--- a/Nominal/Lift.thy Tue Mar 02 20:11:56 2010 +0100
+++ b/Nominal/Lift.thy Tue Mar 02 20:14:21 2010 +0100
@@ -25,7 +25,7 @@
val ntnames = [@{binding trm2}, @{binding as}]
val ncnames = ["Vr2", "Ap2", "Lt2", "As"] *} *)
-datatype rkind =
+(*datatype rkind =
Type
| KPi "rty" "name" "rkind"
and rty =
@@ -48,9 +48,9 @@
val bv_simps = []
val ntnames = [@{binding kind}, @{binding ty}, @{binding trm}]
-val ncnames = ["TYP", "KPI", "TCONST", "TAPP", "TPI", "CONST", "VAR", "APP", "LAM"]
+val ncnames = ["TYP", "KPI", "TCONST", "TAPP", "TPI", "CONST", "VAR", "APP", "LAM"]*}*)
-(*datatype rtrm5 =
+datatype rtrm5 =
rVr5 "name"
| rAp5 "rtrm5" "rtrm5"
| rLt5 "rlts" "rtrm5" --"bind (bv5 lts) in (rtrm5)"
@@ -64,7 +64,7 @@
"rbv5 rLnil = {}"
| "rbv5 (rLcons n t ltl) = {atom n} \<union> (rbv5 ltl)"
-ML
+ML {*
val thy1 = @{theory};
val info = Datatype.the_info @{theory} "Lift.rtrm5"
val number = 2;
@@ -73,7 +73,7 @@
val bv_simps = @{thms rbv5.simps}
val ntnames = [@{binding trm5}, @{binding lts}]
-val ncnames = ["Vr5", "Ap5", "Lt5", "Lnil", "Lcons"]*)
+val ncnames = ["Vr5", "Ap5", "Lt5", "Lnil", "Lcons"]
val descr = #descr info;
--- a/Nominal/Nominal2_Eqvt.thy Tue Mar 02 20:11:56 2010 +0100
+++ b/Nominal/Nominal2_Eqvt.thy Tue Mar 02 20:14:21 2010 +0100
@@ -5,7 +5,7 @@
(Contains most, but not all such lemmas.)
*)
theory Nominal2_Eqvt
-imports Nominal2_Base
+imports Nominal2_Base Nominal2_Atoms
uses ("nominal_thmdecls.ML")
("nominal_permeq.ML")
begin
@@ -248,7 +248,9 @@
(* sets *)
empty_eqvt UNIV_eqvt union_eqvt inter_eqvt mem_eqvt
- Diff_eqvt Compl_eqvt insert_eqvt Collect_eqvt
+ Diff_eqvt Compl_eqvt insert_eqvt Collect_eqvt image_eqvt
+
+ atom_eqvt
thm eqvts
thm eqvts_raw
@@ -301,4 +303,4 @@
oops
-end
\ No newline at end of file
+end
--- a/Nominal/Parser.thy Tue Mar 02 20:11:56 2010 +0100
+++ b/Nominal/Parser.thy Tue Mar 02 20:14:21 2010 +0100
@@ -212,33 +212,51 @@
ML {*
fun nominal_datatype2 dts bn_funs bn_eqs binds lthy =
let
- val (((raw_dt_names, (raw_bn_funs, raw_bn_eqs)), raw_binds), lthy2) =
+ val (((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_binds), lthy2) =
raw_nominal_decls dts bn_funs bn_eqs binds lthy
+ val morphism_2_1 = ProofContext.export_morphism lthy2 lthy
+ val raw_bn_funs = map (Morphism.term morphism_2_1) raw_bn_funs_loc
+ val raw_bn_eqs = ProofContext.export lthy2 lthy raw_bn_eqs_loc
val dtinfo = Datatype.the_info (ProofContext.theory_of lthy2) (hd raw_dt_names);
val descr = #descr dtinfo;
+ val sorts = #sorts dtinfo;
+ val all_typs = map (fn i => typ_of_dtyp descr sorts (DtRec i)) (map fst descr)
val all_full_tnames = map (fn (_, (n, _, _)) => n) descr;
val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy2)) all_full_tnames;
val inject = flat (map #inject dtinfos);
val distinct = flat (map #distinct dtinfos);
+ val induct = #induct dtinfo;
val inducts = #inducts dtinfo;
val ((raw_perm_def, raw_perm_simps, perms), lthy3) =
Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy2;
val raw_binds_flat = map (map flat) raw_binds;
val (((fv_ts_loc, fv_def_loc), alpha), lthy4) = define_fv_alpha dtinfo raw_binds_flat lthy3;
+ val alpha_ts_loc = #preds alpha
+ val morphism_4_3 = ProofContext.export_morphism lthy4 lthy3;
