--- a/Nominal/Fv.thy Thu Mar 04 15:31:21 2010 +0100
+++ b/Nominal/Fv.thy Thu Mar 04 15:31:34 2010 +0100
@@ -1,5 +1,5 @@
theory Fv
-imports "Nominal2_Atoms" "Abs" "Perm" (* For testing *)
+imports "Nominal2_Atoms" "Abs" "Perm" "Rsp"
begin
(* Bindings are given as a list which has a length being equal
@@ -184,8 +184,8 @@
val pi_supps = map ((curry op $) @{term "supp :: perm \<Rightarrow> atom set"}) rpis;
val pi_supps_eq = HOLogic.mk_eq (mk_inter pi_supps, @{term "{} :: atom set"})
in
- if length pi_supps > 1 then
- HOLogic.mk_conj (alpha_gen, pi_supps_eq) else alpha_gen
+ (*if length pi_supps > 1 then
+ HOLogic.mk_conj (alpha_gen, pi_supps_eq) else*) alpha_gen
(* TODO Add some test that is makes sense *)
end else @{term "True"}
end
@@ -312,29 +312,34 @@
*}
ML {*
-fun reflp_tac induct inj =
+fun reflp_tac induct inj ctxt =
rtac induct THEN_ALL_NEW
- asm_full_simp_tac (HOL_ss addsimps inj) THEN_ALL_NEW
-(* TRY o REPEAT_ALL_NEW (CHANGED o rtac conjI) THEN_ALL_NEW*)
- (rtac @{thm exI[of _ "0 :: perm"]} THEN'
- asm_full_simp_tac (HOL_ss addsimps
- @{thms alpha_gen fresh_star_def fresh_zero_perm permute_zero ball_triv}))
+ simp_tac ((mk_minimal_ss ctxt) addsimps inj) THEN_ALL_NEW
+ split_conjs THEN_ALL_NEW REPEAT o rtac @{thm exI[of _ "0 :: perm"]}
+ THEN_ALL_NEW split_conjs THEN_ALL_NEW asm_full_simp_tac (HOL_ss addsimps
+ @{thms alpha_gen fresh_star_def fresh_zero_perm permute_zero ball_triv
+ add_0_left supp_zero_perm Int_empty_left})
*}
+
lemma exi_neg: "\<exists>(pi :: perm). P pi \<Longrightarrow> (\<And>(p :: perm). P p \<Longrightarrow> Q (- p)) \<Longrightarrow> \<exists>pi. Q pi"
apply (erule exE)
apply (rule_tac x="-pi" in exI)
by auto
ML {*
-fun symp_tac induct inj eqvt =
- (((rtac impI THEN' etac induct) ORELSE' rtac induct) THEN_ALL_NEW
- asm_full_simp_tac (HOL_ss addsimps inj) THEN_ALL_NEW
- (REPEAT o etac conjE THEN' etac @{thm exi_neg} 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_sym} THEN'
- (asm_full_simp_tac (HOL_ss addsimps (@{thm atom_eqvt} :: eqvt)))))
+fun symp_tac induct inj eqvt ctxt =
+ ind_tac induct THEN_ALL_NEW
+ simp_tac ((mk_minimal_ss ctxt) addsimps inj) THEN_ALL_NEW split_conjs
+ THEN_ALL_NEW
+ REPEAT o etac @{thm exi_neg}
+ THEN_ALL_NEW
+ split_conjs THEN_ALL_NEW
+ asm_full_simp_tac (HOL_ss addsimps @{thms supp_minus_perm minus_add[symmetric]}) THEN_ALL_NEW
+ (rtac @{thm alpha_gen_compose_sym} THEN' RANGE [
+ (asm_full_simp_tac (HOL_ss addsimps @{thms plus_perm_eq})),
+ (asm_full_simp_tac (HOL_ss addsimps (eqvt @ all_eqvts ctxt)))
+ ])
*}
ML {*
@@ -367,17 +372,38 @@
by auto
ML {*
+fun is_ex (Const ("Ex", _) $ Abs _) = true
+ | is_ex _ = false;
+*}
+
+ML {*
+fun eetac rule = Subgoal.FOCUS_PARAMS
+ (fn (focus) =>
+ let
+ val concl = #concl focus
+ val prems = Logic.strip_imp_prems (term_of concl)
+ val exs = filter (fn x => is_ex (HOLogic.dest_Trueprop x)) prems
+ val cexs = map (SOME o (cterm_of (ProofContext.theory_of (#context focus)))) exs
