nominal2: comparison Nominal/Test.thy

equal deleted inserted replaced

-:cffc5d78ab7f
+:cad5f3851569
 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"
 | WP "weird" "weird"
 thm permute_weird_raw.simps[no_vars]
 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"
 abbreviation "WV \<equiv> WV_raw"
 apply(simp)
 apply(auto)
 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 *}
 (* ML {* set show_hyps *} *)
 term Test.BP_raw
 thm bi_raw.simps
 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
+thm lam_bp_induct
+thm lam_bp_perm
-print_theorems
+thm lam_bp_fv
+thm lam_bp_bn
 text {* example 2 *}
 nominal_datatype trm' =
 Var "name"
 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"
 | App0 "trm0" "trm0"
 | Lam0 x::"name" t::"trm0"          bind x in t
 "f0 PN0 = {}"
 | "f0 (PS0 x) = {atom x}"
 | "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 *}
 (* does not work yet
 nominal_datatype t =
 "bv5 Lnil = {}"
 | "bv5 (Lcons n t ltl) = {atom n} \<union> (bv5 ltl)"
 (* 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
 | Lt6 left::"trm6" right::"trm6"  bind "bv6 left" in right
 binder
 bv6
 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
 | Lt7 l::"trm7" r::"trm7"   bind "bv7 l" in r
 binder
 bv7
 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 *)
 nominal_datatype foo8 =
 Foo0 "name"
 "bv8 (Bar0 x) = {}"
 | "bv8 (Bar1 v x b) = {atom v}"
 (* 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
 and bla9 =
 Bla9 f::"lam9" s::"lam9" bind "bv9 f" in s
 binder
 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
 |  AndL1 n::"name" t::"phd" "name"                              bind n in t
 |  AndL2 n::"name" t::"phd" "name"                              bind n in t
 |  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 *)
 nominal_datatype mexp =
 Acc "path"
 Sref1 "name"
 | Sref2 "path" "name"
 and trmtrm =
 Tref1 "name"
 | Tref2 "path" "name"
-| Lam v::"name" "tyty" M::"trmtrm"  bind v in M
+| Lam' v::"name" "tyty" M::"trmtrm"  bind v in M
-| App "trmtrm" "trmtrm"
+| App' "trmtrm" "trmtrm"
-| Let "body" "trmtrm"
+| Let' "body" "trmtrm"
 binder
 cbinders :: "defn \<Rightarrow> atom set"
 and Cbinders :: "spec \<Rightarrow> atom set"
 where
 "cbinders (Type t T) = {atom t}"
 | "Cbinders (Type2 t T) = {atom t}"
 | "Cbinders (SStru x S) = {atom x}"
 | "Cbinders (SVal v T) = {atom v}"
 (* core haskell *)
+print_theorems
 atom_decl var
 atom_decl tvar
 (*thm bv_raw.simps*)
 (* example 3 from Peter Sewell's bestiary *)
 nominal_datatype exp =
-Var "name"
+VarP "name"
-| App "exp" "exp"
+| AppP "exp" "exp"
-| Lam x::"name" e::"exp" bind x in e
+| LamP 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
+| LetP x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1
 and pat =
 PVar "name"
 | PUnit
 | PPair "pat" "pat"
 binder
 where
 "bp (PVar x) = {atom x}"
 | "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
+PVar' name
-| PUnit
+| PUnit'
-| PPair pat6 pat6
+| PPair' pat6 pat6
 binder
 bp6 :: "pat6 \<Rightarrow> atom set"
 where
-"bp6 (PVar x) = {atom x}"
+"bp6 (PVar' x) = {atom x}"
-| "bp6 (PUnit) = {}"
+| "bp6 (PUnit') = {}"
-| "bp6 (PPair p1 p2) = bp6 p1 \<union> bp6 p2"
+| "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
 | ELetRec l::lrbs e::exp7 bind "b7s l" in e, bind "b7s l" in l
 and lrb =
 b7 :: "lrb \<Rightarrow> atom set" and
 b7s :: "lrbs \<Rightarrow> atom set"
 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
 | ELetRec l::lrbs8 e::exp8 bind "b_lrbs8 l" in e, bind "b_lrbs8 l" in l
 and fnclause =
 | "b_pat (PUnit) = {}"
 | "b_pat (PPair p1 p2) = b_pat p1 \<union> b_pat p2"
 | "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}"*)
 (* example 9 from Peter Sewell's bestiary *)

changeset 1352	cad5f3851569
parent 1351	cffc5d78ab7f
parent 1340	f201eb6acafc
child 1353	3727e234fe6b