1.1 --- a/doc-src/IsarImplementation/Thy/ML.thy Thu Sep 07 15:16:51 2006 +0200
1.2 +++ b/doc-src/IsarImplementation/Thy/ML.thy Thu Sep 07 20:12:08 2006 +0200
1.3 @@ -18,7 +18,7 @@
1.4
1.5 chapter {* Cookbook *}
1.6
1.7 -section {* Defining a method that depends on declarations in the context *}
1.8 +section {* A method that depends on declarations in the context *}
1.9
1.10 text FIXME
1.11
2.1 --- a/doc-src/IsarImplementation/Thy/document/ML.tex Thu Sep 07 15:16:51 2006 +0200
2.2 +++ b/doc-src/IsarImplementation/Thy/document/ML.tex Thu Sep 07 20:12:08 2006 +0200
2.3 @@ -43,7 +43,7 @@
2.4 }
2.5 \isamarkuptrue%
2.6 %
2.7 -\isamarkupsection{Defining a method that depends on declarations in the context%
2.8 +\isamarkupsection{A method that depends on declarations in the context%
2.9 }
2.10 \isamarkuptrue%
2.11 %
3.1 --- a/doc-src/IsarImplementation/Thy/document/integration.tex Thu Sep 07 15:16:51 2006 +0200
3.2 +++ b/doc-src/IsarImplementation/Thy/document/integration.tex Thu Sep 07 20:12:08 2006 +0200
3.3 @@ -510,15 +510,6 @@
3.4 %
3.5 \endisadelimmlref
3.6 %
3.7 -\isamarkupsection{Sessions and document preparation%
3.8 -}
3.9 -\isamarkuptrue%
3.10 -%
3.11 -\begin{isamarkuptext}%
3.12 -FIXME%
3.13 -\end{isamarkuptext}%
3.14 -\isamarkuptrue%
3.15 -%
3.16 \isadelimtheory
3.17 %
3.18 \endisadelimtheory
4.1 --- a/doc-src/IsarImplementation/Thy/document/logic.tex Thu Sep 07 15:16:51 2006 +0200
4.2 +++ b/doc-src/IsarImplementation/Thy/document/logic.tex Thu Sep 07 20:12:08 2006 +0200
4.3 @@ -28,15 +28,18 @@
4.4 which has been introduced as a natural-deduction framework in
4.5 \cite{paulson700}. This is essentially the same logic as ``\isa{{\isasymlambda}HOL}'' in the more abstract framework of Pure Type Systems (PTS)
4.6 \cite{Barendregt-Geuvers:2001}, although there are some key
4.7 - differences in the practical treatment of simple types.
4.8 + differences in the specific treatment of simple types in
4.9 + Isabelle/Pure.
4.10
4.11 Following type-theoretic parlance, the Pure logic consists of three
4.12 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
4.13 \isa{{\isasymLongrightarrow}} for implication (proofs depending on proofs).
4.14
4.15 Pure derivations are relative to a logical theory, which declares
4.16 - type constructors, term constants, and axioms. Term constants and
4.17 - axioms support schematic polymorphism.%
4.18 + type constructors, term constants, and axioms. Theory declarations
4.19 + support schematic polymorphism, which is strictly speaking outside
4.20 + the logic.\footnote{Incidently, this is the main logical reason, why
4.21 + the theory context \isa{{\isasymTheta}} is separate from the context \isa{{\isasymGamma}} of the core calculus.}%
4.22 \end{isamarkuptext}%
4.23 \isamarkuptrue%
4.24 %
4.25 @@ -50,38 +53,42 @@
4.26
4.27 \medskip A \emph{type class} is an abstract syntactic entity
4.28 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
4.29 - generating relation; the transitive closure maintained internally.
4.30 + generating relation; the transitive closure is maintained
4.31 + internally. The resulting relation is an ordering: reflexive,
4.32 + transitive, and antisymmetric.
4.33
4.34 A \emph{sort} is a list of type classes written as \isa{{\isacharbraceleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlisub m{\isacharbraceright}}, which represents symbolic
4.35 intersection. Notationally, the curly braces are omitted for
4.36 singleton intersections, i.e.\ any class \isa{c} may be read as
4.37 a sort \isa{{\isacharbraceleft}c{\isacharbraceright}}. The ordering on type classes is extended to
4.38 - sorts in the canonical fashion: \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
4.39 - universal sort, which is the largest element wrt.\ the sort order.
4.40 - The intersections of all (i.e.\ finitely many) classes declared in
4.41 - the current theory are the minimal elements wrt.\ sort order.
4.42 + 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
4.43 + \isa{{\isasymforall}j{\isachardot}\ {\isasymexists}i{\isachardot}\ c\isactrlisub i\ {\isasymsubseteq}\ d\isactrlisub j}. The empty intersection
4.44 + \isa{{\isacharbraceleft}{\isacharbraceright}} refers to the universal sort, which is the largest
4.45 + element wrt.\ the sort order. The intersections of all (finitely
4.46 + many) classes declared in the current theory are the minimal
4.47 + elements wrt.\ the sort order.
4.48
4.49 - \medskip A \emph{fixed type variable} is pair of a basic name
4.50 + \medskip A \emph{fixed type variable} is a pair of a basic name
4.51 (starting with \isa{{\isacharprime}} character) and a sort constraint. For
4.52 example, \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
4.53 - indexname and a sort constraint. For example, \isa{{\isacharparenleft}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ s{\isacharparenright}} which is usually printed \isa{{\isacharquery}{\isasymalpha}\isactrlisub s}.
4.54 + indexname and a sort constraint. For example, \isa{{\isacharparenleft}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ s{\isacharparenright}} which is usually printed as \isa{{\isacharquery}{\isasymalpha}\isactrlisub s}.
4.55
4.56 Note that \emph{all} syntactic components contribute to the identity
4.57 - of a type variables, including the literal sort constraint. The
4.58 - core logic handles type variables with the same name but different
4.59 - sorts as different, even though the outer layers of the system make
4.60 - it hard to produce anything like this.
4.61 + of type variables, including the literal sort constraint. The core
4.62 + logic handles type variables with the same name but different sorts
4.63 + as different, although some outer layers of the system make it hard
4.64 + to produce anything like this.
4.65
4.66 - A \emph{type constructor} is an \isa{k}-ary type operator
4.67 - declared in the theory.
