--- a/doc-src/IsarImplementation/Thy/document/logic.tex Tue Sep 12 17:12:51 2006 +0200
+++ b/doc-src/IsarImplementation/Thy/document/logic.tex Tue Sep 12 17:23:34 2006 +0200
@@ -103,7 +103,7 @@
\medskip The sort algebra is always maintained as \emph{coregular},
which means that type arities are consistent with the subclass
- relation: for each type constructor \isa{{\isasymkappa}} and classes \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}, any arity \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{1}}{\isacharparenright}c\isactrlisub {\isadigit{1}}} has a corresponding arity \isa{{\isasymkappa}\ {\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 componentwise.
+ relation: for each type constructor \isa{{\isasymkappa}} and classes \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}, any arity \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{1}}{\isacharparenright}c\isactrlisub {\isadigit{1}}} has a corresponding arity \isa{{\isasymkappa}\ {\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 component-wise.
The key property of a coregular order-sorted algebra is that sort
constraints may be always solved in a most general fashion: for each
@@ -128,6 +128,7 @@
\indexmltype{sort}\verb|type sort| \\
\indexmltype{arity}\verb|type arity| \\
\indexmltype{typ}\verb|type typ| \\
+ \indexml{map-atyps}\verb|map_atyps: (typ -> typ) -> typ -> typ| \\
\indexml{fold-atyps}\verb|fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a| \\
\indexml{Sign.subsort}\verb|Sign.subsort: theory -> sort * sort -> bool| \\
\indexml{Sign.of-sort}\verb|Sign.of_sort: theory -> typ * sort -> bool| \\
@@ -153,8 +154,11 @@
\item \verb|typ| represents types; this is a datatype with
constructors \verb|TFree|, \verb|TVar|, \verb|Type|.
- \item \verb|fold_atyps|~\isa{f\ {\isasymtau}} iterates function \isa{f}
- over all occurrences of atoms (\verb|TFree| or \verb|TVar|) of \isa{{\isasymtau}}; the type structure is traversed from left to right.
+ \item \verb|map_atyps|~\isa{f\ {\isasymtau}} applies mapping \isa{f} to
+ all atomic types (\verb|TFree|, \verb|TVar|) occurring in \isa{{\isasymtau}}.
+
+ \item \verb|fold_atyps|~\isa{f\ {\isasymtau}} iterates operation \isa{f}
+ over all occurrences of atoms (\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}}}.
@@ -197,18 +201,18 @@
\glossary{Term}{FIXME}
The language of terms is that of simply-typed \isa{{\isasymlambda}}-calculus
- with de-Bruijn indices for bound variables, and named free variables
- and constants. Terms with loose bound variables are usually
- considered malformed. The types of variables and constants is
- stored explicitly at each occurrence in the term.
+ with de-Bruijn indices for bound variables
+ \cite{debruijn72,paulson-ml2}, and named free variables and
+ constants. Terms with loose bound variables are usually considered
+ malformed. The types of variables and constants is stored
+ explicitly at each occurrence in the term.
\medskip A \emph{bound variable} is a natural number \isa{b},
which refers to the next binder that is \isa{b} steps upwards
from the occurrence of \isa{b} (counting from zero). Bindings
may be introduced as abstractions within the term, or as a separate
context (an inside-out list). This associates each bound variable
- with a type, and a name that is maintained as a comment for parsing
- and printing. A \emph{loose variables} is a bound variable that is
+ with a type. A \emph{loose variables} is a bound variable that is
outside the current scope of local binders or the context. For
example, the de-Bruijn term \isa{{\isasymlambda}\isactrlisub {\isasymtau}{\isachardot}\ {\isasymlambda}\isactrlisub {\isasymtau}{\isachardot}\ {\isadigit{1}}\ {\isacharplus}\ {\isadigit{0}}}
corresponds to \isa{{\isasymlambda}x\isactrlisub {\isasymtau}{\isachardot}\ {\isasymlambda}y\isactrlisub {\isasymtau}{\isachardot}\ x\ {\isacharplus}\ y} in a named
@@ -281,7 +285,20 @@
looks like a constant at the surface, but is fully expanded before
entering the logical core. Abbreviations are usually reverted when
printing terms, using rules \isa{t\ {\isasymrightarrow}\ c\isactrlisub {\isasymsigma}} has a
- higher-order term rewrite system.%
+ higher-order term rewrite system.
