--- a/src/HOL/Nominal/nominal_package.ML Mon Nov 10 17:37:25 2008 +0100
+++ b/src/HOL/Nominal/nominal_package.ML Mon Nov 10 17:38:23 2008 +0100
@@ -134,10 +134,8 @@
val (bT as Type (b, []), _) = dest_permT U
in if aT mem permTs_of u andalso aT <> bT then
let
- val a' = Sign.base_name a;
- val b' = Sign.base_name b;
- val cp = PureThy.get_thm thy ("cp_" ^ a' ^ "_" ^ b' ^ "_inst");
- val dj = PureThy.get_thm thy ("dj_" ^ b' ^ "_" ^ a');
+ val cp = cp_inst_of thy a b;
+ val dj = dj_thm_of thy b a;
val dj_cp' = [cp, dj] MRS dj_cp;
val cert = SOME o cterm_of thy
in
@@ -203,12 +201,6 @@
(tname, length tvs, mx)) dts);
val atoms = atoms_of thy;
- val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms;
- val cp_classes = List.concat (map (fn atom1 => map (fn atom2 =>
- Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^
- Sign.base_name atom2)) atoms) atoms);
- fun augment_sort S = S union classes;
- val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S));
fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
let val (cargs', sorts') = Library.foldl (prep_typ tmp_thy) (([], sorts), cargs)
@@ -219,9 +211,16 @@
in (dts @ [(tvs, tname, mx, constrs')], sorts') end
val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
- val sorts' = map (apsnd augment_sort) sorts;
val tyvars = map #1 dts';
+ fun inter_sort thy S S' = Type.inter_sort (Sign.tsig_of thy) (S, S');
+ fun augment_sort_typ thy S =
+ let val S = Sign.certify_sort thy S
+ in map_type_tfree (fn (s, S') => TFree (s,
+ if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S'))
+ end;
+ fun augment_sort thy S = map_types (augment_sort_typ thy S);
+
val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
@@ -238,7 +237,7 @@
val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn,
map (fn (cname, cargs, mx) => (cname ^ "_Rep",
- map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts';
+ map replace_types cargs, NoSyn)) constrs)) dts';
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
val full_new_type_names' = map (Sign.full_name thy) new_type_names';
@@ -248,7 +247,7 @@
val SOME {descr, ...} = Symtab.lookup
(DatatypePackage.get_datatypes thy1) (hd full_new_type_names');
- fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i);
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
val big_name = space_implode "_" new_type_names;
@@ -271,7 +270,7 @@
let val T = nth_dtyp i
in map (fn (cname, dts) =>
let
- val Ts = map (typ_of_dtyp descr sorts') dts;
+ val Ts = map (typ_of_dtyp descr sorts) dts;
val names = Name.variant_list ["pi"] (DatatypeProp.make_tnames Ts);
val args = map Free (names ~~ Ts);
val c = Const (cname, Ts ---> T);
@@ -336,13 +335,14 @@
let val permT = mk_permT (Type (a, []))
in map standard (List.take (split_conj_thm
(Goal.prove_global thy2 [] []
- (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
- (map (fn ((s, T), x) => HOLogic.mk_eq
- (Const (s, permT --> T --> T) $
- Const ("List.list.Nil", permT) $ Free (x, T),
- Free (x, T)))
- (perm_names ~~
- map body_type perm_types ~~ perm_indnames))))
+ (augment_sort thy2 [pt_class_of thy2 a]
+ (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+ (map (fn ((s, T), x) => HOLogic.mk_eq
+ (Const (s, permT --> T --> T) $
+ Const ("List.list.Nil", permT) $ Free (x, T),
+ Free (x, T)))
+ (perm_names ~~
+ map body_type perm_types ~~ perm_indnames)))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
length new_type_names))
@@ -362,11 +362,12 @@
val permT = mk_permT (Type (a, []));
val pi1 = Free ("pi1", permT);
val pi2 = Free ("pi2", permT);
- val pt_inst = PureThy.get_thm thy2 ("pt_" ^ Sign.base_name a ^ "_inst");
+ val pt_inst = pt_inst_of thy2 a;
val pt2' = pt_inst RS pt2;
val pt2_ax = PureThy.get_thm thy2 (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a);
in List.take (map standard (split_conj_thm
(Goal.prove_global thy2 [] []
+ (augment_sort thy2 [pt_class_of thy2 a]
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn ((s, T), x) =>
let val perm = Const (s, permT --> T --> T)
@@ -376,7 +377,7 @@
perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
end)
(perm_names ~~
- map body_type perm_types ~~ perm_indnames))))