4.68 + A \emph{type constructor} is a \isa{k}-ary operator on types
4.69 + declared in the theory. Type constructor application is usually
4.70 + written postfix. For \isa{k\ {\isacharequal}\ {\isadigit{0}}} the argument tuple is omitted,
4.71 + 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
4.72 + \isa{{\isacharparenleft}{\isasymalpha}{\isacharparenright}list}. Further notation is provided for specific
4.73 + constructors, notably right-associative infix \isa{{\isasymalpha}\ {\isasymRightarrow}\ {\isasymbeta}}
4.74 + instead of \isa{{\isacharparenleft}{\isasymalpha}{\isacharcomma}\ {\isasymbeta}{\isacharparenright}fun} constructor.
4.75
4.76 A \emph{type} is defined inductively over type variables and type
4.77 - constructors: \isa{{\isasymtau}\ {\isacharequal}\ {\isasymalpha}\isactrlisub s\ {\isacharbar}\ {\isacharquery}{\isasymalpha}\isactrlisub s\ {\isacharbar}\ {\isacharparenleft}{\isasymtau}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlsub k{\isacharparenright}c}. Type constructor application is usually written
4.78 - postfix. For \isa{k\ {\isacharequal}\ {\isadigit{0}}} the argument tuple is omitted, e.g.\
4.79 - \isa{prop} instead of \isa{{\isacharparenleft}{\isacharparenright}prop}. For \isa{k\ {\isacharequal}\ {\isadigit{1}}} the
4.80 - parentheses are omitted, e.g.\ \isa{{\isasymtau}\ list} instead of \isa{{\isacharparenleft}{\isasymtau}{\isacharparenright}\ list}. Further notation is provided for specific
4.81 - constructors, notably right-associative infix \isa{{\isasymtau}\isactrlisub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymtau}\isactrlisub {\isadigit{2}}} instead of \isa{{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymtau}\isactrlisub {\isadigit{2}}{\isacharparenright}fun}
4.82 - constructor.
4.83 + 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}c}.
4.84
4.85 A \emph{type abbreviation} is a syntactic abbreviation of an
4.86 arbitrary type expression of the theory. Type abbreviations looks
4.87 @@ -89,21 +96,23 @@
4.88 core logic encounters them.
4.89
4.90 A \emph{type arity} declares the image behavior of a type
4.91 - constructor wrt.\ the algebra of sorts: \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlisub n{\isacharparenright}s} means that \isa{{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub k{\isacharparenright}c} is
4.92 + constructor wrt.\ the algebra of sorts: \isa{c\ {\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}c} is
4.93 of sort \isa{s} if each argument type \isa{{\isasymtau}\isactrlisub i} is of
4.94 - sort \isa{s\isactrlisub i}. The sort algebra is always maintained as
4.95 - \emph{coregular}, which means that type arities are consistent with
4.96 - the subclass relation: for each type constructor \isa{c} and
4.97 - classes \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}, any arity \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{1}}{\isacharparenright}c\isactrlisub {\isadigit{1}}} has a corresponding arity \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{2}}{\isacharparenright}c\isactrlisub {\isadigit{2}}} where \isa{\isactrlvec s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ \isactrlvec s\isactrlisub {\isadigit{2}}} holds pointwise for all argument sorts.
4.98 + sort \isa{s\isactrlisub i}. Arity declarations are implicitly
4.99 + completed, i.e.\ \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c} entails \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isacharprime}} for any \isa{c{\isacharprime}\ {\isasymsupseteq}\ c}.
4.100
4.101 - The key property of the order-sorted algebra of types is that sort
4.102 + \medskip The sort algebra is always maintained as \emph{coregular},
4.103 + which means that type arities are consistent with the subclass
4.104 + relation: for each type constructor \isa{c} and classes \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}, any arity \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{1}}{\isacharparenright}c\isactrlisub {\isadigit{1}}} has a corresponding arity \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{2}}{\isacharparenright}c\isactrlisub {\isadigit{2}}} where \isa{\isactrlvec s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ \isactrlvec s\isactrlisub {\isadigit{2}}} holds pointwise for all argument sorts.
4.105 +
4.106 + The key property of a coregular order-sorted algebra is that sort
4.107 constraints may be always fulfilled in a most general fashion: for
4.108 each type constructor \isa{c} and sort \isa{s} there is a
4.109 - most general vector of argument sorts \isa{{\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlisub k{\isacharparenright}} such that \isa{{\isacharparenleft}{\isasymtau}\isactrlbsub s\isactrlisub {\isadigit{1}}\isactrlesub {\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlbsub s\isactrlisub k\isactrlesub {\isacharparenright}} for arbitrary \isa{{\isasymtau}\isactrlisub i} of
4.110 - sort \isa{s\isactrlisub i}. This means the unification problem on
4.111 - the algebra of types has most general solutions (modulo renaming and
4.112 - equivalence of sorts). As a consequence, type-inference is able to
4.113 - produce primary types.%
4.114 + 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}c} is
4.115 + of sort \isa{s}. Consequently, the unification problem on the
4.116 + algebra of types has most general solutions (modulo renaming and
4.117 + equivalence of sorts). Moreover, the usual type-inference algorithm
4.118 + will produce primary types as expected \cite{nipkow-prehofer}.%
4.119 \end{isamarkuptext}%
4.120 \isamarkuptrue%
4.121 %
4.122 @@ -147,18 +156,18 @@
4.123 tests the subsort relation \isa{s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ s\isactrlisub {\isadigit{2}}}.
4.124
4.125 \item \verb|Sign.of_sort|~\isa{thy\ {\isacharparenleft}{\isasymtau}{\isacharcomma}\ s{\isacharparenright}} tests whether a type
4.126 - expression of of a given sort.
4.127 + is of a given sort.
4.128
4.129 \item \verb|Sign.add_types|~\isa{{\isacharbrackleft}{\isacharparenleft}c{\isacharcomma}\ k{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}} declares new
4.130 - type constructors \isa{c} with \isa{k} arguments, and
4.131 + type constructors \isa{c} with \isa{k} arguments and
4.132 optional mixfix syntax.
4.133
4.134 \item \verb|Sign.add_tyabbrs_i|~\isa{{\isacharbrackleft}{\isacharparenleft}c{\isacharcomma}\ \isactrlvec {\isasymalpha}{\isacharcomma}\ {\isasymtau}{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}}
4.135 - defines type abbreviation \isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}c} (with optional
4.136 - mixfix syntax) as \isa{{\isasymtau}}.
4.137 + defines a new type abbreviation \isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}c\ {\isacharequal}\ {\isasymtau}} with
4.138 + optional mixfix syntax.