+ val thins = map (fn cex => Drule.instantiate' [] [cex] Drule.thin_rl) cexs
+ in
+ (etac rule THEN' RANGE[
+ atac,
+ eresolve_tac thins
+ ]) 1
+ end
+ )
+*}
+
+ML {*
fun transp_tac ctxt induct alpha_inj term_inj distinct cases eqvt =
- ((rtac impI THEN' etac induct) ORELSE' rtac induct) THEN_ALL_NEW
+ ind_tac induct THEN_ALL_NEW
(TRY o rtac allI THEN' imp_elim_tac cases ctxt) THEN_ALL_NEW
- (
- asm_full_simp_tac (HOL_ss addsimps alpha_inj @ term_inj @ distinct)
- THEN_ALL_NEW (REPEAT o etac conjE THEN' etac @{thm exi_sum} THEN' RANGE [atac]) THEN_ALL_NEW
- (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_trans} THEN' RANGE[atac]) THEN_ALL_NEW
- (asm_full_simp_tac (HOL_ss addsimps (@{thm atom_eqvt} :: eqvt)))
- )
+ asm_full_simp_tac ((mk_minimal_ss ctxt) addsimps alpha_inj) THEN_ALL_NEW
+ split_conjs THEN_ALL_NEW REPEAT o (eetac @{thm exi_sum} ctxt) THEN_ALL_NEW split_conjs
+ THEN_ALL_NEW (asm_full_simp_tac (HOL_ss addsimps (term_inj @ distinct)))
+ THEN_ALL_NEW split_conjs THEN_ALL_NEW
+ TRY o (etac @{thm alpha_gen_compose_trans} THEN' RANGE[atac]) THEN_ALL_NEW
+ (asm_full_simp_tac (HOL_ss addsimps (all_eqvts ctxt @ eqvt @ term_inj @ distinct)))
*}
lemma transp_aux:
@@ -400,8 +426,8 @@
let
val ([x, y, z], ctxt') = Variable.variant_fixes ["x","y","z"] ctxt;
val (reflg, (symg, transg)) = build_alpha_refl_gl alphas (x, y, z)
- fun reflp_tac' _ = reflp_tac term_induct alpha_inj 1;
- fun symp_tac' _ = symp_tac alpha_induct alpha_inj eqvt 1;
+ fun reflp_tac' _ = reflp_tac term_induct alpha_inj ctxt 1;
+ fun symp_tac' _ = symp_tac alpha_induct alpha_inj eqvt ctxt 1;
fun transp_tac' _ = transp_tac ctxt alpha_induct alpha_inj term_inj distinct cases eqvt 1;
val reflt = Goal.prove ctxt' [] [] reflg reflp_tac';
val symt = Goal.prove ctxt' [] [] symg symp_tac';
--- a/Nominal/Parser.thy Thu Mar 04 15:31:21 2010 +0100
+++ b/Nominal/Parser.thy Thu Mar 04 15:31:34 2010 +0100
@@ -212,6 +212,8 @@
ML {*
fun nominal_datatype2 dts bn_funs bn_eqs binds lthy =
let
+ val thy = ProofContext.theory_of lthy
+ val thy_name = Context.theory_name thy
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
@@ -233,8 +235,12 @@
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 fv_ts = map (Morphism.term morphism_4_3) fv_ts_loc;
val alpha_ts = map (Morphism.term morphism_4_3) alpha_ts_loc;
val alpha_induct_loc = #induct alpha
+ val [alpha_induct] = ProofContext.export lthy4 lthy3 [alpha_induct_loc];
+ val alpha_inducts = Project_Rule.projects lthy4 (1 upto (length dts)) alpha_induct
+ val fv_def = ProofContext.export lthy4 lthy3 fv_def_loc;
val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo);
val bn_tys = map (domain_type o fastype_of) raw_bn_funs;
val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys;
@@ -242,24 +248,64 @@
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 alpha_inj = ProofContext.export lthy4 lthy3 alpha_inj_loc
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
