * int -> tactic) -> int -> tactic| \\
- \indexdef{}{ML}{CSUBGOAL}\verb|CSUBGOAL: (cterm * int -> tactic) -> int -> tactic| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|tactic| represents tactics. The well-formedness
- conditions described above need to be observed. See also \hyperlink{file.~~/src/Pure/General/seq.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}seq{\isachardot}ML}}}} for the underlying implementation of
- lazy sequences.
-
- \item \verb|int -> tactic| represents tactics with explicit
- subgoal addressing, with well-formedness conditions as described
- above.
-
- \item \verb|no_tac| is a tactic that always fails, returning the
- empty sequence.
-
- \item \verb|all_tac| is a tactic that always succeeds, returning a
- singleton sequence with unchanged goal state.
-
- \item \verb|print_tac|~\isa{message} is like \verb|all_tac|, but
- prints a message together with the goal state on the tracing
- channel.
-
- \item \verb|PRIMITIVE|~\isa{rule} turns a primitive inference rule
- into a tactic with unique result. Exception \verb|THM| is considered
- a regular tactic failure and produces an empty result; other
- exceptions are passed through.
-
- \item \verb|SUBGOAL|~\isa{{\isacharparenleft}fn\ {\isacharparenleft}subgoal{\isacharcomma}\ i{\isacharparenright}\ {\isacharequal}{\isachargreater}\ tactic{\isacharparenright}} is the
- most basic form to produce a tactic with subgoal addressing. The
- given abstraction over the subgoal term and subgoal number allows to
- peek at the relevant information of the full goal state. The
- subgoal range is checked as required above.
-
- \item \verb|CSUBGOAL| is similar to \verb|SUBGOAL|, but passes the
- subgoal as \verb|cterm| instead of raw \verb|term|. This
- avoids expensive re-certification in situations where the subgoal is
- used directly for primitive inferences.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
-{\isafoldmlref}%
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-\isadelimmlref
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-\endisadelimmlref
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-\isamarkupsubsection{Resolution and assumption tactics \label{sec:resolve-assume-tac}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-\emph{Resolution} is the most basic mechanism for refining a
- subgoal using a theorem as object-level rule.
- \emph{Elim-resolution} is particularly suited for elimination rules:
- it resolves with a rule, proves its first premise by assumption, and
- finally deletes that assumption from any new subgoals.
- \emph{Destruct-resolution} is like elim-resolution, but the given
- destruction rules are first turned into canonical elimination
- format. \emph{Forward-resolution} is like destruct-resolution, but
- without deleting the selected assumption. The \isa{r{\isacharslash}e{\isacharslash}d{\isacharslash}f}
- naming convention is maintained for several different kinds of
- resolution rules and tactics.
-
- Assumption tactics close a subgoal by unifying some of its premises
- against its conclusion.
-
- \medskip All the tactics in this section operate on a subgoal
- designated by a positive integer. Other subgoals might be affected
- indirectly, due to instantiation of schematic variables.
-
- There are various sources of non-determinism, the tactic result
- sequence enumerates all possibilities of the following choices (if
- applicable):
-
- \begin{enumerate}
-
- \item selecting one of the rules given as argument to the tactic;
-
- \item selecting a subgoal premise to eliminate, unifying it against
- the first premise of the rule;
-
- \item unifying the conclusion of the subgoal to the conclusion of
- the rule.
-
- \end{enumerate}
-
- Recall that higher-order unification may produce multiple results
- that are enumerated here.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isadelimmlref
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-\endisadelimmlref
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-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{resolve\_tac}\verb|resolve_tac: thm list -> int -> tactic| \\
- \indexdef{}{ML}{eresolve\_tac}\verb|eresolve_tac: thm list -> int -> tactic| \\
- \indexdef{}{ML}{dresolve\_tac}\verb|dresolve_tac: thm list -> int -> tactic| \\
- \indexdef{}{ML}{forward\_tac}\verb|forward_tac: thm list -> int -> tactic| \\[1ex]
- \indexdef{}{ML}{assume\_tac}\verb|assume_tac: int -> tactic| \\
- \indexdef{}{ML}{eq\_assume\_tac}\verb|eq_assume_tac: int -> tactic| \\[1ex]
- \indexdef{}{ML}{match\_tac}\verb|match_tac: thm list -> int -> tactic| \\
- \indexdef{}{ML}{ematch\_tac}\verb|ematch_tac: thm list -> int -> tactic| \\
- \indexdef{}{ML}{dmatch\_tac}\verb|dmatch_tac: thm list -> int -> tactic| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|resolve_tac|~\isa{thms\ i} refines the goal state
- using the given theorems, which should normally be introduction
- rules. The tactic resolves a rule's conclusion with subgoal \isa{i}, replacing it by the corresponding versions of the rule's
- premises.
-
- \item \verb|eresolve_tac|~\isa{thms\ i} performs elim-resolution
- with the given theorems, which should normally be elimination rules.
-
- \item \verb|dresolve_tac|~\isa{thms\ i} performs
- destruct-resolution with the given theorems, which should normally
- be destruction rules. This replaces an assumption by the result of
- applying one of the rules.
-
- \item \verb|forward_tac| is like \verb|dresolve_tac| except that the
- selected assumption is not deleted. It applies a rule to an
- assumption, adding the result as a new assumption.
-
- \item \verb|assume_tac|~\isa{i} attempts to solve subgoal \isa{i}
- by assumption (modulo higher-order unification).
-
- \item \verb|eq_assume_tac| is similar to \verb|assume_tac|, but checks
- only for immediate \isa{{\isasymalpha}}-convertibility instead of using
- unification. It succeeds (with a unique next state) if one of the
- assumptions is equal to the subgoal's conclusion. Since it does not
- instantiate variables, it cannot make other subgoals unprovable.
-
- \item \verb|match_tac|, \verb|ematch_tac|, and \verb|dmatch_tac| are
- similar to \verb|resolve_tac|, \verb|eresolve_tac|, and \verb|dresolve_tac|, respectively, but do not instantiate schematic
- variables in the goal state.
-
- Flexible subgoals are not updated at will, but are left alone.
- Strictly speaking, matching means to treat the unknowns in the goal
- state as constants; these tactics merely discard unifiers that would
- update the goal state.
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\endisatagmlref
-{\isafoldmlref}%
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-\isadelimmlref
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-\endisadelimmlref
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-\isamarkupsubsection{Explicit instantiation within a subgoal context%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The main resolution tactics (\secref{sec:resolve-assume-tac})
- use higher-order unification, which works well in many practical
- situations despite its daunting theoretical properties.
- Nonetheless, there are important problem classes where unguided
- higher-order unification is not so useful. This typically involves
- rules like universal elimination, existential introduction, or
- equational substitution. Here the unification problem involves
- fully flexible \isa{{\isacharquery}P\ {\isacharquery}x} schemes, which are hard to manage
- without further hints.
-
- By providing a (small) rigid term for \isa{{\isacharquery}x} explicitly, the
- remaining unification problem is to assign a (large) term to \isa{{\isacharquery}P}, according to the shape of the given subgoal. This is
- sufficiently well-behaved in most practical situations.
-
- \medskip Isabelle provides separate versions of the standard \isa{r{\isacharslash}e{\isacharslash}d{\isacharslash}f} resolution tactics that allow to provide explicit
- instantiations of unknowns of the given rule, wrt.\ terms that refer
- to the implicit context of the selected subgoal.
-
- An instantiation consists of a list of pairs of the form \isa{{\isacharparenleft}{\isacharquery}x{\isacharcomma}\ t{\isacharparenright}}, where \isa{{\isacharquery}x} is a schematic variable occurring in
- the given rule, and \isa{t} is a term from the current proof
- context, augmented by the local goal parameters of the selected
- subgoal; cf.\ the \isa{focus} operation described in
- \secref{sec:variables}.
-
- Entering the syntactic context of a subgoal is a brittle operation,
- because its exact form is somewhat accidental, and the choice of
- bound variable names depends on the presence of other local and
- global names. Explicit renaming of subgoal parameters prior to
- explicit instantiation might help to achieve a bit more robustness.
-
- Type instantiations may be given as well, via pairs like \isa{{\isacharparenleft}{\isacharquery}{\isacharprime}a{\isacharcomma}\ {\isasymtau}{\isacharparenright}}. Type instantiations are distinguished from term
- instantiations by the syntactic form of the schematic variable.
- Types are instantiated before terms are. Since term instantiation
- already performs type-inference as expected, explicit type
- instantiations are seldom necessary.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
- \indexdef{}{ML}{res\_inst\_tac}\verb|res_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic| \\
- \indexdef{}{ML}{eres\_inst\_tac}\verb|eres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic| \\
- \indexdef{}{ML}{dres\_inst\_tac}\verb|dres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic| \\
- \indexdef{}{ML}{forw\_inst\_tac}\verb|forw_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic| \\[1ex]
- \indexdef{}{ML}{rename\_tac}\verb|rename_tac: string list -> int -> tactic| \\
- \end{mldecls}
-
- \begin{description}
-
- \item \verb|res_inst_tac|~\isa{ctxt\ insts\ thm\ i} instantiates the
- rule \isa{thm} with the instantiations \isa{insts}, as described
- above, and then performs resolution on subgoal \isa{i}.
-
- \item \verb|eres_inst_tac| is like \verb|res_inst_tac|, but performs
- elim-resolution.
-
- \item \verb|dres_inst_tac| is like \verb|res_inst_tac|, but performs
- destruct-resolution.
-
- \item \verb|forw_inst_tac| is like \verb|dres_inst_tac| except that
- the selected assumption is not deleted.
-
- \item \verb|rename_tac|~\isa{names\ i} renames the innermost
- parameters of subgoal \isa{i} according to the provided \isa{names} (which need to be distinct indentifiers).
-
- \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsection{Tacticals \label{sec:tacticals}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-A \emph{tactical} is a functional combinator for building up complex
- tactics from simpler ones. Typical tactical perform sequential
- composition, disjunction (choice), iteration, or goal addressing.
- Various search strategies may be expressed via tacticals.
-
- \medskip FIXME%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\isatagtheory
-\isacommand{end}\isamarkupfalse%
-%
-\endisatagtheory
-{\isafoldtheory}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-\isanewline
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:
--- a/src/HOL/Bali/Basis.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/Basis.thy Wed Mar 04 11:37:50 2009 +0100
@@ -251,8 +251,8 @@
Oex :: "[pttrn, 'a option, bool] => bool" ("(3\<exists>_\<in>_:/ _)" [0,0,10] 10)
translations
- "! x:A: P" == "! x:o2s A. P"
- "? x:A: P" == "? x:o2s A. P"
+ "! x:A: P" == "! x:CONST Option.set A. P"
+ "? x:A: P" == "? x:CONST Option.set A. P"
section "Special map update"
--- a/src/HOL/Bali/Conform.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/Conform.thy Wed Mar 04 11:37:50 2009 +0100
@@ -102,7 +102,7 @@
constdefs
conf :: "prog \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ty \<Rightarrow> bool" ("_,_\<turnstile>_\<Colon>\<preceq>_" [71,71,71,71] 70)
- "G,s\<turnstile>v\<Colon>\<preceq>T \<equiv> \<exists>T'\<in>typeof (\<lambda>a. option_map obj_ty (heap s a)) v:G\<turnstile>T'\<preceq>T"
+ "G,s\<turnstile>v\<Colon>\<preceq>T \<equiv> \<exists>T'\<in>typeof (\<lambda>a. Option.map obj_ty (heap s a)) v:G\<turnstile>T'\<preceq>T"
lemma conf_cong [simp]: "G,set_locals l s\<turnstile>v\<Colon>\<preceq>T = G,s\<turnstile>v\<Colon>\<preceq>T"
by (auto simp: conf_def)
--- a/src/HOL/Bali/Decl.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/Decl.thy Wed Mar 04 11:37:50 2009 +0100
@@ -801,7 +801,7 @@
"imethds G I
\<equiv> iface_rec (G,I)
(\<lambda>I i ts. (Un_tables ts) \<oplus>\<oplus>
- (o2s \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
+ (Option.set \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
--- a/src/HOL/Bali/DeclConcepts.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/DeclConcepts.thy Wed Mar 04 11:37:50 2009 +0100
@@ -1385,7 +1385,7 @@
"imethds G I
\<equiv> iface_rec (G,I)
(\<lambda>I i ts. (Un_tables ts) \<oplus>\<oplus>
- (o2s \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
+ (Option.set \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
text {* methods of an interface, with overriding and inheritance, cf. 9.2 *}
constdefs
@@ -1528,7 +1528,7 @@
lemma imethds_rec: "\<lbrakk>iface G I = Some i; ws_prog G\<rbrakk> \<Longrightarrow>
imethds G I = Un_tables ((\<lambda>J. imethds G J)`set (isuperIfs i)) \<oplus>\<oplus>
- (o2s \<circ> table_of (map (\<lambda>(s,mh). (s,I,mh)) (imethods i)))"