4.139
4.140 \item \verb|Sign.primitive_class|~\isa{{\isacharparenleft}c{\isacharcomma}\ {\isacharbrackleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlisub n{\isacharbrackright}{\isacharparenright}} declares new class \isa{c} derived together with
4.141 - class relations \isa{c\ {\isasymsubseteq}\ c\isactrlisub i}.
4.142 + class relations \isa{c\ {\isasymsubseteq}\ c\isactrlisub i}, for \isa{i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n}.
4.143
4.144 \item \verb|Sign.primitive_classrel|~\isa{{\isacharparenleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ c\isactrlisub {\isadigit{2}}{\isacharparenright}} declares class relation \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}.
4.145
4.146 @@ -183,6 +192,13 @@
4.147 \begin{isamarkuptext}%
4.148 \glossary{Term}{FIXME}
4.149
4.150 + The language of terms is that of simply-typed \isa{{\isasymlambda}}-calculus
4.151 + with de-Bruijn indices for bound variables, and named free
4.152 + variables, and constants. Terms with loose bound variables are
4.153 + usually considered malformed. The types of variables and constants
4.154 + is stored explicitly at each occurrence in the term (which is a
4.155 + known performance issue).
4.156 +
4.157 FIXME de-Bruijn representation of lambda terms
4.158
4.159 Term syntax provides explicit abstraction \isa{{\isasymlambda}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ b{\isacharparenleft}x{\isacharparenright}}
4.160 @@ -203,15 +219,6 @@
4.161 \end{isamarkuptext}%
4.162 \isamarkuptrue%
4.163 %
4.164 -\isamarkupsection{Proof terms%
4.165 -}
4.166 -\isamarkuptrue%
4.167 -%
4.168 -\begin{isamarkuptext}%
4.169 -FIXME%
4.170 -\end{isamarkuptext}%
4.171 -\isamarkuptrue%
4.172 -%
4.173 \isamarkupsection{Theorems \label{sec:thms}%
4.174 }
4.175 \isamarkuptrue%
4.176 @@ -267,22 +274,53 @@
4.177 \end{isamarkuptext}%
4.178 \isamarkuptrue%
4.179 %
4.180 -\isamarkupsubsection{Primitive inferences%
4.181 +\isamarkupsection{Proof terms%
4.182 }
4.183 \isamarkuptrue%
4.184 %
4.185 \begin{isamarkuptext}%
4.186 -FIXME%
4.187 +FIXME !?%
4.188 \end{isamarkuptext}%
4.189 \isamarkuptrue%
4.190 %
4.191 -\isamarkupsubsection{Higher-order resolution%
4.192 +\isamarkupsection{Rules \label{sec:rules}%
4.193 }
4.194 \isamarkuptrue%
4.195 %
4.196 \begin{isamarkuptext}%
4.197 FIXME
4.198
4.199 + A \emph{rule} is any Pure theorem in HHF normal form; there is a
4.200 + separate calculus for rule composition, which is modeled after
4.201 + Gentzen's Natural Deduction \cite{Gentzen:1935}, but allows
4.202 + rules to be nested arbitrarily, similar to \cite{extensions91}.
4.203 +
4.204 + Normally, all theorems accessible to the user are proper rules.
4.205 + Low-level inferences are occasional required internally, but the
4.206 + result should be always presented in canonical form. The higher
4.207 + interfaces of Isabelle/Isar will always produce proper rules. It is
4.208 + important to maintain this invariant in add-on applications!
4.209 +
4.210 + There are two main principles of rule composition: \isa{resolution} (i.e.\ backchaining of rules) and \isa{by{\isacharminus}assumption} (i.e.\ closing a branch); both principles are
4.211 + combined in the variants of \isa{elim{\isacharminus}resosultion} and \isa{dest{\isacharminus}resolution}. Raw \isa{composition} is occasionally
4.212 + useful as well, also it is strictly speaking outside of the proper
4.213 + rule calculus.
4.214 +
4.215 + Rules are treated modulo general higher-order unification, which is
4.216 + unification modulo the equational theory of \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion
4.217 + on \isa{{\isasymlambda}}-terms. Moreover, propositions are understood modulo
4.218 + the (derived) equivalence \isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x{\isacharparenright}{\isacharparenright}\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ A\ {\isasymLongrightarrow}\ B\ x{\isacharparenright}}.
4.219 +
4.220 + This means that any operations within the rule calculus may be
4.221 + subject to spontaneous \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-HHF conversions. It is common
4.222 + practice not to contract or expand unnecessarily. Some mechanisms
4.223 + prefer an one form, others the opposite, so there is a potential
4.224 + danger to produce some oscillation!
4.225 +
4.226 + Only few operations really work \emph{modulo} HHF conversion, but
4.227 + expect a normal form: quantifiers \isa{{\isasymAnd}} before implications
4.228 + \isa{{\isasymLongrightarrow}} at each level of nesting.
4.229 +
4.230 \glossary{Hereditary Harrop Formula}{The set of propositions in HHF
4.231 format is defined inductively as \isa{H\ {\isacharequal}\ {\isacharparenleft}{\isasymAnd}x\isactrlsup {\isacharasterisk}{\isachardot}\ H\isactrlsup {\isacharasterisk}\ {\isasymLongrightarrow}\ A{\isacharparenright}}, for variables \isa{x} and atomic propositions \isa{A}.
4.232 Any proposition may be put into HHF form by normalizing with the rule
4.233 @@ -295,15 +333,6 @@
4.234 \end{isamarkuptext}%
4.235 \isamarkuptrue%
4.236 %
4.237 -\isamarkupsubsection{Equational reasoning%
4.238 -}
4.239 -\isamarkuptrue%
4.240 -%
4.241 -\begin{isamarkuptext}%
4.242 -FIXME%
4.243 -\end{isamarkuptext}%
4.244 -\isamarkuptrue%
4.245 -%
4.246 \isadelimtheory
4.247 %
4.248 \endisadelimtheory
5.1 --- a/doc-src/IsarImplementation/Thy/document/proof.tex Thu Sep 07 15:16:51 2006 +0200
5.2 +++ b/doc-src/IsarImplementation/Thy/document/proof.tex Thu Sep 07 20:12:08 2006 +0200
5.3 @@ -217,7 +217,7 @@
5.4 definition works by fixing \isa{x} and assuming \isa{x\ {\isasymequiv}\ t},
5.5 with the following export rule to reverse the effect:
5.6 \[
5.7 - \infer{\isa{{\isasymGamma}\ {\isacharbackslash}\ x\ {\isasymequiv}\ t\ {\isasymturnstile}\ B\ t}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B\ x}}
5.8 + \infer[(\isa{{\isasymequiv}{\isacharminus}expand})]{\isa{{\isasymGamma}\ {\isacharbackslash}\ x\ {\isasymequiv}\ t\ {\isasymturnstile}\ B\ t}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B\ x}}
5.9 \]
5.10 This works, because the assumption \isa{x\ {\isasymequiv}\ t} was introduced in
5.11 a context with \isa{x} being fresh, so \isa{x} does not
5.12 @@ -291,22 +291,30 @@
5.13 references to free variables or assumptions not present in the proof
5.14 context.
