Nominal/Test.thy
author Christian Urban <urbanc@in.tum.de>
Wed, 17 Mar 2010 06:49:33 +0100
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theory Test
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imports "Parser" "../Attic/Prove"
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begin
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text {* example 1, equivalent to example 2 from Terms *}
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atom_decl name
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ML {* val _ = cheat_alpha_eqvt := false *}
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ML {* val _ = cheat_fv_eqvt := false *}
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ML {* val _ = recursive := false *}
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nominal_datatype lam =
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  VAR "name"
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| APP "lam" "lam"
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| LAM x::"name" t::"lam" bind x in t
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| LET bp::"bp" t::"lam"   bind "bi bp" in t
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and bp =
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  BP "name" "lam"
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binder
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  bi::"bp \<Rightarrow> atom set"
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where
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  "bi (BP x t) = {atom x}"
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thm lam_bp_fv
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thm lam_bp_inject
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thm lam_bp_bn
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thm lam_bp_perm
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thm lam_bp_induct
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thm lam_bp_inducts
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thm lam_bp_distinct
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ML {* Sign.of_sort @{theory} (@{typ lam}, @{sort fs}) *}
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term "supp (x :: lam)"
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(* maybe should be added to Infinite.thy *)
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lemma infinite_Un:
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  shows "infinite (S \<union> T) \<longleftrightarrow> infinite S \<or> infinite T"
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  by simp
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lemma bi_eqvt:
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  shows "(p \<bullet> (bi b)) = bi (p \<bullet> b)"
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  by (rule eqvts)
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lemma supp_fv:
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  shows "supp t = fv_lam t" 
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  and "supp bp = fv_bp bp \<and> fv_bi bp = {a. infinite {b. \<not>alpha_bi ((a \<rightleftharpoons> b) \<bullet> bp) bp}}"
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apply(induct t and bp rule: lam_bp_inducts)
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apply(simp_all add: lam_bp_fv)
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(* VAR case *)
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apply(simp only: supp_def)
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apply(simp only: lam_bp_perm)
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apply(simp only: lam_bp_inject)
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apply(simp only: supp_def[symmetric])
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apply(simp only: supp_at_base)
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(* APP case *)
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apply(simp only: supp_def)
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apply(simp only: lam_bp_perm)
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apply(simp only: lam_bp_inject)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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(* LAM case *)
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apply(rule_tac t="supp (LAM name lam_raw)" and s="supp (Abs {atom name} lam_raw)" in subst)
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apply(simp (no_asm) only: supp_def)
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apply(simp only: lam_bp_perm)
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apply(simp only: permute_ABS)
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apply(simp only: lam_bp_inject)
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apply(simp only: Abs_eq_iff)
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apply(simp only: insert_eqvt atom_eqvt empty_eqvt)
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apply(simp only: alpha_gen)
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apply(simp only: supp_eqvt[symmetric])
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apply(simp only: eqvts)
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apply(simp only: supp_Abs)
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(* LET case *)
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defer
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(* BP case *)
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apply(simp only: supp_def)
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apply(simp only: lam_bp_perm)
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apply(simp only: lam_bp_inject)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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apply(simp only: supp_def[symmetric])
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apply(simp only: supp_at_base)
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apply(simp)
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(* LET case *)
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apply(rule_tac t="supp (LET bp_raw lam_raw)" and s="supp (Abs (bi bp_raw) lam_raw) \<union> fv_bi bp_raw" in subst)
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apply(simp (no_asm) only: supp_def)
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apply(simp only: lam_bp_perm)
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apply(simp only: permute_ABS)
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apply(simp only: lam_bp_inject)
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apply(simp only: eqvts)
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apply(simp only: Abs_eq_iff)
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apply(simp only: ex_simps)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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apply(simp only: alpha_gen)
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apply(simp only: supp_eqvt[symmetric])
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apply(simp only: eqvts)
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apply(blast)
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apply(simp add: supp_Abs)
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apply(blast)
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done
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thm lam_bp_fv[simplified supp_fv(1)[symmetric] supp_fv(2)[THEN conjunct1, symmetric]]
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ML {* val _ = recursive := true *}
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nominal_datatype lam' =
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  VAR' "name"
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| APP' "lam'" "lam'"
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| LAM' x::"name" t::"lam'"  bind x in t
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| LET' bp::"bp'" t::"lam'"   bind "bi' bp" in t
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and bp' =
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  BP' "name" "lam'"
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binder
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  bi'::"bp' \<Rightarrow> atom set"
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where
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  "bi' (BP' x t) = {atom x}"
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thm lam'_bp'_fv
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thm lam'_bp'_inject[no_vars]