+ map body_type perm_types ~~ perm_indnames)))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
length new_type_names)
@@ -394,14 +395,14 @@
val permT = mk_permT (Type (a, []));
val pi1 = Free ("pi1", permT);
val pi2 = Free ("pi2", permT);
- (*FIXME: not robust - better access these theorems using NominalData?*)
- val at_inst = PureThy.get_thm thy2 ("at_" ^ Sign.base_name a ^ "_inst");
- val pt_inst = PureThy.get_thm thy2 ("pt_" ^ Sign.base_name a ^ "_inst");
+ val at_inst = at_inst_of thy2 a;
+ val pt_inst = pt_inst_of thy2 a;
val pt3' = pt_inst RS pt3;
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
val pt3_ax = PureThy.get_thm thy2 (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a);
in List.take (map standard (split_conj_thm
- (Goal.prove_global thy2 [] [] (Logic.mk_implies
+ (Goal.prove_global thy2 [] []
+ (augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies
(HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
@@ -412,7 +413,7 @@
perm $ pi2 $ Free (x, T))
end)
(perm_names ~~
- map body_type perm_types ~~ perm_indnames)))))
+ map body_type perm_types ~~ perm_indnames))))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
length new_type_names)
@@ -428,29 +429,29 @@
fun composition_instance name1 name2 thy =
let
- val name1' = Sign.base_name name1;
- val name2' = Sign.base_name name2;
- val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
+ val cp_class = cp_class_of thy name1 name2;
+ val pt_class =
+ if name1 = name2 then [pt_class_of thy name1]
+ else [];
val permT1 = mk_permT (Type (name1, []));
val permT2 = mk_permT (Type (name2, []));
- val augment = map_type_tfree
- (fn (x, S) => TFree (x, cp_class :: S));
- val Ts = map (augment o body_type) perm_types;
- val cp_inst = PureThy.get_thm thy ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst");
+ val Ts = map body_type perm_types;
+ val cp_inst = cp_inst_of thy name1 name2;
val simps = simpset_of thy addsimps (perm_fun_def ::
(if name1 <> name2 then
- let val dj = PureThy.get_thm thy ("dj_" ^ name2' ^ "_" ^ name1')
+ let val dj = dj_thm_of thy name2 name1
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
else
let
- val at_inst = PureThy.get_thm thy ("at_" ^ name1' ^ "_inst");
- val pt_inst = PureThy.get_thm thy ("pt_" ^ name1' ^ "_inst");
+ val at_inst = at_inst_of thy name1;
+ val pt_inst = pt_inst_of thy name1;
in
[cp_inst RS cp1 RS sym,
at_inst RS (pt_inst RS pt_perm_compose) RS sym,
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
end))
val thms = split_conj_thm (Goal.prove_global thy [] []
+ (augment_sort thy (cp_class :: pt_class)
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn ((s, T), x) =>
let
@@ -463,25 +464,30 @@
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
end)
- (perm_names ~~ Ts ~~ perm_indnames))))
+ (perm_names ~~ Ts ~~ perm_indnames)))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac simps)]))
in
foldl (fn ((s, tvs), thy) => AxClass.prove_arity
- (s, replicate (length tvs) (cp_class :: classes), [cp_class])
+ (s, replicate (length tvs) (cp_class :: pt_class), [cp_class])
(Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
thy (full_new_type_names' ~~ tyvars)
end;
val (perm_thmss,thy3) = thy2 |>
fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
- curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
- AxClass.prove_arity (tyname, replicate (length args) classes, classes)
- (Class.intro_classes_tac [] THEN REPEAT (EVERY
- [resolve_tac perm_empty_thms 1,
- resolve_tac perm_append_thms 1,
- resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
- (List.take (descr, length new_type_names)) |>
+ fold (fn atom => fn thy =>
+ let val pt_name = pt_class_of thy atom
+ in
+ fold (fn (i, (tyname, args, _)) => AxClass.prove_arity
+ (tyname, replicate (length args) [pt_name], [pt_name])
+ (EVERY
+ [Class.intro_classes_tac [],
+ resolve_tac perm_empty_thms 1,
+ resolve_tac perm_append_thms 1,
+ resolve_tac perm_eq_thms 1, assume_tac 1]))
+ (List.take (descr, length new_type_names)) thy
+ end) atoms |>
PureThy.add_thmss
[((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
unfolded_perm_eq_thms), [Simplifier.simp_add]),
