Nominal/Ex/SingleLet.thy
author Christian Urban <urbanc@in.tum.de>
Tue, 27 Jul 2010 09:09:02 +0200
changeset 2384 841b7e34e70a
parent 2382 e8b9c0ebf5dd
child 2385 fe25a3ffeb14
permissions -rw-r--r--
fixed order of fold_union to make alpha and fv agree
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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theory SingleLet
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imports "../NewParser"
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begin
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atom_decl name
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declare [[STEPS = 16]]
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nominal_datatype trm  =
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  Var "name"
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| App "trm" "trm"
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| Lam x::"name" t::"trm"  bind_set x in t
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| Let a::"assg" t::"trm"  bind_set "bn a" in t
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| Foo x::"name" y::"name" t::"trm" t1::"trm" t2::"trm" bind_set x in y t t1 t2
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| Bar x::"name" y::"name" t::"trm" bind y x in t x y
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| Baz x::"name" t1::"trm" t2::"trm" bind x in t1, bind x in t2 
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and assg =
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  As "name" x::"name" t::"trm" bind x in t
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binder
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  bn::"assg \<Rightarrow> atom set"
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where
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  "bn (As x y t) = {atom x}"
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thm alpha_bn_imps
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thm distinct
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thm eq_iff
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thm fv_defs
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thm perm_simps
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thm perm_laws
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typ trm
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typ assg
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term Var 
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term App
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term Baz
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term bn
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term fv_trm
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term alpha_bn
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lemma a2:
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  shows "alpha_trm_raw x1 y1 \<Longrightarrow> fv_trm_raw x1 = fv_trm_raw y1"
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  and   "alpha_assg_raw x2 y2 \<Longrightarrow> fv_assg_raw x2 = fv_assg_raw y2 \<and> bn_raw x2 = bn_raw y2"
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  and   "alpha_bn_raw x3 y3 \<Longrightarrow>  fv_bn_raw x3 = fv_bn_raw y3"
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apply(induct rule: alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.inducts)
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps)
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps)
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps alphas prod_alpha_def ex_simps)
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps alphas prod_alpha_def ex_simps)
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-- ""
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps alphas prod_fv.simps prod_alpha_def ex_simps Un_assoc)
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-- ""
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps alphas prod_fv.simps prod_alpha_def ex_simps)
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apply(simp only: Un_assoc set.simps append.simps)
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apply(simp only: Un_insert_left Un_empty_right Un_empty_left)
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-- ""
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps alphas prod_fv.simps prod_alpha_def ex_simps)
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apply(simp only: Un_assoc set.simps append.simps)
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--""
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps bn_raw.simps alphas prod_fv.simps prod_alpha_def ex_simps)
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apply(simp only: Un_assoc set.simps append.simps)
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apply(simp (no_asm) only: simp_thms)
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--""
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apply(simp only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps bn_raw.simps alphas prod_fv.simps prod_alpha_def ex_simps)
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apply(simp only: Un_assoc set.simps append.simps)
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done
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lemma [quot_respect]: 
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  "(op= ===> alpha_trm_raw) Var_raw Var_raw"
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  "(alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw) App_raw App_raw"
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  "(op= ===> alpha_trm_raw ===> alpha_trm_raw) Lam_raw Lam_raw"
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  "(alpha_assg_raw ===> alpha_trm_raw ===> alpha_trm_raw) Let_raw Let_raw"
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  "(op= ===> op= ===> alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw) 
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     Foo_raw Foo_raw"
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  "(op= ===> op= ===> alpha_trm_raw ===> alpha_trm_raw) Bar_raw Bar_raw"
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  "(op= ===> alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw) Baz_raw Baz_raw"
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  "(op = ===> op = ===> alpha_trm_raw ===> alpha_assg_raw) As_raw As_raw"
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apply(auto)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule refl)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(assumption)
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apply(assumption)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2)
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apply(simp add: a1)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2 prod_alpha_def)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2 prod_alpha_def)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2 prod_alpha_def)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2 prod_alpha_def)
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apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
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apply(rule_tac x="0" in exI)
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apply(simp add: alphas fresh_star_def fresh_zero_perm a2 prod_alpha_def)