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thm lam'_bp'_bn
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thm lam'_bp'_perm
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thm lam'_bp'_induct
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thm lam'_bp'_inducts
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thm lam'_bp'_distinct
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ML {* Sign.of_sort @{theory} (@{typ lam'}, @{sort fs}) *}
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lemma supp_fv:
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  shows "supp t = fv_lam' t" 
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  and "supp bp = fv_bp' bp"
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apply(induct t and bp rule: lam'_bp'_inducts)
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apply(simp_all add: lam'_bp'_fv)
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(* VAR case *)
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apply(simp only: supp_def)
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apply(simp only: lam'_bp'_perm)
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apply(simp only: lam'_bp'_inject)
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apply(simp only: supp_def[symmetric])
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apply(simp only: supp_at_base)
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(* APP case *)
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apply(simp only: supp_def)
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apply(simp only: lam'_bp'_perm)
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apply(simp only: lam'_bp'_inject)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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(* LAM case *)
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apply(rule_tac t="supp (LAM' name lam'_raw)" and s="supp (Abs {atom name} lam'_raw)" in subst)
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apply(simp (no_asm) only: supp_def)
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apply(simp only: lam'_bp'_perm)
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apply(simp only: permute_ABS)
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apply(simp only: lam'_bp'_inject)
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apply(simp only: Abs_eq_iff)
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apply(simp only: insert_eqvt atom_eqvt empty_eqvt)
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apply(simp only: alpha_gen)
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apply(simp only: supp_eqvt[symmetric])
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apply(simp only: eqvts)
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apply(simp only: supp_Abs)
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(* LET case *)
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apply(rule_tac t="supp (LET' bp'_raw lam'_raw)" and 
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               s="supp (Abs (bi' bp'_raw) (bp'_raw, lam'_raw))" in subst)
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apply(simp (no_asm) only: supp_def)
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apply(simp only: lam'_bp'_perm)
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apply(simp only: permute_ABS)
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apply(simp only: lam'_bp'_inject)
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apply(simp only: eqvts)
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apply(simp only: Abs_eq_iff)
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apply(rule Collect_cong)
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apply(tactic {* Cong_Tac.cong_tac @{thm cong} 1 *})
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apply(simp)
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apply(tactic {* Cong_Tac.cong_tac @{thm cong} 1 *})
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apply(simp)
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apply(rule Collect_cong)
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apply(tactic {* Cong_Tac.cong_tac @{thm cong} 1 *})
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apply(simp)
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apply(tactic {* Cong_Tac.cong_tac @{thm cong} 1 *})
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apply(simp)
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apply(rule ext)
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apply(rule sym)
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apply(subgoal_tac "fv_bp' = supp")
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apply(subgoal_tac "fv_lam' = supp")
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apply(simp)
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apply(rule trans)
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apply(rule alpha_abs_Pair[symmetric])
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apply(simp add: alpha_gen supp_Pair)
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oops
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thm lam_bp_fv[simplified supp_fv(1)[symmetric] supp_fv(2)[THEN conjunct1, symmetric]]
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text {* example 2 *}
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ML {* val _ = recursive := false  *}
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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 x in t
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| Let p::"pat'" "trm'" t::"trm'"   bind "f p" in t
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and pat' =
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  PN
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| PS "name"
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| PD "name" "name"
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binder
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  f::"pat' \<Rightarrow> atom set"
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where
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  "f PN = {}"
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| "f (PD x y) = {atom x, atom y}"
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| "f (PS x) = {atom x}"
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thm trm'_pat'_fv
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thm trm'_pat'_inject
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thm trm'_pat'_bn
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thm trm'_pat'_perm
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thm trm'_pat'_induct
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thm trm'_pat'_distinct
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lemma supp_fv_trm'_pat':
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  shows "supp t = fv_trm' t" 
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  and "supp bp = fv_pat' bp \<and> {a. infinite {b. \<not>alpha_f ((a \<rightleftharpoons> b) \<bullet> bp) bp}} = fv_f bp"
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apply(induct t and bp rule: trm'_pat'_inducts)
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apply(simp_all add: trm'_pat'_fv)
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(* VAR case *)
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apply(simp only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: trm'_pat'_inject)
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apply(simp only: supp_def[symmetric])
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apply(simp only: supp_at_base)
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(* APP case *)
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apply(simp only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: trm'_pat'_inject)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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(* LAM case *)
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apply(rule_tac t="supp (Lam name trm'_raw)" and s="supp (Abs {atom name} trm'_raw)" in subst)
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apply(simp (no_asm) only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: permute_ABS)
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apply(simp only: trm'_pat'_inject)
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apply(simp only: Abs_eq_iff)
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apply(simp only: insert_eqvt atom_eqvt empty_eqvt)
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apply(simp only: alpha_gen)
