--- a/src/HOLCF/Fixrec.thy Mon May 24 09:32:52 2010 -0700
+++ b/src/HOLCF/Fixrec.thy Mon May 24 11:29:49 2010 -0700
@@ -64,7 +64,6 @@
"case m of XCONST fail \<Rightarrow> t1 | XCONST succeed\<cdot>x \<Rightarrow> t2"
== "CONST match_case\<cdot>t1\<cdot>(\<Lambda> x. t2)\<cdot>m"
-
subsubsection {* Run operator *}
definition
@@ -109,334 +108,6 @@
lemma mplus_assoc: "(x +++ y) +++ z = x +++ (y +++ z)"
by (cases x, simp_all)
-subsubsection {* Fatbar combinator *}
-
-definition
- fatbar :: "('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match)" where
- "fatbar = (\<Lambda> a b x. a\<cdot>x +++ b\<cdot>x)"
-
-abbreviation
- fatbar_syn :: "['a \<rightarrow> 'b match, 'a \<rightarrow> 'b match] \<Rightarrow> 'a \<rightarrow> 'b match" (infixr "\<parallel>" 60) where
- "m1 \<parallel> m2 == fatbar\<cdot>m1\<cdot>m2"
-
-lemma fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> (m \<parallel> ms)\<cdot>x = \<bottom>"
-by (simp add: fatbar_def)
-
-lemma fatbar2: "m\<cdot>x = fail \<Longrightarrow> (m \<parallel> ms)\<cdot>x = ms\<cdot>x"
-by (simp add: fatbar_def)
-
-lemma fatbar3: "m\<cdot>x = succeed\<cdot>y \<Longrightarrow> (m \<parallel> ms)\<cdot>x = succeed\<cdot>y"
-by (simp add: fatbar_def)
-
-lemmas fatbar_simps = fatbar1 fatbar2 fatbar3
-
-lemma run_fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = \<bottom>"
-by (simp add: fatbar_def)
-
-lemma run_fatbar2: "m\<cdot>x = fail \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = run\<cdot>(ms\<cdot>x)"
-by (simp add: fatbar_def)
-
-lemma run_fatbar3: "m\<cdot>x = succeed\<cdot>y \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = y"
-by (simp add: fatbar_def)
-
-lemmas run_fatbar_simps [simp] = run_fatbar1 run_fatbar2 run_fatbar3
-
-subsection {* Case branch combinator *}
-
-definition
- branch :: "('a \<rightarrow> 'b match) \<Rightarrow> ('b \<rightarrow> 'c) \<rightarrow> ('a \<rightarrow> 'c match)" where
- "branch p \<equiv> \<Lambda> r x. match_case\<cdot>fail\<cdot>(\<Lambda> y. succeed\<cdot>(r\<cdot>y))\<cdot>(p\<cdot>x)"
-
-lemma branch_simps:
- "p\<cdot>x = \<bottom> \<Longrightarrow> branch p\<cdot>r\<cdot>x = \<bottom>"
- "p\<cdot>x = fail \<Longrightarrow> branch p\<cdot>r\<cdot>x = fail"
- "p\<cdot>x = succeed\<cdot>y \<Longrightarrow> branch p\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>y)"
-by (simp_all add: branch_def)
-
-lemma branch_succeed [simp]: "branch succeed\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>x)"
-by (simp add: branch_def)
-
-subsubsection {* Cases operator *}
-
-definition
- cases :: "'a match \<rightarrow> 'a::pcpo" where
- "cases = match_case\<cdot>\<bottom>\<cdot>ID"
-
-text {* rewrite rules for cases *}
-
-lemma cases_strict [simp]: "cases\<cdot>\<bottom> = \<bottom>"
-by (simp add: cases_def)
-
-lemma cases_fail [simp]: "cases\<cdot>fail = \<bottom>"
-by (simp add: cases_def)
-
-lemma cases_succeed [simp]: "cases\<cdot>(succeed\<cdot>x) = x"
-by (simp add: cases_def)
-
-subsection {* Case syntax *}
-
-nonterminals
- Case_syn Cases_syn
-
-syntax
- "_Case_syntax":: "['a, Cases_syn] => 'b" ("(Case _ of/ _)" 10)
- "_Case1" :: "['a, 'b] => Case_syn" ("(2_ =>/ _)" 10)
- "" :: "Case_syn => Cases_syn" ("_")
- "_Case2" :: "[Case_syn, Cases_syn] => Cases_syn" ("_/ | _")
-
-syntax (xsymbols)
- "_Case1" :: "['a, 'b] => Case_syn" ("(2_ \<Rightarrow>/ _)" 10)
-
-translations
- "_Case_syntax x ms" == "CONST Fixrec.cases\<cdot>(ms\<cdot>x)"
- "_Case2 m ms" == "m \<parallel> ms"
-
-text {* Parsing Case expressions *}
-
-syntax
- "_pat" :: "'a"
- "_variable" :: "'a"
- "_noargs" :: "'a"
-
-translations
- "_Case1 p r" => "CONST branch (_pat p)\<cdot>(_variable p r)"
- "_variable (_args x y) r" => "CONST csplit\<cdot>(_variable x (_variable y r))"
- "_variable _noargs r" => "CONST unit_when\<cdot>r"
-
-parse_translation {*
-(* rewrite (_pat x) => (succeed) *)
-(* rewrite (_variable x t) => (Abs_CFun (%x. t)) *)
- [(@{syntax_const "_pat"}, fn _ => Syntax.const @{const_syntax Fixrec.succeed}),
- mk_binder_tr (@{syntax_const "_variable"}, @{const_syntax Abs_CFun})];
-*}
-
-text {* Printing Case expressions *}
-
-syntax
- "_match" :: "'a"
-
-print_translation {*
- let
- fun dest_LAM (Const (@{const_syntax Rep_CFun},_) $ Const (@{const_syntax unit_when},_) $ t) =
- (Syntax.const @{syntax_const "_noargs"}, t)
- | dest_LAM (Const (@{const_syntax Rep_CFun},_) $ Const (@{const_syntax csplit},_) $ t) =
- let
- val (v1, t1) = dest_LAM t;
- val (v2, t2) = dest_LAM t1;
- in (Syntax.const @{syntax_const "_args"} $ v1 $ v2, t2) end
- | dest_LAM (Const (@{const_syntax Abs_CFun},_) $ t) =
- let
- val abs =
- case t of Abs abs => abs
- | _ => ("x", dummyT, incr_boundvars 1 t $ Bound 0);
- val (x, t') = atomic_abs_tr' abs;
- in (Syntax.const @{syntax_const "_variable"} $ x, t') end
- | dest_LAM _ = raise Match; (* too few vars: abort translation *)
-
- fun Case1_tr' [Const(@{const_syntax branch},_) $ p, r] =
- let val (v, t) = dest_LAM r in
- Syntax.const @{syntax_const "_Case1"} $
- (Syntax.const @{syntax_const "_match"} $ p $ v) $ t
- end;
-
- in [(@{const_syntax Rep_CFun}, Case1_tr')] end;
-*}
-
-translations
- "x" <= "_match (CONST Fixrec.succeed) (_variable x)"
-
-
-subsection {* Pattern combinators for data constructors *}
-
-types ('a, 'b) pat = "'a \<rightarrow> 'b match"
-
-definition
- cpair_pat :: "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a \<times> 'b, 'c \<times> 'd) pat" where
- "cpair_pat p1 p2 = (\<Lambda>(x, y).