5.15
5.16 - \medskip The \isa{prove} operation provides an interface for
5.17 - structured backwards reasoning under program control, with some
5.18 - explicit sanity checks of the result. The goal context can be
5.19 - augmented by additional fixed variables (cf.\
5.20 - \secref{sec:variables}) and assumptions (cf.\
5.21 - \secref{sec:assumptions}), which will be available as local facts
5.22 - during the proof and discharged into implications in the result.
5.23 - Type and term variables are generalized as usual, according to the
5.24 - context.
5.25 + \medskip The \isa{SUBPROOF} combinator allows to structure a
5.26 + tactical proof recursively by decomposing a selected sub-goal:
5.27 + \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}}
5.28 + after fixing \isa{x} and assuming \isa{A{\isacharparenleft}x{\isacharparenright}}. This means
5.29 + the tactic needs to solve the conclusion, but may use the premise as
5.30 + a local fact, for locally fixed variables.
5.31
5.32 - The \isa{prove{\isacharunderscore}multi} operation handles several simultaneous
5.33 - claims within a single goal, by using Pure conjunction internally.
5.34 + The \isa{prove} operation provides an interface for structured
5.35 + backwards reasoning under program control, with some explicit sanity
5.36 + checks of the result. The goal context can be augmented by
5.37 + additional fixed variables (cf.\ \secref{sec:variables}) and
5.38 + assumptions (cf.\ \secref{sec:assumptions}), which will be available
5.39 + as local facts during the proof and discharged into implications in
5.40 + the result. Type and term variables are generalized as usual,
5.41 + according to the context.
5.42
5.43 - \medskip Tactical proofs may be structured recursively by
5.44 - decomposing a sub-goal: \isa{{\isacharparenleft}{\isasymAnd}x{\isachardot}\ A{\isacharparenleft}x{\isacharparenright}\ {\isasymLongrightarrow}\ B{\isacharparenleft}x{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}} is turned
5.45 - into \isa{B{\isacharparenleft}x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}} after fixing \isa{x} and assuming \isa{A{\isacharparenleft}x{\isacharparenright}}.%
5.46 + The \isa{obtain} operation produces results by eliminating
5.47 + existing facts by means of a given tactic. This acts like a dual
5.48 + conclusion: the proof demonstrates that the context may be augmented
5.49 + by certain fixed variables and assumptions. See also
5.50 + \cite{isabelle-isar-ref} for the user-level \isa{{\isasymOBTAIN}} and
5.51 + \isa{{\isasymGUESS}} elements. Final results, which may not refer to
5.52 + the parameters in the conclusion, need to exported explicitly into
5.53 + the original context.%
5.54 \end{isamarkuptext}%
5.55 \isamarkuptrue%
5.56 %
5.57 @@ -318,31 +326,39 @@
5.58 %
5.59 \begin{isamarkuptext}%
5.60 \begin{mldecls}
5.61 + \indexml{SUBPROOF}\verb|SUBPROOF: ({context: Proof.context, schematics: ctyp list * cterm list,|\isasep\isanewline%
5.62 +\verb| params: cterm list, asms: cterm list, concl: cterm,|\isasep\isanewline%
5.63 +\verb| prems: thm list} -> tactic) -> Proof.context -> int -> tactic| \\
5.64 \indexml{Goal.prove}\verb|Goal.prove: Proof.context -> string list -> term list -> term ->|\isasep\isanewline%
5.65 \verb| ({prems: thm list, context: Proof.context} -> tactic) -> thm| \\
5.66 \indexml{Goal.prove-multi}\verb|Goal.prove_multi: Proof.context -> string list -> term list -> term list ->|\isasep\isanewline%
5.67 \verb| ({prems: thm list, context: Proof.context} -> tactic) -> thm list| \\
5.68 - \indexml{SUBPROOF}\verb|SUBPROOF: ({context: Proof.context, schematics: ctyp list * cterm list,|\isasep\isanewline%
5.69 -\verb| params: cterm list, asms: cterm list, concl: cterm,|\isasep\isanewline%
5.70 -\verb| prems: thm list} -> tactic) -> Proof.context -> int -> tactic|
5.71 + \indexml{Obtain.result}\verb|Obtain.result: (Proof.context -> tactic) ->|\isasep\isanewline%
5.72 +\verb| thm list -> Proof.context -> (cterm list * thm list) * Proof.context|
5.73 \end{mldecls}
5.74
5.75 \begin{description}
5.76
5.77 + \item \verb|SUBPROOF|~\isa{tac} decomposes the structure of a
5.78 + particular sub-goal, producing an extended context and a reduced
5.79 + goal, which needs to be solved by the given tactic. All schematic
5.80 + parameters of the goal are imported into the context as fixed ones,
5.81 + which may not be instantiated in the sub-proof.
5.82 +
5.83 \item \verb|Goal.prove|~\isa{ctxt\ xs\ As\ C\ tac} states goal \isa{C} in the context augmented by fixed variables \isa{xs} and
5.84 assumptions \isa{As}, and applies tactic \isa{tac} to solve
5.85 it. The latter may depend on the local assumptions being presented
5.86 as facts. The result is in HHF normal form.
5.87
5.88 \item \verb|Goal.prove_multi| is simular to \verb|Goal.prove|, but
5.89 - states several conclusions simultaneously. \verb|Tactic.conjunction_tac| may be used to split these into individual
5.90 - subgoals before commencing the actual proof.
5.91 + states several conclusions simultaneously. The goal is encoded by
5.92 + means of Pure conjunction; \verb|Tactic.conjunction_tac| will turn
5.93 + this into a collection of individual subgoals.