+ val alpha_ts = map (Morphism.term morphism_4_3) alpha_ts_loc;
+ val alpha_induct_loc = #induct alpha
val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo);
- val _ = tracing (PolyML.makestring dts_names);
val bn_tys = map (domain_type o fastype_of) raw_bn_funs;
- val _ = tracing (PolyML.makestring bn_tys);
val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys;
- val _ = tracing (PolyML.makestring bn_nos);
val bns = raw_bn_funs ~~ bn_nos;
val alpha_intros = #intrs alpha;
val alpha_cases = #elims alpha
val alpha_inj_loc = build_alpha_inj alpha_intros (inject @ distinct) alpha_cases lthy4
val (bv_eqvts, lthy5) = fold_map (build_bv_eqvt perms (raw_bn_eqs @ raw_perm_def) inducts) bns lthy4;
-
+ val (fv_eqvts, lthy6) = build_eqvts Binding.empty fv_ts_loc perms
+ ((flat (map snd bv_eqvts)) @ fv_def_loc @ raw_perm_def) induct lthy5;
+ val alpha_eqvt_loc = build_alpha_eqvts alpha_ts_loc perms
+ (raw_perm_def @ alpha_inj_loc) alpha_induct_loc lthy6;
+ val alpha_eqvt = ProofContext.export lthy6 lthy2 alpha_eqvt_loc;
+ val alpha_equivp_loc = build_equivps alpha_ts_loc induct alpha_induct_loc
+ inject alpha_inj_loc distinct alpha_cases alpha_eqvt_loc lthy6;
+ val alpha_equivp = ProofContext.export lthy6 lthy2 alpha_equivp_loc;
+ val qty_names = map (fn (_, b, _, _) => b) dts;
+ val lthy7 = define_quotient_type
+ (map (fn ((b, t), alpha) => (([], b, NoSyn), (t, alpha))) ((qty_names ~~ all_typs) ~~ alpha_ts))
+ (ALLGOALS (resolve_tac alpha_equivp)) lthy6;
in
- ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy5)
+ ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy7)
end
*}
--- a/Nominal/Rsp.thy Tue Mar 02 20:11:56 2010 +0100
+++ b/Nominal/Rsp.thy Tue Mar 02 20:14:21 2010 +0100
@@ -132,7 +132,7 @@
val gl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map eqvtc (funs ~~ (args ~~ perms))))
fun tac _ = (Datatype_Aux.indtac induct indnames THEN_ALL_NEW
(asm_full_simp_tac (HOL_ss addsimps
- (@{thm atom_eqvt} :: (Nominal_ThmDecls.get_eqvts_thms ctxt) @ simps)))) 1
+ (@{thm atom_eqvt} :: (Nominal_ThmDecls.get_eqvts_thms ctxt) @ (Nominal_ThmDecls.get_eqvts_raw_thms ctxt) @ simps)))) 1
val thm = Goal.prove ctxt ("p" :: indnames) [] gl tac
val thms = HOLogic.conj_elims thm
in
@@ -161,14 +161,14 @@
fun tac _ = (((rtac impI THEN' etac induct) ORELSE' rtac induct) THEN_ALL_NEW
(
(asm_full_simp_tac (HOL_ss addsimps
- (@{thm atom_eqvt} :: (Nominal_ThmDecls.get_eqvts_thms ctxt) @ simps)))
+ ((Nominal_ThmDecls.get_eqvts_thms ctxt) @ (Nominal_ThmDecls.get_eqvts_raw_thms ctxt) @ simps)))
THEN_ALL_NEW (REPEAT o etac conjE THEN' etac @{thm exi[of _ _ "p"]} THEN'
REPEAT o etac conjE THEN'
(TRY o REPEAT_ALL_NEW (CHANGED o rtac conjI))) THEN_ALL_NEW
(asm_full_simp_tac HOL_ss) THEN_ALL_NEW
(etac @{thm alpha_gen_compose_eqvt[of _ _ _ _ "p"]}) THEN_ALL_NEW
(asm_full_simp_tac (HOL_ss addsimps
- (@{thm atom_eqvt} :: (Nominal_ThmDecls.get_eqvts_thms ctxt) @ simps))))) 1
+ ((Nominal_ThmDecls.get_eqvts_thms ctxt) @ (Nominal_ThmDecls.get_eqvts_raw_thms ctxt) @ simps))))) 1
val thm = Goal.prove ctxt ("p" :: indnames @ indnames2) [] gl tac
in
map (fn x => mp OF [x]) (HOLogic.conj_elims thm)
--- a/Nominal/Term4.thy Tue Mar 02 20:11:56 2010 +0100
+++ b/Nominal/Term4.thy Tue Mar 02 20:14:21 2010 +0100