@@ -513,9 +519,10 @@
apfst (cons dt) (strip_option dt')
| strip_option dt = ([], dt);
- val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts')
+ val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts)
(List.concat (map (fn (_, (_, _, cs)) => List.concat
(map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
+ val dt_atoms = map (fst o dest_Type) dt_atomTs;
fun make_intr s T (cname, cargs) =
let
@@ -523,9 +530,9 @@
let
val (dts, dt') = strip_option dt;
val (dts', dt'') = strip_dtyp dt';
- val Ts = map (typ_of_dtyp descr sorts') dts;
- val Us = map (typ_of_dtyp descr sorts') dts';
- val T = typ_of_dtyp descr sorts' dt'';
+ val Ts = map (typ_of_dtyp descr sorts) dts;
+ val Us = map (typ_of_dtyp descr sorts) dts';
+ val T = typ_of_dtyp descr sorts dt'';
val free = mk_Free "x" (Us ---> T) j;
val free' = app_bnds free (length Us);
fun mk_abs_fun (T, (i, t)) =
@@ -580,23 +587,22 @@
fun mk_perm_closed name = map (fn th => standard (th RS mp))
(List.take (split_conj_thm (Goal.prove_global thy4 [] []
- (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
- (fn ((s, T), x) =>
- let
- val T = map_type_tfree
- (fn (s, cs) => TFree (s, cs union cp_classes)) T;
- val S = Const (s, T --> HOLogic.boolT);
- val permT = mk_permT (Type (name, []))
- in HOLogic.mk_imp (S $ Free (x, T),
- S $ (Const ("Nominal.perm", permT --> T --> T) $
- Free ("pi", permT) $ Free (x, T)))
- end) (rep_set_names'' ~~ recTs' ~~ perm_indnames'))))
- (fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
+ (augment_sort thy4
+ (pt_class_of thy4 name :: map (cp_class_of thy4 name) (dt_atoms \ name))
+ (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
+ (fn ((s, T), x) =>
+ let
+ val S = Const (s, T --> HOLogic.boolT);
+ val permT = mk_permT (Type (name, []))
+ in HOLogic.mk_imp (S $ Free (x, T),
+ S $ (Const ("Nominal.perm", permT --> T --> T) $
+ Free ("pi", permT) $ Free (x, T)))
+ end) (rep_set_names'' ~~ recTs' ~~ perm_indnames')))))
+ (fn _ => EVERY
[indtac rep_induct [] 1,
ALLGOALS (simp_tac (simpset_of thy4 addsimps
(symmetric perm_fun_def :: abs_perm))),
- ALLGOALS (resolve_tac rep_intrs
- THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
+ ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])),
length new_type_names));
val perm_closed_thmss = map mk_perm_closed atoms;
@@ -617,7 +623,7 @@
let
val permT = mk_permT (TFree (Name.variant tvs "'a", HOLogic.typeS));
val pi = Free ("pi", permT);
- val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
+ val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts s))) tvs;
val T = Type (Sign.intern_type thy name, tvs');
in apfst (pair r o hd)
(PureThy.add_defs_unchecked true [(("prm_" ^ name ^ "_def", Logic.mk_equals
@@ -641,19 +647,23 @@
val _ = warning "prove that new types are in class pt_<name> ...";
- fun pt_instance ((class, atom), perm_closed_thms) =
+ fun pt_instance (atom, perm_closed_thms) =
fold (fn ((((((Abs_inverse, Rep_inverse), Rep),
perm_def), name), tvs), perm_closed) => fn thy =>
- AxClass.prove_arity
+ let
+ val pt_class = pt_class_of thy atom;
+ val cp_sort = map (cp_class_of thy atom) (dt_atoms \ atom)
+ in AxClass.prove_arity
(Sign.intern_type thy name,
- replicate (length tvs) (classes @ cp_classes), [class])
+ replicate (length tvs) (pt_class :: cp_sort), [pt_class])
(EVERY [Class.intro_classes_tac [],
rewrite_goals_tac [perm_def],
asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
asm_full_simp_tac (simpset_of thy addsimps
[Rep RS perm_closed RS Abs_inverse]) 1,
asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
- ("pt_" ^ Sign.base_name atom ^ "3")]) 1]) thy)
+ ("pt_" ^ Sign.base_name atom ^ "3")]) 1]) thy
+ end)
(Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~
new_type_names ~~ tyvars ~~ perm_closed_thms);
@@ -664,14 +674,17 @@
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
let
- val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
- val class = Sign.intern_class thy name;
- val cp1' = PureThy.get_thm thy (name ^ "_inst") RS cp1
+ val cp_class = cp_class_of thy atom1 atom2;
+ val sort =
+ pt_class_of thy atom1 :: map (cp_class_of thy atom1) (dt_atoms \ atom1) @