+ (Option.set \<circ> table_of (map (\<lambda>(s,mh). (s,I,mh)) (imethods i)))"
apply (unfold imethds_def)
apply (rule iface_rec [THEN trans])
apply auto
--- a/src/HOL/Bali/Example.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/Example.thy Wed Mar 04 11:37:50 2009 +0100
@@ -458,7 +458,7 @@
lemmas methd_rec' = methd_rec [OF _ ws_tprg]
lemma imethds_HasFoo [simp]:
- "imethds tprg HasFoo = o2s \<circ> empty(foo_sig\<mapsto>(HasFoo, foo_mhead))"
+ "imethds tprg HasFoo = Option.set \<circ> empty(foo_sig\<mapsto>(HasFoo, foo_mhead))"
apply (rule trans)
apply (rule imethds_rec')
apply (auto simp add: HasFooInt_def)
--- a/src/HOL/Bali/State.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/State.thy Wed Mar 04 11:37:50 2009 +0100
@@ -146,7 +146,7 @@
fields_table::
"prog \<Rightarrow> qtname \<Rightarrow> (fspec \<Rightarrow> field \<Rightarrow> bool) \<Rightarrow> (fspec, ty) table"
"fields_table G C P
- \<equiv> option_map type \<circ> table_of (filter (split P) (DeclConcepts.fields G C))"
+ \<equiv> Option.map type \<circ> table_of (filter (split P) (DeclConcepts.fields G C))"
lemma fields_table_SomeI:
"\<lbrakk>table_of (DeclConcepts.fields G C) n = Some f; P n f\<rbrakk>
@@ -258,8 +258,8 @@
lookup_obj :: "st \<Rightarrow> val \<Rightarrow> obj"
translations
- "val_this s" == "the (locals s This)"
- "lookup_obj s a'" == "the (heap s (the_Addr a'))"
+ "val_this s" == "CONST the (locals s This)"
+ "lookup_obj s a'" == "CONST the (heap s (the_Addr a'))"
subsection "memory allocation"
@@ -290,7 +290,7 @@
init_vals :: "('a, ty) table \<Rightarrow> ('a, val) table"
translations
- "init_vals vs" == "CONST option_map default_val \<circ> vs"
+ "init_vals vs" == "CONST Option.map default_val \<circ> vs"
lemma init_arr_comps_base [simp]: "init_vals (arr_comps T 0) = empty"
apply (unfold arr_comps_def in_bounds_def)
@@ -315,12 +315,12 @@
lupd :: "lname \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st" ("lupd'(_\<mapsto>_')"[10,10]1000)
"lupd vn v \<equiv> st_case (\<lambda>g l. st g (l(vn\<mapsto>v)))"
- upd_gobj :: "oref \<Rightarrow> vn \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st"
+ upd_gobj :: "oref \<Rightarrow> vn \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st"
"upd_gobj r n v \<equiv> st_case (\<lambda>g l. st (chg_map (upd_obj n v) r g) l)"
set_locals :: "locals \<Rightarrow> st \<Rightarrow> st"
"set_locals l \<equiv> st_case (\<lambda>g l'. st g l)"
-
+
init_obj :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> st \<Rightarrow> st"
"init_obj G oi r \<equiv> gupd(r\<mapsto>\<lparr>tag=oi, values=init_vals (var_tys G oi r)\<rparr>)"
--- a/src/HOL/Bali/Table.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/Table.thy Wed Mar 04 11:37:50 2009 +0100
@@ -194,7 +194,7 @@
done
lemma Ball_set_tableD:
- "\<lbrakk>(\<forall> (x,y)\<in> set l. P x y); x \<in> o2s (table_of l xa)\<rbrakk> \<Longrightarrow> P xa x"
+ "\<lbrakk>(\<forall> (x,y)\<in> set l. P x y); x \<in> Option.set (table_of l xa)\<rbrakk> \<Longrightarrow> P xa x"
apply (frule Ball_set_table)
by auto
--- a/src/HOL/Bali/WellForm.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/WellForm.thy Wed Mar 04 11:37:50 2009 +0100
@@ -236,7 +236,7 @@
under (\<lambda> new old. accmodi old \<noteq> Private)
entails (\<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old \<and>
is_static new = is_static old)) \<and>
- (o2s \<circ> table_of (imethods i)
+ (Option.set \<circ> table_of (imethods i)
hidings Un_tables((\<lambda>J.(imethds G J))`set (isuperIfs i))
entails (\<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old))"
@@ -248,7 +248,7 @@
lemma wf_idecl_hidings:
"wf_idecl G (I, i) \<Longrightarrow>
- (\<lambda>s. o2s (table_of (imethods i) s))
+ (\<lambda>s. Option.set (table_of (imethods i) s))
hidings Un_tables ((\<lambda>J. imethds G J) ` set (isuperIfs i))
entails \<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old"
apply (unfold wf_idecl_def o_def)
@@ -751,7 +751,7 @@
show "\<not>is_static im \<and> accmodi im = Public"
proof -
let ?inherited = "Un_tables (imethds G ` set (isuperIfs i))"
- let ?new = "(o2s \<circ> table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)))"
+ let ?new = "(Option.set \<circ> table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)))"
from if_I wf im have imethds:"im \<in> (?inherited \<oplus>\<oplus> ?new) sig"
by (simp add: imethds_rec)
from wf if_I have
@@ -1783,7 +1783,7 @@
by (blast dest: subint1D)
let ?newMethods
- = "(o2s \<circ> table_of (map (\<lambda>(sig, mh). (sig, I, mh)) (imethods i)))"
+ = "(Option.set \<circ> table_of (map (\<lambda>(sig, mh). (sig, I, mh)) (imethods i)))"
show "?Concl I"
proof (cases "?newMethods sig = {}")
case True
@@ -1864,7 +1864,7 @@
apply (drule (1) wf_prog_idecl)
apply (frule (3) imethds_wf_mhead [OF _ _ wf_idecl_supD [THEN conjunct1
[THEN is_acc_ifaceD [THEN conjunct1]]]])
-apply (case_tac "(o2s \<circ> table_of (map (\<lambda>(s, mh). (s, y, mh)) (imethods i)))
+apply (case_tac "(Option.set \<circ> table_of (map (\<lambda>(s, mh). (s, y, mh)) (imethods i)))
sig ={}")
apply force
--- a/src/HOL/Bali/WellType.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Bali/WellType.thy Wed Mar 04 11:37:50 2009 +0100
@@ -87,11 +87,11 @@
defs
cmheads_def:
"cmheads G S C
- \<equiv> \<lambda>sig. (\<lambda>(Cls,mthd). (ClassT Cls,(mhead mthd))) ` o2s (accmethd G S C sig)"
+ \<equiv> \<lambda>sig. (\<lambda>(Cls,mthd). (ClassT Cls,(mhead mthd))) ` Option.set (accmethd G S C sig)"
Objectmheads_def:
"Objectmheads G S
\<equiv> \<lambda>sig. (\<lambda>(Cls,mthd). (ClassT Cls,(mhead mthd)))
- ` o2s (filter_tab (\<lambda>sig m. accmodi m \<noteq> Private) (accmethd G S Object) sig)"
+ ` Option.set (filter_tab (\<lambda>sig m. accmodi m \<noteq> Private) (accmethd G S Object) sig)"
accObjectmheads_def:
"accObjectmheads G S T
\<equiv> if G\<turnstile>RefT T accessible_in (pid S)
--- a/src/HOL/Datatype.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Datatype.thy Wed Mar 04 11:37:50 2009 +0100
@@ -576,122 +576,4 @@
hide (open) const Suml Sumr Projl Projr
-
-subsection {* The option datatype *}
-
-datatype 'a option = None | Some 'a
-
-lemma not_None_eq [iff]: "(x ~= None) = (EX y. x = Some y)"
- by (induct x) auto
-
-lemma not_Some_eq [iff]: "(ALL y. x ~= Some y) = (x = None)"
- by (induct x) auto
-
-text{*Although it may appear that both of these equalities are helpful
-only when applied to assumptions, in practice it seems better to give
-them the uniform iff attribute. *}
-
-lemma option_caseE:
- assumes c: "(case x of None => P | Some y => Q y)"
- obtains
- (None) "x = None" and P
- | (Some) y where "x = Some y" and "Q y"
- using c by (cases x) simp_all
-
-lemma insert_None_conv_UNIV: "insert None (range Some) = UNIV"
- by (rule set_ext, case_tac x) auto
-
-lemma inj_Some [simp]: "inj_on Some A"
- by (rule inj_onI) simp
-
-
-subsubsection {* Operations *}
-
-consts
- the :: "'a option => 'a"
-primrec
- "the (Some x) = x"
-
-consts
- o2s :: "'a option => 'a set"
-primrec
- "o2s None = {}"
- "o2s (Some x) = {x}"
-
-lemma ospec [dest]: "(ALL x:o2s A. P x) ==> A = Some x ==> P x"
- by simp
-
-declaration {* fn _ =>
- Classical.map_cs (fn cs => cs addSD2 ("ospec", thm "ospec"))
-*}
-
-lemma elem_o2s [iff]: "(x : o2s xo) = (xo = Some x)"
- by (cases xo) auto
-
-lemma o2s_empty_eq [simp]: "(o2s xo = {}) = (xo = None)"
- by (cases xo) auto
-
-definition
- option_map :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a option \<Rightarrow> 'b option"
-where
- [code del]: "option_map = (%f y. case y of None => None | Some x => Some (f x))"
-
-lemma option_map_None [simp, code]: "option_map f None = None"
- by (simp add: option_map_def)
-
-lemma option_map_Some [simp, code]: "option_map f (Some x) = Some (f x)"
- by (simp add: option_map_def)
-
-lemma option_map_is_None [iff]:
- "(option_map f opt = None) = (opt = None)"
- by (simp add: option_map_def split add: option.split)
-
-lemma option_map_eq_Some [iff]:
- "(option_map f xo = Some y) = (EX z. xo = Some z & f z = y)"
- by (simp add: option_map_def split add: option.split)
-
-lemma option_map_comp:
- "option_map f (option_map g opt) = option_map (f o g) opt"
- by (simp add: option_map_def split add: option.split)
-
-lemma option_map_o_sum_case [simp]:
- "option_map f o sum_case g h = sum_case (option_map f o g) (option_map f o h)"
- by (rule ext) (simp split: sum.split)
-
-
-subsubsection {* Code generator setup *}
-
-definition
- is_none :: "'a option \<Rightarrow> bool" where
- is_none_none [code post, symmetric, code inline]: "is_none x \<longleftrightarrow> x = None"
-
-lemma is_none_code [code]:
- shows "is_none None \<longleftrightarrow> True"
- and "is_none (Some x) \<longleftrightarrow> False"
- unfolding is_none_none [symmetric] by simp_all
-
-hide (open) const is_none
-
-code_type option
- (SML "_ option")
- (OCaml "_ option")
- (Haskell "Maybe _")
-
-code_const None and Some
- (SML "NONE" and "SOME")
- (OCaml "None" and "Some _")
- (Haskell "Nothing" and "Just")
-
-code_instance option :: eq
- (Haskell -)
-
-code_const "eq_class.eq \<Colon> 'a\<Colon>eq option \<Rightarrow> 'a option \<Rightarrow> bool"
- (Haskell infixl 4 "==")
-
-code_reserved SML
- option NONE SOME
-
-code_reserved OCaml
- option None Some
-
end
--- a/src/HOL/Extraction.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Extraction.thy Wed Mar 04 11:37:50 2009 +0100
@@ -6,7 +6,7 @@
header {* Program extraction for HOL *}
theory Extraction
-imports Datatype
+imports Option
uses "Tools/rewrite_hol_proof.ML"
begin
--- a/src/HOL/Import/Generate-HOL/GenHOL4Base.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Import/Generate-HOL/GenHOL4Base.thy Wed Mar 04 11:37:50 2009 +0100
@@ -88,14 +88,14 @@
import_theory option;
type_maps
- option > Datatype.option;
+ option > Option.option;
const_maps
- NONE > Datatype.option.None
- SOME > Datatype.option.Some
- option_case > Datatype.option.option_case
- OPTION_MAP > Datatype.option_map
- THE > Datatype.the
+ NONE > Option.option.None
+ SOME > Option.option.Some
+ option_case > Option.option.option_case
+ OPTION_MAP > Option.map
+ THE > Option.the
IS_SOME > HOL4Compat.IS_SOME
IS_NONE > HOL4Compat.IS_NONE
OPTION_JOIN > HOL4Compat.OPTION_JOIN;
--- a/src/HOL/Import/HOL4Compat.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Import/HOL4Compat.thy Wed Mar 04 11:37:50 2009 +0100
@@ -73,7 +73,7 @@
lemma option_case_def: "(!u f. option_case u f None = u) & (!u f x. option_case u f (Some x) = f x)"
by simp
-lemma OPTION_MAP_DEF: "(!f x. option_map f (Some x) = Some (f x)) & (!f. option_map f None = None)"
+lemma OPTION_MAP_DEF: "(!f x. Option.map f (Some x) = Some (f x)) & (!f. Option.map f None = None)"
by simp
consts
--- a/src/HOL/IsaMakefile Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/IsaMakefile Wed Mar 04 11:37:50 2009 +0100
@@ -127,6 +127,7 @@
Nat.thy \
OrderedGroup.thy \
Orderings.thy \
+ Option.thy \
Plain.thy \
Power.thy \
Predicate.thy \
--- a/src/HOL/Library/AssocList.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Library/AssocList.thy Wed Mar 04 11:37:50 2009 +0100
@@ -429,7 +429,7 @@
subsection {* @{const map_ran} *}
-lemma map_ran_conv: "map_of (map_ran f al) k = option_map (f k) (map_of al k)"
+lemma map_ran_conv: "map_of (map_ran f al) k = Option.map (f k) (map_of al k)"
by (induct al) auto
lemma dom_map_ran: "fst ` set (map_ran f al) = fst ` set al"
--- a/src/HOL/Library/RBT.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Library/RBT.thy Wed Mar 04 11:37:50 2009 +0100
@@ -891,7 +891,7 @@
theorem mapwk_isrbt[simp]: "isrbt (mapwithkey f t) = isrbt t"
unfolding isrbt_def by (simp add: mapwk_inv1 mapwk_inv2 mapwk_st mapwk_treec)
-theorem map_of_mapwk[simp]: "map_of (mapwithkey f t) x = option_map (f x) (map_of t x)"
+theorem map_of_mapwk[simp]: "map_of (mapwithkey f t) x = Option.map (f x) (map_of t x)"
by (induct t) auto
definition map
@@ -899,7 +899,7 @@
theorem map_keys[simp]: "keys (map f t) = keys t" unfolding map_def by simp
theorem map_isrbt[simp]: "isrbt (map f t) = isrbt t" unfolding map_def by simp
-theorem map_of_map[simp]: "map_of (map f t) = option_map f o map_of t"
+theorem map_of_map[simp]: "map_of (map f t) = Option.map f o map_of t"
by (rule ext) (simp add:map_def)
subsection {* Fold *}
--- a/src/HOL/Map.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Map.thy Wed Mar 04 11:37:50 2009 +0100
@@ -242,17 +242,17 @@
"map_of xs k = Some z \<Longrightarrow> P k z \<Longrightarrow> map_of (filter (split P) xs) k = Some z"
by (induct xs) auto
-lemma map_of_map: "map_of (map (%(a,b). (a,f b)) xs) x = option_map f (map_of xs x)"
+lemma map_of_map: "map_of (map (%(a,b). (a,f b)) xs) x = Option.map f (map_of xs x)"
by (induct xs) auto
-subsection {* @{term [source] option_map} related *}
+subsection {* @{const Option.map} related *}
-lemma option_map_o_empty [simp]: "option_map f o empty = empty"
+lemma option_map_o_empty [simp]: "Option.map f o empty = empty"
by (rule ext) simp
lemma option_map_o_map_upd [simp]:
- "option_map f o m(a|->b) = (option_map f o m)(a|->f b)"
+ "Option.map f o m(a|->b) = (Option.map f o m)(a|->f b)"
by (rule ext) simp
--- a/src/HOL/MicroJava/BV/Effect.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/BV/Effect.thy Wed Mar 04 11:37:50 2009 +0100
@@ -105,7 +105,7 @@
(xcpt_names (i,G,pc,et))"
norm_eff :: "instr \<Rightarrow> jvm_prog \<Rightarrow> state_type option \<Rightarrow> state_type option"
- "norm_eff i G == option_map (\<lambda>s. eff' (i,G,s))"
+ "norm_eff i G == Option.map (\<lambda>s. eff' (i,G,s))"