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apply(simp only: supp_eqvt[symmetric])
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apply(simp only: eqvts)
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apply(simp only: supp_Abs)
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(* LET case *)
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apply(rule_tac t="supp (Let pat'_raw trm'_raw1 trm'_raw2)" 
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           and s="supp (Abs (f pat'_raw) trm'_raw2) \<union> supp trm'_raw1 \<union> fv_f pat'_raw" in subst)
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apply(simp (no_asm) only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: permute_ABS)
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apply(simp only: trm'_pat'_inject)
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apply(simp only: eqvts)
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apply(simp only: Abs_eq_iff)
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apply(simp only: ex_simps)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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apply(simp only: alpha_gen)
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apply(simp only: supp_eqvt[symmetric])
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apply(simp only: eqvts)
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apply(blast)
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apply(simp add: supp_Abs)
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apply(blast)
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(* PN case *)
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apply(simp only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: trm'_pat'_inject)
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apply(simp)
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(* PS case *)
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apply(simp only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: trm'_pat'_inject)
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apply(simp only: supp_def[symmetric])
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apply(simp only: supp_at_base)
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apply(simp)
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(* PD case *)
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apply(simp only: supp_def)
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apply(simp only: trm'_pat'_perm)
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apply(simp only: trm'_pat'_inject)
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apply(simp only: de_Morgan_conj)
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apply(simp only: Collect_disj_eq)
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apply(simp only: infinite_Un)
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apply(simp only: Collect_disj_eq)
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apply(simp only: supp_def[symmetric])
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apply(simp add: supp_at_base)
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done
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thm trm'_pat'_fv[simplified supp_fv_trm'_pat'(1)[symmetric] supp_fv_trm'_pat'(2)[THEN conjunct1, symmetric]]
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nominal_datatype trm0 =
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  Var0 "name"
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| App0 "trm0" "trm0"
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| Lam0 x::"name" t::"trm0"          bind x in t
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| Let0 p::"pat0" "trm0" t::"trm0"   bind "f0 p" in t
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and pat0 =
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  PN0
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| PS0 "name"
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| PD0 "pat0" "pat0"
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binder
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  f0::"pat0 \<Rightarrow> atom set"
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where
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  "f0 PN0 = {}"
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| "f0 (PS0 x) = {atom x}"
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| "f0 (PD0 p1 p2) = (f0 p1) \<union> (f0 p2)"
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thm trm0_pat0_fv
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thm trm0_pat0_inject
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thm trm0_pat0_bn
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thm trm0_pat0_perm
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thm trm0_pat0_induct
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thm trm0_pat0_distinct
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text {* example type schemes *}
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nominal_datatype t =
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  VarTS "name"
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| FunTS "t" "t"
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and  tyS =
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  All xs::"name set" ty::"t" bind xs in ty
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thm t_tyS_fv
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thm t_tyS_inject
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thm t_tyS_bn
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thm t_tyS_perm
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thm t_tyS_induct
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thm t_tyS_distinct
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(* example 1 from Terms.thy *)
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nominal_datatype trm1 =
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  Vr1 "name"
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| Ap1 "trm1" "trm1"
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| Lm1 x::"name" t::"trm1"       bind x in t
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| Lt1 p::"bp1" "trm1" t::"trm1" bind "bv1 p" in t
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and bp1 =
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  BUnit1
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| BV1 "name"
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| BP1 "bp1" "bp1"
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binder
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  bv1
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where
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  "bv1 (BUnit1) = {}"
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| "bv1 (BP1 bp1 bp2) = (bv1 bp1) \<union> (bv1 bp2)"
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| "bv1 (BV1 x) = {atom x}"
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thm trm1_bp1_fv
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thm trm1_bp1_inject
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thm trm1_bp1_bn
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thm trm1_bp1_perm
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thm trm1_bp1_induct
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thm trm1_bp1_distinct
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text {* example 3 from Terms.thy *}
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nominal_datatype trm3 =
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  Vr3 "name"
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| Ap3 "trm3" "trm3"
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| Lm3 x::"name" t::"trm3"        bind x in t
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| Lt3 r::"rassigns3" t::"trm3"   bind "bv3 r" in t
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and rassigns3 =
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  ANil
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| ACons "name" "trm3" "rassigns3"
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binder
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  bv3
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where
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  "bv3 ANil = {}"
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| "bv3 (ACons x t as) = {atom x} \<union> (bv3 as)"
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parents: 1232
diff changeset
   379
1418
632b08744613 With the 4 cheats, all examples fully lift.