5.94
5.95 - \item \verb|SUBPROOF|~\isa{tac} decomposes the structure of a
5.96 - particular sub-goal, producing an extended context and a reduced
5.97 - goal, which needs to be solved by the given tactic. All schematic
5.98 - parameters of the goal are imported into the context as fixed ones,
5.99 - which may not be instantiated in the sub-proof.
5.100 + \item \verb|Obtain.result|~\isa{tac\ thms\ ctxt} eliminates the
5.101 + given facts using a tactic, which results in additional fixed
5.102 + variables and assumptions in the context. Final results need to be
5.103 + exported explicitly.
5.104
5.105 \end{description}%
5.106 \end{isamarkuptext}%
6.1 --- a/doc-src/IsarImplementation/Thy/integration.thy Thu Sep 07 15:16:51 2006 +0200
6.2 +++ b/doc-src/IsarImplementation/Thy/integration.thy Thu Sep 07 20:12:08 2006 +0200
6.3 @@ -432,9 +432,4 @@
6.4 \end{description}
6.5 *}
6.6
6.7 -
6.8 -section {* Sessions and document preparation *}
6.9 -
6.10 -text FIXME
6.11 -
6.12 end
7.1 --- a/doc-src/IsarImplementation/Thy/logic.thy Thu Sep 07 15:16:51 2006 +0200
7.2 +++ b/doc-src/IsarImplementation/Thy/logic.thy Thu Sep 07 20:12:08 2006 +0200
7.3 @@ -11,7 +11,8 @@
7.4 \cite{paulson700}. This is essentially the same logic as ``@{text
7.5 "\<lambda>HOL"}'' in the more abstract framework of Pure Type Systems (PTS)
7.6 \cite{Barendregt-Geuvers:2001}, although there are some key
7.7 - differences in the practical treatment of simple types.
7.8 + differences in the specific treatment of simple types in
7.9 + Isabelle/Pure.
7.10
7.11 Following type-theoretic parlance, the Pure logic consists of three
7.12 levels of @{text "\<lambda>"}-calculus with corresponding arrows: @{text
7.13 @@ -20,8 +21,11 @@
7.14 @{text "\<Longrightarrow>"} for implication (proofs depending on proofs).
7.15
7.16 Pure derivations are relative to a logical theory, which declares
7.17 - type constructors, term constants, and axioms. Term constants and
7.18 - axioms support schematic polymorphism.
7.19 + type constructors, term constants, and axioms. Theory declarations
7.20 + support schematic polymorphism, which is strictly speaking outside
7.21 + the logic.\footnote{Incidently, this is the main logical reason, why
7.22 + the theory context @{text "\<Theta>"} is separate from the context @{text
7.23 + "\<Gamma>"} of the core calculus.}
7.24 *}
7.25
7.26
7.27 @@ -34,46 +38,48 @@
7.28 \medskip A \emph{type class} is an abstract syntactic entity
7.29 declared in the theory context. The \emph{subclass relation} @{text
7.30 "c\<^isub>1 \<subseteq> c\<^isub>2"} is specified by stating an acyclic
7.31 - generating relation; the transitive closure maintained internally.
7.32 + generating relation; the transitive closure is maintained
7.33 + internally. The resulting relation is an ordering: reflexive,
7.34 + transitive, and antisymmetric.
7.35
7.36 A \emph{sort} is a list of type classes written as @{text
7.37 "{c\<^isub>1, \<dots>, c\<^isub>m}"}, which represents symbolic
7.38 intersection. Notationally, the curly braces are omitted for
7.39 singleton intersections, i.e.\ any class @{text "c"} may be read as
7.40 a sort @{text "{c}"}. The ordering on type classes is extended to
7.41 - sorts in the canonical fashion: @{text "{c\<^isub>1, \<dots> c\<^isub>m} \<subseteq>
7.42 - {d\<^isub>1, \<dots>, d\<^isub>n}"} iff @{text "\<forall>j. \<exists>i. c\<^isub>i \<subseteq>
7.43 - d\<^isub>j"}. The empty intersection @{text "{}"} refers to the
7.44 - universal sort, which is the largest element wrt.\ the sort order.
7.45 - The intersections of all (i.e.\ finitely many) classes declared in
7.46 - the current theory are the minimal elements wrt.\ sort order.
7.47 + sorts according to the meaning of intersections: @{text
7.48 + "{c\<^isub>1, \<dots> c\<^isub>m} \<subseteq> {d\<^isub>1, \<dots>, d\<^isub>n}"} iff
7.49 + @{text "\<forall>j. \<exists>i. c\<^isub>i \<subseteq> d\<^isub>j"}. The empty intersection
7.50 + @{text "{}"} refers to the universal sort, which is the largest
7.51 + element wrt.\ the sort order. The intersections of all (finitely
7.52 + many) classes declared in the current theory are the minimal
7.53 + elements wrt.\ the sort order.
7.54
7.55 - \medskip A \emph{fixed type variable} is pair of a basic name
7.56 + \medskip A \emph{fixed type variable} is a pair of a basic name
7.57 (starting with @{text "'"} character) and a sort constraint. For
7.58 example, @{text "('a, s)"} which is usually printed as @{text
7.59 "\<alpha>\<^isub>s"}. A \emph{schematic type variable} is a pair of an
7.60 indexname and a sort constraint. For example, @{text "(('a, 0),
7.61 - s)"} which is usually printed @{text "?\<alpha>\<^isub>s"}.
7.62 + s)"} which is usually printed as @{text "?\<alpha>\<^isub>s"}.
7.63
7.64 Note that \emph{all} syntactic components contribute to the identity
7.65 - of a type variables, including the literal sort constraint. The
7.66 - core logic handles type variables with the same name but different
7.67 - sorts as different, even though the outer layers of the system make
7.68 - it hard to produce anything like this.
7.69 + of type variables, including the literal sort constraint. The core
7.70 + logic handles type variables with the same name but different sorts
7.71 + as different, although some outer layers of the system make it hard
7.72 + to produce anything like this.
7.73
7.74 - A \emph{type constructor} is an @{text "k"}-ary type operator
7.75 - declared in the theory.
7.76 + A \emph{type constructor} is a @{text "k"}-ary operator on types
7.77 + declared in the theory. Type constructor application is usually
7.78 + written postfix. For @{text "k = 0"} the argument tuple is omitted,
7.79 + e.g.\ @{text "prop"} instead of @{text "()prop"}. For @{text "k =
7.80 + 1"} the parentheses are omitted, e.g.\ @{text "\<alpha> list"} instead of
7.81 + @{text "(\<alpha>)list"}. Further notation is provided for specific
7.82 + constructors, notably right-associative infix @{text "\<alpha> \<Rightarrow> \<beta>"}
7.83 + instead of @{text "(\<alpha>, \<beta>)fun"} constructor.