+ 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 qty_binds = map (fn (_, b, _, _) => b) dts;
+ val qty_names = map Name.of_binding qty_binds;
+ val qty_full_names = map (Long_Name.qualify thy_name) qty_names
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;*)
+ (map (fn ((b, t), alpha) => (([], b, NoSyn), (t, alpha))) ((qty_binds ~~ all_typs) ~~ alpha_ts))
+ (ALLGOALS (resolve_tac alpha_equivp)) lthy6;
+ val const_names = map Name.of_binding (flat (map (fn (_, _, _, t) => map (fn (b, _, _) => b) t) dts));
+ val raw_consts =
+ flat (map (fn (i, (_, _, l)) =>
+ map (fn (cname, dts) =>
+ Const (cname, map (typ_of_dtyp descr sorts) dts --->
+ typ_of_dtyp descr sorts (DtRec i))) l) descr);
+ val (consts_defs, lthy8) = fold_map Quotient_Def.quotient_lift_const (const_names ~~ raw_consts) lthy7;
+ val (consts, const_defs) = split_list consts_defs;
+ val (bns_rsp_pre, lthy9) = fold_map (
+ fn (bn_t, i) => prove_const_rsp Binding.empty [bn_t]
+ (fn _ => fvbv_rsp_tac (nth alpha_inducts i) raw_bn_eqs 1)) bns lthy8;
+ val bns_rsp = flat (map snd bns_rsp_pre);
+ val ((_, fv_rsp), lthy10) = prove_const_rsp Binding.empty fv_ts
+ (fn _ => fvbv_rsp_tac alpha_induct fv_def 1) lthy9;
+ val (const_rsps, lthy11) = fold_map (fn cnst => prove_const_rsp Binding.empty [cnst]
+ (fn _ => constr_rsp_tac alpha_inj (fv_rsp @ bns_rsp) alpha_equivp 1)) raw_consts lthy10
+ val (perms_rsp, lthy12) = prove_const_rsp Binding.empty perms
+ (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy11;
+ val qfv_names = map (fn x => "fv_" ^ x) qty_names
+ val (qfv_defs, lthy12a) = fold_map Quotient_Def.quotient_lift_const (qfv_names ~~ fv_ts) lthy12;
+ val qbn_names = map (fn (b, _ , _) => Name.of_binding b) bn_funs
+ val (qbn_defs, lthy12b) = fold_map Quotient_Def.quotient_lift_const (qbn_names ~~ raw_bn_funs) lthy12a;
+ val thy = Local_Theory.exit_global lthy12b;
+ val perm_names = map (fn x => "permute_" ^ x) qty_names
+ val thy' = define_lifted_perms qty_full_names (perm_names ~~ perms) raw_perm_simps thy;
+ val lthy13 = Theory_Target.init NONE thy';
+ val q_name = space_implode "_" qty_names;
+ val q_induct = snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy13, induct));
+ val (_, lthy14) = Local_Theory.note ((Binding.name (q_name ^ "_induct"), []), [q_induct]) lthy13;
+ val q_perm = map (fn th => snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy14, th))) raw_perm_def;
+ val (_, lthy15) = Local_Theory.note ((Binding.name (q_name ^ "_perm"), []), q_perm) lthy14;
+ val q_fv = map (fn th => snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy15, th))) fv_def;
+ val (_, lthy16) = Local_Theory.note ((Binding.name (q_name ^ "_fv"), []), q_fv) lthy15;
+ val q_bn = map (fn th => snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy16, th))) raw_bn_eqs;
+ val (_, lthy17) = Local_Theory.note ((Binding.name (q_name ^ "_bn"), []), q_bn) lthy16;
in
- ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy6)
+ ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy17)