- match_case\<cdot>fail\<cdot>(\<Lambda> a. match_case\<cdot>fail\<cdot>(\<Lambda> b. succeed\<cdot>(a, b))\<cdot>(p2\<cdot>y))\<cdot>(p1\<cdot>x))"
-
-definition
- spair_pat ::
- "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a::pcpo \<otimes> 'b::pcpo, 'c \<times> 'd) pat" where
- "spair_pat p1 p2 = (\<Lambda>(:x, y:). cpair_pat p1 p2\<cdot>(x, y))"
-
-definition
- sinl_pat :: "('a, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where
- "sinl_pat p = sscase\<cdot>p\<cdot>(\<Lambda> x. fail)"
-
-definition
- sinr_pat :: "('b, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where
- "sinr_pat p = sscase\<cdot>(\<Lambda> x. fail)\<cdot>p"
-
-definition
- up_pat :: "('a, 'b) pat \<Rightarrow> ('a u, 'b) pat" where
- "up_pat p = fup\<cdot>p"
-
-definition
- TT_pat :: "(tr, unit) pat" where
- "TT_pat = (\<Lambda> b. If b then succeed\<cdot>() else fail fi)"
-
-definition
- FF_pat :: "(tr, unit) pat" where
- "FF_pat = (\<Lambda> b. If b then fail else succeed\<cdot>() fi)"
-
-definition
- ONE_pat :: "(one, unit) pat" where
- "ONE_pat = (\<Lambda> ONE. succeed\<cdot>())"
-
-text {* Parse translations (patterns) *}
-translations
- "_pat (XCONST Pair x y)" => "CONST cpair_pat (_pat x) (_pat y)"
- "_pat (XCONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)"
- "_pat (XCONST sinl\<cdot>x)" => "CONST sinl_pat (_pat x)"
- "_pat (XCONST sinr\<cdot>x)" => "CONST sinr_pat (_pat x)"
- "_pat (XCONST up\<cdot>x)" => "CONST up_pat (_pat x)"
- "_pat (XCONST TT)" => "CONST TT_pat"
- "_pat (XCONST FF)" => "CONST FF_pat"
- "_pat (XCONST ONE)" => "CONST ONE_pat"
-
-text {* CONST version is also needed for constructors with special syntax *}
-translations
- "_pat (CONST Pair x y)" => "CONST cpair_pat (_pat x) (_pat y)"
- "_pat (CONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)"
-
-text {* Parse translations (variables) *}
-translations
- "_variable (XCONST Pair x y) r" => "_variable (_args x y) r"
- "_variable (XCONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
- "_variable (XCONST sinl\<cdot>x) r" => "_variable x r"
- "_variable (XCONST sinr\<cdot>x) r" => "_variable x r"
- "_variable (XCONST up\<cdot>x) r" => "_variable x r"
- "_variable (XCONST TT) r" => "_variable _noargs r"
- "_variable (XCONST FF) r" => "_variable _noargs r"
- "_variable (XCONST ONE) r" => "_variable _noargs r"
-
-translations
- "_variable (CONST Pair x y) r" => "_variable (_args x y) r"
- "_variable (CONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
-
-text {* Print translations *}
-translations
- "CONST Pair (_match p1 v1) (_match p2 v2)"
- <= "_match (CONST cpair_pat p1 p2) (_args v1 v2)"
- "CONST spair\<cdot>(_match p1 v1)\<cdot>(_match p2 v2)"
- <= "_match (CONST spair_pat p1 p2) (_args v1 v2)"
- "CONST sinl\<cdot>(_match p1 v1)" <= "_match (CONST sinl_pat p1) v1"
- "CONST sinr\<cdot>(_match p1 v1)" <= "_match (CONST sinr_pat p1) v1"
- "CONST up\<cdot>(_match p1 v1)" <= "_match (CONST up_pat p1) v1"
- "CONST TT" <= "_match (CONST TT_pat) _noargs"
- "CONST FF" <= "_match (CONST FF_pat) _noargs"
- "CONST ONE" <= "_match (CONST ONE_pat) _noargs"
-
-lemma cpair_pat1:
- "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = \<bottom>"
-apply (simp add: branch_def cpair_pat_def)
-apply (cases "p\<cdot>x", simp_all)
-done
-
-lemma cpair_pat2:
- "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = fail"
-apply (simp add: branch_def cpair_pat_def)
-apply (cases "p\<cdot>x", simp_all)
-done
-
-lemma cpair_pat3:
- "branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow>
- branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = branch q\<cdot>s\<cdot>y"
-apply (simp add: branch_def cpair_pat_def)
-apply (cases "p\<cdot>x", simp_all)
-apply (cases "q\<cdot>y", simp_all)
-done
-
-lemmas cpair_pat [simp] =
- cpair_pat1 cpair_pat2 cpair_pat3
-
-lemma spair_pat [simp]:
- "branch (spair_pat p1 p2)\<cdot>r\<cdot>\<bottom> = \<bottom>"
- "\<lbrakk>x \<noteq> \<bottom>; y \<noteq> \<bottom>\<rbrakk>
- \<Longrightarrow> branch (spair_pat p1 p2)\<cdot>r\<cdot>(:x, y:) =
- branch (cpair_pat p1 p2)\<cdot>r\<cdot>(x, y)"
-by (simp_all add: branch_def spair_pat_def)
-
-lemma sinl_pat [simp]:
- "branch (sinl_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
- "x \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = branch p\<cdot>r\<cdot>x"
- "y \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = fail"
-by (simp_all add: branch_def sinl_pat_def)
-
-lemma sinr_pat [simp]:
- "branch (sinr_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
- "x \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = fail"
- "y \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = branch p\<cdot>r\<cdot>y"
-by (simp_all add: branch_def sinr_pat_def)
-
-lemma up_pat [simp]:
- "branch (up_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
- "branch (up_pat p)\<cdot>r\<cdot>(up\<cdot>x) = branch p\<cdot>r\<cdot>x"
-by (simp_all add: branch_def up_pat_def)
-
-lemma TT_pat [simp]:
- "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
- "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = succeed\<cdot>r"
- "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = fail"
-by (simp_all add: branch_def TT_pat_def)
-
-lemma FF_pat [simp]:
- "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
- "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = fail"
