author wenzelm Tue, 12 Sep 2006 17:23:34 +0200 changeset 20519 d7ad1217c24a parent 20518 9125f0d95449 child 20520 05fd007bdeb9
more on terms;
--- 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

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.

@@ -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
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| \\
+\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.