
diff -r 5256f256edd8 -r f201eb6acafc Nominal/Test.thy
--- a/Nominal/Test.thy	Thu Mar 04 12:00:11 2010 +0100
+++ b/Nominal/Test.thy	Thu Mar 04 15:15:44 2010 +0100
@@ -4,7 +4,7 @@
 
 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"
@@ -23,39 +23,10 @@
 (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)) *}
 
-ML {*
-fun is_ex (Const ("Ex", _) $ Abs _) = true
-  | is_ex _ = false;
-*}
+(*prove {* (snd o snd) (build_alpha_refl_gl [@{term alpha_weird_raw}] ("x","y","z")) *}
 
-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 =
-  ind_tac induct THEN_ALL_NEW
-  (TRY o rtac allI THEN' imp_elim_tac cases ctxt) THEN_ALL_NEW
-  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
-*}
-(*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 *})*)
-
+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)
@@ -90,27 +61,30 @@
 apply (erule alpha_gen_compose_trans)
 apply assumption
 apply (simp add: alpha_eqvt)
-done
+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)
-defer (* simple *)
-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)
-apply (rule_tac x="- pic" in exI)
-apply (erule alpha_gen_compose_sym)
-apply (simp_all add: alpha_eqvt)
 done
 
 
@@ -144,7 +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 *}
 
@@ -170,9 +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 *}
 
@@ -196,6 +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"
@@ -214,6 +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 *}
 
@@ -313,6 +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
@@ -322,10 +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
@@ -335,7 +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 *)
 
@@ -353,6 +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
@@ -362,13 +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
@@ -377,10 +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 *)
 
@@ -419,9 +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"
@@ -436,6 +421,7 @@
 | "Cbinders (SVal v T) = {atom v}"  
 
 (* core haskell *)
+print_theorems
 
 atom_decl var
 atom_decl tvar
@@ -495,10 +481,10 @@
 
 (* 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
@@ -510,24 +496,25 @@
 | "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
@@ -543,10 +530,10 @@
 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
@@ -580,7 +567,7 @@
 | "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}"*)
 
 
 