+ (if atom1 = atom2 then [cp_class_of thy atom1 atom1] else
+ pt_class_of thy atom2 :: map (cp_class_of thy atom2) (dt_atoms \ atom2));
+ val cp1' = cp_inst_of thy atom1 atom2 RS cp1
in fold (fn ((((((Abs_inverse, Rep),
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
AxClass.prove_arity
(Sign.intern_type thy name,
- replicate (length tvs) (classes @ cp_classes), [class])
+ replicate (length tvs) sort, [cp_class])
(EVERY [Class.intro_classes_tac [],
rewrite_goals_tac [perm_def],
asm_full_simp_tac (simpset_of thy addsimps
@@ -687,8 +700,8 @@
val thy7 = fold (fn x => fn thy => thy |>
pt_instance x |>
- fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
- (classes ~~ atoms ~~ perm_closed_thmss) thy6;
+ fold (cp_instance x) (atoms ~~ perm_closed_thmss))
+ (atoms ~~ perm_closed_thmss) thy6;
(**** constructors ****)
@@ -741,14 +754,14 @@
map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs))
(constrs ~~ idxss)))) (descr'' ~~ ndescr);
- fun nth_dtyp' i = typ_of_dtyp descr'' sorts' (DtRec i);
+ fun nth_dtyp' i = typ_of_dtyp descr'' sorts (DtRec i);
val rep_names = map (fn s =>
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
val abs_names = map (fn s =>
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
- val recTs = get_rec_types descr'' sorts';
+ val recTs = get_rec_types descr'' sorts;
val newTs' = Library.take (length new_type_names, recTs');
val newTs = Library.take (length new_type_names, recTs);
@@ -759,17 +772,17 @@
let
fun constr_arg ((dts, dt), (j, l_args, r_args)) =
let
- val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts' dt) i)
+ val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts dt) i)
(dts ~~ (j upto j + length dts - 1))
- val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
+ val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
in
(j + length dts + 1,
xs @ x :: l_args,
foldr mk_abs_fun
(case dt of
DtRec k => if k < length new_type_names then
- Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts' dt -->
- typ_of_dtyp descr sorts' dt) $ x
+ Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts dt -->
+ typ_of_dtyp descr sorts dt) $ x
else error "nested recursion not (yet) supported"
| _ => x) xs :: r_args)
end
@@ -834,9 +847,12 @@
val permT = mk_permT (Type (atom, []));
val pi = Free ("pi", permT);
in
- Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
- Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x))))
+ Goal.prove_global thy8 [] []
+ (augment_sort thy8
+ (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom))
+ (HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
+ Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x)))))
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
perm_closed_thms @ Rep_thms)) 1)
end) Rep_thms;
@@ -846,7 +862,7 @@
(* prove distinctness theorems *)
- val distinct_props = DatatypeProp.make_distincts descr' sorts';
+ val distinct_props = DatatypeProp.make_distincts descr' sorts;
val dist_rewrites = map2 (fn rep_thms => fn dist_lemma =>
dist_lemma :: rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])
constr_rep_thmss dist_lemmas;
@@ -881,10 +897,10 @@
fun constr_arg ((dts, dt), (j, l_args, r_args)) =
let
- val Ts = map (typ_of_dtyp descr'' sorts') dts;
+ val Ts = map (typ_of_dtyp descr'' sorts) dts;
val xs = map (fn (T, i) => mk_Free "x" T i)
(Ts ~~ (j upto j + length dts - 1))
- val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
+ val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
in
(j + length dts + 1,
xs @ x :: l_args,
@@ -895,8 +911,10 @@
val c = Const (cname, map fastype_of l_args ---> T)
in
Goal.prove_global thy8 [] []
- (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (perm (list_comb (c, l_args)), list_comb (c, r_args))))
+ (augment_sort thy8
+ (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom))
+ (HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (perm (list_comb (c, l_args)), list_comb (c, r_args)))))
(fn _ => EVERY
[simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
@@ -915,6 +933,10 @@
val alpha = PureThy.get_thms thy8 "alpha";
val abs_fresh = PureThy.get_thms thy8 "abs_fresh";