eff :: "instr \<Rightarrow> jvm_prog \<Rightarrow> p_count \<Rightarrow> exception_table \<Rightarrow> state_type option \<Rightarrow> succ_type"
"eff i G pc et s == (map (\<lambda>pc'. (pc',norm_eff i G s)) (succs i pc)) @ (xcpt_eff i G pc s et)"
--- a/src/HOL/MicroJava/BV/Opt.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/BV/Opt.thy Wed Mar 04 11:37:50 2009 +0100
@@ -286,8 +286,8 @@
lemma option_map_in_optionI:
"\<lbrakk> ox : opt S; !x:S. ox = Some x \<longrightarrow> f x : S \<rbrakk>
- \<Longrightarrow> option_map f ox : opt S";
-apply (unfold option_map_def)
+ \<Longrightarrow> Option.map f ox : opt S";
+apply (unfold Option.map_def)
apply (simp split: option.split)
apply blast
done
--- a/src/HOL/MicroJava/Comp/AuxLemmas.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/Comp/AuxLemmas.thy Wed Mar 04 11:37:50 2009 +0100
@@ -126,11 +126,11 @@
by (induct xs,auto)
lemma map_of_map2: "\<forall> x \<in> set xs. (fst (f x)) = (fst x) \<Longrightarrow>
- map_of (map f xs) a = option_map (\<lambda> b. (snd (f (a, b)))) (map_of xs a)"
+ map_of (map f xs) a = Option.map (\<lambda> b. (snd (f (a, b)))) (map_of xs a)"
by (induct xs, auto)
-lemma option_map_of [simp]: "(option_map f (map_of xs k) = None) = ((map_of xs k) = None)"
-by (simp add: option_map_def split: option.split)
+lemma option_map_of [simp]: "(Option.map f (map_of xs k) = None) = ((map_of xs k) = None)"
+by (simp add: Option.map_def split: option.split)
--- a/src/HOL/MicroJava/Comp/CorrCompTp.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/Comp/CorrCompTp.thy Wed Mar 04 11:37:50 2009 +0100
@@ -553,7 +553,7 @@
lemma match_xctable_offset: "
(match_exception_table G cn (pc + n) (offset_xctable n et)) =
- (option_map (\<lambda> pc'. pc' + n) (match_exception_table G cn pc et))"
+ (Option.map (\<lambda> pc'. pc' + n) (match_exception_table G cn pc et))"
apply (induct et)
apply (simp add: offset_xctable_def)+
apply (case_tac "match_exception_entry G cn pc a")
@@ -675,7 +675,7 @@
in app_jumps_lem)
apply (simp add: nth_append)+
(* subgoal \<exists> st. mt ! pc'' = Some st *)
- apply (simp add: norm_eff_def option_map_def nth_append)
+ apply (simp add: norm_eff_def Option.map_def nth_append)
apply (case_tac "mt ! pc''")
apply simp+
done
--- a/src/HOL/MicroJava/Comp/LemmasComp.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/Comp/LemmasComp.thy Wed Mar 04 11:37:50 2009 +0100
@@ -271,7 +271,7 @@
lemma map_of_map_fst: "\<lbrakk> inj f;
\<forall>x\<in>set xs. fst (f x) = fst x; \<forall>x\<in>set xs. fst (g x) = fst x \<rbrakk>
\<Longrightarrow> map_of (map g xs) k
- = option_map (\<lambda> e. (snd (g ((inv f) (k, e))))) (map_of (map f xs) k)"
+ = Option.map (\<lambda> e. (snd (g ((inv f) (k, e))))) (map_of (map f xs) k)"
apply (induct xs)
apply simp
apply (simp del: split_paired_All)
@@ -288,13 +288,13 @@
lemma comp_method [rule_format (no_asm)]: "\<lbrakk> ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>
((method (comp G, C) S) =
- option_map (\<lambda> (D,rT,b). (D, rT, mtd_mb (compMethod G D (S, rT, b))))
+ Option.map (\<lambda> (D,rT,b). (D, rT, mtd_mb (compMethod G D (S, rT, b))))
(method (G, C) S))"
apply (simp add: method_def)
apply (frule wf_subcls1)
apply (simp add: comp_class_rec)
apply (simp add: map_compose [THEN sym] split_iter split_compose del: map_compose)
-apply (rule_tac R="%x y. ((x S) = (option_map (\<lambda>(D, rT, b).
+apply (rule_tac R="%x y. ((x S) = (Option.map (\<lambda>(D, rT, b).
(D, rT, snd (snd (compMethod G D (S, rT, b))))) (y S)))"
in class_rec_relation)
apply assumption
--- a/src/HOL/MicroJava/J/Conform.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/J/Conform.thy Wed Mar 04 11:37:50 2009 +0100
@@ -17,7 +17,7 @@
conf :: "'c prog => aheap => val => ty => bool"
("_,_ |- _ ::<= _" [51,51,51,51] 50)
- "G,h|-v::<=T == \<exists>T'. typeof (option_map obj_ty o h) v = Some T' \<and> G\<turnstile>T'\<preceq>T"
+ "G,h|-v::<=T == \<exists>T'. typeof (Option.map obj_ty o h) v = Some T' \<and> G\<turnstile>T'\<preceq>T"
lconf :: "'c prog => aheap => ('a \<rightharpoonup> val) => ('a \<rightharpoonup> ty) => bool"
("_,_ |- _ [::<=] _" [51,51,51,51] 50)
--- a/src/HOL/MicroJava/J/Exceptions.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/J/Exceptions.thy Wed Mar 04 11:37:50 2009 +0100
@@ -21,7 +21,7 @@
cname_of :: "aheap \<Rightarrow> val \<Rightarrow> cname"
translations
- "cname_of hp v" == "fst (the (hp (the_Addr v)))"
+ "cname_of hp v" == "fst (CONST the (hp (the_Addr v)))"
constdefs
--- a/src/HOL/MicroJava/J/State.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/MicroJava/J/State.thy Wed Mar 04 11:37:50 2009 +0100
@@ -41,7 +41,7 @@
"Norm s" == "(None,s)"
"abrupt" => "fst"
"store" => "snd"
- "lookup_obj s a'" == "the (heap s (the_Addr a'))"
+ "lookup_obj s a'" == "CONST the (heap s (the_Addr a'))"
constdefs
--- a/src/HOL/NanoJava/State.thy Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/NanoJava/State.thy Wed Mar 04 11:37:50 2009 +0100
@@ -33,7 +33,7 @@
constdefs
init_vars:: "('a \<rightharpoonup> 'b) => ('a \<rightharpoonup> val)"
- "init_vars m == option_map (\<lambda>T. Null) o m"
+ "init_vars m == Option.map (\<lambda>T. Null) o m"
text {* private: *}
types heap = "loc \<rightharpoonup> obj"
--- a/src/HOL/Nominal/nominal_atoms.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Nominal/nominal_atoms.ML Wed Mar 04 11:37:50 2009 +0100
@@ -539,7 +539,7 @@
thy
|> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
|> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn)
- |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
+ |> AxClass.prove_arity ("Option.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
|> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
|> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
|> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name])
@@ -606,7 +606,7 @@
|> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name])
(fs_proof fs_thm_nprod)
|> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
- |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
+ |> AxClass.prove_arity ("Option.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
end) ak_names thy20;
(******** cp_<ak>_<ai> class instances ********)
@@ -687,7 +687,7 @@
|> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
|> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
|> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
- |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
+ |> AxClass.prove_arity ("Option.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
|> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
end) ak_names thy) ak_names thy25;
--- a/src/HOL/Nominal/nominal_inductive.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Nominal/nominal_inductive.ML Wed Mar 04 11:37:50 2009 +0100
@@ -546,7 +546,7 @@
Proof.theorem_i NONE (fn thss => fn ctxt =>
let
val rec_name = space_implode "_" (map Sign.base_name names);
- val rec_qualified = Binding.qualify rec_name;
+ val rec_qualified = Binding.qualify false rec_name;
val ind_case_names = RuleCases.case_names induct_cases;
val induct_cases' = InductivePackage.partition_rules' raw_induct
(intrs ~~ induct_cases);
--- a/src/HOL/Nominal/nominal_inductive2.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Nominal/nominal_inductive2.ML Wed Mar 04 11:37:50 2009 +0100
@@ -453,7 +453,7 @@
Proof.theorem_i NONE (fn thss => fn ctxt =>
let
val rec_name = space_implode "_" (map Sign.base_name names);
- val rec_qualified = Binding.qualify rec_name;
+ val rec_qualified = Binding.qualify false rec_name;
val ind_case_names = RuleCases.case_names induct_cases;
val induct_cases' = InductivePackage.partition_rules' raw_induct
(intrs ~~ induct_cases);
--- a/src/HOL/Nominal/nominal_primrec.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Nominal/nominal_primrec.ML Wed Mar 04 11:37:50 2009 +0100
@@ -210,7 +210,7 @@
val def_name = Thm.def_name (Sign.base_name fname);
val rhs = singleton (Syntax.check_terms ctxt) raw_rhs;
val SOME var = get_first (fn ((b, _), mx) =>
- if Binding.base_name b = fname then SOME (b, mx) else NONE) fixes;
+ if Binding.name_of b = fname then SOME (b, mx) else NONE) fixes;
in
((var, ((Binding.name def_name, []), rhs)),
subst_bounds (rev (map Free frees), strip_abs_body rhs))
@@ -248,7 +248,7 @@
val (names_atts, spec') = split_list spec;
val eqns' = map unquantify spec'
val eqns = fold_rev (process_eqn lthy (fn v => Variable.is_fixed lthy v
- orelse exists (fn ((w, _), _) => v = Binding.base_name w) fixes)) spec' [];
+ orelse exists (fn ((w, _), _) => v = Binding.name_of w) fixes)) spec' [];
val dt_info = NominalPackage.get_nominal_datatypes (ProofContext.theory_of lthy);
val lsrs :: lsrss = maps (fn (_, (_, _, eqns)) =>
map (fn (_, (ls, _, rs, _, _)) => ls @ rs) eqns) eqns
@@ -285,7 +285,7 @@
set_group ? LocalTheory.set_group (serial_string ()) |>
fold_map (apfst (snd o snd) oo
LocalTheory.define Thm.definitionK o fst) defs';
- val qualify = Binding.qualify
+ val qualify = Binding.qualify false
(space_implode "_" (map (Sign.base_name o #1) defs));
val names_atts' = map (apfst qualify) names_atts;
val cert = cterm_of (ProofContext.theory_of lthy');
--- a/src/HOL/Tools/function_package/fundef_common.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/function_package/fundef_common.ML Wed Mar 04 11:37:50 2009 +0100
@@ -82,7 +82,7 @@
psimps, pinducts, termination, defname}) phi =
let
val term = Morphism.term phi val thm = Morphism.thm phi val fact = Morphism.fact phi
- val name = Binding.base_name o Morphism.binding phi o Binding.name
+ val name = Binding.name_of o Morphism.binding phi o Binding.name
in
FundefCtxData { add_simps = add_simps, case_names = case_names,
fs = map term fs, R = term R, psimps = fact psimps,
--- a/src/HOL/Tools/function_package/fundef_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/function_package/fundef_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -99,8 +99,8 @@
val constrn_fxs = map (fn (b, T, mx) => (b, SOME (the_default default_constraint T), mx))
val ((fixes0, spec0), ctxt') =
prep (constrn_fxs fixspec) (map (single o apsnd single) eqnss) lthy
- val fixes = map (apfst (apfst Binding.base_name)) fixes0;
- val spec = map (apfst (apfst Binding.base_name)) spec0;
+ val fixes = map (apfst (apfst Binding.name_of)) fixes0;
+ val spec = map (apfst (apfst Binding.name_of)) spec0;
val (eqs, post, sort_cont, cnames) = FundefCommon.get_preproc lthy config flags ctxt' fixes spec
val defname = mk_defname fixes
--- a/src/HOL/Tools/inductive_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/inductive_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -260,7 +260,7 @@
fun check_rule ctxt cs params ((binding, att), rule) =
let
- val err_name = Binding.display binding;
+ val err_name = Binding.str_of binding;
val params' = Term.variant_frees rule (Logic.strip_params rule);
val frees = rev (map Free params');
val concl = subst_bounds (frees, Logic.strip_assums_concl rule);
@@ -639,7 +639,7 @@
val rec_name =
if Binding.is_empty alt_name then
- Binding.name (space_implode "_" (map (Binding.base_name o fst) cnames_syn))
+ Binding.name (space_implode "_" (map (Binding.name_of o fst) cnames_syn))
else alt_name;
val ((rec_const, (_, fp_def)), ctxt') = ctxt |>
@@ -674,9 +674,9 @@
fun declare_rules kind rec_binding coind no_ind cnames intrs intr_bindings intr_atts
elims raw_induct ctxt =
let
- val rec_name = Binding.base_name rec_binding;
- val rec_qualified = Binding.qualify rec_name;
- val intr_names = map Binding.base_name intr_bindings;
+ val rec_name = Binding.name_of rec_binding;
+ val rec_qualified = Binding.qualify false rec_name;
+ val intr_names = map Binding.name_of intr_bindings;
val ind_case_names = RuleCases.case_names intr_names;
val induct =
if coind then
@@ -734,7 +734,7 @@
cs intros monos params cnames_syn ctxt =
let
val _ = null cnames_syn andalso error "No inductive predicates given";
- val names = map (Binding.base_name o fst) cnames_syn;
+ val names = map (Binding.name_of o fst) cnames_syn;
val _ = message (quiet_mode andalso not verbose)
("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^ commas_quote names);
@@ -749,7 +749,7 @@
val (intrs, unfold) = prove_intrs quiet_mode coind mono fp_def (length bs + length xs)
params intr_ts rec_preds_defs ctxt1;
val elims = if no_elim then [] else
- prove_elims quiet_mode cs params intr_ts (map Binding.base_name intr_names)
+ prove_elims quiet_mode cs params intr_ts (map Binding.name_of intr_names)
unfold rec_preds_defs ctxt1;
val raw_induct = zero_var_indexes
(if no_ind then Drule.asm_rl else
@@ -793,7 +793,7 @@
(* abbrevs *)
- val (_, ctxt1) = Variable.add_fixes (map (Binding.base_name o fst o fst) cnames_syn) lthy;
+ val (_, ctxt1) = Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn) lthy;
fun get_abbrev ((name, atts), t) =
if can (Logic.strip_assums_concl #> Logic.dest_equals) t then
@@ -802,7 +802,7 @@
error "Abbreviations may not have names or attributes";
val ((x, T), rhs) = LocalDefs.abs_def (snd (LocalDefs.cert_def ctxt1 t));
val var =
- (case find_first (fn ((c, _), _) => Binding.base_name c = x) cnames_syn of
+ (case find_first (fn ((c, _), _) => Binding.name_of c = x) cnames_syn of
NONE => error ("Undeclared head of abbreviation " ^ quote x)
| SOME ((b, T'), mx) =>
if T <> T' then error ("Bad type specification for abbreviation " ^ quote x)
@@ -811,17 +811,17 @@
else NONE;
val abbrevs = map_filter get_abbrev spec;
- val bs = map (Binding.base_name o fst o fst) abbrevs;
+ val bs = map (Binding.name_of o fst o fst) abbrevs;
(* predicates *)