- "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = succeed\<cdot>r"
-by (simp_all add: branch_def FF_pat_def)
-
-lemma ONE_pat [simp]:
- "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
- "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>ONE = succeed\<cdot>r"
-by (simp_all add: branch_def ONE_pat_def)
-
-
-subsection {* Wildcards, as-patterns, and lazy patterns *}
-
-definition
- wild_pat :: "'a \<rightarrow> unit match" where
- "wild_pat = (\<Lambda> x. succeed\<cdot>())"
-
-definition
- as_pat :: "('a \<rightarrow> 'b match) \<Rightarrow> 'a \<rightarrow> ('a \<times> 'b) match" where
- "as_pat p = (\<Lambda> x. match_case\<cdot>fail\<cdot>(\<Lambda> a. succeed\<cdot>(x, a))\<cdot>(p\<cdot>x))"
-
-definition
- lazy_pat :: "('a \<rightarrow> 'b::pcpo match) \<Rightarrow> ('a \<rightarrow> 'b match)" where
- "lazy_pat p = (\<Lambda> x. succeed\<cdot>(cases\<cdot>(p\<cdot>x)))"
-
-text {* Parse translations (patterns) *}
-translations
- "_pat _" => "CONST wild_pat"
-
-text {* Parse translations (variables) *}
-translations
- "_variable _ r" => "_variable _noargs r"
-
-text {* Print translations *}
-translations
- "_" <= "_match (CONST wild_pat) _noargs"
-
-lemma wild_pat [simp]: "branch wild_pat\<cdot>(unit_when\<cdot>r)\<cdot>x = succeed\<cdot>r"
-by (simp add: branch_def wild_pat_def)
-
-lemma as_pat [simp]:
- "branch (as_pat p)\<cdot>(csplit\<cdot>r)\<cdot>x = branch p\<cdot>(r\<cdot>x)\<cdot>x"
-apply (simp add: branch_def as_pat_def)
-apply (cases "p\<cdot>x", simp_all)
-done
-
-lemma lazy_pat [simp]:
- "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)"
- "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)"
- "branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>s"
-apply (simp_all add: branch_def lazy_pat_def)
-apply (cases "p\<cdot>x", simp_all)+
-done
-
-
subsection {* Match functions for built-in types *}
default_sort pcpo
@@ -584,6 +255,6 @@
(@{const_name UU}, @{const_name match_UU}) ]
*}
-hide_const (open) succeed fail run cases
+hide_const (open) succeed fail run
end
--- a/src/HOLCF/IsaMakefile Mon May 24 09:32:52 2010 -0700
+++ b/src/HOLCF/IsaMakefile Mon May 24 11:29:49 2010 -0700
@@ -115,6 +115,7 @@
ex/Hoare.thy \
ex/Letrec.thy \
ex/Loop.thy \
+ ex/Pattern_Match.thy \
ex/Powerdomain_ex.thy \
ex/Stream.thy \
ex/Strict_Fun.thy \
--- a/src/HOLCF/Tools/Domain/domain_constructors.ML Mon May 24 09:32:52 2010 -0700
+++ b/src/HOLCF/Tools/Domain/domain_constructors.ML Mon May 24 11:29:49 2010 -0700
@@ -25,8 +25,7 @@
cases : thm list,
sel_rews : thm list,
dis_rews : thm list,
- match_rews : thm list,
- pat_rews : thm list
+ match_rews : thm list
} * theory;
end;
@@ -824,162 +823,6 @@
end;
(******************************************************************************)
-(************** definitions and theorems for pattern combinators **************)
-(******************************************************************************)
-
-fun add_pattern_combinators
- (bindings : binding list)
- (spec : (term * (bool * typ) list) list)
- (lhsT : typ)
- (exhaust : thm)
- (case_const : typ -> term)
- (case_rews : thm list)
- (thy : theory) =
- let
-
- (* utility functions *)
- fun mk_pair_pat (p1, p2) =
- let
- val T1 = fastype_of p1;
- val T2 = fastype_of p2;
- val (U1, V1) = apsnd dest_matchT (dest_cfunT T1);
- val (U2, V2) = apsnd dest_matchT (dest_cfunT T2);
- val pat_typ = [T1, T2] --->
- (mk_prodT (U1, U2) ->> mk_matchT (mk_prodT (V1, V2)));
- val pat_const = Const (@{const_name cpair_pat}, pat_typ);
- in
- pat_const $ p1 $ p2
- end;
- fun mk_tuple_pat [] = succeed_const HOLogic.unitT
- | mk_tuple_pat ps = foldr1 mk_pair_pat ps;
- fun branch_const (T,U,V) =
- Const (@{const_name branch},
- (T ->> mk_matchT U) --> (U ->> V) ->> T ->> mk_matchT V);
-
- (* define pattern combinators *)
- local
- val tns = map (fst o dest_TFree) (snd (dest_Type lhsT));
-
- fun pat_eqn (i, (bind, (con, args))) : binding * term * mixfix =
- let
- val pat_bind = Binding.suffix_name "_pat" bind;
- val Ts = map snd args;
- val Vs =
- (map (K "'t") args)
- |> Datatype_Prop.indexify_names
- |> Name.variant_list tns
- |> map (fn t => TFree (t, @{sort pcpo}));
- val patNs = Datatype_Prop.indexify_names (map (K "pat") args);
- val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs;
- val pats = map Free (patNs ~~ patTs);
- val fail = mk_fail (mk_tupleT Vs);
- val (vs, nonlazy) = get_vars_avoiding patNs args;
- val rhs = big_lambdas vs (mk_tuple_pat pats ` mk_tuple vs);
- fun one_fun (j, (_, args')) =
- let
- val (vs', nonlazy) = get_vars_avoiding patNs args';
- in if i = j then rhs else big_lambdas vs' fail end;
- val funs = map_index one_fun spec;
- val body = list_ccomb (case_const (mk_matchT (mk_tupleT Vs)), funs);
- in
- (pat_bind, lambdas pats body, NoSyn)
- end;
- in
- val ((pat_consts, pat_defs), thy) =
- define_consts (map_index pat_eqn (bindings ~~ spec)) thy
- end;
-
- (* syntax translations for pattern combinators *)
- local
- open Syntax
- fun syntax c = Syntax.mark_const (fst (dest_Const c));
- fun app s (l, r) = Syntax.mk_appl (Constant s) [l, r];
- val capp = app @{const_syntax Rep_CFun};
- val capps = Library.foldl capp
-
- fun app_var x = Syntax.mk_appl (Constant "_variable") [x, Variable "rhs"];
- fun app_pat x = Syntax.mk_appl (Constant "_pat") [x];
- fun args_list [] = Constant "_noargs"
- | args_list xs = foldr1 (app "_args") xs;
- fun one_case_trans (pat, (con, args)) =
