--- a/src/HOLCF/Tools/Domain/domain_constructors.ML Wed Feb 24 17:37:59 2010 -0800
+++ b/src/HOLCF/Tools/Domain/domain_constructors.ML Thu Feb 25 13:16:28 2010 -0800
@@ -14,7 +14,8 @@
-> thm * thm
-> theory
-> { con_consts : term list,
- con_defs : thm list }
+ con_defs : thm list,
+ sel_rews : thm list }
* theory;
end;
@@ -33,6 +34,7 @@
fun mk_cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
infixr 6 ->>; val (op ->>) = mk_cfunT;
+infix -->>; val (op -->>) = Library.foldr mk_cfunT;
fun dest_cfunT (Type(@{type_name "->"}, [T, U])) = (T, U)
| dest_cfunT T = raise TYPE ("dest_cfunT", [T], []);
@@ -64,6 +66,25 @@
infix 9 ` ; val (op `) = mk_capply;
+val list_ccomb : term * term list -> term = Library.foldl mk_capply;
+
+fun mk_ID T = Const (@{const_name ID}, T ->> T);
+
+fun cfcomp_const (T, U, V) =
+ Const (@{const_name cfcomp}, (U ->> V) ->> (T ->> U) ->> (T ->> V));
+
+fun mk_cfcomp (f, g) =
+ let
+ val (U, V) = dest_cfunT (Term.fastype_of f);
+ val (T, U') = dest_cfunT (Term.fastype_of g);
+ in
+ if U = U'
+ then mk_capply (mk_capply (cfcomp_const (T, U, V), f), g)
+ else raise TYPE ("mk_cfcomp", [U, U'], [f, g])
+ end;
+
+fun mk_bottom T = Const (@{const_name UU}, T);
+
(*** Product type ***)
@@ -87,10 +108,18 @@
fun mk_upT T = Type(@{type_name "u"}, [T]);
+fun dest_upT (Type(@{type_name "u"}, [T])) = T
+ | dest_upT T = raise TYPE ("dest_upT", [T], []);
+
fun up_const T = Const(@{const_name up}, T ->> mk_upT T);
fun mk_up t = up_const (Term.fastype_of t) ` t;
+fun fup_const (T, U) =
+ Const(@{const_name fup}, (T ->> U) ->> mk_upT T ->> U);
+
+fun from_up T = fup_const (T, T) ` mk_ID T;
+
(*** Strict product type ***)
@@ -98,6 +127,9 @@
fun mk_sprodT (T, U) = Type(@{type_name "**"}, [T, U]);
+fun dest_sprodT (Type(@{type_name "**"}, [T, U])) = (T, U)
+ | dest_sprodT T = raise TYPE ("dest_sprodT", [T], []);
+
fun spair_const (T, U) =
Const(@{const_name spair}, T ->> U ->> mk_sprodT (T, U));
@@ -110,6 +142,12 @@
| mk_stuple (t::[]) = t
| mk_stuple (t::ts) = mk_spair (t, mk_stuple ts);
+fun sfst_const (T, U) =
+ Const(@{const_name sfst}, mk_sprodT (T, U) ->> T);
+
+fun ssnd_const (T, U) =
+ Const(@{const_name ssnd}, mk_sprodT (T, U) ->> U);
+
(*** Strict sum type ***)
@@ -139,6 +177,16 @@
fst (inj (ts ~~ Ts))
end;
+fun sscase_const (T, U, V) =
+ Const(@{const_name sscase},
+ (T ->> V) ->> (U ->> V) ->> mk_ssumT (T, U) ->> V);
+
+fun from_sinl (T, U) =
+ sscase_const (T, U, T) ` mk_ID T ` mk_bottom (U ->> T);
+
+fun from_sinr (T, U) =
+ sscase_const (T, U, U) ` mk_bottom (T ->> U) ` mk_ID U;
+
(*** miscellaneous constructions ***)
@@ -151,7 +199,7 @@
fun argTs (Type (_, Ts)) = Ts | argTs _ = [];
fun auto T = T ->> T;
in
- Library.foldr mk_cfunT (map auto (argTs T), auto T)
+ map auto (argTs T) -->> auto T
end;
val mk_equals = Logic.mk_equals;
@@ -159,6 +207,13 @@
val mk_trp = HOLogic.mk_Trueprop;
val mk_fst = HOLogic.mk_fst;
val mk_snd = HOLogic.mk_snd;
+val mk_not = HOLogic.mk_not;
+
+fun mk_strict t =
+ let val (T, U) = dest_cfunT (Term.fastype_of t);
+ in mk_eq (t ` mk_bottom T, mk_bottom U) end;
+