val pre_intros = filter_out (is_some o get_abbrev) spec;
- val cnames_syn' = filter_out (member (op =) bs o Binding.base_name o fst o fst) cnames_syn;
- val cs = map (Free o apfst Binding.base_name o fst) cnames_syn';
+ val cnames_syn' = filter_out (member (op =) bs o Binding.name_of o fst o fst) cnames_syn;
+ val cs = map (Free o apfst Binding.name_of o fst) cnames_syn';
val ps = map Free pnames;
- val (_, ctxt2) = lthy |> Variable.add_fixes (map (Binding.base_name o fst o fst) cnames_syn');
+ val (_, ctxt2) = lthy |> Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn');
val _ = map (fn abbr => LocalDefs.fixed_abbrev abbr ctxt2) abbrevs;
val ctxt3 = ctxt2 |> fold (snd oo LocalDefs.fixed_abbrev) abbrevs;
val expand = Assumption.export_term ctxt3 lthy #> ProofContext.cert_term lthy;
@@ -854,7 +854,7 @@
in
lthy
|> LocalTheory.set_group (serial_string ())
- |> gen_add_inductive_i mk_def flags cs (map (apfst Binding.base_name o fst) ps) intrs monos
+ |> gen_add_inductive_i mk_def flags cs (map (apfst Binding.name_of o fst) ps) intrs monos
end;
val add_inductive_i = gen_add_inductive_i add_ind_def;
@@ -954,7 +954,7 @@
else if Binding.is_empty b then ((a, atts), B)
else error "Illegal nested case names"
| ((b, _), _) => error "Illegal simultaneous specification")
- | (a, _) => error ("Illegal local specification parameters for " ^ quote (Binding.base_name a)));
+ | (a, _) => error ("Illegal local specification parameters for " ^ quote (Binding.str_of a)));
fun gen_ind_decl mk_def coind =
P.fixes -- P.for_fixes --
--- a/src/HOL/Tools/inductive_set_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/inductive_set_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -464,7 +464,7 @@
| NONE => u)) |>
Pattern.rewrite_term thy [] [to_pred_proc thy eqns'] |>
eta_contract (member op = cs' orf is_pred pred_arities))) intros;
- val cnames_syn' = map (fn (b, _) => (Binding.map_base (suffix "p") b, NoSyn)) cnames_syn;
+ val cnames_syn' = map (fn (b, _) => (Binding.map_name (suffix "p") b, NoSyn)) cnames_syn;
val monos' = map (to_pred [] (Context.Proof ctxt)) monos;
val ({preds, intrs, elims, raw_induct, ...}, ctxt1) =
InductivePackage.add_ind_def
@@ -501,7 +501,7 @@
(* convert theorems to set notation *)
val rec_name =
if Binding.is_empty alt_name then
- Binding.name (space_implode "_" (map (Binding.base_name o fst) cnames_syn))
+ Binding.name (space_implode "_" (map (Binding.name_of o fst) cnames_syn))
else alt_name;
val cnames = map (LocalTheory.full_name ctxt3 o #1) cnames_syn; (* FIXME *)
val (intr_names, intr_atts) = split_list (map fst intros);
--- a/src/HOL/Tools/primrec_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/primrec_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -194,7 +194,7 @@
val def_name = Thm.def_name (Sign.base_name fname);
val rhs = singleton (Syntax.check_terms ctxt) raw_rhs;
val SOME var = get_first (fn ((b, _), mx) =>
- if Binding.base_name b = fname then SOME (b, mx) else NONE) fixes;
+ if Binding.name_of b = fname then SOME (b, mx) else NONE) fixes;
in (var, ((Binding.name def_name, []), rhs)) end;
@@ -231,7 +231,7 @@
let
val (fixes, spec) = prepare_spec prep_spec lthy raw_fixes raw_spec;
val eqns = fold_rev (process_eqn (fn v => Variable.is_fixed lthy v
- orelse exists (fn ((w, _), _) => v = Binding.base_name w) fixes) o snd) spec [];
+ orelse exists (fn ((w, _), _) => v = Binding.name_of w) fixes) o snd) spec [];
val tnames = distinct (op =) (map (#1 o snd) eqns);
val dts = find_dts (DatatypePackage.get_datatypes (ProofContext.theory_of lthy)) tnames tnames;
val main_fns = map (fn (tname, {index, ...}) =>
@@ -248,7 +248,7 @@
else primrec_error ("functions " ^ commas_quote names2 ^
"\nare not mutually recursive");
val prefix = space_implode "_" (map (Sign.base_name o #1) defs);
- val qualify = Binding.qualify prefix;
+ val qualify = Binding.qualify false prefix;
val spec' = (map o apfst)
(fn (b, attrs) => (qualify b, Code.add_default_eqn_attrib :: attrs)) spec;
val simp_atts = map (Attrib.internal o K)
@@ -299,7 +299,7 @@
P.name >> pair false) --| P.$$$ ")")) (false, "");
val old_primrec_decl =
- opt_unchecked_name -- Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name) -- P.prop);
+ opt_unchecked_name -- Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.name_of) -- P.prop);
fun pipe_error t = P.!!! (Scan.fail_with (K
(cat_lines ["Equations must be separated by " ^ quote "|", quote t])));
--- a/src/HOL/Tools/recdef_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/recdef_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -320,7 +320,7 @@
val _ =
OuterSyntax.local_theory_to_proof' "recdef_tc" "recommence proof of termination condition (TFL)"
K.thy_goal
- ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name) -- P.xname --
+ ((SpecParse.opt_thm_name ":" >> apfst Binding.name_of) -- P.xname --
Scan.option (P.$$$ "(" |-- P.nat --| P.$$$ ")")
>> (fn ((thm_name, name), i) => recdef_tc thm_name name i));
--- a/src/HOL/Tools/specification_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOL/Tools/specification_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -232,7 +232,7 @@
val specification_decl =
P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" --
- Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name) -- P.prop)
+ Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.name_of) -- P.prop)
val _ =
OuterSyntax.command "specification" "define constants by specification" K.thy_goal
@@ -243,7 +243,7 @@
val ax_specification_decl =
P.name --
(P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" --
- Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name) -- P.prop))
+ Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.name_of) -- P.prop))
val _ =
OuterSyntax.command "ax_specification" "define constants by specification" K.thy_goal
--- a/src/HOLCF/Tools/fixrec_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/HOLCF/Tools/fixrec_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -16,7 +16,7 @@
-> (Attrib.binding * term) list -> local_theory -> local_theory
val add_fixpat: Attrib.binding * string list -> theory -> theory
- val add_fixpat_i: (binding * attribute list) * term list -> theory -> theory
+ val add_fixpat_i: Thm.binding * term list -> theory -> theory
val add_matchers: (string * string) list -> theory -> theory
val setup: theory -> theory
end;
@@ -175,7 +175,7 @@
(spec : (Attrib.binding * term) list)
(lthy : local_theory) =
let
- val names = map (Binding.base_name o fst o fst) fixes;
+ val names = map (Binding.name_of o fst o fst) fixes;
val all_names = space_implode "_" names;
val (lhss,rhss) = ListPair.unzip (map (dest_eqs o snd) spec);
val fixpoint = mk_fix (lambda_ctuple lhss (mk_ctuple rhss));
--- a/src/Pure/General/binding.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/General/binding.ML Wed Mar 04 11:37:50 2009 +0100
@@ -1,98 +1,104 @@
(* Title: Pure/General/binding.ML
Author: Florian Haftmann, TU Muenchen
+ Author: Makarius
Structured name bindings.
*)
-signature BASIC_BINDING =
-sig
- type binding
- val long_names: bool ref
- val short_names: bool ref
- val unique_names: bool ref
-end;
+type bstring = string; (*primitive names to be bound*)
signature BINDING =
sig
- include BASIC_BINDING
- val name_pos: string * Position.T -> binding
- val name: string -> binding
+ type binding
+ val dest: binding -> (string * bool) list * (string * bool) list * bstring
+ val verbose: bool ref
+ val str_of: binding -> string
+ val make: bstring * Position.T -> binding
+ val name: bstring -> binding
+ val pos_of: binding -> Position.T
+ val name_of: binding -> string
+ val map_name: (bstring -> bstring) -> binding -> binding
val empty: binding
- val map_base: (string -> string) -> binding -> binding
- val qualify: string -> binding -> binding
+ val is_empty: binding -> bool
+ val qualify: bool -> string -> binding -> binding
+ val map_prefix: ((string * bool) list -> (string * bool) list) -> binding -> binding
val add_prefix: bool -> string -> binding -> binding
- val map_prefix: ((string * bool) list -> binding -> binding) -> binding -> binding
- val is_empty: binding -> bool
- val base_name: binding -> string
- val pos_of: binding -> Position.T
- val dest: binding -> (string * bool) list * string
- val separator: string
- val is_qualified: string -> bool
- val display: binding -> string
end;
-structure Binding : BINDING =
+structure Binding: BINDING =
struct
-(** global flags **)
+(** representation **)
-val long_names = ref false;
-val short_names = ref false;
-val unique_names = ref true;
+(* datatype *)
+type component = string * bool; (*name with mandatory flag*)
-(** qualification **)
-
-val separator = ".";
-val is_qualified = exists_string (fn s => s = separator);
+datatype binding = Binding of
+ {prefix: component list, (*system prefix*)
+ qualifier: component list, (*user qualifier*)
+ name: bstring, (*base name*)
+ pos: Position.T}; (*source position*)
-fun reject_qualified kind s =
- if is_qualified s then
- error ("Attempt to declare qualified " ^ kind ^ " " ^ quote s)
- else s;
+fun make_binding (prefix, qualifier, name, pos) =
+ Binding {prefix = prefix, qualifier = qualifier, name = name, pos = pos};
+
+fun map_binding f (Binding {prefix, qualifier, name, pos}) =
+ make_binding (f (prefix, qualifier, name, pos));
+
+fun dest (Binding {prefix, qualifier, name, ...}) = (prefix, qualifier, name);
-(** binding representation **)
+(* diagnostic output *)
-datatype binding = Binding of ((string * bool) list * string) * Position.T;
- (* (prefix components (with mandatory flag), base name, position) *)
+val verbose = ref false;
-fun name_pos (name, pos) = Binding (([], name), pos);
-fun name name = name_pos (name, Position.none);
-val empty = name "";
+val str_of_components = implode o map (fn (s, true) => s ^ "!" | (s, false) => s ^ "?");
-fun map_binding f (Binding (prefix_name, pos)) = Binding (f prefix_name, pos);
-
-val map_base = map_binding o apsnd;
+fun str_of (Binding {prefix, qualifier, name, pos}) =
+ let
+ val text =
+ if ! verbose then
+ (if null prefix then "" else enclose "(" ")" (str_of_components prefix)) ^
+ str_of_components qualifier ^ name
+ else name;
+ val props = Position.properties_of pos;
+ in Markup.markup (Markup.properties props (Markup.binding name)) text end;
-fun qualify_base path name =
- if path = "" orelse name = "" then name
- else path ^ separator ^ name;
+
-val qualify = map_base o qualify_base;
- (*FIXME should all operations on bare names move here from name_space.ML ?*)
+(** basic operations **)
+
+(* name and position *)
-fun add_prefix sticky "" b = b
- | add_prefix sticky prfx b = (map_binding o apfst)
- (cons ((*reject_qualified "prefix"*) prfx, sticky)) b;
+fun make (name, pos) = make_binding ([], [], name, pos);
+fun name name = make (name, Position.none);
+
+fun pos_of (Binding {pos, ...}) = pos;
+fun name_of (Binding {name, ...}) = name;
-fun map_prefix f (Binding ((prefix, name), pos)) =
- f prefix (name_pos (name, pos));
+fun map_name f = map_binding (fn (prefix, qualifier, name, pos) => (prefix, qualifier, f name, pos));
+
+val empty = name "";
+fun is_empty b = name_of b = "";
+
-fun is_empty (Binding ((_, name), _)) = name = "";
-fun base_name (Binding ((_, name), _)) = name;
-fun pos_of (Binding (_, pos)) = pos;
-fun dest (Binding (prefix_name, _)) = prefix_name;
+(* user qualifier *)
+
+fun qualify _ "" = I
+ | qualify mandatory qual = map_binding (fn (prefix, qualifier, name, pos) =>
+ (prefix, (qual, mandatory) :: qualifier, name, pos));
+
-fun display (Binding ((prefix, name), _)) =
- let
- fun mk_prefix (prfx, true) = prfx
- | mk_prefix (prfx, false) = enclose "(" ")" prfx
- in if not (! long_names) orelse null prefix orelse name = "" then name
- else space_implode "." (map mk_prefix prefix) ^ ":" ^ name
- end;
+(* system prefix *)
+
+fun map_prefix f = map_binding (fn (prefix, qualifier, name, pos) =>
+ (f prefix, qualifier, name, pos));
+
+fun add_prefix _ "" = I
+ | add_prefix mandatory prfx = map_prefix (cons (prfx, mandatory));
end;
-structure Basic_Binding : BASIC_BINDING = Binding;
-open Basic_Binding;
+type binding = Binding.binding;
+
--- a/src/Pure/General/markup.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/General/markup.ML Wed Mar 04 11:37:50 2009 +0100
@@ -12,9 +12,9 @@
val properties: (string * string) list -> T -> T
val nameN: string
val name: string -> T -> T
+ val bindingN: string val binding: string -> T
val groupN: string
val theory_nameN: string
- val idN: string
val kindN: string
val internalK: string
val property_internal: Properties.property
@@ -25,6 +25,7 @@
val end_columnN: string
val end_offsetN: string
val fileN: string
+ val idN: string
val position_properties': string list
val position_properties: string list
val positionN: string val position: T
@@ -107,6 +108,8 @@
structure Markup: MARKUP =
struct
+(** markup elements **)
+
(* basic markup *)
type T = string * Properties.T;
@@ -130,6 +133,8 @@
val nameN = "name";
fun name a = properties [(nameN, a)];
+val (bindingN, binding) = markup_string "binding" nameN;
+
val groupN = "group";
val theory_nameN = "theory_name";
@@ -278,7 +283,7 @@
-(* print mode operations *)
+(** print mode operations **)
val no_output = ("", "");
fun default_output (_: T) = no_output;
--- a/src/Pure/General/name_space.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/General/name_space.ML Wed Mar 04 11:37:50 2009 +0100
@@ -3,15 +3,20 @@
Generic name spaces with declared and hidden entries. Unknown names
are considered global; no support for absolute addressing.