- let
- val cname = Constant (syntax con);
- val pname = Constant (syntax pat);
- val ns = 1 upto length args;
- val xs = map (fn n => Variable ("x"^(string_of_int n))) ns;
- val ps = map (fn n => Variable ("p"^(string_of_int n))) ns;
- val vs = map (fn n => Variable ("v"^(string_of_int n))) ns;
- in
- [ParseRule (app_pat (capps (cname, xs)),
- mk_appl pname (map app_pat xs)),
- ParseRule (app_var (capps (cname, xs)),
- app_var (args_list xs)),
- PrintRule (capps (cname, ListPair.map (app "_match") (ps,vs)),
- app "_match" (mk_appl pname ps, args_list vs))]
- end;
- val trans_rules : Syntax.ast Syntax.trrule list =
- maps one_case_trans (pat_consts ~~ spec);
- in
- val thy = Sign.add_trrules_i trans_rules thy;
- end;
-
- (* prove strictness and reduction rules of pattern combinators *)
- local
- val tns = map (fst o dest_TFree) (snd (dest_Type lhsT));
- val rn = Name.variant tns "'r";
- val R = TFree (rn, @{sort pcpo});
- fun pat_lhs (pat, args) =
- let
- val Ts = map snd args;
- val Vs =
- (map (K "'t") args)
- |> Datatype_Prop.indexify_names
- |> Name.variant_list (rn::tns)
- |> map (fn t => TFree (t, @{sort pcpo}));
- val patNs = Datatype_Prop.indexify_names (map (K "pat") args);
- val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs;
- val pats = map Free (patNs ~~ patTs);
- val k = Free ("rhs", mk_tupleT Vs ->> R);
- val branch1 = branch_const (lhsT, mk_tupleT Vs, R);
- val fun1 = (branch1 $ list_comb (pat, pats)) ` k;
- val branch2 = branch_const (mk_tupleT Ts, mk_tupleT Vs, R);
- val fun2 = (branch2 $ mk_tuple_pat pats) ` k;
- val taken = "rhs" :: patNs;
- in (fun1, fun2, taken) end;
- fun pat_strict (pat, (con, args)) =
- let
- val (fun1, fun2, taken) = pat_lhs (pat, args);
- val defs = @{thm branch_def} :: pat_defs;
- val goal = mk_trp (mk_strict fun1);
- val rules = @{thms match_case_simps} @ case_rews;
- val tacs = [simp_tac (beta_ss addsimps rules) 1];
- in prove thy defs goal (K tacs) end;
- fun pat_apps (i, (pat, (con, args))) =
- let
- val (fun1, fun2, taken) = pat_lhs (pat, args);
- fun pat_app (j, (con', args')) =
- let
- val (vs, nonlazy) = get_vars_avoiding taken args';
- val con_app = list_ccomb (con', vs);
- val assms = map (mk_trp o mk_defined) nonlazy;
- val rhs = if i = j then fun2 ` mk_tuple vs else mk_fail R;
- val concl = mk_trp (mk_eq (fun1 ` con_app, rhs));
- val goal = Logic.list_implies (assms, concl);
- val defs = @{thm branch_def} :: pat_defs;
- val rules = @{thms match_case_simps} @ case_rews;
- val tacs = [asm_simp_tac (beta_ss addsimps rules) 1];
- in prove thy defs goal (K tacs) end;
- in map_index pat_app spec end;
- in
- val pat_stricts = map pat_strict (pat_consts ~~ spec);
- val pat_apps = flat (map_index pat_apps (pat_consts ~~ spec));
- end;
-
- in
- (pat_stricts @ pat_apps, thy)
- end
-
-(******************************************************************************)
(******************************* main function ********************************)
(******************************************************************************)
@@ -1061,18 +904,6 @@
exhaust case_const cases thy
end
- (* define and prove theorems for pattern combinators *)
- val (pat_thms : thm list, thy : theory) =
- let
- val bindings = map #1 spec;
- fun prep_arg (lazy, sel, T) = (lazy, T);
- fun prep_con c (b, args, mx) = (c, map prep_arg args);
- val pat_spec = map2 prep_con con_consts spec;
- in
- add_pattern_combinators bindings pat_spec lhsT
- exhaust case_const cases thy
- end
-
(* restore original signature path *)
val thy = Sign.parent_path thy;
@@ -1090,8 +921,7 @@
cases = cases,
sel_rews = sel_thms,
dis_rews = dis_thms,
- match_rews = match_thms,
- pat_rews = pat_thms };
+ match_rews = match_thms };
in
(result, thy)
end;
--- a/src/HOLCF/Tools/Domain/domain_theorems.ML Mon May 24 09:32:52 2010 -0700
+++ b/src/HOLCF/Tools/Domain/domain_theorems.ML Mon May 24 11:29:49 2010 -0700
@@ -145,7 +145,6 @@
val when_strict = hd when_rews;
val dis_rews = #dis_rews result;
val mat_rews = #match_rews result;
-val pat_rews = #pat_rews result;
(* ----- theorems concerning the isomorphism -------------------------------- *)
@@ -211,7 +210,6 @@
((qualified "con_rews" , con_rews ), [simp]),
((qualified "sel_rews" , sel_rews ), [simp]),
((qualified "dis_rews" , dis_rews ), [simp]),
- ((qualified "pat_rews" , pat_rews ), [simp]),
((qualified "dist_les" , dist_les ), [simp]),
((qualified "dist_eqs" , dist_eqs ), [simp]),
((qualified "inverts" , inverts ), [simp]),
@@ -220,7 +218,7 @@
((qualified "match_rews", mat_rews ), [simp])]
|> snd
|> pair (iso_rews @ when_rews @ con_rews @ sel_rews @ dis_rews @
- pat_rews @ dist_les @ dist_eqs)
+ dist_les @ dist_eqs)
end; (* let *)
(******************************************************************************)
--- a/src/HOLCF/Tutorial/Domain_ex.thy Mon May 24 09:32:52 2010 -0700
+++ b/src/HOLCF/Tutorial/Domain_ex.thy Mon May 24 11:29:49 2010 -0700
@@ -154,11 +154,6 @@
term is_Node
thm tree.dis_rews
-text {* Rules about pattern match combinators *}
-term Leaf_pat
-term Node_pat
-thm tree.pat_rews
-
text {* Rules about monadic pattern match combinators *}
term match_Leaf
term match_Node
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/ex/Pattern_Match.thy Mon May 24 11:29:49 2010 -0700
@@ -0,0 +1,591 @@
+(* Title: HOLCF/ex/Pattern_Match.thy
+ Author: Brian Huffman
+*)
+
+header {* An experimental pattern-matching notation *}