@@ -1,5 +1,5 @@
theory Term4
-imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove"
+imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove" "Quotient_List"
begin
atom_decl name
@@ -33,14 +33,32 @@
[[[], [], [(NONE, 0,1)]], [[], []] ] *}
print_theorems
+lemma fix2: "alpha_rtrm4_list = list_rel alpha_rtrm4"
+apply (rule ext)+
+apply (induct_tac x xa rule: list_induct2')
+apply (simp_all add: alpha_rtrm4_alpha_rtrm4_list.intros)
+apply clarify apply (erule alpha_rtrm4_list.cases) apply(simp_all)
+apply clarify apply (erule alpha_rtrm4_list.cases) apply(simp_all)
+apply rule
+apply (erule alpha_rtrm4_list.cases)
+apply simp_all
+apply (rule alpha_rtrm4_alpha_rtrm4_list.intros)
+apply simp_all
+done
+
+(* We need sth like:
+lemma fix3: "fv_rtrm4_list = set o map fv_rtrm4" *)
+
notation
alpha_rtrm4 ("_ \<approx>4 _" [100, 100] 100) and
alpha_rtrm4_list ("_ \<approx>4l _" [100, 100] 100)
-thm alpha_rtrm4_alpha_rtrm4_list.intros
+thm alpha_rtrm4_alpha_rtrm4_list.intros[simplified fix2]
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_inj}, []), (build_alpha_inj @{thms alpha_rtrm4_alpha_rtrm4_list.intros} @{thms rtrm4.distinct rtrm4.inject list.distinct list.inject} @{thms alpha_rtrm4.cases alpha_rtrm4_list.cases} ctxt)) ctxt)) *}
+local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_inj}, []), (build_alpha_inj @{thms alpha_rtrm4_alpha_rtrm4_list.intros[simplified fix2]} @{thms rtrm4.distinct rtrm4.inject list.distinct list.inject} @{thms alpha_rtrm4.cases[simplified fix2] alpha_rtrm4_list.cases[simplified fix2]} ctxt)) ctxt)) *}
thm alpha4_inj
-thm alpha_rtrm4_alpha_rtrm4_list.induct
+
+local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_inj_no}, []), (build_alpha_inj @{thms alpha_rtrm4_alpha_rtrm4_list.intros} @{thms rtrm4.distinct rtrm4.inject list.distinct list.inject} @{thms alpha_rtrm4.cases alpha_rtrm4_list.cases} ctxt)) ctxt)) *}
+thm alpha4_inj_no
local_setup {*
snd o build_eqvts @{binding fv_rtrm4_fv_rtrm4_list_eqvt} [@{term fv_rtrm4}, @{term fv_rtrm4_list}] [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"},@{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}] (@{thms fv_rtrm4_fv_rtrm4_list.simps permute_rtrm4_permute_rtrm4_list.simps[simplified repaired]}) @{thm rtrm4.induct}
@@ -48,18 +66,56 @@
print_theorems
local_setup {*
-(fn ctxt => snd (Local_Theory.note ((@{binding alpha4_eqvt}, []),
- build_alpha_eqvts [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"},@{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}] @{thms permute_rtrm4_permute_rtrm4_list.simps[simplified repaired] alpha4_inj} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} ctxt) ctxt))
+(fn ctxt => snd (Local_Theory.note ((@{binding alpha4_eqvt_no}, []),
+ build_alpha_eqvts [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"},@{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}] @{thms permute_rtrm4_permute_rtrm4_list.simps[simplified repaired] alpha4_inj_no} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} ctxt) ctxt))
+*}
+lemmas alpha4_eqvt = alpha4_eqvt_no[simplified fix2]
+
+local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_equivp_no}, []),