+
+ \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 some 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
+ \isa{{\isadigit{0}}} does not occur in \isa{f}.
+
+ Terms are almost always treated module \isa{{\isasymalpha}}-conversion, which
+ is implicit in the de-Bruijn representation. The names in
+ abstractions of bound variables are maintained only as a comment for
+ parsing and printing. Full \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-equivalence is usually
+ taken for granted higher rules (\secref{sec:rules}), anything
+ depending on higher-order unification or rewriting.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -294,15 +311,68 @@
\begin{isamarkuptext}%
\begin{mldecls}
\indexmltype{term}\verb|type term| \\
+ \indexml{op aconv}\verb|op aconv: term * term -> bool| \\
+ \indexml{map-term-types}\verb|map_term_types: (typ -> typ) -> term -> term| \\ %FIXME rename map_types
+ \indexml{fold-types}\verb|fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a| \\
\indexml{map-aterms}\verb|map_aterms: (term -> term) -> term -> term| \\
\indexml{fold-aterms}\verb|fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a| \\
\indexml{fastype-of}\verb|fastype_of: term -> typ| \\
- \indexml{fold-types}\verb|fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a| \\
+ \indexml{lambda}\verb|lambda: term -> term -> term| \\
+ \indexml{betapply}\verb|betapply: term * term -> term| \\
+ \indexml{Sign.add-consts-i}\verb|Sign.add_consts_i: (bstring * typ * mixfix) list -> theory -> theory| \\
+ \indexml{Sign.add-abbrevs}\verb|Sign.add_abbrevs: string * bool ->|\isasep\isanewline%
+\verb| ((bstring * mixfix) * term) list -> theory -> theory| \\
+ \indexml{Sign.const-typargs}\verb|Sign.const_typargs: theory -> string * typ -> typ list| \\
+ \indexml{Sign.const-instance}\verb|Sign.const_instance: theory -> string * typ list -> typ| \\
\end{mldecls}
\begin{description}
- \item \verb|term| FIXME
+ \item \verb|term| represents de-Bruijn terms with comments in
+ abstractions for bound variable names. 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_term_types|~\isa{f\ t} applies mapping \isa{f}
+ to all types occurring in \isa{t}.
+
+ \item \verb|fold_types|~\isa{f\ t} iterates 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 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 operation \isa{f}
+ over all occurrences of atomic terms in (\verb|Bound|, \verb|Free|,
+ \verb|Var|, \verb|Const|) \isa{t}; the term structure is traversed
+ from left to right.
+
+ \item \verb|fastype_of|~\isa{t} recomputes the type of a
+ well-formed term, while omitting any sanity checks. This operation
+ is relatively slow.
+
+ \item \verb|lambda|~\isa{a\ b} produces an abstraction \isa{{\isasymlambda}a{\isachardot}\ b}, where occurrences of the original (atomic) term \isa{a} are replaced by bound variables.
+
+ \item \verb|betapply|~\isa{t\ u} produces an application \isa{t\ u}, with topmost \isa{{\isasymbeta}}-conversion \isa{t} is an
+ abstraction.
+
+ \item \verb|Sign.add_consts_i|~\isa{{\isacharbrackleft}{\isacharparenleft}c{\isacharcomma}\ {\isasymsigma}{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}} declares a
+ new constant \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} with optional mixfix syntax.
+
+ \item \verb|Sign.add_abbrevs|~\isa{print{\isacharunderscore}mode\ {\isacharbrackleft}{\isacharparenleft}{\isacharparenleft}c{\isacharcomma}\ t{\isacharparenright}{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}}
+ declares a new term abbreviation \isa{c\ {\isasymequiv}\ t} with optional
+ mixfix syntax.
+
+ \item \verb|Sign.const_typargs|~\isa{thy\ {\isacharparenleft}c{\isacharcomma}\ {\isasymtau}{\isacharparenright}} produces the
+ type arguments of the instance \isa{c\isactrlisub {\isasymtau}} wrt.\ its
+ declaration in the theory.
+
+ \item \verb|Sign.const_instance|~\isa{thy\ {\isacharparenleft}c{\isacharcomma}\ {\isacharbrackleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharbrackright}{\isacharparenright}} produces the full instance \isa{c{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharparenright}} wrt.\ its declaration in the theory.