+
+theory Pattern_Match
+imports HOLCF
+begin
+
+text {* FIXME: Find a proper way to un-hide constants. *}
+
+abbreviation fail :: "'a match"
+where "fail \<equiv> Fixrec.fail"
+
+abbreviation succeed :: "'a \<rightarrow> 'a match"
+where "succeed \<equiv> Fixrec.succeed"
+
+abbreviation run :: "'a match \<rightarrow> 'a"
+where "run \<equiv> Fixrec.run"
+
+subsection {* Fatbar combinator *}
+
+definition
+ fatbar :: "('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match)" where
+ "fatbar = (\<Lambda> a b x. a\<cdot>x +++ b\<cdot>x)"
+
+abbreviation
+ fatbar_syn :: "['a \<rightarrow> 'b match, 'a \<rightarrow> 'b match] \<Rightarrow> 'a \<rightarrow> 'b match" (infixr "\<parallel>" 60) where
+ "m1 \<parallel> m2 == fatbar\<cdot>m1\<cdot>m2"
+
+lemma fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> (m \<parallel> ms)\<cdot>x = \<bottom>"
+by (simp add: fatbar_def)
+
+lemma fatbar2: "m\<cdot>x = fail \<Longrightarrow> (m \<parallel> ms)\<cdot>x = ms\<cdot>x"
+by (simp add: fatbar_def)
+
+lemma fatbar3: "m\<cdot>x = succeed\<cdot>y \<Longrightarrow> (m \<parallel> ms)\<cdot>x = succeed\<cdot>y"
+by (simp add: fatbar_def)
+
+lemmas fatbar_simps = fatbar1 fatbar2 fatbar3
+
+lemma run_fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = \<bottom>"
+by (simp add: fatbar_def)
+
+lemma run_fatbar2: "m\<cdot>x = fail \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = run\<cdot>(ms\<cdot>x)"
+by (simp add: fatbar_def)
+
+lemma run_fatbar3: "m\<cdot>x = succeed\<cdot>y \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = y"
+by (simp add: fatbar_def)
+
+lemmas run_fatbar_simps [simp] = run_fatbar1 run_fatbar2 run_fatbar3
+
+subsection {* Case branch combinator *}
+
+definition
+ branch :: "('a \<rightarrow> 'b match) \<Rightarrow> ('b \<rightarrow> 'c) \<rightarrow> ('a \<rightarrow> 'c match)" where
+ "branch p \<equiv> \<Lambda> r x. match_case\<cdot>fail\<cdot>(\<Lambda> y. succeed\<cdot>(r\<cdot>y))\<cdot>(p\<cdot>x)"
+
+lemma branch_simps:
+ "p\<cdot>x = \<bottom> \<Longrightarrow> branch p\<cdot>r\<cdot>x = \<bottom>"
+ "p\<cdot>x = fail \<Longrightarrow> branch p\<cdot>r\<cdot>x = fail"
+ "p\<cdot>x = succeed\<cdot>y \<Longrightarrow> branch p\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>y)"
+by (simp_all add: branch_def)
+
+lemma branch_succeed [simp]: "branch succeed\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>x)"
+by (simp add: branch_def)
+
+subsection {* Cases operator *}
+
+definition
+ cases :: "'a match \<rightarrow> 'a::pcpo" where
+ "cases = match_case\<cdot>\<bottom>\<cdot>ID"
+
+text {* rewrite rules for cases *}
+
+lemma cases_strict [simp]: "cases\<cdot>\<bottom> = \<bottom>"
+by (simp add: cases_def)
+
+lemma cases_fail [simp]: "cases\<cdot>fail = \<bottom>"
+by (simp add: cases_def)
+
+lemma cases_succeed [simp]: "cases\<cdot>(succeed\<cdot>x) = x"
+by (simp add: cases_def)
+
+subsection {* Case syntax *}
+
+nonterminals
+ Case_syn Cases_syn
+
+syntax
+ "_Case_syntax":: "['a, Cases_syn] => 'b" ("(Case _ of/ _)" 10)
+ "_Case1" :: "['a, 'b] => Case_syn" ("(2_ =>/ _)" 10)
+ "" :: "Case_syn => Cases_syn" ("_")
+ "_Case2" :: "[Case_syn, Cases_syn] => Cases_syn" ("_/ | _")
+
+syntax (xsymbols)
+ "_Case1" :: "['a, 'b] => Case_syn" ("(2_ \<Rightarrow>/ _)" 10)
+
+translations
+ "_Case_syntax x ms" == "CONST cases\<cdot>(ms\<cdot>x)"
+ "_Case2 m ms" == "m \<parallel> ms"
+
+text {* Parsing Case expressions *}
+
+syntax
+ "_pat" :: "'a"
+ "_variable" :: "'a"
+ "_noargs" :: "'a"
+
+translations
+ "_Case1 p r" => "CONST branch (_pat p)\<cdot>(_variable p r)"
+ "_variable (_args x y) r" => "CONST csplit\<cdot>(_variable x (_variable y r))"
+ "_variable _noargs r" => "CONST unit_when\<cdot>r"
+
+parse_translation {*
+(* rewrite (_pat x) => (succeed) *)
+(* rewrite (_variable x t) => (Abs_CFun (%x. t)) *)
+ [(@{syntax_const "_pat"}, fn _ => Syntax.const @{const_syntax Fixrec.succeed}),
+ mk_binder_tr (@{syntax_const "_variable"}, @{const_syntax Abs_CFun})];
+*}
+
+text {* Printing Case expressions *}
+
+syntax
+ "_match" :: "'a"
+
+print_translation {*
+ let
+ fun dest_LAM (Const (@{const_syntax Rep_CFun},_) $ Const (@{const_syntax unit_when},_) $ t) =
+ (Syntax.const @{syntax_const "_noargs"}, t)
+ | dest_LAM (Const (@{const_syntax Rep_CFun},_) $ Const (@{const_syntax csplit},_) $ t) =
+ let
+ val (v1, t1) = dest_LAM t;
+ val (v2, t2) = dest_LAM t1;
+ in (Syntax.const @{syntax_const "_args"} $ v1 $ v2, t2) end
+ | dest_LAM (Const (@{const_syntax Abs_CFun},_) $ t) =
+ let
+ val abs =
+ case t of Abs abs => abs
+ | _ => ("x", dummyT, incr_boundvars 1 t $ Bound 0);
+ val (x, t') = atomic_abs_tr' abs;
+ in (Syntax.const @{syntax_const "_variable"} $ x, t') end
+ | dest_LAM _ = raise Match; (* too few vars: abort translation *)
+
+ fun Case1_tr' [Const(@{const_syntax branch},_) $ p, r] =
+ let val (v, t) = dest_LAM r in
+ Syntax.const @{syntax_const "_Case1"} $
+ (Syntax.const @{syntax_const "_match"} $ p $ v) $ t
+ end;
+
+ in [(@{const_syntax Rep_CFun}, Case1_tr')] end;
+*}
+
+translations
+ "x" <= "_match (CONST succeed) (_variable x)"
+
+
+subsection {* Pattern combinators for data constructors *}
+
+types ('a, 'b) pat = "'a \<rightarrow> 'b match"
+
+definition
+ cpair_pat :: "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a \<times> 'b, 'c \<times> 'd) pat" where
+ "cpair_pat p1 p2 = (\<Lambda>(x, y).