+ val pt_cp_sort =
+ map (pt_class_of thy8) dt_atoms @
+ maps (fn s => map (cp_class_of thy8 s) (dt_atoms \ s)) dt_atoms;
+
val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
let val T = nth_dtyp' i
in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
@@ -925,11 +947,11 @@
fun make_inj ((dts, dt), (j, args1, args2, eqs)) =
let
- val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1);
+ val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts - 1);
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
- val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts);
- val y = mk_Free "y" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
+ val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts);
+ val y = mk_Free "y" (typ_of_dtyp descr'' sorts dt) (j + length dts)
in
(j + length dts + 1,
xs @ (x :: args1), ys @ (y :: args2),
@@ -941,17 +963,17 @@
val Ts = map fastype_of args1;
val c = Const (cname, Ts ---> T)
in
- Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
- foldr1 HOLogic.mk_conj eqs)))
+ Goal.prove_global thy8 [] []
+ (augment_sort thy8 pt_cp_sort
+ (HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
+ foldr1 HOLogic.mk_conj eqs))))
(fn _ => EVERY
[asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
rep_inject_thms')) 1,
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
- perm_rep_perm_thms)) 1),
- TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
- @{thm expand_fun_eq} :: rep_inject_thms @ perm_rep_perm_thms)) 1)])
+ perm_rep_perm_thms)) 1)])
end) (constrs ~~ constr_rep_thms)
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
@@ -968,9 +990,9 @@
fun process_constr ((dts, dt), (j, args1, args2)) =
let
- val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1);
+ val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts - 1);
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
- val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
+ val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
in
(j + length dts + 1,
xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
@@ -983,10 +1005,11 @@
Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t;
val supp_thm = Goal.prove_global thy8 [] []
+ (augment_sort thy8 pt_cp_sort
(HOLogic.mk_Trueprop (HOLogic.mk_eq
(supp c,
if null dts then Const ("{}", HOLogic.mk_setT atomT)
- else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
+ else foldr1 (HOLogic.mk_binop "op Un") (map supp args2)))))
(fn _ =>
simp_tac (HOL_basic_ss addsimps (supp_def ::
Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
@@ -994,10 +1017,11 @@
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)
in
(supp_thm,
- Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (fresh c,
- if null dts then HOLogic.true_const
- else foldr1 HOLogic.mk_conj (map fresh args2))))
+ Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort
+ (HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (fresh c,
+ if null dts then HOLogic.true_const
+ else foldr1 HOLogic.mk_conj (map fresh args2)))))
(fn _ =>
simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1))
end) atoms) constrs)
@@ -1038,7 +1062,7 @@
val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms;
- val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
+ val dt_induct_prop = DatatypeProp.make_ind descr' sorts;
val dt_induct = Goal.prove_global thy8 []
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
(fn {prems, ...} => EVERY
@@ -1064,11 +1088,13 @@
val finite_supp_thms = map (fn atom =>
let val atomT = Type (atom, [])
in map standard (List.take
- (split_conj_thm (Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop
- (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
- Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $
- (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T)))
- (indnames ~~ recTs))))
+ (split_conj_thm (Goal.prove_global thy8 [] []
+ (augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort)
+ (HOLogic.mk_Trueprop
+ (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
+ Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $
+ (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T)))