end
*}
+ML name_of_typ
+
ML {*
(* parsing the datatypes and declaring *)
(* constructors in the local theory *)
--- a/Nominal/Rsp.thy Thu Mar 04 15:31:21 2010 +0100
+++ b/Nominal/Rsp.thy Thu Mar 04 15:31:34 2010 +0100
@@ -146,7 +146,9 @@
by auto
ML {*
- fun indtac induct = (rtac impI THEN' etac induct) ORELSE' rtac induct
+fun ind_tac induct = (rtac impI THEN' etac induct) ORELSE' rtac induct
+*}
+ML {*
fun all_eqvts ctxt =
Nominal_ThmDecls.get_eqvts_thms ctxt @ Nominal_ThmDecls.get_eqvts_raw_thms ctxt
val split_conjs = REPEAT o etac conjE THEN' TRY o REPEAT_ALL_NEW (CHANGED o rtac conjI)
@@ -161,7 +163,7 @@
ML {*
fun alpha_eqvt_tac induct simps ctxt =
- indtac induct THEN_ALL_NEW
+ ind_tac induct THEN_ALL_NEW
simp_tac ((mk_minimal_ss ctxt) addsimps simps) THEN_ALL_NEW
REPEAT o etac @{thm exi[of _ _ "p"]} THEN' split_conjs THEN_ALL_NEW
asm_full_simp_tac (HOL_ss addsimps (all_eqvts ctxt @ simps)) THEN_ALL_NEW
--- a/Nominal/Test.thy Thu Mar 04 15:31:21 2010 +0100
+++ b/Nominal/Test.thy Thu Mar 04 15:31:34 2010 +0100
@@ -1,10 +1,10 @@
theory Test
-imports "Parser"
+imports "Parser" "../Attic/Prove"
begin
text {* weirdo example from Peter Sewell's bestiary *}
-nominal_datatype weird =
+(*nominal_datatype weird =
WBind x::"name" y::"name" p1::"weird" p2::"weird" p3::"weird"
bind x in p1, bind x in p2, bind y in p2, bind y in p3
| WV "name"
@@ -14,6 +14,79 @@
thm alpha_weird_raw.intros[no_vars]
thm fv_weird_raw.simps[no_vars]
+thm eqvts
+
+local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding weird_inj}, []), (build_alpha_inj @{thms alpha_weird_raw.intros} @{thms weird_raw.distinct weird_raw.inject} @{thms alpha_weird_raw.cases} ctxt)) ctxt)) *}
+thm weird_inj
+
+local_setup {*
+(fn ctxt => snd (Local_Theory.note ((@{binding alpha_eqvt}, []),
+build_alpha_eqvts [@{term alpha_weird_raw}] [@{term "permute :: perm \<Rightarrow> weird_raw \<Rightarrow> weird_raw"}] @{thms permute_weird_raw.simps weird_inj} @{thm alpha_weird_raw.induct} ctxt) ctxt)) *}
+
+(*prove {* (snd o snd) (build_alpha_refl_gl [@{term alpha_weird_raw}] ("x","y","z")) *}
+
+apply (tactic {* transp_tac @{context} @{thm alpha_weird_raw.induct} @{thms weird_inj} @{thms weird_raw.inject} @{thms weird_raw.distinct} @{thms alpha_weird_raw.cases} @{thms alpha_eqvt} 1 *})
+*)
+lemma "alpha_weird_raw x y \<longrightarrow> (\<forall>z. alpha_weird_raw y z \<longrightarrow> alpha_weird_raw x z)"
+apply (rule impI)
+apply (erule alpha_weird_raw.induct)
+apply (simp_all add: weird_inj)
+defer
+apply (rule allI)
+apply (rule impI)
+apply (erule alpha_weird_raw.cases)
+apply (simp_all add: weird_inj)
+apply (rule allI)
+apply (rule impI)
+apply (erule alpha_weird_raw.cases)
+apply (simp_all add: weird_inj)
+apply (erule conjE)+
+apply (erule exE)+
+apply (erule conjE)+
+apply (erule exE)+
+apply (rule conjI)
+apply (rule_tac x="pica + pic" in exI)
+apply (erule alpha_gen_compose_trans)
+apply assumption
+apply (simp add: alpha_eqvt)