7.84
7.85 A \emph{type} is defined inductively over type variables and type
7.86 - constructors: @{text "\<tau> = \<alpha>\<^isub>s | ?\<alpha>\<^isub>s | (\<tau>\<^sub>1, \<dots>,
7.87 - \<tau>\<^sub>k)c"}. Type constructor application is usually written
7.88 - postfix. For @{text "k = 0"} the argument tuple is omitted, e.g.\
7.89 - @{text "prop"} instead of @{text "()prop"}. For @{text "k = 1"} the
7.90 - parentheses are omitted, e.g.\ @{text "\<tau> list"} instead of @{text
7.91 - "(\<tau>) list"}. Further notation is provided for specific
7.92 - constructors, notably right-associative infix @{text "\<tau>\<^isub>1 \<Rightarrow>
7.93 - \<tau>\<^isub>2"} instead of @{text "(\<tau>\<^isub>1, \<tau>\<^isub>2)fun"}
7.94 - constructor.
7.95 + constructors as follows: @{text "\<tau> = \<alpha>\<^isub>s | ?\<alpha>\<^isub>s |
7.96 + (\<tau>\<^sub>1, \<dots>, \<tau>\<^sub>k)c"}.
7.97
7.98 A \emph{type abbreviation} is a syntactic abbreviation of an
7.99 arbitrary type expression of the theory. Type abbreviations looks
7.100 @@ -82,26 +88,30 @@
7.101
7.102 A \emph{type arity} declares the image behavior of a type
7.103 constructor wrt.\ the algebra of sorts: @{text "c :: (s\<^isub>1, \<dots>,
7.104 - s\<^isub>n)s"} means that @{text "(\<tau>\<^isub>1, \<dots>, \<tau>\<^isub>k)c"} is
7.105 + s\<^isub>k)s"} means that @{text "(\<tau>\<^isub>1, \<dots>, \<tau>\<^isub>k)c"} is
7.106 of sort @{text "s"} if each argument type @{text "\<tau>\<^isub>i"} is of
7.107 - sort @{text "s\<^isub>i"}. The sort algebra is always maintained as
7.108 - \emph{coregular}, which means that type arities are consistent with
7.109 - the subclass relation: for each type constructor @{text "c"} and
7.110 - classes @{text "c\<^isub>1 \<subseteq> c\<^isub>2"}, any arity @{text "c ::
7.111 + sort @{text "s\<^isub>i"}. Arity declarations are implicitly
7.112 + completed, i.e.\ @{text "c :: (\<^vec>s)c"} entails @{text "c ::
7.113 + (\<^vec>s)c'"} for any @{text "c' \<supseteq> c"}.
7.114 +
7.115 + \medskip The sort algebra is always maintained as \emph{coregular},
7.116 + which means that type arities are consistent with the subclass
7.117 + relation: for each type constructor @{text "c"} and classes @{text
7.118 + "c\<^isub>1 \<subseteq> c\<^isub>2"}, any arity @{text "c ::
7.119 (\<^vec>s\<^isub>1)c\<^isub>1"} has a corresponding arity @{text "c
7.120 :: (\<^vec>s\<^isub>2)c\<^isub>2"} where @{text "\<^vec>s\<^isub>1 \<subseteq>
7.121 \<^vec>s\<^isub>2"} holds pointwise for all argument sorts.
7.122
7.123 - The key property of the order-sorted algebra of types is that sort
7.124 + The key property of a coregular order-sorted algebra is that sort
7.125 constraints may be always fulfilled in a most general fashion: for
7.126 each type constructor @{text "c"} and sort @{text "s"} there is a
7.127 most general vector of argument sorts @{text "(s\<^isub>1, \<dots>,
7.128 - s\<^isub>k)"} such that @{text "(\<tau>\<^bsub>s\<^isub>1\<^esub>, \<dots>,
7.129 - \<tau>\<^bsub>s\<^isub>k\<^esub>)"} for arbitrary @{text "\<tau>\<^isub>i"} of
7.130 - sort @{text "s\<^isub>i"}. This means the unification problem on
7.131 - the algebra of types has most general solutions (modulo renaming and
7.132 - equivalence of sorts). As a consequence, type-inference is able to
7.133 - produce primary types.
7.134 + s\<^isub>k)"} such that a type scheme @{text
7.135 + "(\<alpha>\<^bsub>s\<^isub>1\<^esub>, \<dots>, \<alpha>\<^bsub>s\<^isub>k\<^esub>)c"} is
7.136 + of sort @{text "s"}. Consequently, the unification problem on the
7.137 + algebra of types has most general solutions (modulo renaming and
7.138 + equivalence of sorts). Moreover, the usual type-inference algorithm
7.139 + will produce primary types as expected \cite{nipkow-prehofer}.
7.140 *}
7.141
7.142 text %mlref {*
7.143 @@ -139,19 +149,19 @@
7.144 tests the subsort relation @{text "s\<^isub>1 \<subseteq> s\<^isub>2"}.
7.145
7.146 \item @{ML Sign.of_sort}~@{text "thy (\<tau>, s)"} tests whether a type
7.147 - expression of of a given sort.
7.148 + is of a given sort.
7.149
7.150 \item @{ML Sign.add_types}~@{text "[(c, k, mx), \<dots>]"} declares new
7.151 - type constructors @{text "c"} with @{text "k"} arguments, and
7.152 + type constructors @{text "c"} with @{text "k"} arguments and
7.153 optional mixfix syntax.
7.154
7.155 \item @{ML Sign.add_tyabbrs_i}~@{text "[(c, \<^vec>\<alpha>, \<tau>, mx), \<dots>]"}
7.156 - defines type abbreviation @{text "(\<^vec>\<alpha>)c"} (with optional
7.157 - mixfix syntax) as @{text "\<tau>"}.
7.158 + defines a new type abbreviation @{text "(\<^vec>\<alpha>)c = \<tau>"} with
7.159 + optional mixfix syntax.
7.160
7.161 \item @{ML Sign.primitive_class}~@{text "(c, [c\<^isub>1, \<dots>,
7.162 c\<^isub>n])"} declares new class @{text "c"} derived together with
7.163 - class relations @{text "c \<subseteq> c\<^isub>i"}.