+ (indnames ~~ recTs)))))
(fn _ => indtac dt_induct indnames 1 THEN
ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
(abs_supp @ supp_atm @
@@ -1096,10 +1122,10 @@
DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
fold (fn (atom, ths) => fn thy =>
- let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
+ let val class = fs_class_of thy atom
in fold (fn T => AxClass.prove_arity
(fst (dest_Type T),
- replicate (length sorts) [class], [class])
+ replicate (length sorts) (class :: pt_cp_sort), [class])
(Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
end) (atoms ~~ finite_supp_thms);
@@ -1108,8 +1134,7 @@
val pnames = if length descr'' = 1 then ["P"]
else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
val ind_sort = if null dt_atomTs then HOLogic.typeS
- else Sign.certify_sort thy9 (map (fn T => Sign.intern_class thy9 ("fs_" ^
- Sign.base_name (fst (dest_Type T)))) dt_atomTs);
+ else Sign.certify_sort thy9 (map (fs_class_of thy9) dt_atoms);
val fsT = TFree ("'n", ind_sort);
val fsT' = TFree ("'n", HOLogic.typeS);
@@ -1134,8 +1159,8 @@
fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
let
val recs = List.filter is_rec_type cargs;
- val Ts = map (typ_of_dtyp descr'' sorts') cargs;
- val recTs' = map (typ_of_dtyp descr'' sorts') recs;
+ val Ts = map (typ_of_dtyp descr'' sorts) cargs;
+ val recTs' = map (typ_of_dtyp descr'' sorts) recs;
val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts);
val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
val frees = tnames ~~ Ts;
@@ -1199,12 +1224,10 @@
(Free (tname, T))))
(descr'' ~~ recTs ~~ tnames)));
- val fin_set_supp = map (fn Type (s, _) =>
- PureThy.get_thm thy9 ("at_" ^ Sign.base_name s ^ "_inst") RS
- at_fin_set_supp) dt_atomTs;
- val fin_set_fresh = map (fn Type (s, _) =>
- PureThy.get_thm thy9 ("at_" ^ Sign.base_name s ^ "_inst") RS
- at_fin_set_fresh) dt_atomTs;
+ val fin_set_supp = map (fn s =>
+ at_inst_of thy9 s RS at_fin_set_supp) dt_atoms;
+ val fin_set_fresh = map (fn s =>
+ at_inst_of thy9 s RS at_fin_set_fresh) dt_atoms;
val pt1_atoms = map (fn Type (s, _) =>
PureThy.get_thm thy9 ("pt_" ^ Sign.base_name s ^ "1")) dt_atomTs;
val pt2_atoms = map (fn Type (s, _) =>
@@ -1248,6 +1271,10 @@
[SOME (cterm_of thy a), NONE, SOME (cterm_of thy b)] th
end;
+ val fs_cp_sort =
+ map (fs_class_of thy9) dt_atoms @
+ maps (fn s => map (cp_class_of thy9 s) (dt_atoms \ s)) dt_atoms;
+
(**********************************************************************
The subgoals occurring in the proof of induct_aux have the
following parameters:
@@ -1263,7 +1290,9 @@
val _ = warning "proving strong induction theorem ...";
- val induct_aux = Goal.prove_global thy9 [] ind_prems' ind_concl' (fn {prems, context} =>
+ val induct_aux = Goal.prove_global thy9 []
+ (map (augment_sort thy9 fs_cp_sort) ind_prems')
+ (augment_sort thy9 fs_cp_sort ind_concl') (fn {prems, context} =>
let
val (prems1, prems2) = chop (length dt_atomTs) prems;
val ind_ss2 = HOL_ss addsimps
@@ -1276,7 +1305,8 @@
fin_set_fresh @ calc_atm;
val ind_ss5 = HOL_basic_ss addsimps pt1_atoms;
val ind_ss6 = HOL_basic_ss addsimps flat perm_simps';
- val th = Goal.prove context [] [] aux_ind_concl
+ val th = Goal.prove context [] []
+ (augment_sort thy9 fs_cp_sort aux_ind_concl)
(fn {context = context1, ...} =>
EVERY (indtac dt_induct tnames 1 ::
maps (fn ((_, (_, _, constrs)), (_, constrs')) =>
@@ -1351,17 +1381,19 @@
end);
val induct_aux' = Thm.instantiate ([],
- map (fn (s, T) =>
- let val pT = TVar (("'n", 0), HOLogic.typeS) --> T --> HOLogic.boolT
- in (cterm_of thy9 (Var ((s, 0), pT)), cterm_of thy9 (Free (s, pT))) end)
- (pnames ~~ recTs) @
+ map (fn (s, v as Var (_, T)) =>
+ (cterm_of thy9 v, cterm_of thy9 (Free (s, T))))
+ (pnames ~~ map head_of (HOLogic.dest_conj
+ (HOLogic.dest_Trueprop (concl_of induct_aux)))) @
map (fn (_, f) =>
let val f' = Logic.varify f
in (cterm_of thy9 f',
cterm_of thy9 (Const ("Nominal.supp", fastype_of f')))
end) fresh_fs) induct_aux;
- val induct = Goal.prove_global thy9 [] ind_prems ind_concl
+ val induct = Goal.prove_global thy9 []
+ (map (augment_sort thy9 fs_cp_sort) ind_prems)
+ (augment_sort thy9 fs_cp_sort ind_concl)