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apply(rule refl)
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done
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lemma [quot_respect]:
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  "(alpha_trm_raw ===> op =) fv_trm_raw fv_trm_raw"
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  "(alpha_assg_raw ===> op =) fv_bn_raw fv_bn_raw"
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  "(alpha_assg_raw ===> op =) bn_raw bn_raw"
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  "(alpha_assg_raw ===> op =) fv_assg_raw fv_assg_raw"
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  "(op = ===> alpha_trm_raw ===> alpha_trm_raw) permute permute"
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apply(simp_all add: a2 a1)
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sorry
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ML {*
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  val thms_d = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms distinct}
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*}
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ML {* 
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  val thms_i = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw_assg_raw.inducts}
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*}
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ML {*
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms fv_defs}
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*}
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thm perm_defs[no_vars]
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instance trm :: pt sorry
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instance assg :: pt sorry
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lemma b1:
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  "p \<bullet> Var name = Var (p \<bullet> name)"
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  "p \<bullet> App trm1 trm2 = App (p \<bullet> trm1) (p \<bullet> trm2)"
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  "p \<bullet> Lam name trm = Lam (p \<bullet> name) (p \<bullet> trm)"
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  "p \<bullet> Let assg trm = Let (p \<bullet> assg) (p \<bullet> trm)"
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  "p \<bullet> Foo name1 name2 trm1 trm2 trm3 =
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     Foo (p \<bullet> name1) (p \<bullet> name2) (p \<bullet> trm1) (p \<bullet> trm2) (p \<bullet> trm3)"
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  "p \<bullet> Bar name1 name2 trm = Bar (p \<bullet> name1) (p \<bullet> name2) (p \<bullet> trm)"
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  "p \<bullet> Baz name trm1 trm2 = Baz (p \<bullet> name) (p \<bullet> trm1) (p \<bullet> trm2)"
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  "p \<bullet> As name1 name2 trm = As (p \<bullet> name1) (p \<bullet> name2) (p \<bullet> trm)"
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sorry
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(*
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ML {*
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  val thms_p = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms perm_defs}
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*}
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*)
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thm eq_iff[no_vars]
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ML {*
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  val q1 = lift_thm [@{typ trm}, @{typ assg}] @{context} @{thm "eq_iff"(1)}
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*}
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local_setup {* Local_Theory.note ((@{binding d1}, []), thms_d) #> snd *}
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local_setup {* Local_Theory.note ((@{binding i1}, []), thms_i) #> snd *}
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local_setup {* Local_Theory.note ((@{binding f1}, []), thms_f) #> snd *}
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local_setup {* Local_Theory.note ((@{binding q1}, []), [q1]) #> snd *}
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thm perm_defs
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thm perm_simps
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lemma supp_fv:
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  "supp t = fv_trm t"
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  "supp b = fv_bn b"
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apply(induct t and b rule: i1)
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apply(simp_all add: f1)
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apply(simp_all add: supp_def)
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apply(simp_all add: b1)
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consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm"
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consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg"
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lemma y:
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  "perm_bn_trm p (Var x) = (Var x)"
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  "perm_bn_trm p (App t1 t2) = (App t1 t2)"
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  "perm_bn_trm p ("
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ML {*
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  map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms eq_iff}
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*}
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lemma "Var x \<noteq> App y1 y2"
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apply(descending)
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apply(simp add: trm_raw.distinct)
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ML {*
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  map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw.distinct(1)}
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*}
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typ trm
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typ assg
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thm trm_assg.fv
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thm trm_assg.supp
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thm trm_assg.eq_iff
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thm trm_assg.bn
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thm trm_assg.perm
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thm trm_assg.induct
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thm trm_assg.inducts
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thm trm_assg.distinct
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ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
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(* TEMPORARY
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thm trm_assg.fv[simplified trm_assg.supp(1-2)]
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*)
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end
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