+ match_case\<cdot>fail\<cdot>(\<Lambda> a. match_case\<cdot>fail\<cdot>(\<Lambda> b. succeed\<cdot>(a, b))\<cdot>(p2\<cdot>y))\<cdot>(p1\<cdot>x))"
+
+definition
+ spair_pat ::
+ "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a::pcpo \<otimes> 'b::pcpo, 'c \<times> 'd) pat" where
+ "spair_pat p1 p2 = (\<Lambda>(:x, y:). cpair_pat p1 p2\<cdot>(x, y))"
+
+definition
+ sinl_pat :: "('a, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where
+ "sinl_pat p = sscase\<cdot>p\<cdot>(\<Lambda> x. fail)"
+
+definition
+ sinr_pat :: "('b, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where
+ "sinr_pat p = sscase\<cdot>(\<Lambda> x. fail)\<cdot>p"
+
+definition
+ up_pat :: "('a, 'b) pat \<Rightarrow> ('a u, 'b) pat" where
+ "up_pat p = fup\<cdot>p"
+
+definition
+ TT_pat :: "(tr, unit) pat" where
+ "TT_pat = (\<Lambda> b. If b then succeed\<cdot>() else fail fi)"
+
+definition
+ FF_pat :: "(tr, unit) pat" where
+ "FF_pat = (\<Lambda> b. If b then fail else succeed\<cdot>() fi)"
+
+definition
+ ONE_pat :: "(one, unit) pat" where
+ "ONE_pat = (\<Lambda> ONE. succeed\<cdot>())"
+
+text {* Parse translations (patterns) *}
+translations
+ "_pat (XCONST Pair x y)" => "CONST cpair_pat (_pat x) (_pat y)"
+ "_pat (XCONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)"
+ "_pat (XCONST sinl\<cdot>x)" => "CONST sinl_pat (_pat x)"
+ "_pat (XCONST sinr\<cdot>x)" => "CONST sinr_pat (_pat x)"
+ "_pat (XCONST up\<cdot>x)" => "CONST up_pat (_pat x)"
+ "_pat (XCONST TT)" => "CONST TT_pat"
+ "_pat (XCONST FF)" => "CONST FF_pat"
+ "_pat (XCONST ONE)" => "CONST ONE_pat"
+
+text {* CONST version is also needed for constructors with special syntax *}
+translations
+ "_pat (CONST Pair x y)" => "CONST cpair_pat (_pat x) (_pat y)"
+ "_pat (CONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)"
+
+text {* Parse translations (variables) *}
+translations
+ "_variable (XCONST Pair x y) r" => "_variable (_args x y) r"
+ "_variable (XCONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
+ "_variable (XCONST sinl\<cdot>x) r" => "_variable x r"
+ "_variable (XCONST sinr\<cdot>x) r" => "_variable x r"
+ "_variable (XCONST up\<cdot>x) r" => "_variable x r"
+ "_variable (XCONST TT) r" => "_variable _noargs r"
+ "_variable (XCONST FF) r" => "_variable _noargs r"
+ "_variable (XCONST ONE) r" => "_variable _noargs r"
+
+translations
+ "_variable (CONST Pair x y) r" => "_variable (_args x y) r"
+ "_variable (CONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
+
+text {* Print translations *}
+translations
+ "CONST Pair (_match p1 v1) (_match p2 v2)"
+ <= "_match (CONST cpair_pat p1 p2) (_args v1 v2)"
+ "CONST spair\<cdot>(_match p1 v1)\<cdot>(_match p2 v2)"
+ <= "_match (CONST spair_pat p1 p2) (_args v1 v2)"
+ "CONST sinl\<cdot>(_match p1 v1)" <= "_match (CONST sinl_pat p1) v1"
+ "CONST sinr\<cdot>(_match p1 v1)" <= "_match (CONST sinr_pat p1) v1"
+ "CONST up\<cdot>(_match p1 v1)" <= "_match (CONST up_pat p1) v1"
+ "CONST TT" <= "_match (CONST TT_pat) _noargs"
+ "CONST FF" <= "_match (CONST FF_pat) _noargs"
+ "CONST ONE" <= "_match (CONST ONE_pat) _noargs"
+
+lemma cpair_pat1:
+ "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = \<bottom>"
+apply (simp add: branch_def cpair_pat_def)
+apply (cases "p\<cdot>x", simp_all)
+done
+
+lemma cpair_pat2:
+ "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = fail"
+apply (simp add: branch_def cpair_pat_def)
+apply (cases "p\<cdot>x", simp_all)
+done
+
+lemma cpair_pat3:
+ "branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow>
+ branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = branch q\<cdot>s\<cdot>y"
+apply (simp add: branch_def cpair_pat_def)
+apply (cases "p\<cdot>x", simp_all)
+apply (cases "q\<cdot>y", simp_all)
+done
+
+lemmas cpair_pat [simp] =
+ cpair_pat1 cpair_pat2 cpair_pat3
+
+lemma spair_pat [simp]:
+ "branch (spair_pat p1 p2)\<cdot>r\<cdot>\<bottom> = \<bottom>"
+ "\<lbrakk>x \<noteq> \<bottom>; y \<noteq> \<bottom>\<rbrakk>
+ \<Longrightarrow> branch (spair_pat p1 p2)\<cdot>r\<cdot>(:x, y:) =
+ branch (cpair_pat p1 p2)\<cdot>r\<cdot>(x, y)"
+by (simp_all add: branch_def spair_pat_def)
+
+lemma sinl_pat [simp]:
+ "branch (sinl_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
+ "x \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = branch p\<cdot>r\<cdot>x"
+ "y \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = fail"
+by (simp_all add: branch_def sinl_pat_def)
+
+lemma sinr_pat [simp]:
+ "branch (sinr_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
+ "x \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = fail"
+ "y \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = branch p\<cdot>r\<cdot>y"
+by (simp_all add: branch_def sinr_pat_def)
+
+lemma up_pat [simp]:
+ "branch (up_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
+ "branch (up_pat p)\<cdot>r\<cdot>(up\<cdot>x) = branch p\<cdot>r\<cdot>x"
+by (simp_all add: branch_def up_pat_def)
+
+lemma TT_pat [simp]:
+ "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
+ "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = succeed\<cdot>r"
+ "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = fail"