-Cf. Pure/General/binding.ML
*)
-type bstring = string; (*simple names to be bound -- legacy*)
type xstring = string; (*external names*)
+signature BASIC_NAME_SPACE =
+sig
+ val long_names: bool ref
+ val short_names: bool ref
+ val unique_names: bool ref
+end;
+
signature NAME_SPACE =
sig
- include BASIC_BINDING
+ include BASIC_NAME_SPACE
val hidden: string -> string
val is_hidden: string -> bool
val separator: string (*single char*)
@@ -27,8 +32,9 @@
val empty: T
val intern: T -> xstring -> string
val extern: T -> string -> xstring
+ val extern_flags: {long_names: bool, short_names: bool, unique_names: bool} ->
+ T -> string -> xstring
val hide: bool -> string -> T -> T
- val get_accesses: T -> string -> xstring list
val merge: T * T -> T
type naming
val default_naming: naming
@@ -41,12 +47,11 @@
val qualified_names: naming -> naming
val sticky_prefix: string -> naming -> naming
type 'a table = T * 'a Symtab.table
+ val bind: naming -> binding * 'a -> 'a table -> string * 'a table (*exception Symtab.DUP*)
val empty_table: 'a table
- val bind: naming -> binding * 'a
- -> 'a table -> string * 'a table (*exception Symtab.DUP*)
- val merge_tables: ('a * 'a -> bool) -> 'a table * 'a table -> 'a table
- val join_tables: (string -> 'a * 'a -> 'a)
- -> 'a table * 'a table -> 'a table
+ val merge_tables: ('a * 'a -> bool) -> 'a table * 'a table -> 'a table (*exception Symtab.DUP*)
+ val join_tables: (string -> 'a * 'a -> 'a) (*exception Symtab.DUP/Symtab.SAME*) ->
+ 'a table * 'a table -> 'a table (*exception Symtab.DUP*)
val dest_table: 'a table -> (string * 'a) list
val extern_table: 'a table -> (xstring * 'a) list
end;
@@ -54,16 +59,13 @@
structure NameSpace: NAME_SPACE =
struct
-open Basic_Binding;
-
-
(** long identifiers **)
fun hidden name = "??." ^ name;
val is_hidden = String.isPrefix "??.";
-val separator = Binding.separator;
-val is_qualified = Binding.is_qualified;
+val separator = ".";
+val is_qualified = exists_string (fn s => s = separator);
val implode_name = space_implode separator;
val explode_name = space_explode separator;
@@ -120,37 +122,28 @@
datatype T =
NameSpace of
- ((string list * string list) * stamp) Symtab.table * (*internals, hidden internals*)
- (string list * stamp) Symtab.table; (*externals*)
+ (string list * string list) Symtab.table * (*internals, hidden internals*)
+ string list Symtab.table; (*externals*)
val empty = NameSpace (Symtab.empty, Symtab.empty);
fun lookup (NameSpace (tab, _)) xname =
(case Symtab.lookup tab xname of
NONE => (xname, true)
- | SOME (([], []), _) => (xname, true)
- | SOME (([name], _), _) => (name, true)
- | SOME ((name :: _, _), _) => (name, false)
- | SOME (([], name' :: _), _) => (hidden name', true));
+ | SOME ([], []) => (xname, true)
+ | SOME ([name], _) => (name, true)
+ | SOME (name :: _, _) => (name, false)
+ | SOME ([], name' :: _) => (hidden name', true));
-fun ex_mapsto_in (NameSpace (tab, _)) name xname =
- (case Symtab.lookup tab xname of
- SOME ((name'::_, _), _) => name' = name
- | _ => false);
-
-fun get_accesses' valid_only (ns as (NameSpace (_, tab))) name =
- (case Symtab.lookup tab name of
+fun get_accesses (NameSpace (_, xtab)) name =
+ (case Symtab.lookup xtab name of
NONE => [name]
- | SOME (xnames, _) => if valid_only
- then filter (ex_mapsto_in ns name) xnames
- else xnames);
-
-val get_accesses = get_accesses' true;
+ | SOME xnames => xnames);
fun put_accesses name xnames (NameSpace (tab, xtab)) =
- NameSpace (tab, Symtab.update (name, (xnames, stamp ())) xtab);
+ NameSpace (tab, Symtab.update (name, xnames) xtab);
-fun valid_accesses (NameSpace (tab, _)) name = Symtab.fold (fn (xname, ((names, _), _)) =>
+fun valid_accesses (NameSpace (tab, _)) name = Symtab.fold (fn (xname, (names, _)) =>
if not (null names) andalso hd names = name then cons xname else I) tab [];
@@ -158,28 +151,37 @@
fun intern space xname = #1 (lookup space xname);
-fun extern space name =
+fun extern_flags {long_names, short_names, unique_names} space name =
let
fun valid unique xname =
let val (name', uniq) = lookup space xname
in name = name' andalso (uniq orelse not unique) end;
fun ext [] = if valid false name then name else hidden name
- | ext (nm :: nms) = if valid (! unique_names) nm then nm else ext nms;
+ | ext (nm :: nms) = if valid unique_names nm then nm else ext nms;
in
- if ! long_names then name
- else if ! short_names then base name
- else ext (get_accesses' false space name)
+ if long_names then name
+ else if short_names then base name
+ else ext (get_accesses space name)
end;
+val long_names = ref false;
+val short_names = ref false;
+val unique_names = ref true;
+
+fun extern space name =
+ extern_flags
+ {long_names = ! long_names,
+ short_names = ! short_names,
+ unique_names = ! unique_names} space name;
+
(* basic operations *)
local
fun map_space f xname (NameSpace (tab, xtab)) =
- NameSpace (Symtab.map_default (xname, (([], []), stamp ()))
- (fn (entry, _) => (f entry, stamp ())) tab, xtab);
+ NameSpace (Symtab.map_default (xname, ([], [])) f tab, xtab);
in
@@ -203,7 +205,7 @@
space
|> add_name' name name
|> fold (del_name name) (if fully then names else names inter_string [base name])
- |> fold (del_name_extra name) (get_accesses' false space name)
+ |> fold (del_name_extra name) (get_accesses space name)
end;
@@ -212,15 +214,13 @@
fun merge (NameSpace (tab1, xtab1), NameSpace (tab2, xtab2)) =
let
val tab' = (tab1, tab2) |> Symtab.join
- (K (fn (((names1, names1'), stamp1), ((names2, names2'), stamp2)) =>
- if stamp1 = stamp2 then raise Symtab.SAME
- else
- ((Library.merge (op =) (names1, names2),
- Library.merge (op =) (names1', names2')), stamp ())));
+ (K (fn names as ((names1, names1'), (names2, names2')) =>
+ if pointer_eq names then raise Symtab.SAME
+ else (Library.merge (op =) (names1, names2), Library.merge (op =) (names1', names2'))));
val xtab' = (xtab1, xtab2) |> Symtab.join
- (K (fn ((xnames1, stamp1), (xnames2, stamp2)) =>
- if stamp1 = stamp2 then raise Symtab.SAME
- else (Library.merge (op =) (xnames1, xnames2), stamp ())));
+ (K (fn xnames =>
+ if pointer_eq xnames then raise Symtab.SAME
+ else (Library.merge (op =) xnames)));
in NameSpace (tab', xtab') end;
@@ -272,32 +272,33 @@
in fold mk_prefix end;
-(* declarations *)
+(* full name *)
+
+fun full (Naming (path, (qualify, _))) = qualify path;
-fun full_internal (Naming (path, (qualify, _))) = qualify path;
+fun full_name naming binding =
+ let
+ val (prefix, qualifier, bname) = Binding.dest binding;
+ val naming' = apply_prefix (prefix @ qualifier) naming;
+ in full naming' bname end;
+
+
+(* declaration *)
-fun declare_internal naming name space =
- if is_hidden name then
- error ("Attempt to declare hidden name " ^ quote name)
- else
- let
- val names = explode_name name;
- val _ = (null names orelse exists (fn s => s = "") names
- orelse exists_string (fn s => s = "\"") name) andalso
- error ("Bad name declaration " ^ quote name);
- val (accs, accs') = pairself (map implode_name) (accesses naming names);
- in space |> fold (add_name name) accs |> put_accesses name accs' end;
+fun declare naming binding space =
+ let
+ val (prefix, qualifier, bname) = Binding.dest binding;
+ val naming' = apply_prefix (prefix @ qualifier) naming;
+ val name = full naming' bname;
+ val names = explode_name name;
-fun full_name naming b =
- let val (prefix, bname) = Binding.dest b
- in full_internal (apply_prefix prefix naming) bname end;
+ val _ = (null names orelse exists (fn s => s = "" orelse s = "??") names
+ orelse exists_string (fn s => s = "\"") name) andalso
+ error ("Bad name declaration " ^ quote (Binding.str_of binding));
-fun declare bnaming b =
- let
- val (prefix, bname) = Binding.dest b;
- val naming = apply_prefix prefix bnaming;
- val name = full_internal naming bname;
- in declare_internal naming name #> pair name end;
+ val (accs, accs') = pairself (map implode_name) (accesses naming' names);
+ val space' = space |> fold (add_name name) accs |> put_accesses name accs';
+ in (name, space') end;
@@ -305,12 +306,11 @@
type 'a table = T * 'a Symtab.table;
-val empty_table = (empty, Symtab.empty);
+fun bind naming (binding, x) (space, tab) =
+ let val (name, space') = declare naming binding space
+ in (name, (space', Symtab.update_new (name, x) tab)) end;
-fun bind naming (b, x) (space, tab) =
- let
- val (name, space') = declare naming b space;
- in (name, (space', Symtab.update_new (name, x) tab)) end;
+val empty_table = (empty, Symtab.empty);
fun merge_tables eq ((space1, tab1), (space2, tab2)) =
(merge (space1, space2), Symtab.merge eq (tab1, tab2));
@@ -331,3 +331,7 @@
val explode = explode_name;
end;
+
+structure BasicNameSpace: BASIC_NAME_SPACE = NameSpace;
+open BasicNameSpace;
+
--- a/src/Pure/Isar/args.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/args.ML Wed Mar 04 11:37:50 2009 +0100
@@ -170,7 +170,7 @@
val name_source_position = named >> T.source_position_of;
val name = named >> T.content_of;
-val binding = P.position name >> Binding.name_pos;
+val binding = P.position name >> Binding.make;
val alt_name = alt_string >> T.content_of;
val symbol = symbolic >> T.content_of;
val liberal_name = symbol || name;
--- a/src/Pure/Isar/attrib.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/attrib.ML Wed Mar 04 11:37:50 2009 +0100
@@ -118,8 +118,7 @@
fun attribute thy = attribute_i thy o intern_src thy;
fun eval_thms ctxt args = ProofContext.note_thmss Thm.theoremK
- [((Binding.empty, []),
- map (apsnd (map (attribute (ProofContext.theory_of ctxt)))) args)] ctxt
+ [(Thm.empty_binding, map (apsnd (map (attribute (ProofContext.theory_of ctxt)))) args)] ctxt
|> fst |> maps snd;
--- a/src/Pure/Isar/class.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/class.ML Wed Mar 04 11:37:50 2009 +0100
@@ -201,7 +201,7 @@
| check_element e = [()];
val _ = map check_element syntax_elems;
fun fork_syn (Element.Fixes xs) =
- fold_map (fn (c, ty, syn) => cons (Binding.base_name c, syn) #> pair (c, ty, NoSyn)) xs
+ fold_map (fn (c, ty, syn) => cons (Binding.name_of c, syn) #> pair (c, ty, NoSyn)) xs
#>> Element.Fixes
| fork_syn x = pair x;
val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
@@ -228,7 +228,7 @@
val raw_params = (snd o chop (length supparams)) all_params;
fun add_const (b, SOME raw_ty, _) thy =
let
- val v = Binding.base_name b;
+ val v = Binding.name_of b;
val c = Sign.full_bname thy v;
val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
val ty0 = Type.strip_sorts ty;
@@ -265,8 +265,7 @@
|> add_consts bname class base_sort sups supparams global_syntax
|-> (fn (param_map, params) => AxClass.define_class (bname, supsort)
(map (fst o snd) params)
- [((Binding.empty, []),
- Option.map (globalize param_map) raw_pred |> the_list)]
+ [(Thm.empty_binding, Option.map (globalize param_map) raw_pred |> the_list)]
#> snd
#> `get_axiom
#-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
--- a/src/Pure/Isar/constdefs.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/constdefs.ML Wed Mar 04 11:37:50 2009 +0100
@@ -9,11 +9,9 @@
signature CONSTDEFS =
sig
val add_constdefs: (binding * string option) list *
- ((binding * string option * mixfix) option *
- (Attrib.binding * string)) list -> theory -> theory
+ ((binding * string option * mixfix) option * (Attrib.binding * string)) list -> theory -> theory
val add_constdefs_i: (binding * typ option) list *
- ((binding * typ option * mixfix) option *
- ((binding * attribute list) * term)) list -> theory -> theory
+ ((binding * typ option * mixfix) option * (Thm.binding * term)) list -> theory -> theory
end;
structure Constdefs: CONSTDEFS =
@@ -38,7 +36,7 @@
val prop = prep_prop var_ctxt raw_prop;
val (c, T) = #1 (LocalDefs.cert_def thy_ctxt (Logic.strip_imp_concl prop));
val _ =
- (case Option.map Binding.base_name d of
+ (case Option.map Binding.name_of d of
NONE => ()
| SOME c' =>
if c <> c' then
@@ -46,7 +44,7 @@
else ());
val def = Term.subst_atomic [(Free (c, T), Const (Sign.full_bname thy c, T))] prop;
- val name = Thm.def_name_optional c (Binding.base_name raw_name);
+ val name = Thm.def_name_optional c (Binding.name_of raw_name);
val atts = map (prep_att thy) raw_atts;
val thy' =
