(* Title: HOL/HOLCF/ex/Pattern_Match.thy
Author: Brian Huffman
*)
header {* An experimental pattern-matching notation *}
theory Pattern_Match
imports HOLCF
begin
default_sort pcpo
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 {* Bind operator for match monad *}
definition match_bind :: "'a match \<rightarrow> ('a \<rightarrow> 'b match) \<rightarrow> 'b match" where
"match_bind = (\<Lambda> m k. sscase\<cdot>(\<Lambda> _. fail)\<cdot>(fup\<cdot>k)\<cdot>(Rep_match m))"
lemma match_bind_simps [simp]:
"match_bind\<cdot>\<bottom>\<cdot>k = \<bottom>"
"match_bind\<cdot>fail\<cdot>k = fail"
"match_bind\<cdot>(succeed\<cdot>x)\<cdot>k = k\<cdot>x"
unfolding match_bind_def fail_def succeed_def
by (simp_all add: cont_Rep_match cont_Abs_match
Rep_match_strict Abs_match_inverse)
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_bind\<cdot>(p\<cdot>x)\<cdot>(\<Lambda> y. succeed\<cdot>(r\<cdot>y))"
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 = Fixrec.run"
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 *}
nonterminal Case_pat and Case_syn and Cases_syn
syntax
"_Case_syntax":: "['a, Cases_syn] => 'b" ("(Case _ of/ _)" 10)
"_Case1" :: "[Case_pat, 'b] => Case_syn" ("(2_ =>/ _)" 10)
"" :: "Case_syn => Cases_syn" ("_")
"_Case2" :: "[Case_syn, Cases_syn] => Cases_syn" ("_/ | _")
"_strip_positions" :: "'a => Case_pat" ("_")
syntax (xsymbols)
"_Case1" :: "[Case_pat, '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 _ => fn _ => Syntax.const @{const_syntax Fixrec.succeed}),
Syntax_Trans.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') = Syntax_Trans.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}, K Case1_tr')] end;
*}
translations
"x" <= "_match (CONST succeed) (_variable x)"
subsection {* Pattern combinators for data constructors *}
type_synonym ('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_bind\<cdot>(p1\<cdot>x)\<cdot>(\<Lambda> a. match_bind\<cdot>(p2\<cdot>y)\<cdot>(\<Lambda> b. succeed\<cdot>(a, b))))"
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)"
definition
FF_pat :: "(tr, unit) pat" where
"FF_pat = (\<Lambda> b. If b then fail else succeed\<cdot>())"
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_bind\<cdot>(p\<cdot>x)\<cdot>(\<Lambda> a. succeed\<cdot>(x, a)))"
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
infixr 6 ->>;
infix 9 ` ;
val beta_rules =
@{thms beta_cfun cont_id cont_const cont2cont_APP cont2cont_LAM'} @
@{thms cont2cont_fst cont2cont_snd cont2cont_Pair};
val beta_ss =
simpset_of (put_simpset HOL_basic_ss @{context} addsimps (@{thms 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) =
(Thm.def_binding b, Logic.mk_equals (c, t));
val defs = map2 mk_def consts specs;
val (def_thms, thy) =
Global_Theory.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
fun syntax c = Lexicon.mark_const (fst (dest_Const c));
fun app s (l, r) = Ast.mk_appl (Ast.Constant s) [l, r];
val capp = app @{const_syntax Rep_cfun};
val capps = Library.foldl capp
fun app_var x = Ast.mk_appl (Ast.Constant "_variable") [x, Ast.Variable "rhs"];
fun app_pat x = Ast.mk_appl (Ast.Constant "_pat") [x];
fun args_list [] = Ast.Constant "_noargs"
| args_list xs = foldr1 (app "_args") xs;
fun one_case_trans (pat, (con, args)) =
let
val cname = Ast.Constant (syntax con);
val pname = Ast.Constant (syntax pat);
val ns = 1 upto length args;
val xs = map (fn n => Ast.Variable ("x"^(string_of_int n))) ns;
val ps = map (fn n => Ast.Variable ("p"^(string_of_int n))) ns;
val vs = map (fn n => Ast.Variable ("v"^(string_of_int n))) ns;
in
[Syntax.Parse_Rule (app_pat (capps (cname, xs)),
Ast.mk_appl pname (map app_pat xs)),
Syntax.Parse_Rule (app_var (capps (cname, xs)),
app_var (args_list xs)),
Syntax.Print_Rule (capps (cname, ListPair.map (app "_match") (ps,vs)),
app "_match" (Ast.mk_appl pname ps, args_list vs))]
end;
val trans_rules : Ast.ast Syntax.trrule list =
maps one_case_trans (pat_consts ~~ spec);
in
val thy = Sign.add_trrules 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 = singleton (Name.variant_list 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_bind_simps} @ case_rews;
val tacs = [simp_tac (Simplifier.global_context thy 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_bind_simps} @ case_rews;
val tacs = [asm_simp_tac (Simplifier.global_context thy 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