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parents: 1416
diff changeset
   380
thm trm3_rassigns3_fv
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   381
thm trm3_rassigns3_inject
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   382
thm trm3_rassigns3_bn
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   383
thm trm3_rassigns3_perm
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   384
thm trm3_rassigns3_induct
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   385
thm trm3_rassigns3_distinct
1367
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parents: 1365
diff changeset
   386
9bbf56cdeb88 added compat definitions to some examples
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parents: 1365
diff changeset
   387
(* compat should be
9bbf56cdeb88 added compat definitions to some examples
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parents: 1365
diff changeset
   388
compat (ANil) pi (PNil) \<equiv> TRue
9bbf56cdeb88 added compat definitions to some examples
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parents: 1365
diff changeset
   389
compat (ACons x t ts) pi (ACons x' t' ts') \<equiv> pi o x = x' \<and> alpha t t' \<and> compat ts pi ts'
9bbf56cdeb88 added compat definitions to some examples
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parents: 1365
diff changeset
   390
*)
9bbf56cdeb88 added compat definitions to some examples
Christian Urban <urbanc@in.tum.de>
parents: 1365
diff changeset
   391
1251
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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parents: 1232
diff changeset
   392
(* example 5 from Terms.thy *)
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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parents: 1232
diff changeset
   393
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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parents: 1232
diff changeset
   394
nominal_datatype trm5 =
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   395
  Vr5 "name"
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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parents: 1232
diff changeset
   396
| Ap5 "trm5" "trm5"
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   397
| Lt5 l::"lts" t::"trm5"  bind "bv5 l" in t
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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diff changeset
   398
and lts =
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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parents: 1232
diff changeset
   399
  Lnil
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
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parents: 1232
diff changeset
   400
| Lcons "name" "trm5" "lts"
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   401
binder
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   402
  bv5
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   403
where
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   404
  "bv5 Lnil = {}"
11b8798dea5d parsing and definition of raw datatype and bv-function work (not very beautiful)
Christian Urban <urbanc@in.tum.de>
parents: 1232
diff changeset
   405
| "bv5 (Lcons n t ltl) = {atom n} \<union> (bv5 ltl)"
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parents: 1232
diff changeset
   406
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   407
thm trm5_lts_fv
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   408
thm trm5_lts_inject
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   409
thm trm5_lts_bn
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   410
thm trm5_lts_perm
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   411
thm trm5_lts_induct
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   412
thm trm5_lts_distinct
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   413
1285
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diff changeset
   414
(* example from my PHD *)
e3ac56d3b7af added example from my phd
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parents: 1284
diff changeset
   415
e3ac56d3b7af added example from my phd
Christian Urban <urbanc@in.tum.de>
parents: 1284
diff changeset
   416
atom_decl coname
1272
6d140b2c751f added ott-example about Leroy96
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parents: 1265
diff changeset
   417
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   418
nominal_datatype phd =
1290
a7e7ffb7f362 modified for new binding format - hope it is the intended one
Christian Urban <urbanc@in.tum.de>
parents: 1287
diff changeset
   419
   Ax "name" "coname"
a7e7ffb7f362 modified for new binding format - hope it is the intended one
Christian Urban <urbanc@in.tum.de>
parents: 1287
diff changeset
   420
|  Cut n::"coname" t1::"phd" c::"coname" t2::"phd"              bind n in t1, bind c in t2
a7e7ffb7f362 modified for new binding format - hope it is the intended one
Christian Urban <urbanc@in.tum.de>
parents: 1287
diff changeset
   421
|  AndR c1::"coname" t1::"phd" c2::"coname" t2::"phd" "coname"  bind c1 in t1, bind c2 in t2
a7e7ffb7f362 modified for new binding format - hope it is the intended one
Christian Urban <urbanc@in.tum.de>
parents: 1287
diff changeset
   422
|  AndL1 n::"name" t::"phd" "name"                              bind n in t
a7e7ffb7f362 modified for new binding format - hope it is the intended one
Christian Urban <urbanc@in.tum.de>
parents: 1287
diff changeset
   423
|  AndL2 n::"name" t::"phd" "name"                              bind n in t
a7e7ffb7f362 modified for new binding format - hope it is the intended one
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parents: 1287
diff changeset
   424
|  ImpL c::"coname" t1::"phd" n::"name" t2::"phd" "name"        bind c in t1, bind n in t2
1319
d793ce9cd06f potential problem with the phd-example, where two permutations are generated, but only one is used
Christian Urban <urbanc@in.tum.de>
parents: 1313
diff changeset
   425
|  ImpR c::"coname" n::"name" t::"phd" "coname"                 bind n in t, bind c in t
d793ce9cd06f potential problem with the phd-example, where two permutations are generated, but only one is used
Christian Urban <urbanc@in.tum.de>
parents: 1313
diff changeset
   426
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   427
thm phd_fv
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   428
thm phd_inject
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   429
thm phd_bn
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   430
thm phd_perm
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   431
thm phd_induct
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   432
thm phd_distinct
1285
e3ac56d3b7af added example from my phd
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parents: 1284
diff changeset
   433
e3ac56d3b7af added example from my phd
Christian Urban <urbanc@in.tum.de>
parents: 1284
diff changeset
   434
(* example form Leroy 96 about modules; OTT *)
1284
212f3ab40cc2 streamlined parser
