--- 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}"*)