Nominal/Term4.thy
author Cezary Kaliszyk <kaliszyk@in.tum.de>
Tue, 02 Mar 2010 11:04:49 +0100
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permissions -rw-r--r--
Fixed eqvt code.
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theory Term4
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imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove"
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begin
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atom_decl name
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section {*** lam with indirect list recursion ***}
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datatype rtrm4 =
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  rVr4 "name"
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| rAp4 "rtrm4" "rtrm4 list"
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| rLm4 "name" "rtrm4"  --"bind (name) in (trm)"
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print_theorems
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thm rtrm4.recs
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(* there cannot be a clause for lists, as *)
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(* permutations are  already defined in Nominal (also functions, options, and so on) *)
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setup {* snd o define_raw_perms (Datatype.the_info @{theory} "Term4.rtrm4") 1 *}
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(* "repairing" of the permute function *)
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lemma repaired:
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  fixes ts::"rtrm4 list"
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  shows "permute_rtrm4_list p ts = p \<bullet> ts"
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  apply(induct ts)
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  apply(simp_all)
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  done
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thm permute_rtrm4_permute_rtrm4_list.simps
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thm permute_rtrm4_permute_rtrm4_list.simps[simplified repaired]
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local_setup {* snd o define_fv_alpha (Datatype.the_info @{theory} "Term4.rtrm4")
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  [[[], [], [(NONE, 0,1)]], [[], []]  ] *}
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print_theorems
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notation
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  alpha_rtrm4 ("_ \<approx>4 _" [100, 100] 100) and
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  alpha_rtrm4_list ("_ \<approx>4l _" [100, 100] 100)
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thm alpha_rtrm4_alpha_rtrm4_list.intros
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local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_inj}, []), (build_alpha_inj @{thms alpha_rtrm4_alpha_rtrm4_list.intros} @{thms rtrm4.distinct rtrm4.inject list.distinct list.inject} @{thms alpha_rtrm4.cases alpha_rtrm4_list.cases} ctxt)) ctxt)) *}
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thm alpha4_inj
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thm alpha_rtrm4_alpha_rtrm4_list.induct
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local_setup {*
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snd o build_eqvts @{binding fv_rtrm4_fv_rtrm4_list_eqvt} [@{term fv_rtrm4}, @{term fv_rtrm4_list}] [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"},@{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}] (@{thms fv_rtrm4_fv_rtrm4_list.simps permute_rtrm4_permute_rtrm4_list.simps[simplified repaired]}) @{thm rtrm4.induct}
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*}
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print_theorems
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local_setup {*
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(fn ctxt => snd (Local_Theory.note ((@{binding alpha4_eqvt}, []),
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  build_alpha_eqvts [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"},@{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}] @{thms permute_rtrm4_permute_rtrm4_list.simps[simplified repaired] alpha4_inj} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} ctxt) ctxt))
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*}
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print_theorems
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local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_equivp}, []),
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  (build_equivps [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] @{thm rtrm4.induct} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} @{thms rtrm4.inject list.inject} @{thms alpha4_inj} @{thms rtrm4.distinct list.distinct} @{thms alpha_rtrm4_list.cases alpha_rtrm4.cases} @{thms alpha4_eqvt} ctxt)) ctxt)) *}
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thm alpha4_equivp
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quotient_type 
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  qrtrm4 = rtrm4 / alpha_rtrm4 and
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  qrtrm4list = "rtrm4 list" / alpha_rtrm4_list
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  by (simp_all add: alpha4_equivp)
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end