+by (simp_all add: branch_def TT_pat_def)
+
+lemma FF_pat [simp]:
+ "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
+ "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = fail"
+ "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = succeed\<cdot>r"
+by (simp_all add: branch_def FF_pat_def)
+
+lemma ONE_pat [simp]:
+ "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
+ "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>ONE = succeed\<cdot>r"
+by (simp_all add: branch_def ONE_pat_def)
+
+
+subsection {* Wildcards, as-patterns, and lazy patterns *}
+
+definition
+ wild_pat :: "'a \<rightarrow> unit match" where
+ "wild_pat = (\<Lambda> x. succeed\<cdot>())"
+
+definition
+ as_pat :: "('a \<rightarrow> 'b match) \<Rightarrow> 'a \<rightarrow> ('a \<times> 'b) match" where
+ "as_pat p = (\<Lambda> x. match_case\<cdot>fail\<cdot>(\<Lambda> a. succeed\<cdot>(x, a))\<cdot>(p\<cdot>x))"
+
+definition
+ lazy_pat :: "('a \<rightarrow> 'b::pcpo match) \<Rightarrow> ('a \<rightarrow> 'b match)" where
+ "lazy_pat p = (\<Lambda> x. succeed\<cdot>(cases\<cdot>(p\<cdot>x)))"
+
+text {* Parse translations (patterns) *}
+translations
+ "_pat _" => "CONST wild_pat"
+
+text {* Parse translations (variables) *}
+translations
+ "_variable _ r" => "_variable _noargs r"
+
+text {* Print translations *}
+translations
+ "_" <= "_match (CONST wild_pat) _noargs"
+
+lemma wild_pat [simp]: "branch wild_pat\<cdot>(unit_when\<cdot>r)\<cdot>x = succeed\<cdot>r"
+by (simp add: branch_def wild_pat_def)
+
+lemma as_pat [simp]:
+ "branch (as_pat p)\<cdot>(csplit\<cdot>r)\<cdot>x = branch p\<cdot>(r\<cdot>x)\<cdot>x"
+apply (simp add: branch_def as_pat_def)
+apply (cases "p\<cdot>x", simp_all)
+done
+
+lemma lazy_pat [simp]:
+ "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)"
+ "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)"
+ "branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>s"
+apply (simp_all add: branch_def lazy_pat_def)
+apply (cases "p\<cdot>x", simp_all)+
+done
+
+subsection {* Examples *}
+
+term "Case t of (:up\<cdot>(sinl\<cdot>x), sinr\<cdot>y:) \<Rightarrow> (x, y)"
+
+term "\<Lambda> t. Case t of up\<cdot>(sinl\<cdot>a) \<Rightarrow> a | up\<cdot>(sinr\<cdot>b) \<Rightarrow> b"
+
+term "\<Lambda> t. Case t of (:up\<cdot>(sinl\<cdot>_), sinr\<cdot>x:) \<Rightarrow> x"
+
+subsection {* ML code for generating definitions *}
+
+ML {*
+local open HOLCF_Library in
+
+val beta_rules =
+ @{thms beta_cfun cont_id cont_const cont2cont_Rep_CFun cont2cont_LAM'} @
+ @{thms cont2cont_fst cont2cont_snd cont2cont_Pair};
+
+val beta_ss = HOL_basic_ss addsimps (simp_thms @ beta_rules);
+
+fun define_consts
+ (specs : (binding * term * mixfix) list)
+ (thy : theory)
+ : (term list * thm list) * theory =
+ let
+ fun mk_decl (b, t, mx) = (b, fastype_of t, mx);
+ val decls = map mk_decl specs;
+ val thy = Cont_Consts.add_consts decls thy;
+ fun mk_const (b, T, mx) = Const (Sign.full_name thy b, T);
+ val consts = map mk_const decls;
+ fun mk_def c (b, t, mx) =
+ (Binding.suffix_name "_def" b, Logic.mk_equals (c, t));
+ val defs = map2 mk_def consts specs;
+ val (def_thms, thy) =
+ PureThy.add_defs false (map Thm.no_attributes defs) thy;
+ in
+ ((consts, def_thms), thy)
+ end;
+
+fun prove
+ (thy : theory)
+ (defs : thm list)
+ (goal : term)
+ (tacs : {prems: thm list, context: Proof.context} -> tactic list)
+ : thm =
+ let
+ fun tac {prems, context} =
+ rewrite_goals_tac defs THEN
+ EVERY (tacs {prems = map (rewrite_rule defs) prems, context = context})
+ in
+ Goal.prove_global thy [] [] goal tac
+ end;
+
+fun get_vars_avoiding
+ (taken : string list)
+ (args : (bool * typ) list)
+ : (term list * term list) =
+ let
+ val Ts = map snd args;
+ val ns = Name.variant_list taken (Datatype_Prop.make_tnames Ts);
+ val vs = map Free (ns ~~ Ts);
+ val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs));
+ in
+ (vs, nonlazy)
+ end;
+
+(******************************************************************************)
+(************** definitions and theorems for pattern combinators **************)
+(******************************************************************************)
+
+fun add_pattern_combinators
+ (bindings : binding list)
+ (spec : (term * (bool * typ) list) list)
+ (lhsT : typ)
+ (exhaust : thm)
+ (case_const : typ -> term)
+ (case_rews : thm list)
+ (thy : theory) =
+ let
+
+ (* utility functions *)
+ fun mk_pair_pat (p1, p2) =
+ let
+ val T1 = fastype_of p1;
+ val T2 = fastype_of p2;
+ val (U1, V1) = apsnd dest_matchT (dest_cfunT T1);
+ val (U2, V2) = apsnd dest_matchT (dest_cfunT T2);
+ val pat_typ = [T1, T2] --->
+ (mk_prodT (U1, U2) ->> mk_matchT (mk_prodT (V1, V2)));
+ val pat_const = Const (@{const_name cpair_pat}, pat_typ);
+ in
+ pat_const $ p1 $ p2
+ end;
+ fun mk_tuple_pat [] = succeed_const HOLogic.unitT
+ | mk_tuple_pat ps = foldr1 mk_pair_pat ps;
+ fun branch_const (T,U,V) =
+ Const (@{const_name branch},
+ (T ->> mk_matchT U) --> (U ->> V) ->> T ->> mk_matchT V);
+
+ (* define pattern combinators *)
+ local
+ val tns = map (fst o dest_TFree) (snd (dest_Type lhsT));