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parents: 1283
diff changeset
   435
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   436
nominal_datatype mexp =
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   437
  Acc "path"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   438
| Stru "body"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   439
| Funct x::"name" "sexp" m::"mexp"    bind x in m
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   440
| FApp "mexp" "path"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   441
| Ascr "mexp" "sexp"
1272
6d140b2c751f added ott-example about Leroy96
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parents: 1265
diff changeset
   442
and body =
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   443
  Empty
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   444
| Seq c::defn d::"body"     bind "cbinders c" in d
1398
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   445
and defn =
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   446
  Type "name" "tyty"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   447
| Dty "name"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   448
| DStru "name" "mexp"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   449
| Val "name" "trmtrm"
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   450
and sexp =
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   451
  Sig sbody
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   452
| SFunc "name" "sexp" "sexp"
1398
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   453
and sbody =
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   454
  SEmpty
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   455
| SSeq C::spec D::sbody    bind "Cbinders C" in D
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   456
and spec =
1398
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   457
  Type1 "name"
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   458
| Type2 "name" "tyty"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   459
| SStru "name" "sexp"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   460
| SVal "name" "tyty"
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   461
and tyty =
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   462
  Tyref1 "name"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   463
| Tyref2 "path" "tyty"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   464
| Fun "tyty" "tyty"
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   465
and path =
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   466
  Sref1 "name"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   467
| Sref2 "path" "name"
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   468
and trmtrm =
1296
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   469
  Tref1 "name"
790940e90db2 some tuning
Christian Urban <urbanc@in.tum.de>
parents: 1295
diff changeset
   470
| Tref2 "path" "name"
1340
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   471
| Lam' v::"name" "tyty" M::"trmtrm"  bind v in M
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   472
| App' "trmtrm" "trmtrm"
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   473
| Let' "body" "trmtrm"
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   474
binder
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   475
    cbinders :: "defn \<Rightarrow> atom set"
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   476
and Cbinders :: "spec \<Rightarrow> atom set"
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   477
where
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   478
  "cbinders (Type t T) = {atom t}"
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   479
| "cbinders (Dty t) = {atom t}"
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   480
| "cbinders (DStru x s) = {atom x}"
1396
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   481
| "cbinders (Val v M) = {atom v}"
1272
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   482
| "Cbinders (Type1 t) = {atom t}"
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   483
| "Cbinders (Type2 t T) = {atom t}"
6d140b2c751f added ott-example about Leroy96
Christian Urban <urbanc@in.tum.de>
parents: 1265
diff changeset
   484
| "Cbinders (SStru x S) = {atom x}"
1396
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   485
| "Cbinders (SVal v T) = {atom v}"
1265
fc8f5897b00a first attempt to make sense out of the core-haskell definition
Christian Urban <urbanc@in.tum.de>
parents: 1261
diff changeset
   486
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   487
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_fv
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   488
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_inject
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   489
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_bn
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   490
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_perm
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   491
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_induct
1447
378b8c791de8 derive "inducts" from "induct" instead of lifting again is much faster.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1445
diff changeset
   492
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_inducts
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   493
thm mexp_body_defn_sexp_sbody_spec_tyty_path_trmtrm_distinct
1392
baa67b07f436 parser produces ordered bn-fun information
Christian Urban <urbanc@in.tum.de>
parents: 1380
diff changeset
   494
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   495
(* example 3 from Peter Sewell's bestiary *)
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   496
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   497
nominal_datatype exp =
1340
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   498
  VarP "name"
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   499
| AppP "exp" "exp"
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   500
| LamP x::"name" e::"exp" bind x in e
1396
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   501
| LetP x::"name" p::"pat3" e1::"exp" e2::"exp" bind x in e2, bind "bp' p" in e1
1378
5c6c950812b1 All examples should work.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1368
diff changeset
   502
and pat3 =
1319
d793ce9cd06f potential problem with the phd-example, where two permutations are generated, but only one is used
Christian Urban <urbanc@in.tum.de>
parents: 1313
diff changeset
   503
  PVar "name"
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   504
| PUnit
1378
5c6c950812b1 All examples should work.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1368
diff changeset
   505
| PPair "pat3" "pat3"
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   506
binder
1396
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   507
  bp' :: "pat3 \<Rightarrow> atom set"
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   508
where