--- a/src/Pure/Isar/element.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/element.ML Wed Mar 04 11:37:50 2009 +0100
@@ -96,7 +96,7 @@
fun map_ctxt {binding, typ, term, pattern, fact, attrib} =
fn Fixes fixes => Fixes (fixes |> map (fn (x, T, mx) => (binding x, Option.map typ T, mx)))
| Constrains xs => Constrains (xs |> map (fn (x, T) =>
- (Binding.base_name (binding (Binding.name x)), typ T)))
+ (Binding.name_of (binding (Binding.name x)), typ T)))
| Assumes asms => Assumes (asms |> map (fn ((a, atts), propps) =>
((binding a, map attrib atts), propps |> map (fn (t, ps) => (term t, map pattern ps)))))
| Defines defs => Defines (defs |> map (fn ((a, atts), (t, ps)) =>
@@ -125,11 +125,9 @@
map (fn y => Pretty.block [Pretty.str " ", Pretty.keyword sep, Pretty.brk 1, y]) ys;
fun pretty_name_atts ctxt (b, atts) sep =
- let val name = Binding.display b in
- if name = "" andalso null atts then []
- else [Pretty.block
- (Pretty.breaks (Pretty.str name :: Attrib.pretty_attribs ctxt atts @ [Pretty.str sep]))]
- end;
+ if Binding.is_empty b andalso null atts then []
+ else [Pretty.block (Pretty.breaks
+ (Pretty.str (Binding.str_of b) :: Attrib.pretty_attribs ctxt atts @ [Pretty.str sep]))];
(* pretty_stmt *)
@@ -145,8 +143,8 @@
Pretty.block (Pretty.breaks (prt_name_atts a ":" @ prt_terms (map fst ts)));
fun prt_var (x, SOME T) = Pretty.block
- [Pretty.str (Binding.base_name x ^ " ::"), Pretty.brk 1, prt_typ T]
- | prt_var (x, NONE) = Pretty.str (Binding.base_name x);
+ [Pretty.str (Binding.name_of x ^ " ::"), Pretty.brk 1, prt_typ T]
+ | prt_var (x, NONE) = Pretty.str (Binding.name_of x);
val prt_vars = separate (Pretty.keyword "and") o map prt_var;
fun prt_obtain (_, ([], ts)) = Pretty.block (Pretty.breaks (prt_terms ts))
@@ -170,9 +168,9 @@
fun prt_mixfix NoSyn = []
| prt_mixfix mx = [Pretty.brk 2, Syntax.pretty_mixfix mx];
- fun prt_fix (x, SOME T, mx) = Pretty.block (Pretty.str (Binding.base_name x ^ " ::") ::
+ fun prt_fix (x, SOME T, mx) = Pretty.block (Pretty.str (Binding.name_of x ^ " ::") ::
Pretty.brk 1 :: prt_typ T :: Pretty.brk 1 :: prt_mixfix mx)
- | prt_fix (x, NONE, mx) = Pretty.block (Pretty.str (Binding.base_name x) ::
+ | prt_fix (x, NONE, mx) = Pretty.block (Pretty.str (Binding.name_of x) ::
Pretty.brk 1 :: prt_mixfix mx);
fun prt_constrain (x, T) = prt_fix (Binding.name x, SOME T, NoSyn);
@@ -296,7 +294,7 @@
gen_witness_proof (fn after_qed' => fn propss =>
Proof.map_context (K goal_ctxt)
#> Proof.local_goal (ProofDisplay.print_results int) (K I) ProofContext.bind_propp_i
- cmd NONE after_qed' (map (pair (Binding.empty, [])) propss))
+ cmd NONE after_qed' (map (pair Thm.empty_binding) propss))
(fn wits => fn _ => after_qed wits) wit_propss [];
end;
@@ -504,7 +502,7 @@
val defs' = Attrib.map_specs (Attrib.attribute_i (ProofContext.theory_of ctxt)) defs;
val asms = defs' |> map (fn ((name, atts), (t, ps)) =>
let val ((c, _), t') = LocalDefs.cert_def ctxt t
- in (t', ((Binding.map_base (Thm.def_name_optional c) name, atts), [(t', ps)])) end);
+ in (t', ((Binding.map_name (Thm.def_name_optional c) name, atts), [(t', ps)])) end);
val (_, ctxt') =
ctxt |> fold (Variable.auto_fixes o #1) asms
|> ProofContext.add_assms_i LocalDefs.def_export (map #2 asms);
@@ -529,7 +527,7 @@
fun prep_facts prep_name get intern ctxt =
map_ctxt
- {binding = Binding.map_base prep_name,
+ {binding = Binding.map_name prep_name,
typ = I,
term = I,
pattern = I,
--- a/src/Pure/Isar/expression.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/expression.ML Wed Mar 04 11:37:50 2009 +0100
@@ -88,17 +88,13 @@
if null dups then () else error (message ^ commas dups)
end;
- fun match_bind (n, b) = (n = Binding.base_name b);
+ fun match_bind (n, b) = (n = Binding.name_of b);
fun parm_eq ((b1, mx1: mixfix), (b2, mx2)) =
(* FIXME: cannot compare bindings for equality, instead check for equal name and syntax *)
- (Binding.base_name b1 = Binding.base_name b2) andalso
- (if mx1 = mx2 then true
- else error ("Conflicting syntax for parameter" ^ quote (Binding.display b1) ^
- " in expression."));
+ Binding.name_of b1 = Binding.name_of b2 andalso
+ (mx1 = mx2 orelse
+ error ("Conflicting syntax for parameter " ^ quote (Binding.str_of b1) ^ " in expression"));
- fun bind_eq (b1, b2) = (Binding.base_name b1 = Binding.base_name b2);
- (* FIXME: cannot compare bindings for equality. *)
-
fun params_loc loc =
(Locale.params_of thy loc |> map (fn (p, _, mx) => (p, mx)), loc);
fun params_inst (expr as (loc, (prfx, Positional insts))) =
@@ -133,8 +129,8 @@
val (implicit, expr') = params_expr expr;
- val implicit' = map (#1 #> Binding.base_name) implicit;
- val fixed' = map (#1 #> Binding.base_name) fixed;
+ val implicit' = map (#1 #> Binding.name_of) implicit;
+ val fixed' = map (#1 #> Binding.name_of) fixed;
val _ = reject_dups "Duplicate fixed parameter(s): " fixed';
val implicit'' = if strict then []
else let val _ = reject_dups
@@ -310,14 +306,12 @@
(a, map (fn (t, ps) => (close_frees t, no_binds ps)) propps)))
| Defines defs => Defines (defs |> map (fn ((name, atts), (t, ps)) =>
let val ((c, _), t') = LocalDefs.cert_def ctxt (close_frees t)
- in
- ((Binding.map_base (Thm.def_name_optional c) name, atts), (t', no_binds ps))
- end))
+ in ((Binding.map_name (Thm.def_name_optional c) name, atts), (t', no_binds ps)) end))
| e => e)
end;
fun finish_primitive parms _ (Fixes fixes) = Fixes (map (fn (binding, _, mx) =>
- let val x = Binding.base_name binding
+ let val x = Binding.name_of binding
in (binding, AList.lookup (op =) parms x, mx) end) fixes)
| finish_primitive _ _ (Constrains _) = Constrains []
| finish_primitive _ close (Assumes asms) = close (Assumes asms)
@@ -328,7 +322,7 @@
let
val thy = ProofContext.theory_of ctxt;
val (parm_names, parm_types) = Locale.params_of thy loc |>
- map_split (fn (b, SOME T, _) => (Binding.base_name b, T));
+ map_split (fn (b, SOME T, _) => (Binding.name_of b, T));
val (morph, _) = inst_morph (parm_names, parm_types) (prfx, inst) ctxt;
in (loc, morph) end;
@@ -360,7 +354,7 @@
fun prep_insts (loc, (prfx, inst)) (i, insts, ctxt) =
let
val (parm_names, parm_types) = Locale.params_of thy loc |>
- map_split (fn (b, SOME T, _) => (Binding.base_name b, T))
+ map_split (fn (b, SOME T, _) => (Binding.name_of b, T))
(*FIXME return value of Locale.params_of has strange type*)
val inst' = prep_inst ctxt parm_names inst;
val parm_types' = map (TypeInfer.paramify_vars o
@@ -394,7 +388,7 @@
prep_concl raw_concl (insts', elems, ctxt5);
(* Retrieve parameter types *)
- val xs = fold (fn Fixes fixes => (fn ps => ps @ map (Binding.base_name o #1) fixes)
+ val xs = fold (fn Fixes fixes => (fn ps => ps @ map (Binding.name_of o #1) fixes)
| _ => fn ps => ps) (Fixes fors :: elems') [];
val (Ts, ctxt7) = fold_map ProofContext.inferred_param xs ctxt6;
val parms = xs ~~ Ts; (* params from expression and elements *)
--- a/src/Pure/Isar/isar_cmd.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/isar_cmd.ML Wed Mar 04 11:37:50 2009 +0100
@@ -161,7 +161,7 @@
(* axioms *)
fun add_axms f args thy =
- f (map (fn ((b, ax), srcs) => ((Binding.base_name b, ax), map (Attrib.attribute thy) srcs)) args) thy;
+ f (map (fn ((b, ax), srcs) => ((Binding.name_of b, ax), map (Attrib.attribute thy) srcs)) args) thy;
val add_axioms = add_axms (snd oo PureThy.add_axioms_cmd);
--- a/src/Pure/Isar/local_defs.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/local_defs.ML Wed Mar 04 11:37:50 2009 +0100
@@ -11,8 +11,8 @@
val mk_def: Proof.context -> (string * term) list -> term list
val expand: cterm list -> thm -> thm
val def_export: Assumption.export
- val add_defs: ((binding * mixfix) * ((binding * attribute list) * term)) list ->
- Proof.context -> (term * (string * thm)) list * Proof.context
+ val add_defs: ((binding * mixfix) * (Thm.binding * term)) list -> Proof.context ->
+ (term * (string * thm)) list * Proof.context
val add_def: (binding * mixfix) * term -> Proof.context -> (term * thm) * Proof.context
val fixed_abbrev: (binding * mixfix) * term -> Proof.context ->
(term * term) * Proof.context
@@ -90,8 +90,8 @@
let
val ((bvars, mxs), specs) = defs |> split_list |>> split_list;
val ((bfacts, atts), rhss) = specs |> split_list |>> split_list;
- val xs = map Binding.base_name bvars;
- val names = map2 (Binding.map_base o Thm.def_name_optional) xs bfacts;
+ val xs = map Binding.name_of bvars;
+ val names = map2 (Binding.map_name o Thm.def_name_optional) xs bfacts;
val eqs = mk_def ctxt (xs ~~ rhss);
val lhss = map (fst o Logic.dest_equals) eqs;
in
@@ -104,7 +104,7 @@
end;
fun add_def (var, rhs) ctxt =
- let val ([(lhs, (_, th))], ctxt') = add_defs [(var, ((Binding.empty, []), rhs))] ctxt
+ let val ([(lhs, (_, th))], ctxt') = add_defs [(var, (Thm.empty_binding, rhs))] ctxt
in ((lhs, th), ctxt') end;
--- a/src/Pure/Isar/locale.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/locale.ML Wed Mar 04 11:37:50 2009 +0100
@@ -194,7 +194,7 @@
fun axioms_of thy = #axioms o the_locale thy;
fun instance_of thy name morph = params_of thy name |>
- map ((fn (b, T, _) => Free (Binding.base_name b, the T)) #> Morphism.term morph);
+ map ((fn (b, T, _) => Free (Binding.name_of b, the T)) #> Morphism.term morph);
fun specification_of thy = #spec o the_locale thy;
@@ -464,8 +464,7 @@
fun decl_attrib decl phi = Thm.declaration_attribute (K (decl phi));
fun add_decls add loc decl =
- ProofContext.theory ((change_locale loc o apfst o apfst) (add (decl, stamp ())))
- #>
+ ProofContext.theory ((change_locale loc o apfst o apfst) (add (decl, stamp ()))) #>
add_thmss loc Thm.internalK
[((Binding.empty, [Attrib.internal (decl_attrib decl)]), [([Drule.dummy_thm], [])])];
--- a/src/Pure/Isar/method.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/method.ML Wed Mar 04 11:37:50 2009 +0100
@@ -38,7 +38,7 @@
val atomize: bool -> method
val this: method
val fact: thm list -> Proof.context -> method
- val assumption_tac: Proof.context -> int -> tactic
+ val assm_tac: Proof.context -> int -> tactic
val assumption: Proof.context -> method
val close: bool -> Proof.context -> method
val trace: Proof.context -> thm list -> unit
@@ -224,20 +224,20 @@
in
-fun assumption_tac ctxt =
+fun assm_tac ctxt =
assume_tac APPEND'
Goal.assume_rule_tac ctxt APPEND'
cond_rtac (can Logic.dest_equals) Drule.reflexive_thm APPEND'
cond_rtac (can Logic.dest_term) Drule.termI;
fun assumption ctxt = METHOD (HEADGOAL o
- (fn [] => assumption_tac ctxt
+ (fn [] => assm_tac ctxt
| [fact] => solve_tac [fact]
| _ => K no_tac));
fun close immed ctxt = METHOD (K
(FILTER Thm.no_prems
- ((if immed then ALLGOALS (assumption_tac ctxt) else all_tac) THEN flexflex_tac)));
+ ((if immed then ALLGOALS (assm_tac ctxt) else all_tac) THEN flexflex_tac)));
end;
--- a/src/Pure/Isar/obtain.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/obtain.ML Wed Mar 04 11:37:50 2009 +0100
@@ -40,11 +40,9 @@
sig
val thatN: string
val obtain: string -> (binding * string option * mixfix) list ->
- (Attrib.binding * (string * string list) list) list ->
- bool -> Proof.state -> Proof.state
+ (Attrib.binding * (string * string list) list) list -> bool -> Proof.state -> Proof.state
val obtain_i: string -> (binding * typ option * mixfix) list ->
- ((binding * attribute list) * (term * term list) list) list ->
- bool -> Proof.state -> Proof.state
+ (Thm.binding * (term * term list) list) list -> bool -> Proof.state -> Proof.state
val result: (Proof.context -> tactic) -> thm list -> Proof.context ->
(cterm list * thm list) * Proof.context
val guess: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state
@@ -121,7 +119,7 @@
(*obtain vars*)
val (vars, vars_ctxt) = prep_vars raw_vars ctxt;
val (_, fix_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
- val xs = map (Binding.base_name o #1) vars;
+ val xs = map (Binding.name_of o #1) vars;
(*obtain asms*)
val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
@@ -155,14 +153,14 @@
in
state
|> Proof.enter_forward
- |> Proof.have_i NONE (K I) [((Binding.empty, []), [(obtain_prop, [])])] int
+ |> Proof.have_i NONE (K I) [(Thm.empty_binding, [(obtain_prop, [])])] int
|> Proof.proof (SOME Method.succeed_text) |> Seq.hd
|> Proof.fix_i [(Binding.name thesisN, NONE, NoSyn)]
|> Proof.assume_i
[((Binding.name that_name, [ContextRules.intro_query NONE]), [(that_prop, [])])]