+ (build_equivps [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] @{thm rtrm4.induct} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} @{thms rtrm4.inject list.inject} @{thms alpha4_inj_no} @{thms rtrm4.distinct list.distinct} @{thms alpha_rtrm4_list.cases alpha_rtrm4.cases} @{thms alpha4_eqvt_no} ctxt)) ctxt)) *}
+lemmas alpha4_equivp = alpha4_equivp_no[simplified fix2]
+
+(*lemma fv_rtrm4_rsp:
+ "xa \<approx>4 ya \<Longrightarrow> fv_rtrm4 xa = fv_rtrm4 ya"
+ "x \<approx>4l y \<Longrightarrow> fv_rtrm4_list x = fv_rtrm4_list y"
+ apply (induct rule: alpha_rtrm4_alpha_rtrm4_list.inducts)
+ apply (simp_all add: alpha_gen)
+done*)
+
+
+quotient_type
+ trm4 = rtrm4 / alpha_rtrm4
+(*and
+ trm4list = "rtrm4 list" / alpha_rtrm4_list*)
+ by (simp_all add: alpha4_equivp)
+
+local_setup {*
+(fn ctxt => ctxt
+ |> snd o (Quotient_Def.quotient_lift_const ("Vr4", @{term rVr4}))
+ |> snd o (Quotient_Def.quotient_lift_const ("Ap4", @{term rAp4}))
+ |> snd o (Quotient_Def.quotient_lift_const ("Lm4", @{term rLm4})))
*}
print_theorems
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_equivp}, []),
- (build_equivps [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] @{thm rtrm4.induct} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} @{thms rtrm4.inject list.inject} @{thms alpha4_inj} @{thms rtrm4.distinct list.distinct} @{thms alpha_rtrm4_list.cases alpha_rtrm4.cases} @{thms alpha4_eqvt} ctxt)) ctxt)) *}
-thm alpha4_equivp
+local_setup {* snd o prove_const_rsp @{binding fv_rtrm4_rsp} [@{term fv_rtrm4}]
+ (fn _ => fvbv_rsp_tac @{thm alpha_rtrm4_alpha_rtrm4_list.inducts(1)} @{thms fv_rtrm4_fv_rtrm4_list.simps} 1) *}
+print_theorems
-quotient_type
- qrtrm4 = rtrm4 / alpha_rtrm4 and
- qrtrm4list = "rtrm4 list" / alpha_rtrm4_list
- by (simp_all add: alpha4_equivp)
+local_setup {* snd o prove_const_rsp @{binding rVr4_rsp} [@{term rVr4}]
+ (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp} @{thms alpha4_equivp} 1) *}
+lemma "(alpha_rtrm4 ===> list_rel alpha_rtrm4 ===> alpha_rtrm4) rAp4 rAp4"
+apply simp
+apply clarify
+apply (simp add: alpha4_inj)
+
+
+local_setup {* snd o prove_const_rsp @{binding rLm4_rsp} [@{term rLm4}]
+ (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp} @{thms alpha4_equivp} 1) *}
+local_setup {* snd o prove_const_rsp @{binding permute_rtrm4_rsp}
+ [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"}, @{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}]
+ (fn _ => asm_simp_tac (HOL_ss addsimps @{thms alpha4_eqvt}) 1) *}
+
+thm rtrm4.induct
+lemmas trm1_bp_induct = rtrm4.induct[quot_lifted]
end
--- a/Nominal/Test.thy Tue Mar 02 20:11:56 2010 +0100
+++ b/Nominal/Test.thy Tue Mar 02 20:14:21 2010 +0100
@@ -71,6 +71,8 @@
text {* example 1 *}
+(* ML {* set show_hyps *} *)
+
nominal_datatype lam =
VAR "name"
| APP "lam" "lam"
@@ -147,11 +149,13 @@
All xs::"name list" ty::"t_raw" bind xs in ty
*)
+
+(* alpha_eqvt fails...
nominal_datatype t =
Var "name"
| Fun "t" "t"
and tyS =
- All xs::"name set" ty::"t" bind xs in ty
+ All xs::"name set" ty::"t" bind xs in ty *)
(* example 1 from Terms.thy *)
@@ -205,6 +209,7 @@
(* example 4 from Terms.thy *)
+(* fv_eqvt does not work, we need to repaire defined permute functions...
nominal_datatype trm4 =
Vr4 "name"
| Ap4 "trm4" "trm4 list"