+fun mk_defined t = mk_not (mk_eq (t, mk_bottom (Term.fastype_of t)));
fun mk_cont t =
let val T = Term.fastype_of t
@@ -168,21 +223,6 @@
let val (T, _) = dest_cfunT (Term.fastype_of t)
in mk_capply (Const(@{const_name fix}, (T ->> T) ->> T), t) end;
-fun ID_const T = Const (@{const_name ID}, T ->> T);
-
-fun cfcomp_const (T, U, V) =
- Const (@{const_name cfcomp}, (U ->> V) ->> (T ->> U) ->> (T ->> V));
-
-fun mk_cfcomp (f, g) =
- let
- val (U, V) = dest_cfunT (Term.fastype_of f);
- val (T, U') = dest_cfunT (Term.fastype_of g);
- in
- if U = U'
- then mk_capply (mk_capply (cfcomp_const (T, U, V), f), g)
- else raise TYPE ("mk_cfcomp", [U, U'], [f, g])
- end;
-
fun mk_Rep_of T =
Const (@{const_name Rep_of}, Term.itselfT T --> deflT) $ Logic.mk_type T;
@@ -196,8 +236,10 @@
fun mk_eqs (t, u) = HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u));
-(*** miscellaneous ***)
+(************************** miscellaneous functions ***************************)
+
+(*
fun declare_consts
(decls : (binding * typ * mixfix) list)
(thy : theory)
@@ -208,6 +250,7 @@
in
(map con decls, thy)
end;
+*)
fun define_consts
(specs : (binding * term * mixfix) list)
@@ -228,6 +271,16 @@
((consts, def_thms), thy)
end;
+fun define_const
+ (spec : binding * term * mixfix)
+ (thy : theory)
+ : (term * thm) * theory =
+ let
+ val ((consts, def_thms), thy) = define_consts [spec] thy;
+ in
+ ((hd consts, hd def_thms), thy)
+ end;
+
(************** generating beta reduction rules from definitions **************)
@@ -243,7 +296,7 @@
let
val (con, lam) = Logic.dest_equals (concl_of def_thm);
val (args, rhs) = arglist lam;
- val lhs = Library.foldl mk_capply (con, args);
+ val lhs = list_ccomb (con, args);
val goal = mk_equals (lhs, rhs);
val cs = ContProc.cont_thms lam;
val betas = map (fn c => mk_meta_eq (c RS @{thm beta_cfun})) cs;
@@ -255,45 +308,211 @@
end;
end;
-(******************************* main function ********************************)
+(******************************************************************************)
+(************** definitions and theorems for selector functions ***************)
+(******************************************************************************)
+
+fun add_selectors
+ (spec : (term * (bool * binding option * typ) list) list)
+ (rep_const : term)
+ (abs_inv : thm)
+ (rep_strict : thm)
+ (rep_strict_iff : thm)
+ (con_betas : thm list)
+ (thy : theory)
+ : thm list * theory =
+ let
+
+ (* define selector functions *)
+ val ((sel_consts, sel_defs), thy) =
+ let
+ fun rangeT s = snd (dest_cfunT (Term.fastype_of s));
+ fun mk_outl s = mk_cfcomp (from_sinl (dest_ssumT (rangeT s)), s);
+ fun mk_outr s = mk_cfcomp (from_sinr (dest_ssumT (rangeT s)), s);
+ fun mk_sfst s = mk_cfcomp (sfst_const (dest_sprodT (rangeT s)), s);
+ fun mk_ssnd s = mk_cfcomp (ssnd_const (dest_sprodT (rangeT s)), s);
+ fun mk_down s = mk_cfcomp (from_up (dest_upT (rangeT s)), s);
+
+ fun sels_of_arg s (lazy, NONE, T) = []
+ | sels_of_arg s (lazy, SOME b, T) =
+ [(b, if lazy then mk_down s else s, NoSyn)];
+ fun sels_of_args s [] = []
+ | sels_of_args s (v :: []) = sels_of_arg s v