|> `Proof.the_facts
||> Proof.chain_facts chain_facts
- ||> Proof.show_i NONE after_qed [((Binding.empty, []), [(thesis, [])])] false
+ ||> Proof.show_i NONE after_qed [(Thm.empty_binding, [(thesis, [])])] false
|-> Proof.refine_insert
end;
@@ -260,7 +258,7 @@
fun inferred_type (binding, _, mx) ctxt =
let
- val x = Binding.base_name binding;
+ val x = Binding.name_of binding;
val (T, ctxt') = ProofContext.inferred_param x ctxt
in ((x, T, mx), ctxt') end;
@@ -295,7 +293,7 @@
|> Proof.map_context (K ctxt')
|> Proof.fix_i (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms)
|> `Proof.context_of |-> (fn fix_ctxt => Proof.assm_i
- (obtain_export fix_ctxt rule (map cert ts)) [((Binding.empty, []), asms)])
+ (obtain_export fix_ctxt rule (map cert ts)) [(Thm.empty_binding, asms)])
|> Proof.add_binds_i AutoBind.no_facts
end;
@@ -313,7 +311,7 @@
|> Proof.fix_i [(Binding.name AutoBind.thesisN, NONE, NoSyn)]
|> Proof.chain_facts chain_facts
|> Proof.local_goal print_result (K I) (apsnd (rpair I))
- "guess" before_qed after_qed [((Binding.empty, []), [Logic.mk_term goal, goal])]
+ "guess" before_qed after_qed [(Thm.empty_binding, [Logic.mk_term goal, goal])]
|> Proof.refine (Method.primitive_text (K (Goal.init (cert thesis)))) |> Seq.hd
end;
--- a/src/Pure/Isar/outer_parse.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/outer_parse.ML Wed Mar 04 11:37:50 2009 +0100
@@ -228,7 +228,7 @@
(* names and text *)
val name = group "name declaration" (short_ident || sym_ident || string || number);
-val binding = position name >> Binding.name_pos;
+val binding = position name >> Binding.make;
val xname = group "name reference" (short_ident || long_ident || sym_ident || string || number);
val text = group "text" (short_ident || long_ident || sym_ident || string || number || verbatim);
val path = group "file name/path specification" name >> Path.explode;
--- a/src/Pure/Isar/proof.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/proof.ML Wed Mar 04 11:37:50 2009 +0100
@@ -48,23 +48,18 @@
val assm: Assumption.export ->
(Attrib.binding * (string * string list) list) list -> state -> state
val assm_i: Assumption.export ->
- ((binding * attribute list) * (term * term list) list) list -> state -> state
+ (Thm.binding * (term * term list) list) list -> state -> state
val assume: (Attrib.binding * (string * string list) list) list -> state -> state
- val assume_i: ((binding * attribute list) * (term * term list) list) list ->
- state -> state
+ val assume_i: (Thm.binding * (term * term list) list) list -> state -> state
val presume: (Attrib.binding * (string * string list) list) list -> state -> state
- val presume_i: ((binding * attribute list) * (term * term list) list) list ->
- state -> state
- val def: (Attrib.binding * ((binding * mixfix) * (string * string list))) list ->
- state -> state
- val def_i: ((binding * attribute list) *
- ((binding * mixfix) * (term * term list))) list -> state -> state
+ val presume_i: (Thm.binding * (term * term list) list) list -> state -> state
+ val def: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
+ val def_i: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
val chain: state -> state
val chain_facts: thm list -> state -> state
val get_thmss: state -> (Facts.ref * Attrib.src list) list -> thm list
val note_thmss: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
- val note_thmss_i: ((binding * attribute list) *
- (thm list * attribute list) list) list -> state -> state
+ val note_thmss_i: (Thm.binding * (thm list * attribute list) list) list -> state -> state
val from_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
val with_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
@@ -107,11 +102,11 @@
val have: Method.text option -> (thm list list -> state -> state) ->
(Attrib.binding * (string * string list) list) list -> bool -> state -> state
val have_i: Method.text option -> (thm list list -> state -> state) ->
- ((binding * attribute list) * (term * term list) list) list -> bool -> state -> state
+ (Thm.binding * (term * term list) list) list -> bool -> state -> state
val show: Method.text option -> (thm list list -> state -> state) ->
(Attrib.binding * (string * string list) list) list -> bool -> state -> state
val show_i: Method.text option -> (thm list list -> state -> state) ->
- ((binding * attribute list) * (term * term list) list) list -> bool -> state -> state
+ (Thm.binding * (term * term list) list) list -> bool -> state -> state
val schematic_goal: state -> bool
val is_relevant: state -> bool
val local_future_proof: (state -> ('a * state) Future.future) ->
--- a/src/Pure/Isar/proof_context.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/proof_context.ML Wed Mar 04 11:37:50 2009 +0100
@@ -103,12 +103,10 @@
val sticky_prefix: string -> Proof.context -> Proof.context
val restore_naming: Proof.context -> Proof.context -> Proof.context
val reset_naming: Proof.context -> Proof.context
- val note_thmss: string ->
- ((binding * attribute list) * (Facts.ref * attribute list) list) list ->
- Proof.context -> (string * thm list) list * Proof.context
- val note_thmss_i: string ->
- ((binding * attribute list) * (thm list * attribute list) list) list ->
- Proof.context -> (string * thm list) list * Proof.context
+ val note_thmss: string -> (Thm.binding * (Facts.ref * attribute list) list) list ->
+ Proof.context -> (string * thm list) list * Proof.context
+ val note_thmss_i: string -> (Thm.binding * (thm list * attribute list) list) list ->
+ Proof.context -> (string * thm list) list * Proof.context
val put_thms: bool -> string * thm list option -> Proof.context -> Proof.context
val read_vars: (binding * string option * mixfix) list -> Proof.context ->
(binding * typ option * mixfix) list * Proof.context
@@ -121,10 +119,10 @@
val auto_fixes: Proof.context * (term list list * 'a) -> Proof.context * (term list list * 'a)
val bind_fixes: string list -> Proof.context -> (term -> term) * Proof.context
val add_assms: Assumption.export ->
- ((binding * attribute list) * (string * string list) list) list ->
+ (Thm.binding * (string * string list) list) list ->
Proof.context -> (string * thm list) list * Proof.context
val add_assms_i: Assumption.export ->
- ((binding * attribute list) * (term * term list) list) list ->
+ (Thm.binding * (term * term list) list) list ->
Proof.context -> (string * thm list) list * Proof.context
val add_cases: bool -> (string * RuleCases.T option) list -> Proof.context -> Proof.context
val apply_case: RuleCases.T -> Proof.context -> (string * term list) list * Proof.context
@@ -1010,7 +1008,7 @@
fun prep_vars prep_typ internal =
fold_map (fn (raw_b, raw_T, raw_mx) => fn ctxt =>
let
- val raw_x = Binding.base_name raw_b;
+ val raw_x = Binding.name_of raw_b;
val (x, mx) = Syntax.const_mixfix raw_x raw_mx;
val _ = Syntax.is_identifier (no_skolem internal x) orelse
error ("Illegal variable name: " ^ quote x);
@@ -1019,7 +1017,7 @@
if internal then T
else Type.no_tvars T handle TYPE (msg, _, _) => error msg;
val opt_T = Option.map (cond_tvars o cert_typ ctxt o prep_typ ctxt) raw_T;
- val var = (Binding.map_base (K x) raw_b, opt_T, mx);
+ val var = (Binding.map_name (K x) raw_b, opt_T, mx);
in (var, ctxt |> declare_var (x, opt_T, mx) |> #2) end);
in
@@ -1093,7 +1091,7 @@
fun add_abbrev mode tags (b, raw_t) ctxt =
let
val t0 = cert_term (ctxt |> set_mode mode_abbrev) raw_t
- handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote (Binding.display b));
+ handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote (Binding.str_of b));
val [t] = Variable.exportT_terms (Variable.declare_term t0 ctxt) ctxt [t0];
val ((lhs, rhs), consts') = consts_of ctxt
|> Consts.abbreviate (Syntax.pp ctxt) (tsig_of ctxt) (naming_of ctxt) mode tags (b, t);
@@ -1120,7 +1118,7 @@
fun gen_fixes prep raw_vars ctxt =
let
val (vars, _) = prep raw_vars ctxt;
- val (xs', ctxt') = Variable.add_fixes (map (Binding.base_name o #1) vars) ctxt;
+ val (xs', ctxt') = Variable.add_fixes (map (Binding.name_of o #1) vars) ctxt;
val ctxt'' =
ctxt'
|> fold_map declare_var (map2 (fn x' => fn (_, T, mx) => (x', T, mx)) xs' vars)
--- a/src/Pure/Isar/specification.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/specification.ML Wed Mar 04 11:37:50 2009 +0100
@@ -140,7 +140,7 @@
fun gen_axioms do_print prep raw_vars raw_specs thy =
let
val ((vars, specs), _) = prep raw_vars [raw_specs] (ProofContext.init thy);
- val xs = map (fn ((b, T), _) => (Binding.base_name b, T)) vars;
+ val xs = map (fn ((b, T), _) => (Binding.name_of b, T)) vars;
(*consts*)
val (consts, consts_thy) = thy |> fold_map (Theory.specify_const []) vars;
@@ -148,8 +148,8 @@
(*axioms*)
val (axioms, axioms_thy) = consts_thy |> fold_map (fn ((b, atts), props) =>
- fold_map Thm.add_axiom
- ((map o apfst) Binding.name (PureThy.name_multi (Binding.base_name b) (map subst props)))
+ fold_map Thm.add_axiom (* FIXME proper use of binding!? *)
+ ((map o apfst) Binding.name (PureThy.name_multi (Binding.name_of b) (map subst props)))
#>> (fn ths => ((b, atts), [(map Drule.standard' ths, [])]))) specs;
val (facts, thy') = axioms_thy |> PureThy.note_thmss Thm.axiomK
(Attrib.map_facts (Attrib.attribute_i axioms_thy) axioms);
@@ -169,19 +169,19 @@
val (vars, [((raw_name, atts), [prop])]) =
fst (prep (the_list raw_var) [(raw_a, [raw_prop])] lthy);
val (((x, T), rhs), prove) = LocalDefs.derived_def lthy true prop;
- val name = Binding.map_base (Thm.def_name_optional x) raw_name;
+ val name = Binding.map_name (Thm.def_name_optional x) raw_name;
val var =
(case vars of
[] => (Binding.name x, NoSyn)
| [((b, _), mx)] =>
let
- val y = Binding.base_name b;
+ val y = Binding.name_of b;
val _ = x = y orelse
error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote y ^
Position.str_of (Binding.pos_of b));
in (b, mx) end);
val ((lhs, (_, th)), lthy2) = lthy |> LocalTheory.define Thm.definitionK
- (var, ((Binding.map_base (suffix "_raw") name, []), rhs));
+ (var, ((Binding.map_name (suffix "_raw") name, []), rhs));
val ((def_name, [th']), lthy3) = lthy2 |> LocalTheory.note Thm.definitionK
((name, Code.add_default_eqn_attrib :: atts), [prove lthy2 th]);
@@ -208,7 +208,7 @@
[] => (Binding.name x, NoSyn)
| [((b, _), mx)] =>
let
- val y = Binding.base_name b;
+ val y = Binding.name_of b;
val _ = x = y orelse
error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y ^
Position.str_of (Binding.pos_of b));
@@ -269,11 +269,10 @@
| Element.Obtains obtains =>
let
val case_names = obtains |> map_index (fn (i, (b, _)) =>
- let val name = Binding.base_name b
- in if name = "" then string_of_int (i + 1) else name end);
+ if Binding.is_empty b then string_of_int (i + 1) else Binding.name_of b);
val constraints = obtains |> map (fn (_, (vars, _)) =>
Element.Constrains
- (vars |> map_filter (fn (x, SOME T) => SOME (Binding.base_name x, T) | _ => NONE)));
+ (vars |> map_filter (fn (x, SOME T) => SOME (Binding.name_of x, T) | _ => NONE)));
val raw_propp = obtains |> map (fn (_, (_, props)) => map (rpair []) props);
val (propp, elems_ctxt) = prep_stmt (elems @ constraints) raw_propp ctxt;
@@ -283,7 +282,7 @@
fun assume_case ((name, (vars, _)), asms) ctxt' =
let
val bs = map fst vars;
- val xs = map Binding.base_name bs;
+ val xs = map Binding.name_of bs;
val props = map fst asms;
val (Ts, _) = ctxt'
|> fold Variable.declare_term props
--- a/src/Pure/Isar/theory_target.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Isar/theory_target.ML Wed Mar 04 11:37:50 2009 +0100
@@ -188,8 +188,8 @@
val arg = (b', Term.close_schematic_term rhs');
val similar_body = Type.similar_types (rhs, rhs');
(* FIXME workaround based on educated guess *)
- val (prefix', _) = Binding.dest b';
- val class_global = Binding.base_name b = Binding.base_name b'
+ val (prefix', _, _) = Binding.dest b';
+ val class_global = Binding.name_of b = Binding.name_of b'
andalso not (null prefix')
andalso (fst o snd o split_last) prefix' = Class_Target.class_prefix target;
in
@@ -206,14 +206,15 @@
Morphism.form (ProofContext.target_notation true prmode [(lhs', mx)]))))
end;
+fun syntax_error c = error ("Illegal mixfix syntax for overloaded constant " ^ quote c);
+