7.164 + class relations @{text "c \<subseteq> c\<^isub>i"}, for @{text "i = 1, \<dots>, n"}.
7.165
7.166 \item @{ML Sign.primitive_classrel}~@{text "(c\<^isub>1,
7.167 c\<^isub>2)"} declares class relation @{text "c\<^isub>1 \<subseteq>
7.168 @@ -170,6 +180,13 @@
7.169 text {*
7.170 \glossary{Term}{FIXME}
7.171
7.172 + The language of terms is that of simply-typed @{text "\<lambda>"}-calculus
7.173 + with de-Bruijn indices for bound variables, and named free
7.174 + variables, and constants. Terms with loose bound variables are
7.175 + usually considered malformed. The types of variables and constants
7.176 + is stored explicitly at each occurrence in the term (which is a
7.177 + known performance issue).
7.178 +
7.179 FIXME de-Bruijn representation of lambda terms
7.180
7.181 Term syntax provides explicit abstraction @{text "\<lambda>x :: \<alpha>. b(x)"}
7.182 @@ -193,13 +210,6 @@
7.183 *}
7.184
7.185
7.186 -section {* Proof terms *}
7.187 -
7.188 -text {*
7.189 - FIXME
7.190 -*}
7.191 -
7.192 -
7.193 section {* Theorems \label{sec:thms} *}
7.194
7.195 text {*
7.196 @@ -258,17 +268,54 @@
7.197
7.198 *}
7.199
7.200 -subsection {* Primitive inferences *}
7.201
7.202 -text FIXME
7.203 +section {* Proof terms *}
7.204
7.205 +text {*
7.206 + FIXME !?
7.207 +*}
7.208
7.209 -subsection {* Higher-order resolution *}
7.210 +
7.211 +section {* Rules \label{sec:rules} *}
7.212
7.213 text {*
7.214
7.215 FIXME
7.216
7.217 + A \emph{rule} is any Pure theorem in HHF normal form; there is a
7.218 + separate calculus for rule composition, which is modeled after
7.219 + Gentzen's Natural Deduction \cite{Gentzen:1935}, but allows
7.220 + rules to be nested arbitrarily, similar to \cite{extensions91}.
7.221 +
7.222 + Normally, all theorems accessible to the user are proper rules.
7.223 + Low-level inferences are occasional required internally, but the
7.224 + result should be always presented in canonical form. The higher
7.225 + interfaces of Isabelle/Isar will always produce proper rules. It is
7.226 + important to maintain this invariant in add-on applications!
7.227 +
7.228 + There are two main principles of rule composition: @{text
7.229 + "resolution"} (i.e.\ backchaining of rules) and @{text
7.230 + "by-assumption"} (i.e.\ closing a branch); both principles are
7.231 + combined in the variants of @{text "elim-resosultion"} and @{text
7.232 + "dest-resolution"}. Raw @{text "composition"} is occasionally
7.233 + useful as well, also it is strictly speaking outside of the proper
7.234 + rule calculus.
7.235 +
7.236 + Rules are treated modulo general higher-order unification, which is
7.237 + unification modulo the equational theory of @{text "\<alpha>\<beta>\<eta>"}-conversion
7.238 + on @{text "\<lambda>"}-terms. Moreover, propositions are understood modulo
7.239 + the (derived) equivalence @{text "(A \<Longrightarrow> (\<And>x. B x)) \<equiv> (\<And>x. A \<Longrightarrow> B x)"}.
7.240 +
7.241 + This means that any operations within the rule calculus may be
7.242 + subject to spontaneous @{text "\<alpha>\<beta>\<eta>"}-HHF conversions. It is common
7.243 + practice not to contract or expand unnecessarily. Some mechanisms
7.244 + prefer an one form, others the opposite, so there is a potential
7.245 + danger to produce some oscillation!
7.246 +
7.247 + Only few operations really work \emph{modulo} HHF conversion, but
7.248 + expect a normal form: quantifiers @{text "\<And>"} before implications
7.249 + @{text "\<Longrightarrow>"} at each level of nesting.
7.250 +
7.251 \glossary{Hereditary Harrop Formula}{The set of propositions in HHF
7.252 format is defined inductively as @{text "H = (\<And>x\<^sup>*. H\<^sup>* \<Longrightarrow>
7.253 A)"}, for variables @{text "x"} and atomic propositions @{text "A"}.
7.254 @@ -282,9 +329,4 @@
7.255
7.256 *}
7.257
7.258 -subsection {* Equational reasoning *}
7.259 -
7.260 -text FIXME
7.261 -
7.262 -
7.263 end
8.1 --- a/doc-src/IsarImplementation/Thy/proof.thy Thu Sep 07 15:16:51 2006 +0200
8.2 +++ b/doc-src/IsarImplementation/Thy/proof.thy Thu Sep 07 20:12:08 2006 +0200
8.3 @@ -196,7 +196,7 @@
8.4 definition works by fixing @{text "x"} and assuming @{text "x \<equiv> t"},
8.5 with the following export rule to reverse the effect:
8.6 \[
8.7 - \infer{@{text "\<Gamma> \\ x \<equiv> t \<turnstile> B t"}}{@{text "\<Gamma> \<turnstile> B x"}}
8.8 + \infer[(@{text "\<equiv>-expand"})]{@{text "\<Gamma> \\ x \<equiv> t \<turnstile> B t"}}{@{text "\<Gamma> \<turnstile> B x"}}
8.9 \]
8.10 This works, because the assumption @{text "x \<equiv> t"} was introduced in
8.11 a context with @{text "x"} being fresh, so @{text "x"} does not
8.12 @@ -258,39 +258,54 @@
8.13 references to free variables or assumptions not present in the proof
8.14 context.
8.15
8.16 - \medskip The @{text "prove"} operation provides an interface for
8.17 - structured backwards reasoning under program control, with some
8.18 - explicit sanity checks of the result. The goal context can be
8.19 - augmented by additional fixed variables (cf.\
8.20 - \secref{sec:variables}) and assumptions (cf.\
8.21 - \secref{sec:assumptions}), which will be available as local facts
8.22 - during the proof and discharged into implications in the result.
8.23 - Type and term variables are generalized as usual, according to the
8.24 - context.