+apply (rule_tac x="pia + pib" in exI)
+apply (rule_tac x="piaa + piba" in exI)
+apply (rule conjI)
+apply (erule alpha_gen_compose_trans)
+apply assumption
+apply (simp add: alpha_eqvt)
+apply (rule conjI)
+defer
+apply (rule_tac x="pid + pi" in exI)
+apply (erule alpha_gen_compose_trans)
+apply assumption
+apply (simp add: alpha_eqvt)
+sorry
+
+lemma "alpha_weird_raw x y \<Longrightarrow> alpha_weird_raw y x"
+apply (erule alpha_weird_raw.induct)
+apply (simp_all add: weird_inj)
+apply (erule conjE)+
+apply (erule exE)+
+apply (erule conjE)+
+apply (erule exE)+
+apply (rule conjI)
+apply (rule_tac x="- pic" in exI)
+apply (erule alpha_gen_compose_sym)
+apply (simp_all add: alpha_eqvt)
+apply (rule_tac x="- pia" in exI)
+apply (rule_tac x="- pib" in exI)
+apply (simp add: minus_add[symmetric])
+apply (rule conjI)
+apply (erule alpha_gen_compose_sym)
+apply (simp_all add: alpha_eqvt)
+apply (rule conjI)
+apply (simp add: supp_minus_perm Int_commute)
+apply (rule_tac x="- pi" in exI)
+apply (erule alpha_gen_compose_sym)
+apply (simp_all add: alpha_eqvt)
+done
+
abbreviation "WBind \<equiv> WBind_raw"
abbreviation "WP \<equiv> WP_raw"
@@ -45,7 +118,7 @@
apply(simp add: flip_def fresh_def supp_swap)
apply(rule alpha_weird_raw.intros)
apply(simp add: alpha_weird_raw.intros(2))
-done
+done*)
text {* example 1 *}
@@ -71,9 +144,10 @@
thm permute_lam_raw_permute_bp_raw.simps
thm alpha_lam_raw_alpha_bp_raw.intros[no_vars]
thm fv_lam_raw_fv_bp_raw.simps[no_vars]
-thm eqvts
-
-print_theorems
+thm lam_bp_induct
+thm lam_bp_perm
+thm lam_bp_fv
+thm lam_bp_bn
text {* example 2 *}
@@ -97,6 +171,10 @@
thm alpha_trm'_raw_alpha_pat'_raw.intros[no_vars]
thm fv_trm'_raw_fv_pat'_raw.simps[no_vars]
thm f_raw.simps
+thm trm'_pat'_induct
+thm trm'_pat'_perm
+thm trm'_pat'_fv
+thm trm'_pat'_bn
nominal_datatype trm0 =
Var0 "name"
@@ -115,6 +193,10 @@
| "f0 (PD0 p1 p2) = (f0 p1) \<union> (f0 p2)"
thm f0_raw.simps
+thm trm0_pat0_induct
+thm trm0_pat0_perm
+thm trm0_pat0_fv
+thm trm0_pat0_bn
text {* example type schemes *}
@@ -214,6 +296,7 @@
(* example 6 from Terms.thy *)
+(* BV is not respectful, needs to fail
nominal_datatype trm6 =
Vr6 "name"
| Lm6 x::"name" t::"trm6" bind x in t
@@ -223,10 +306,11 @@
where
"bv6 (Vr6 n) = {}"
| "bv6 (Lm6 n t) = {atom n} \<union> bv6 t"
-| "bv6 (Lt6 l r) = bv6 l \<union> bv6 r"
+| "bv6 (Lt6 l r) = bv6 l \<union> bv6 r" *)
(* example 7 from Terms.thy *)
+(* BV is not respectful, needs to fail
nominal_datatype trm7 =
Vr7 "name"
| Lm7 l::"name" r::"trm7" bind l in r
@@ -236,7 +320,7 @@
where
"bv7 (Vr7 n) = {atom n}"
| "bv7 (Lm7 n t) = bv7 t - {atom n}"
-| "bv7 (Lt7 l r) = bv7 l \<union> bv7 r"
+| "bv7 (Lt7 l r) = bv7 l \<union> bv7 r" *)
(* example 8 from Terms.thy *)
@@ -254,6 +338,7 @@
(* example 9 from Terms.thy *)
+(* BV is not respectful, needs to fail
nominal_datatype lam9 =
Var9 "name"
| Lam9 n::"name" l::"lam9" bind n in l
@@ -263,13 +348,13 @@
bv9
where
"bv9 (Var9 x) = {}"
-| "bv9 (Lam9 x b) = {atom x}"