(fn {prems, ...} => EVERY
[rtac induct_aux' 1,
REPEAT (resolve_tac fs_atoms 1),
@@ -1380,16 +1412,10 @@
val used = foldr add_typ_tfree_names [] recTs;
- val (rec_result_Ts', rec_fn_Ts') = DatatypeProp.make_primrec_Ts descr' sorts' used;
+ val (rec_result_Ts', rec_fn_Ts') = DatatypeProp.make_primrec_Ts descr' sorts used;
val rec_sort = if null dt_atomTs then HOLogic.typeS else
- let val names = map (Sign.base_name o fst o dest_Type) dt_atomTs
- in Sign.certify_sort thy10 (map (Sign.intern_class thy10)
- (map (fn s => "pt_" ^ s) names @
- List.concat (map (fn s => List.mapPartial (fn s' =>
- if s = s' then NONE
- else SOME ("cp_" ^ s ^ "_" ^ s')) names) names)))
- end;
+ Sign.certify_sort thy10 pt_cp_sort;
val rec_result_Ts = map (fn TFree (s, _) => TFree (s, rec_sort)) rec_result_Ts';
val rec_fn_Ts = map (typ_subst_atomic (rec_result_Ts' ~~ rec_result_Ts)) rec_fn_Ts';
@@ -1429,7 +1455,7 @@
fun make_rec_intr T p rec_set ((rec_intr_ts, rec_prems, rec_prems',
rec_eq_prems, l), ((cname, cargs), idxs)) =
let
- val Ts = map (typ_of_dtyp descr'' sorts') cargs;
+ val Ts = map (typ_of_dtyp descr'' sorts) cargs;
val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts;
val frees' = partition_cargs idxs frees;
val binders = List.concat (map fst frees');
@@ -1508,7 +1534,8 @@
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs));
val ths = map (fn th => standard (th RS mp)) (split_conj_thm
(Goal.prove_global thy11 [] []
- (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps)))
+ (augment_sort thy1 pt_cp_sort
+ (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps))))
(fn _ => rtac rec_induct 1 THEN REPEAT
(simp_tac (Simplifier.theory_context thy11 HOL_basic_ss
addsimps flat perm_simps'
@@ -1517,7 +1544,8 @@
asm_simp_tac (HOL_ss addsimps (fresh_bij @ perm_bij))) 1))))
val ths' = map (fn ((P, Q), th) =>
Goal.prove_global thy11 [] []
- (Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P))
+ (augment_sort thy1 pt_cp_sort
+ (Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P)))
(fn _ => dtac (Thm.instantiate ([],
[(cterm_of thy11 (Var (("pi", 0), permT)),
cterm_of thy11 (Const ("List.rev", permT --> permT) $ pi))]) th) 1 THEN
@@ -1537,16 +1565,19 @@
(rec_fns ~~ rec_fn_Ts)
in
map (fn th => standard (th RS mp)) (split_conj_thm
- (Goal.prove_global thy11 [] fins
- (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
- (map (fn (((T, U), R), i) =>
- let
- val x = Free ("x" ^ string_of_int i, T);
- val y = Free ("y" ^ string_of_int i, U)
- in
- HOLogic.mk_imp (R $ x $ y,
- finite $ (Const ("Nominal.supp", U --> aset) $ y))
- end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ (1 upto length recTs)))))
+ (Goal.prove_global thy11 []
+ (map (augment_sort thy11 fs_cp_sort) fins)
+ (augment_sort thy11 fs_cp_sort
+ (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+ (map (fn (((T, U), R), i) =>
+ let
+ val x = Free ("x" ^ string_of_int i, T);
+ val y = Free ("y" ^ string_of_int i, U)
+ in
+ HOLogic.mk_imp (R $ x $ y,
+ finite $ (Const ("Nominal.supp", U --> aset) $ y))
+ end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~
+ (1 upto length recTs))))))
(fn {prems = fins, ...} =>
(rtac rec_induct THEN_ALL_NEW cut_facts_tac fins) 1 THEN REPEAT
(NominalPermeq.finite_guess_tac (HOL_ss addsimps [fs_name]) 1))))
@@ -1560,6 +1591,8 @@
(Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ f)))
(rec_fns ~~ rec_fn_Ts)) dt_atomTs;
+ val rec_fns' = map (augment_sort thy11 fs_cp_sort) rec_fns;
+
val rec_fresh_thms = map (fn ((aT, eqvt_ths), finite_prems) =>
let
val name = Sign.base_name (fst (dest_Type aT));
@@ -1570,16 +1603,18 @@
in
map (fn (((T, U), R), eqvt_th) =>
let
- val x = Free ("x", T);
+ val x = Free ("x", augment_sort_typ thy11 fs_cp_sort T);
val y = Free ("y", U);
val y' = Free ("y'", U)
in
- standard (Goal.prove (ProofContext.init thy11) [] (finite_prems @
- [HOLogic.mk_Trueprop (R $ x $ y),
- HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U,
- HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))),
- HOLogic.mk_Trueprop (fresh_const aT T $ a $ x)] @
- freshs)
+ standard (Goal.prove (ProofContext.init thy11) []