\end{description}%
\end{isamarkuptext}%
@@ -333,7 +403,7 @@
rarely spelled out explicitly. Theorems are usually normalized
according to the \seeglossary{HHF} format. FIXME}
- \glossary{Fact}{Sometimes used interchangably for
+ \glossary{Fact}{Sometimes used interchangeably for
\seeglossary{theorem}. Strictly speaking, a list of theorems,
essentially an extra-logical conjunction. Facts emerge either as
local assumptions, or as results of local goal statements --- both
@@ -501,7 +571,7 @@
important to maintain this invariant in add-on applications!
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
- combined in the variants of \isa{elim{\isacharminus}resosultion} and \isa{dest{\isacharminus}resolution}. Raw \isa{composition} is occasionally
+ combined in the variants of \isa{elim{\isacharminus}resolution} and \isa{dest{\isacharminus}resolution}. Raw \isa{composition} is occasionally
useful as well, also it is strictly speaking outside of the proper
rule calculus.
--- a/doc-src/IsarImplementation/Thy/logic.thy Tue Sep 12 17:12:51 2006 +0200
+++ b/doc-src/IsarImplementation/Thy/logic.thy Tue Sep 12 17:23:34 2006 +0200
@@ -102,7 +102,7 @@
"c\<^isub>1 \<subseteq> c\<^isub>2"}, any arity @{text "\<kappa> ::
(\<^vec>s\<^isub>1)c\<^isub>1"} has a corresponding arity @{text "\<kappa>
:: (\<^vec>s\<^isub>2)c\<^isub>2"} where @{text "\<^vec>s\<^isub>1 \<subseteq>
- \<^vec>s\<^isub>2"} holds componentwise.
+ \<^vec>s\<^isub>2"} holds component-wise.
The key property of a coregular order-sorted algebra is that sort
constraints may be always solved in a most general fashion: for each
@@ -122,6 +122,7 @@
@{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"} \\
@{index_ML Sign.subsort: "theory -> sort * sort -> bool"} \\
@{index_ML Sign.of_sort: "theory -> typ * sort -> bool"} \\
@@ -148,8 +149,11 @@
\item @{ML_type typ} represents types; this is a datatype with
constructors @{ML TFree}, @{ML TVar}, @{ML Type}.
- \item @{ML fold_atyps}~@{text "f \<tau>"} iterates function @{text "f"}
- over all occurrences of atoms (@{ML TFree} or @{ML TVar}) of @{text
+ \item @{ML map_atyps}~@{text "f \<tau>"} applies mapping @{text "f"} to
+ all atomic types (@{ML TFree}, @{ML TVar}) occurring in @{text "\<tau>"}.
+
+ \item @{ML fold_atyps}~@{text "f \<tau>"} iterates operation @{text "f"}
+ over all occurrences of atoms (@{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)"}
@@ -188,18 +192,18 @@
\glossary{Term}{FIXME}
The language of terms is that of simply-typed @{text "\<lambda>"}-calculus
- with de-Bruijn indices for bound variables, and named free variables
- and constants. Terms with loose bound variables are usually
- considered malformed. The types of variables and constants is
- stored explicitly at each occurrence in the term.
+ with de-Bruijn indices for bound variables
+ \cite{debruijn72,paulson-ml2}, and named free variables and
+ constants. Terms with loose bound variables are usually considered
+ malformed. The types of variables and constants is stored
+ explicitly at each occurrence in the term.
\medskip A \emph{bound variable} is a natural number @{text "b"},
which refers to the next binder that is @{text "b"} steps upwards
from the occurrence of @{text "b"} (counting from zero). Bindings
may be introduced as abstractions within the term, or as a separate
context (an inside-out list). This associates each bound variable
- with a type, and a name that is maintained as a comment for parsing
- and printing. A \emph{loose variables} is a bound variable that is
+ with a type. A \emph{loose variables} is a bound variable that is
outside the current scope of local binders or the context. For
example, the de-Bruijn term @{text "\<lambda>\<^isub>\<tau>. \<lambda>\<^isub>\<tau>. 1 + 0"}
corresponds to @{text "\<lambda>x\<^isub>\<tau>. \<lambda>y\<^isub>\<tau>. x + y"} in a named
@@ -284,20 +288,96 @@
entering the logical core. Abbreviations are usually reverted when
printing terms, using rules @{text "t \<rightarrow> c\<^isub>\<sigma>"} has a
higher-order term rewrite system.