+| "bv9 (Lam9 x b) = {atom x}" *)
(* example from my PHD *)
atom_decl coname
-nominal_datatype phd =
+(*nominal_datatype phd =
Ax "name" "coname"
| Cut n::"coname" t1::"phd" c::"coname" t2::"phd" bind n in t1, bind c in t2
| AndR c1::"coname" t1::"phd" c2::"coname" t2::"phd" "coname" bind c1 in t1, bind c2 in t2
@@ -278,10 +363,9 @@
| ImpL c::"coname" t1::"phd" n::"name" t2::"phd" "name" bind c in t1, bind n in t2
| ImpR c::"coname" n::"name" t::"phd" "coname" bind n in t, bind c in t
-(* PROBLEM?: why does it create for the Cut AndR ImpL cases
-two permutations, but only one is used *)
thm alpha_phd_raw.intros[no_vars]
thm fv_phd_raw.simps[no_vars]
+*)
(* example form Leroy 96 about modules; OTT *)
@@ -320,9 +404,9 @@
and trmtrm =
Tref1 "name"
| Tref2 "path" "name"
-| Lam v::"name" "tyty" M::"trmtrm" bind v in M
-| App "trmtrm" "trmtrm"
-| Let "body" "trmtrm"
+| Lam' v::"name" "tyty" M::"trmtrm" bind v in M
+| App' "trmtrm" "trmtrm"
+| Let' "body" "trmtrm"
binder
cbinders :: "defn \<Rightarrow> atom set"
and Cbinders :: "spec \<Rightarrow> atom set"
@@ -337,6 +421,7 @@
| "Cbinders (SVal v T) = {atom v}"
(* core haskell *)
+print_theorems
atom_decl var
atom_decl tvar
@@ -399,10 +484,10 @@
(* example 3 from Peter Sewell's bestiary *)
nominal_datatype exp =
- Var "name"
-| App "exp" "exp"
-| Lam x::"name" e::"exp" bind x in e
-| Let x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1
+ VarP "name"
+| AppP "exp" "exp"
+| LamP x::"name" e::"exp" bind x in e
+| LetP x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1
and pat =
PVar "name"
| PUnit
@@ -414,24 +499,25 @@
| "bp (PUnit) = {}"
| "bp (PPair p1 p2) = bp p1 \<union> bp p2"
+thm quot_respect
(* example 6 from Peter Sewell's bestiary *)
-nominal_datatype exp6 =
+(*nominal_datatype exp6 =
EVar name
| EPair exp6 exp6
| ELetRec x::name p::pat6 e1::exp6 e2::exp6 bind x in e1, bind x in e2, bind "bp6 p" in e1
and pat6 =
- PVar name
-| PUnit
-| PPair pat6 pat6
+ PVar' name
+| PUnit'
+| PPair' pat6 pat6
binder
bp6 :: "pat6 \<Rightarrow> atom set"
where
- "bp6 (PVar x) = {atom x}"
-| "bp6 (PUnit) = {}"
-| "bp6 (PPair p1 p2) = bp6 p1 \<union> bp6 p2"
+ "bp6 (PVar' x) = {atom x}"
+| "bp6 (PUnit') = {}"
+| "bp6 (PPair' p1 p2) = bp6 p1 \<union> bp6 p2"*)
(* example 7 from Peter Sewell's bestiary *)
-nominal_datatype exp7 =
+(*nominal_datatype exp7 =
EVar name
| EUnit
| EPair exp7 exp7
@@ -447,10 +533,10 @@
where
"b7 (Assign x e) = {atom x}"
| "b7s (Single a) = b7 a"
-| "b7s (More a as) = (b7 a) \<union> (b7s as)"
+| "b7s (More a as) = (b7 a) \<union> (b7s as)"*)
(* example 8 from Peter Sewell's bestiary *)
-nominal_datatype exp8 =
+(*nominal_datatype exp8 =
EVar name
| EUnit
| EPair exp8 exp8
@@ -484,7 +570,7 @@
| "b_fnclauses (S fc) = (b_fnclause fc)"
| "b_fnclauses (ORs fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"
| "b_lrb8 (Clause fcs) = (b_fnclauses fcs)"
-| "b_fnclause (K x pat exp8) = {atom x}"
+| "b_fnclause (K x pat exp8) = {atom x}"*)