fun declare_const (ta as Target {target, is_locale, is_class, ...}) depends ((b, T), mx) lthy =
let
- val c = Binding.base_name b;
+ val c = Binding.name_of b;
val tags = LocalTheory.group_position_of lthy;
val xs = filter depends (#1 (ProofContext.inferred_fixes (LocalTheory.target_of lthy)));
val U = map #2 xs ---> T;
val (mx1, mx2, mx3) = fork_mixfix ta mx;
- fun syntax_error c = error ("Illegal mixfix syntax for overloaded constant " ^ quote c);
val declare_const =
(case Class_Target.instantiation_param lthy c of
SOME c' =>
@@ -241,7 +242,7 @@
fun abbrev (ta as Target {target, is_locale, is_class, ...}) prmode ((b, mx), t) lthy =
let
- val c = Binding.base_name b;
+ val c = Binding.name_of b;
val tags = LocalTheory.group_position_of lthy;
val thy_ctxt = ProofContext.init (ProofContext.theory_of lthy);
val target_ctxt = LocalTheory.target_of lthy;
@@ -278,8 +279,8 @@
val thy = ProofContext.theory_of lthy;
val thy_ctxt = ProofContext.init thy;
- val c = Binding.base_name b;
- val name' = Binding.map_base (Thm.def_name_optional c) name;
+ val c = Binding.name_of b;
+ val name' = Binding.map_name (Thm.def_name_optional c) name;
val (rhs', rhs_conv) =
LocalDefs.export_cterm lthy thy_ctxt (Thm.cterm_of thy rhs) |>> Thm.term_of;
val xs = Variable.add_fixed (LocalTheory.target_of lthy) rhs' [];
@@ -299,7 +300,7 @@
then (fn name => fn eq => Thm.add_def false false (Binding.name name, Logic.mk_equals eq))
else (fn name => fn (Const (c, _), rhs) => AxClass.define_overloaded name (c, rhs)));
val (global_def, lthy3) = lthy2
- |> LocalTheory.theory_result (define_const (Binding.base_name name') (lhs', rhs'));
+ |> LocalTheory.theory_result (define_const (Binding.name_of name') (lhs', rhs'));
val def = LocalDefs.trans_terms lthy3
[(*c == global.c xs*) local_def,
(*global.c xs == rhs'*) global_def,
--- a/src/Pure/ML/ml_antiquote.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/ML/ml_antiquote.ML Wed Mar 04 11:37:50 2009 +0100
@@ -59,12 +59,13 @@
-(** concrete antiquotations **)
+(** misc antiquotations **)
structure P = OuterParse;
-
-(* misc *)
+val _ = inline "binding" (Scan.lift (P.position Args.name) >> (fn b =>
+ ML_Syntax.atomic ("Binding.make " ^
+ ML_Syntax.print_pair ML_Syntax.print_string ML_Syntax.print_position b)));
val _ = value "theory"
(Scan.lift Args.name >> (fn name => "ThyInfo.get_theory " ^ ML_Syntax.print_string name)
--- a/src/Pure/ML/ml_syntax.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/ML/ml_syntax.ML Wed Mar 04 11:37:50 2009 +0100
@@ -18,6 +18,8 @@
val print_char: string -> string
val print_string: string -> string
val print_strings: string list -> string
+ val print_properties: Properties.T -> string
+ val print_position: Position.T -> string
val print_indexname: indexname -> string
val print_class: class -> string
val print_sort: sort -> string
@@ -68,6 +70,9 @@
val print_string = quote o translate_string print_char;
val print_strings = print_list print_string;
+val print_properties = print_list (print_pair print_string print_string);
+fun print_position pos = "Position.of_properties " ^ print_properties (Position.properties_of pos);
+
val print_indexname = print_pair print_string print_int;
val print_class = print_string;
--- a/src/Pure/Thy/thy_output.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Thy/thy_output.ML Wed Mar 04 11:37:50 2009 +0100
@@ -519,9 +519,9 @@
fun ml_type txt = "val _ = NONE : (" ^ txt ^ ") option;";
fun ml_struct txt = "functor DUMMY_FUNCTOR() = struct structure DUMMY = " ^ txt ^ " end;"
-fun output_ml ml src ctxt (txt, pos) =
+fun output_ml ml _ ctxt (txt, pos) =
(ML_Context.eval_in (SOME ctxt) false pos (ml txt);
- (if ! source then str_of_source src else SymbolPos.content (SymbolPos.explode (txt, pos)))
+ SymbolPos.content (SymbolPos.explode (txt, pos))
|> (if ! quotes then quote else I)
|> (if ! display then enclose "\\begin{verbatim}\n" "\n\\end{verbatim}"
else
--- a/src/Pure/Tools/find_theorems.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/Tools/find_theorems.ML Wed Mar 04 11:37:50 2009 +0100
@@ -169,8 +169,7 @@
fun try_thm thm =
if Thm.no_prems thm then rtac thm 1 goal
else (etacn thm THEN_ALL_NEW
- (Goal.norm_hhf_tac THEN'
- Method.assumption_tac ctxt)) 1 goal;
+ (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
in
fn (_, thm) =>
if (is_some o Seq.pull o try_thm) thm
@@ -306,14 +305,11 @@
fun nicer_shortest ctxt =
let
- val ns = ProofContext.theory_of ctxt
- |> PureThy.facts_of
- |> Facts.space_of;
+ (* FIXME global name space!? *)
+ val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));
- val len_sort = sort (int_ord o (pairself size));
- fun shorten s = (case len_sort (NameSpace.get_accesses ns s) of
- [] => s
- | s'::_ => s');
+ val shorten =
+ NameSpace.extern_flags {long_names = false, short_names = false, unique_names = false} space;
fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
nicer_name (shorten x, i) (shorten y, j)
--- a/src/Pure/axclass.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/axclass.ML Wed Mar 04 11:37:50 2009 +0100
@@ -8,7 +8,7 @@
signature AX_CLASS =
sig
val define_class: bstring * class list -> string list ->
- ((binding * attribute list) * term list) list -> theory -> class * theory
+ (Thm.binding * term list) list -> theory -> class * theory
val add_classrel: thm -> theory -> theory
val add_arity: thm -> theory -> theory
val prove_classrel: class * class -> tactic -> theory -> theory
--- a/src/Pure/more_thm.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/more_thm.ML Wed Mar 04 11:37:50 2009 +0100
@@ -40,6 +40,8 @@
val close_derivation: thm -> thm
val add_axiom: binding * term -> theory -> thm * theory
val add_def: bool -> bool -> binding * term -> theory -> thm * theory
+ type binding = binding * attribute list
+ val empty_binding: binding
val rule_attribute: (Context.generic -> thm -> thm) -> attribute
val declaration_attribute: (thm -> Context.generic -> Context.generic) -> attribute
val theory_attributes: attribute list -> theory * thm -> theory * thm
@@ -301,6 +303,9 @@
(** attributes **)
+type binding = binding * attribute list;
+val empty_binding: binding = (Binding.empty, []);
+
fun rule_attribute f (x, th) = (x, f x th);
fun declaration_attribute f (x, th) = (f th x, th);
--- a/src/Pure/pure_setup.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/pure_setup.ML Wed Mar 04 11:37:50 2009 +0100
@@ -33,7 +33,7 @@
map (fn (x, y) => Pretty.str (x ^ "=" ^ y)) o Position.properties_of));
install_pp (make_pp ["Thm", "thm"] ProofDisplay.pprint_thm);
install_pp (make_pp ["Thm", "cterm"] ProofDisplay.pprint_cterm);
-install_pp (make_pp ["Binding", "binding"] (Pretty.pprint o Pretty.str o Binding.display));
+install_pp (make_pp ["Binding", "binding"] (Pretty.pprint o Pretty.str o Binding.str_of));
install_pp (make_pp ["Thm", "ctyp"] ProofDisplay.pprint_ctyp);
install_pp (make_pp ["Context", "theory"] Context.pprint_thy);
install_pp (make_pp ["Context", "theory_ref"] Context.pprint_thy_ref);
--- a/src/Pure/pure_thy.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/pure_thy.ML Wed Mar 04 11:37:50 2009 +0100
@@ -31,10 +31,10 @@
val add_thm: (binding * thm) * attribute list -> theory -> thm * theory
val add_thmss: ((binding * thm list) * attribute list) list -> theory -> thm list list * theory
val add_thms_dynamic: binding * (Context.generic -> thm list) -> theory -> theory
- val note_thmss: string -> ((binding * attribute list) *
- (thm list * attribute list) list) list -> theory -> (string * thm list) list * theory
- val note_thmss_grouped: string -> string -> ((binding * attribute list) *
- (thm list * attribute list) list) list -> theory -> (string * thm list) list * theory
+ val note_thmss: string -> (Thm.binding *
+ (thm list * attribute list) list) list -> theory -> (string * thm list) list * theory
+ val note_thmss_grouped: string -> string -> (Thm.binding *
+ (thm list * attribute list) list) list -> theory -> (string * thm list) list * theory
val add_axioms: ((binding * term) * attribute list) list -> theory -> thm list * theory
val add_axioms_cmd: ((bstring * string) * attribute list) list -> theory -> thm list * theory
val add_defs: bool -> ((binding * term) * attribute list) list ->
@@ -151,14 +151,15 @@
fun enter_thms pre_name post_name app_att (b, thms) thy =
if Binding.is_empty b
then swap (enter_proofs (app_att (thy, thms)))
- else let
- val naming = Sign.naming_of thy;
- val name = NameSpace.full_name naming b;
- val (thy', thms') =
- enter_proofs (apsnd (post_name name) (app_att (thy, pre_name name thms)));
- val thms'' = map (Thm.transfer thy') thms';
- val thy'' = thy' |> (FactsData.map o apfst) (Facts.add_global naming (b, thms'') #> snd);
- in (thms'', thy'') end;
+ else
+ let
+ val naming = Sign.naming_of thy;
+ val name = NameSpace.full_name naming b;
+ val (thy', thms') =
+ enter_proofs (apsnd (post_name name) (app_att (thy, pre_name name thms)));
+ val thms'' = map (Thm.transfer thy') thms';
+ val thy'' = thy' |> (FactsData.map o apfst) (Facts.add_global naming (b, thms'') #> snd);
+ in (thms'', thy'') end;
(* store_thm(s) *)
--- a/src/Pure/sign.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/sign.ML Wed Mar 04 11:37:50 2009 +0100
@@ -507,12 +507,12 @@
val prepT = Type.no_tvars o Term.no_dummyT o certify_typ thy o parse_typ ctxt;
fun prep (raw_b, raw_T, raw_mx) =
let
- val (mx_name, mx) = Syntax.const_mixfix (Binding.base_name raw_b) raw_mx;
- val b = Binding.map_base (K mx_name) raw_b;
+ val (mx_name, mx) = Syntax.const_mixfix (Binding.name_of raw_b) raw_mx;
+ val b = Binding.map_name (K mx_name) raw_b;
val c = full_name thy b;
- val c_syn = if authentic then Syntax.constN ^ c else Binding.base_name b;
+ val c_syn = if authentic then Syntax.constN ^ c else Binding.name_of b;
val T = (prepT raw_T handle TYPE (msg, _, _) => error msg) handle ERROR msg =>
- cat_error msg ("in declaration of constant " ^ quote (Binding.display b));
+ cat_error msg ("in declaration of constant " ^ quote (Binding.str_of b));
val T' = Logic.varifyT T;
in ((b, T'), (c_syn, T', mx), Const (c, T)) end;
val args = map prep raw_args;
@@ -549,7 +549,7 @@
val pp = Syntax.pp_global thy;
val prep_tm = no_frees pp o Term.no_dummy_patterns o cert_term_abbrev thy;
val t = (prep_tm raw_t handle TYPE (msg, _, _) => error msg | TERM (msg, _) => error msg)
- handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote (Binding.display b));
+ handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote (Binding.str_of b));
val (res, consts') = consts_of thy
|> Consts.abbreviate pp (tsig_of thy) (naming_of thy) mode tags (b, t);
in (res, thy |> map_consts (K consts')) end;
--- a/src/Pure/theory.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Pure/theory.ML Wed Mar 04 11:37:50 2009 +0100
@@ -258,7 +258,7 @@
val _ = check_overloading thy overloaded lhs_const;
in defs |> dependencies thy unchecked true name lhs_const rhs_consts end
handle ERROR msg => cat_error msg (Pretty.string_of (Pretty.block
- [Pretty.str ("The error(s) above occurred in definition " ^ quote (Binding.display b) ^ ":"),
+ [Pretty.str ("The error(s) above occurred in definition " ^ quote (Binding.str_of b) ^ ":"),
Pretty.fbrk, Pretty.quote (Syntax.pretty_term_global thy tm)]));
--- a/src/Tools/induct.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/Tools/induct.ML Wed Mar 04 11:37:50 2009 +0100
@@ -552,7 +552,7 @@
let
fun add (SOME (SOME x, t)) ctxt =
let val ([(lhs, (_, th))], ctxt') =
- LocalDefs.add_defs [((x, NoSyn), ((Binding.empty, []), t))] ctxt
+ LocalDefs.add_defs [((x, NoSyn), (Thm.empty_binding, t))] ctxt
in ((SOME lhs, [th]), ctxt') end
| add (SOME (NONE, t)) ctxt = ((SOME t, []), ctxt)
| add NONE ctxt = ((NONE, []), ctxt);
--- a/src/ZF/Tools/inductive_package.ML Wed Mar 04 10:52:47 2009 +0100
+++ b/src/ZF/Tools/inductive_package.ML Wed Mar 04 11:37:50 2009 +0100
@@ -65,7 +65,7 @@
val _ = Theory.requires thy "Inductive_ZF" "(co)inductive definitions";
val ctxt = ProofContext.init thy;
- val intr_specs = map (apfst (apfst Binding.base_name)) raw_intr_specs;
+ val intr_specs = map (apfst (apfst Binding.name_of)) raw_intr_specs;
val (intr_names, intr_tms) = split_list (map fst intr_specs);
val case_names = RuleCases.case_names intr_names;