+ | sels_of_args s (v :: vs) =
+ sels_of_arg (mk_sfst s) v @ sels_of_args (mk_ssnd s) vs;
+ fun sels_of_cons s [] = []
+ | sels_of_cons s ((con, args) :: []) = sels_of_args s args
+ | sels_of_cons s ((con, args) :: cs) =
+ sels_of_args (mk_outl s) args @ sels_of_cons (mk_outr s) cs;
+ val sel_eqns : (binding * term * mixfix) list =
+ sels_of_cons rep_const spec;
+ in
+ define_consts sel_eqns thy
+ end
+
+ (* replace bindings with terms in constructor spec *)
+ val spec2 : (term * (bool * term option * typ) list) list =
+ let
+ fun prep_arg (lazy, NONE, T) sels = ((lazy, NONE, T), sels)
+ | prep_arg (lazy, SOME _, T) sels =
+ ((lazy, SOME (hd sels), T), tl sels);
+ fun prep_con (con, args) sels =
+ apfst (pair con) (fold_map prep_arg args sels);
+ in
+ fst (fold_map prep_con spec sel_consts)
+ end;
+
+ (* prove selector strictness rules *)
+ val sel_stricts : thm list =
+ let
+ val rules = rep_strict :: sel_defs @ @{thms sel_strict_rules};
+ val tac = simp_tac (HOL_basic_ss addsimps rules) 1;
+ fun sel_strict sel =
+ let
+ val goal = mk_trp (mk_strict sel);
+ in
+ Goal.prove_global thy [] [] goal (K tac)
+ end
+ in
+ map sel_strict sel_consts
+ end
+
+ (* prove selector application rules *)
+ val sel_apps : thm list =
+ let
+ val rules = @{thms sel_app_rules};
+ val simps = simp_thms @ [abs_inv] @ con_betas @ sel_defs @ rules;
+ val tac = asm_simp_tac (HOL_basic_ss addsimps simps) 1;
+ fun sel_apps_of (i, (con, args)) =
+ let
+ val Ts : typ list = map #3 args;
+ val ns : string list = Datatype_Prop.make_tnames Ts;
+ val vs : term list = map Free (ns ~~ Ts);
+ val con_app : term = list_ccomb (con, vs);
+ val vs' : (bool * term) list = map #1 args ~~ vs;
+ fun one_same (n, sel, T) =
+ let
+ val xs = map snd (filter_out fst (nth_drop n vs'));
+ val assms = map (mk_trp o mk_defined) xs;
+ val concl = mk_trp (mk_eq (sel ` con_app, nth vs n));
+ val goal = Logic.list_implies (assms, concl);
+ in
+ Goal.prove_global thy [] [] goal (K tac)
+ end;
+ fun one_diff (n, sel, T) =
+ let
+ val goal = mk_trp (mk_eq (sel ` con_app, mk_bottom T));
+ in
+ Goal.prove_global thy [] [] goal (K tac)
+ end;
+ fun one_con (j, (_, args')) : thm list =
+ let
+ fun prep (i, (lazy, NONE, T)) = NONE
+ | prep (i, (lazy, SOME sel, T)) = SOME (i, sel, T);
+ val sels : (int * term * typ) list =
+ map_filter prep (map_index I args');
+ in
+ if i = j
+ then map one_same sels
+ else map one_diff sels
+ end
+ in
+ flat (map_index one_con spec2)
+ end
+ in
+ flat (map_index sel_apps_of spec2)
+ end
+
+ (* prove selector definedness rules *)
+ val sel_defins : thm list =
+ let
+ val rules = @{thms sel_defined_iff_rules};
+ val simps = rep_strict_iff :: sel_defs @ rules;
+ val tac = simp_tac (HOL_basic_ss addsimps simps) 1;
+ fun sel_defin sel =
+ let
+ val (T, U) = dest_cfunT (Term.fastype_of sel);
+ val x = Free ("x", T);
+ val lhs = mk_eq (sel ` x, mk_bottom U);
+ val rhs = mk_eq (x, mk_bottom T);
+ val goal = mk_trp (mk_eq (lhs, rhs));
+ in
+ Goal.prove_global thy [] [] goal (K tac)
+ end
+ fun one_arg (false, SOME sel, T) = SOME (sel_defin sel)