1396
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   509
  "bp' (PVar x) = {atom x}"
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   510
| "bp' (PUnit) = {}"
08294f4d6c08 Linked parser to fv and alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1392
diff changeset
   511
| "bp' (PPair p1 p2) = bp' p1 \<union> bp' p2"
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   512
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   513
thm exp_pat3_fv
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   514
thm exp_pat3_inject
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   515
thm exp_pat3_bn
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   516
thm exp_pat3_perm
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   517
thm exp_pat3_induct
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   518
thm exp_pat3_distinct
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   519
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   520
(* example 6 from Peter Sewell's bestiary *)
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   521
nominal_datatype exp6 =
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   522
  EVar name
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   523
| EPair exp6 exp6
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   524
| ELetRec x::name p::pat6 e1::exp6 e2::exp6 bind x in e1, bind x in e2, bind "bp6 p" in e1
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   525
and pat6 =
1340
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   526
  PVar' name
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   527
| PUnit'
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   528
| PPair' pat6 pat6
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   529
binder
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   530
  bp6 :: "pat6 \<Rightarrow> atom set"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   531
where
1340
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   532
  "bp6 (PVar' x) = {atom x}"
f201eb6acafc Lift BV,FV,Permutations and injection :).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1338
diff changeset
   533
| "bp6 (PUnit') = {}"
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   534
| "bp6 (PPair' p1 p2) = bp6 p1 \<union> bp6 p2"
1418
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   535
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   536
thm exp6_pat6_fv
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   537
thm exp6_pat6_inject
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   538
thm exp6_pat6_bn
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   539
thm exp6_pat6_perm
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   540
thm exp6_pat6_induct
632b08744613 With the 4 cheats, all examples fully lift.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1416
diff changeset
   541
thm exp6_pat6_distinct
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   542
1398
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   543
(* THE REST ARE NOT SUPPOSED TO WORK YET *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   544
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   545
(* example 7 from Peter Sewell's bestiary *)
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   546
nominal_datatype exp7 =
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   547
  EVar name
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   548
| EUnit
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   549
| EPair exp7 exp7
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   550
| ELetRec l::lrbs e::exp7 bind "b7s l" in e, bind "b7s l" in l
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   551
and lrb =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   552
  Assign name exp7
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   553
and lrbs =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   554
  Single lrb
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   555
| More lrb lrbs
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   556
binder
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   557
  b7 :: "lrb \<Rightarrow> atom set" and
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   558
  b7s :: "lrbs \<Rightarrow> atom set"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   559
where
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   560
  "b7 (Assign x e) = {atom x}"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   561
| "b7s (Single a) = b7 a"
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   562
| "b7s (More a as) = (b7 a) \<union> (b7s as)"
1361
1e811e3424f3 With restricted_nominal=1, exp7 and exp8 work. Not sure about proving bn_rsp there.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1355
diff changeset
   563
thm alpha_exp7_raw_alpha_lrb_raw_alpha_lrbs_raw.intros
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   564
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   565
(* example 8 from Peter Sewell's bestiary *)
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   566
nominal_datatype exp8 =
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   567
  EVar name
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   568
| EUnit
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   569
| EPair exp8 exp8
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   570
| ELetRec l::lrbs8 e::exp8 bind "b_lrbs8 l" in e, bind "b_lrbs8 l" in l
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   571
and fnclause =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   572
  K x::name p::pat8 e::exp8 bind "b_pat p" in e
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   573
and fnclauses =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   574
  S fnclause
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   575
| ORs fnclause fnclauses
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   576
and lrb8 =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   577
  Clause fnclauses
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   578
and lrbs8 =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   579
  Single lrb8
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   580
| More lrb8 lrbs8
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   581
and pat8 =
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   582
  PVar name
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   583
| PUnit
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   584
| PPair pat8 pat8
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   585
binder
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   586
  b_lrbs8 :: "lrbs8 \<Rightarrow> atom set" and
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   587
  b_pat :: "pat8 \<Rightarrow> atom set" and
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   588
  b_fnclauses :: "fnclauses \<Rightarrow> atom set" and
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   589
  b_fnclause :: "fnclause \<Rightarrow> atom set" and
