author | Cezary Kaliszyk <kaliszyk@in.tum.de> |
Tue, 02 Mar 2010 11:04:49 +0100 | |
changeset 1300 | 22a084c9316b |
parent 1277 | 6eacf60ce41d |
child 1318 | cce1b6d1b761 |
permissions | -rw-r--r-- |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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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 |