+ | one_arg _ = NONE;
+ in
+ case spec2 of
+ [(con, args)] => map_filter one_arg args
+ | _ => []
+ end;
+
+ in
+ (sel_stricts @ sel_defins @ sel_apps, thy)
+ end
+
+(******************************************************************************)
+(************* definitions and theorems for constructor functions *************)
+(******************************************************************************)
fun add_domain_constructors
(dname : string)
(lhsT : typ,
- cons : (binding * (bool * binding option * typ) list * mixfix) list)
+ spec : (binding * (bool * binding option * typ) list * mixfix) list)
(rep_const : term, abs_const : term)
(rep_iso_thm : thm, abs_iso_thm : thm)
(thy : theory) =
let
- (* TODO: re-enable this *)
- (* val thy = Sign.add_path dname thy; *)
+
+ (* prove rep/abs strictness rules *)
+ val iso_locale = @{thm iso.intro} OF [abs_iso_thm, rep_iso_thm];
+ val rep_strict = iso_locale RS @{thm iso.rep_strict};
+ val abs_strict = iso_locale RS @{thm iso.abs_strict};
+ val rep_defined_iff = iso_locale RS @{thm iso.rep_defined_iff};
+ val abs_defined_iff = iso_locale RS @{thm iso.abs_defined_iff};
(* define constructor functions *)
val ((con_consts, con_def_thms), thy) =
let
- fun prep_con (bind, args, mx) =
- (bind, args ~~ Datatype_Prop.make_tnames (map #3 args), mx);
- fun var_of ((lazy, sel, T), name) = Free (name, T);
- fun is_lazy ((lazy, sel, T), name) = lazy;
- val cons' = map prep_con cons;
- fun one_arg arg = (if is_lazy arg then mk_up else I) (var_of arg);
- fun one_con (bind, args, mx) = mk_stuple (map one_arg args);
+ fun vars_of args =
+ let
+ val Ts = map (fn (lazy,sel,T) => T) args;
+ val ns = Datatype_Prop.make_tnames Ts;
+ in
+ map Free (ns ~~ Ts)
+ end;
+ fun one_arg (lazy,_,_) var = if lazy then mk_up var else var;
+ fun one_con (_,args,_) = mk_stuple (map2 one_arg args (vars_of args));
fun mk_abs t = abs_const ` t;
- val rhss = map mk_abs (mk_sinjects (map one_con cons'));
+ val rhss = map mk_abs (mk_sinjects (map one_con spec));
fun mk_def (bind, args, mx) rhs =
- (bind, big_lambdas (map var_of args) rhs, mx);
+ (bind, big_lambdas (vars_of args) rhs, mx);
in
- define_consts (map2 mk_def cons' rhss) thy
+ define_consts (map2 mk_def spec rhss) thy
end;
+ (* prove beta reduction rules for constructors *)
val con_beta_thms = map (beta_of_def thy) con_def_thms;
- (* TODO: re-enable this *)
- (* val thy = Sign.parent_path thy; *)
+ (* TODO: enable this earlier *)
+ val thy = Sign.add_path dname thy;
+
+ (* replace bindings with terms in constructor spec *)
+ val spec2 : (term * (bool * binding option * typ) list) list =
+ map2 (fn con => fn (b, args, mx) => (con, args)) con_consts spec;
+
+ (* define and prove theorems for selector functions *)
+ val (sel_thms : thm list, thy : theory) =
+ add_selectors spec2 rep_const
+ abs_iso_thm rep_strict rep_defined_iff con_beta_thms thy;
+
+ (* restore original signature path *)
+ val thy = Sign.parent_path thy;
val result =
{ con_consts = con_consts,
- con_defs = con_def_thms };
+ con_defs = con_def_thms,
+ sel_rews = sel_thms };
in
(result, thy)
end;