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   590
  b_lrb8 :: "lrb8 \<Rightarrow> atom set"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   591
where
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   592
  "b_lrbs8 (Single l) = b_lrb8 l"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   593
| "b_lrbs8 (More l ls) = b_lrb8 l \<union> b_lrbs8 ls"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   594
| "b_pat (PVar x) = {atom x}"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   595
| "b_pat (PUnit) = {}"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   596
| "b_pat (PPair p1 p2) = b_pat p1 \<union> b_pat p2"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   597
| "b_fnclauses (S fc) = (b_fnclause fc)"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   598
| "b_fnclauses (ORs fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   599
| "b_lrb8 (Clause fcs) = (b_fnclauses fcs)"
1341
c25f797c7e6e Added lifting of pseudo-injectivity, commented out the code again and enabled the weird examples.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1340
diff changeset
   600
| "b_fnclause (K x pat exp8) = {atom x}"
1361
1e811e3424f3 With restricted_nominal=1, exp7 and exp8 work. Not sure about proving bn_rsp there.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1355
diff changeset
   601
thm alpha_exp8_raw_alpha_fnclause_raw_alpha_fnclauses_raw_alpha_lrb8_raw_alpha_lrbs8_raw_alpha_pat8_raw.intros
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   602
1398
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   603
(* example 4 from Terms.thy *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   604
(* fv_eqvt does not work, we need to repaire defined permute functions
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   605
   defined fv and defined alpha... *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   606
nominal_datatype trm4 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   607
  Vr4 "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   608
| Ap4 "trm4" "trm4 list"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   609
| Lm4 x::"name" t::"trm4"  bind x in t
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   610
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   611
thm alpha_trm4_raw_alpha_trm4_raw_list.intros[no_vars]
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   612
thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   613
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   614
(* core haskell *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   615
atom_decl var
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   616
atom_decl tvar
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   617
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   618
(* there are types, coercion types and regular types *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   619
nominal_datatype tkind =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   620
  KStar
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   621
| KFun "tkind" "tkind"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   622
and ckind =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   623
  CKEq "ty" "ty"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   624
and ty =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   625
  TVar "tvar"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   626
| TC "string"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   627
| TApp "ty" "ty"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   628
| TFun "string" "ty list"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   629
| TAll tv::"tvar" "tkind" T::"ty"  bind tv in T
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   630
| TEq "ty" "ty" "ty"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   631
and co =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   632
  CC "string"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   633
| CApp "co" "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   634
| CFun "string" "co list"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   635
| CAll tv::"tvar" "ckind" C::"co"  bind tv in C
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   636
| CEq "co" "co" "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   637
| CSym "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   638
| CCir "co" "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   639
| CLeft "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   640
| CRight "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   641
| CSim "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   642
| CRightc "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   643
| CLeftc "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   644
| CCoe "co" "co"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   645
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   646
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   647
typedecl ty --"hack since ty is not yet defined"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   648
typedecl kind
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   649
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   650
instance ty and kind:: pt
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   651
sorry
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   652
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   653
abbreviation
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   654
  "atoms A \<equiv> atom ` A"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   655
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   656
nominal_datatype trm =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   657
  Var "var"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   658
| C "string"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   659
| LAM tv::"tvar" "kind" t::"trm"   bind tv in t
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   660
| APP "trm" "ty"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   661
| Lam v::"var" "ty" t::"trm"       bind v in t
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   662
| App "trm" "trm"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   663
| Let x::"var" "ty" "trm" t::"trm" bind x in t
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   664
| Case "trm" "assoc list"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   665
| Cast "trm" "ty"                   --"ty is supposed to be a coercion type only"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   666
and assoc =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   667
  A p::"pat" t::"trm" bind "bv p" in t
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   668
and pat =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   669
  K "string" "(tvar \<times> kind) list" "(var \<times> ty) list"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   670
binder
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   671