+
+ \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 some 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
+ @{text "0"} does not occur in @{text "f"}.
+
+ Terms are almost always treated module @{text "\<alpha>"}-conversion, which
+ is implicit in the de-Bruijn representation. The names in
+ abstractions of bound variables are maintained only as a comment for
+ parsing and printing. Full @{text "\<alpha>\<beta>\<eta>"}-equivalence is usually
+ taken for granted higher rules (\secref{sec:rules}), anything
+ depending on higher-order unification or rewriting.
*}
text %mlref {*
\begin{mldecls}
@{index_ML_type term} \\
+ @{index_ML "op aconv": "term * term -> bool"} \\
+ @{index_ML map_term_types: "(typ -> typ) -> term -> term"} \\ %FIXME rename map_types
+ @{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"} \\
@{index_ML fastype_of: "term -> typ"} \\
- @{index_ML fold_types: "(typ -> 'a -> 'a) -> term -> 'a -> 'a"} \\
+ @{index_ML lambda: "term -> term -> term"} \\
+ @{index_ML betapply: "term * term -> term"} \\
+ @{index_ML Sign.add_consts_i: "(bstring * typ * mixfix) list -> theory -> theory"} \\
+ @{index_ML Sign.add_abbrevs: "string * bool ->
+ ((bstring * mixfix) * term) list -> theory -> 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} FIXME
+ \item @{ML_type term} represents de-Bruijn terms with comments in
+ abstractions for bound variable names. 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_term_types}~@{text "f t"} applies mapping @{text "f"}
+ to all types occurring in @{text "t"}.
+
+ \item @{ML fold_types}~@{text "f t"} iterates 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 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 operation @{text "f"}
+ over all occurrences of atomic terms in (@{ML Bound}, @{ML Free},
+ @{ML Var}, @{ML Const}) @{text "t"}; the term structure is traversed
+ from left to right.
+
+ \item @{ML fastype_of}~@{text "t"} recomputes the type of a
+ well-formed term, while omitting any sanity checks. This operation
+ is relatively slow.
+
+ \item @{ML lambda}~@{text "a b"} produces an abstraction @{text
+ "\<lambda>a. b"}, where occurrences of the original (atomic) term @{text
+ "a"} are replaced by bound variables.
+
+ \item @{ML betapply}~@{text "t u"} produces an application @{text "t
+ u"}, with topmost @{text "\<beta>"}-conversion @{text "t"} is an
+ abstraction.
+
+ \item @{ML Sign.add_consts_i}~@{text "[(c, \<sigma>, mx), \<dots>]"} declares a
+ new constant @{text "c :: \<sigma>"} with optional mixfix syntax.
+
+ \item @{ML Sign.add_abbrevs}~@{text "print_mode [((c, t), mx), \<dots>]"}
+ declares a new term abbreviation @{text "c \<equiv> t"} with optional
+ mixfix syntax.
+
+ \item @{ML Sign.const_typargs}~@{text "thy (c, \<tau>)"} produces the
+ type arguments of the instance @{text "c\<^isub>\<tau>"} wrt.\ its
+ declaration in the theory.
+
+ \item @{ML Sign.const_instance}~@{text "thy (c, [\<tau>\<^isub>1, \<dots>,
+ \<tau>\<^isub>n])"} produces the full instance @{text "c(\<tau>\<^isub>1, \<dots>,
+ \<tau>\<^isub>n)"} wrt.\ its declaration in the theory.
\end{description}
*}
@@ -319,7 +399,7 @@
rarely spelled out explicitly. Theorems are usually normalized
according to the \seeglossary{HHF} format. FIXME}
- \glossary{Fact}{Sometimes used interchangably for
+ \glossary{Fact}{Sometimes used interchangeably for
\seeglossary{theorem}. Strictly speaking, a list of theorems,
essentially an extra-logical conjunction. Facts emerge either as
local assumptions, or as results of local goal statements --- both
@@ -495,7 +575,7 @@
There are two main principles of rule composition: @{text
"resolution"} (i.e.\ backchaining of rules) and @{text
"by-assumption"} (i.e.\ closing a branch); both principles are
- combined in the variants of @{text "elim-resosultion"} and @{text
+ combined in the variants of @{text "elim-resolution"} and @{text
"dest-resolution"}. Raw @{text "composition"} is occasionally
useful as well, also it is strictly speaking outside of the proper
rule calculus.