+
+ fun pat_eqn (i, (bind, (con, args))) : binding * term * mixfix =
+ let
+ val pat_bind = Binding.suffix_name "_pat" bind;
+ val Ts = map snd args;
+ val Vs =
+ (map (K "'t") args)
+ |> Datatype_Prop.indexify_names
+ |> Name.variant_list tns
+ |> map (fn t => TFree (t, @{sort pcpo}));
+ val patNs = Datatype_Prop.indexify_names (map (K "pat") args);
+ val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs;
+ val pats = map Free (patNs ~~ patTs);
+ val fail = mk_fail (mk_tupleT Vs);
+ val (vs, nonlazy) = get_vars_avoiding patNs args;
+ val rhs = big_lambdas vs (mk_tuple_pat pats ` mk_tuple vs);
+ fun one_fun (j, (_, args')) =
+ let
+ val (vs', nonlazy) = get_vars_avoiding patNs args';
+ in if i = j then rhs else big_lambdas vs' fail end;
+ val funs = map_index one_fun spec;
+ val body = list_ccomb (case_const (mk_matchT (mk_tupleT Vs)), funs);
+ in
+ (pat_bind, lambdas pats body, NoSyn)
+ end;
+ in
+ val ((pat_consts, pat_defs), thy) =
+ define_consts (map_index pat_eqn (bindings ~~ spec)) thy
+ end;
+
+ (* syntax translations for pattern combinators *)
+ local
+ open Syntax
+ fun syntax c = Syntax.mark_const (fst (dest_Const c));
+ fun app s (l, r) = Syntax.mk_appl (Constant s) [l, r];
+ val capp = app @{const_syntax Rep_CFun};
+ val capps = Library.foldl capp
+
+ fun app_var x = Syntax.mk_appl (Constant "_variable") [x, Variable "rhs"];
+ fun app_pat x = Syntax.mk_appl (Constant "_pat") [x];
+ fun args_list [] = Constant "_noargs"
+ | args_list xs = foldr1 (app "_args") xs;
+ fun one_case_trans (pat, (con, args)) =
+ let
+ val cname = Constant (syntax con);
+ val pname = Constant (syntax pat);
+ val ns = 1 upto length args;
+ val xs = map (fn n => Variable ("x"^(string_of_int n))) ns;
+ val ps = map (fn n => Variable ("p"^(string_of_int n))) ns;
+ val vs = map (fn n => Variable ("v"^(string_of_int n))) ns;
+ in
+ [ParseRule (app_pat (capps (cname, xs)),
+ mk_appl pname (map app_pat xs)),
+ ParseRule (app_var (capps (cname, xs)),
+ app_var (args_list xs)),
+ PrintRule (capps (cname, ListPair.map (app "_match") (ps,vs)),
+ app "_match" (mk_appl pname ps, args_list vs))]
+ end;
+ val trans_rules : Syntax.ast Syntax.trrule list =
+ maps one_case_trans (pat_consts ~~ spec);
+ in
+ val thy = Sign.add_trrules_i trans_rules thy;
+ end;
+
+ (* prove strictness and reduction rules of pattern combinators *)
+ local
+ val tns = map (fst o dest_TFree) (snd (dest_Type lhsT));
+ val rn = Name.variant tns "'r";
+ val R = TFree (rn, @{sort pcpo});
+ fun pat_lhs (pat, args) =
+ let
+ val Ts = map snd args;
+ val Vs =
+ (map (K "'t") args)
+ |> Datatype_Prop.indexify_names
+ |> Name.variant_list (rn::tns)
+ |> map (fn t => TFree (t, @{sort pcpo}));
+ val patNs = Datatype_Prop.indexify_names (map (K "pat") args);
+ val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs;
+ val pats = map Free (patNs ~~ patTs);
+ val k = Free ("rhs", mk_tupleT Vs ->> R);
+ val branch1 = branch_const (lhsT, mk_tupleT Vs, R);
+ val fun1 = (branch1 $ list_comb (pat, pats)) ` k;
+ val branch2 = branch_const (mk_tupleT Ts, mk_tupleT Vs, R);
+ val fun2 = (branch2 $ mk_tuple_pat pats) ` k;
+ val taken = "rhs" :: patNs;
+ in (fun1, fun2, taken) end;
+ fun pat_strict (pat, (con, args)) =
+ let
+ val (fun1, fun2, taken) = pat_lhs (pat, args);
+ val defs = @{thm branch_def} :: pat_defs;
+ val goal = mk_trp (mk_strict fun1);
+ val rules = @{thms match_case_simps} @ case_rews;
+ val tacs = [simp_tac (beta_ss addsimps rules) 1];
+ in prove thy defs goal (K tacs) end;
+ fun pat_apps (i, (pat, (con, args))) =
+ let
+ val (fun1, fun2, taken) = pat_lhs (pat, args);
+ fun pat_app (j, (con', args')) =
+ let
+ val (vs, nonlazy) = get_vars_avoiding taken args';
+ val con_app = list_ccomb (con', vs);
+ val assms = map (mk_trp o mk_defined) nonlazy;
+ val rhs = if i = j then fun2 ` mk_tuple vs else mk_fail R;
+ val concl = mk_trp (mk_eq (fun1 ` con_app, rhs));
+ val goal = Logic.list_implies (assms, concl);
+ val defs = @{thm branch_def} :: pat_defs;
+ val rules = @{thms match_case_simps} @ case_rews;
+ val tacs = [asm_simp_tac (beta_ss addsimps rules) 1];
+ in prove thy defs goal (K tacs) end;
+ in map_index pat_app spec end;
+ in
+ val pat_stricts = map pat_strict (pat_consts ~~ spec);
+ val pat_apps = flat (map_index pat_apps (pat_consts ~~ spec));
+ end;
+
+ in
+ (pat_stricts @ pat_apps, thy)
+ end
+
+end
+*}
+
+(*
+Cut from HOLCF/Tools/domain_constructors.ML
+in function add_domain_constructors:
+
+ ( * define and prove theorems for pattern combinators * )
+ val (pat_thms : thm list, thy : theory) =
+ let
+ val bindings = map #1 spec;
+ fun prep_arg (lazy, sel, T) = (lazy, T);
+ fun prep_con c (b, args, mx) = (c, map prep_arg args);
+ val pat_spec = map2 prep_con con_consts spec;
+ in
+ add_pattern_combinators bindings pat_spec lhsT
+ exhaust case_const cases thy
+ end
+
+*)
+
+end
--- a/src/HOLCF/ex/ROOT.ML Mon May 24 09:32:52 2010 -0700
+++ b/src/HOLCF/ex/ROOT.ML Mon May 24 11:29:49 2010 -0700
@@ -6,4 +6,5 @@
use_thys ["Dnat", "Stream", "Dagstuhl", "Focus_ex", "Fix2", "Hoare",
"Loop", "Powerdomain_ex", "Domain_Proofs",
"Letrec",
+ "Pattern_Match",
"Strict_Fun"];