8.25 + \medskip The @{text "SUBPROOF"} combinator allows to structure a
8.26 + tactical proof recursively by decomposing a selected sub-goal:
8.27 + @{text "(\<And>x. A(x) \<Longrightarrow> B(x)) \<Longrightarrow> \<dots>"} is turned into @{text "B(x) \<Longrightarrow> \<dots>"}
8.28 + after fixing @{text "x"} and assuming @{text "A(x)"}. This means
8.29 + the tactic needs to solve the conclusion, but may use the premise as
8.30 + a local fact, for locally fixed variables.
8.31
8.32 - The @{text "prove_multi"} operation handles several simultaneous
8.33 - claims within a single goal, by using Pure conjunction internally.
8.34 + The @{text "prove"} operation provides an interface for structured
8.35 + backwards reasoning under program control, with some explicit sanity
8.36 + checks of the result. The goal context can be augmented by
8.37 + additional fixed variables (cf.\ \secref{sec:variables}) and
8.38 + assumptions (cf.\ \secref{sec:assumptions}), which will be available
8.39 + as local facts during the proof and discharged into implications in
8.40 + the result. Type and term variables are generalized as usual,
8.41 + according to the context.
8.42
8.43 - \medskip Tactical proofs may be structured recursively by
8.44 - decomposing a sub-goal: @{text "(\<And>x. A(x) \<Longrightarrow> B(x)) \<Longrightarrow> \<dots>"} is turned
8.45 - into @{text "B(x) \<Longrightarrow> \<dots>"} after fixing @{text "x"} and assuming @{text
8.46 - "A(x)"}.
8.47 + The @{text "obtain"} operation produces results by eliminating
8.48 + existing facts by means of a given tactic. This acts like a dual
8.49 + conclusion: the proof demonstrates that the context may be augmented
8.50 + by certain fixed variables and assumptions. See also
8.51 + \cite{isabelle-isar-ref} for the user-level @{text "\<OBTAIN>"} and
8.52 + @{text "\<GUESS>"} elements. Final results, which may not refer to
8.53 + the parameters in the conclusion, need to exported explicitly into
8.54 + the original context.
8.55 *}
8.56
8.57 text %mlref {*
8.58 \begin{mldecls}
8.59 + @{index_ML SUBPROOF:
8.60 + "({context: Proof.context, schematics: ctyp list * cterm list,
8.61 + params: cterm list, asms: cterm list, concl: cterm,
8.62 + prems: thm list} -> tactic) -> Proof.context -> int -> tactic"} \\
8.63 @{index_ML Goal.prove: "Proof.context -> string list -> term list -> term ->
8.64 ({prems: thm list, context: Proof.context} -> tactic) -> thm"} \\
8.65 @{index_ML Goal.prove_multi: "Proof.context -> string list -> term list -> term list ->
8.66 ({prems: thm list, context: Proof.context} -> tactic) -> thm list"} \\
8.67 - @{index_ML SUBPROOF:
8.68 - "({context: Proof.context, schematics: ctyp list * cterm list,
8.69 - params: cterm list, asms: cterm list, concl: cterm,
8.70 - prems: thm list} -> tactic) -> Proof.context -> int -> tactic"}
8.71 + @{index_ML Obtain.result: "(Proof.context -> tactic) ->
8.72 + thm list -> Proof.context -> (cterm list * thm list) * Proof.context"}
8.73 \end{mldecls}
8.74
8.75 \begin{description}
8.76
8.77 + \item @{ML SUBPROOF}~@{text "tac"} decomposes the structure of a
8.78 + particular sub-goal, producing an extended context and a reduced
8.79 + goal, which needs to be solved by the given tactic. All schematic
8.80 + parameters of the goal are imported into the context as fixed ones,
8.81 + which may not be instantiated in the sub-proof.
8.82 +
8.83 \item @{ML Goal.prove}~@{text "ctxt xs As C tac"} states goal @{text
8.84 "C"} in the context augmented by fixed variables @{text "xs"} and
8.85 assumptions @{text "As"}, and applies tactic @{text "tac"} to solve
8.86 @@ -298,15 +313,14 @@
8.87 as facts. The result is in HHF normal form.
8.88
8.89 \item @{ML Goal.prove_multi} is simular to @{ML Goal.prove}, but
8.90 - states several conclusions simultaneously. @{ML
8.91 - Tactic.conjunction_tac} may be used to split these into individual
8.92 - subgoals before commencing the actual proof.
8.93 + states several conclusions simultaneously. The goal is encoded by
8.94 + means of Pure conjunction; @{ML Tactic.conjunction_tac} will turn
8.95 + this into a collection of individual subgoals.
8.96
8.97 - \item @{ML SUBPROOF}~@{text "tac"} decomposes the structure of a
8.98 - particular sub-goal, producing an extended context and a reduced
8.99 - goal, which needs to be solved by the given tactic. All schematic
8.100 - parameters of the goal are imported into the context as fixed ones,
8.101 - which may not be instantiated in the sub-proof.
8.102 + \item @{ML Obtain.result}~@{text "tac thms ctxt"} eliminates the
8.103 + given facts using a tactic, which results in additional fixed
8.104 + variables and assumptions in the context. Final results need to be
8.105 + exported explicitly.
8.106
8.107 \end{description}
8.108 *}
9.1 --- a/doc-src/IsarImplementation/Thy/unused.thy Thu Sep 07 15:16:51 2006 +0200
9.2 +++ b/doc-src/IsarImplementation/Thy/unused.thy Thu Sep 07 20:12:08 2006 +0200
9.3 @@ -1,3 +1,6 @@
9.4 +
9.5 +section {* Sessions and document preparation *}
9.6 +
9.7 section {* Structured output *}
9.8
9.9 subsection {* Pretty printing *}
10.1 --- a/doc-src/IsarImplementation/style.sty Thu Sep 07 15:16:51 2006 +0200
10.2 +++ b/doc-src/IsarImplementation/style.sty Thu Sep 07 20:12:08 2006 +0200
10.3 @@ -49,6 +49,8 @@
10.4 \renewcommand{\isatagmlref}{\subsection*{\makebox[0pt][r]{\fbox{\ML}~~}Reference}\begingroup\def\isastyletext{\rm}\small}
10.5 \renewcommand{\endisatagmlref}{\endgroup}
10.6
10.7 +\newcommand{\isasymGUESS}{\isakeyword{guess}}
10.8 +\newcommand{\isasymOBTAIN}{\isakeyword{obtain}}
10.9 \newcommand{\isasymTHEORY}{\isakeyword{theory}}
10.10 \newcommand{\isasymIMPORTS}{\isakeyword{imports}}
10.11 \newcommand{\isasymUSES}{\isakeyword{uses}}