+ (map (augment_sort thy11 fs_cp_sort)
+ (finite_prems @
+ [HOLogic.mk_Trueprop (R $ x $ y),
+ HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U,
+ HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))),
+ HOLogic.mk_Trueprop (fresh_const aT T $ a $ x)] @
+ freshs))
(HOLogic.mk_Trueprop (fresh_const aT U $ a $ y))
(fn {prems, context} =>
let
@@ -1588,7 +1623,7 @@
val unique_prem' = unique_prem RS spec RS mp;
val unique = [unique_prem', unique_prem' RS sym] MRS trans;
val _ $ (_ $ (_ $ S $ _)) $ _ = prop_of supports_fresh;
- val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns)
+ val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns')
in EVERY
[rtac (Drule.cterm_instantiate
[(cterm_of thy11 S,
@@ -1631,7 +1666,7 @@
(rec_unique_frees ~~ rec_result_Ts ~~ rec_sets);
val induct_aux_rec = Drule.cterm_instantiate
- (map (pairself (cterm_of thy11))
+ (map (pairself (cterm_of thy11) o apsnd (augment_sort thy11 fs_cp_sort))
(map (fn (aT, f) => (Logic.varify f, Abs ("z", HOLogic.unitT,
Const ("Nominal.supp", fun_tupleT --> HOLogic.mk_setT aT) $ fun_tuple)))
fresh_fs @
@@ -1668,8 +1703,10 @@
val rec_unique_thms = split_conj_thm (Goal.prove
(ProofContext.init thy11) (map fst rec_unique_frees)
- (List.concat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems')
- (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls))
+ (map (augment_sort thy11 fs_cp_sort)
+ (List.concat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems'))
+ (augment_sort thy11 fs_cp_sort
+ (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls)))
(fn {prems, context} =>
let
val k = length rec_fns;
@@ -1680,10 +1717,12 @@
val P_ths = map (fn th => th RS mp) (split_conj_thm
(Goal.prove context
(map fst (rec_unique_frees'' @ rec_unique_frees')) []
- (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
- (map (fn (((x, y), S), P) => HOLogic.mk_imp
- (S $ Free x $ Free y, P $ (Free y)))
- (rec_unique_frees'' ~~ rec_unique_frees' ~~ rec_sets ~~ rec_preds))))
+ (augment_sort thy11 fs_cp_sort
+ (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+ (map (fn (((x, y), S), P) => HOLogic.mk_imp
+ (S $ Free x $ Free y, P $ (Free y)))
+ (rec_unique_frees'' ~~ rec_unique_frees' ~~
+ rec_sets ~~ rec_preds)))))
(fn _ =>
rtac rec_induct 1 THEN
REPEAT ((resolve_tac P_ind_ths THEN_ALL_NEW assume_tac) 1))));
@@ -1722,7 +1761,10 @@
chop (length params div 2) (map term_of params);
val params' = params1 @ params2;
val rec_prems = filter (fn th => case prop_of th of
- _ $ (S $ _ $ _) => S mem rec_sets | _ => false) prems';
+ _ $ p => (case head_of p of
+ Const (s, _) => s mem rec_set_names
+ | _ => false)
+ | _ => false) prems';
val fresh_prems = filter (fn th => case prop_of th of
_ $ (Const ("Nominal.fresh", _) $ _ $ _) => true
| _ $ (Const ("Not", _) $ _) => true
@@ -1731,7 +1773,7 @@
val _ = warning "step 1: obtaining fresh names";
val (freshs1, freshs2, context'') = fold
- (obtain_fresh_name (rec_ctxt :: rec_fns @ params')
+ (obtain_fresh_name (rec_ctxt :: rec_fns' @ params')
(List.concat (map snd finite_thss) @
finite_ctxt_ths @ rec_prems)
rec_fin_supp_thms')
@@ -1802,7 +1844,8 @@
val rec_prems' = map (fn th =>
let
val _ $ (S $ x $ y) = prop_of th;
- val k = find_index (equal S) rec_sets;
+ val Const (s, _) = head_of S;
+ val k = find_index (equal s) rec_set_names;
val pi = rpi1 @ pi2;
fun mk_pi z = fold_rev (mk_perm []) pi z;
fun eqvt_tac p =
@@ -1988,7 +2031,9 @@
fun solve rules prems = resolve_tac rules THEN_ALL_NEW
(resolve_tac prems THEN_ALL_NEW atac)
in
- Goal.prove_global thy12 [] prems' concl'
+ Goal.prove_global thy12 []
+ (map (augment_sort thy12 fs_cp_sort) prems')
+ (augment_sort thy12 fs_cp_sort concl')
(fn {prems, ...} => EVERY
[rewrite_goals_tac reccomb_defs,
rtac the1_equality 1,
@@ -1996,7 +2041,7 @@
resolve_tac rec_intrs 1,
REPEAT (solve (prems @ rec_total_thms) prems 1)])
end) (rec_eq_prems ~~
- DatatypeProp.make_primrecs new_type_names descr' sorts' thy12);
+ DatatypeProp.make_primrecs new_type_names descr' sorts thy12);
val dt_infos = map (make_dt_info pdescr sorts induct reccomb_names rec_thms)
((0 upto length descr1 - 1) ~~ descr1 ~~ distinct_thms ~~ inject_thms);