 bv :: "pat \<Rightarrow> atom set"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   672
where
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   673
 "bv (K s ts vs) = (atoms (set (map fst ts))) \<union> (atoms (set (map fst vs)))"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   674
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   675
(*
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   676
compat (K s ts vs) pi (K s' ts' vs') ==
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   677
  s = s' &
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   678
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   679
*)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   680
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   681
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   682
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   683
text {* weirdo example from Peter Sewell's bestiary *}
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   684
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   685
nominal_datatype weird =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   686
  WBind x::"name" y::"name" p1::"weird" p2::"weird" p3::"weird"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   687
    bind x in p1, bind x in p2, bind y in p2, bind y in p3
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   688
| WV "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   689
| WP "weird" "weird"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   690
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   691
thm permute_weird_raw.simps[no_vars]
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   692
thm alpha_weird_raw.intros[no_vars]
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   693
thm fv_weird_raw.simps[no_vars]
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   694
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   695
(* example 6 from Terms.thy *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   696
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   697
(* BV is not respectful, needs to fail*)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   698
nominal_datatype trm6 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   699
  Vr6 "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   700
| Lm6 x::"name" t::"trm6"         bind x in t
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   701
| Lt6 left::"trm6" right::"trm6"  bind "bv6 left" in right
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   702
binder
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   703
  bv6
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   704
where
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   705
  "bv6 (Vr6 n) = {}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   706
| "bv6 (Lm6 n t) = {atom n} \<union> bv6 t"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   707
| "bv6 (Lt6 l r) = bv6 l \<union> bv6 r"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   708
(* example 7 from Terms.thy *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   709
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   710
(* BV is not respectful, needs to fail*)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   711
nominal_datatype trm7 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   712
  Vr7 "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   713
| Lm7 l::"name" r::"trm7"   bind l in r
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   714
| Lt7 l::"trm7" r::"trm7"   bind "bv7 l" in r
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   715
binder
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   716
  bv7
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   717
where
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   718
  "bv7 (Vr7 n) = {atom n}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   719
| "bv7 (Lm7 n t) = bv7 t - {atom n}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   720
| "bv7 (Lt7 l r) = bv7 l \<union> bv7 r"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   721
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   722
(* example 8 from Terms.thy *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   723
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   724
(* Binding in a term under a bn, needs to fail *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   725
nominal_datatype foo8 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   726
  Foo0 "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   727
| Foo1 b::"bar8" f::"foo8" bind "bv8 b" in f --"check fo error if this is called foo"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   728
and bar8 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   729
  Bar0 "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   730
| Bar1 "name" s::"name" b::"bar8" bind s in b
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   731
binder
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   732
  bv8
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   733
where
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   734
  "bv8 (Bar0 x) = {}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   735
| "bv8 (Bar1 v x b) = {atom v}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   736
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   737
(* example 9 from Terms.thy *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   738
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   739
(* BV is not respectful, needs to fail*)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   740
nominal_datatype lam9 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   741
  Var9 "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   742
| Lam9 n::"name" l::"lam9" bind n in l
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   743
and bla9 =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   744
  Bla9 f::"lam9" s::"lam9" bind "bv9 f" in s
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   745
binder
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   746
  bv9
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   747
where
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   748
  "bv9 (Var9 x) = {}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   749
| "bv9 (Lam9 x b) = {atom x}"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   750
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   751
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   752
(* Type schemes with separate datatypes *)
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   753
nominal_datatype t =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   754
  Var "name"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   755
| Fun "t" "t"
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   756
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   757
nominal_datatype tyS =
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   758
  All xs::"name list" ty::"t_raw" bind xs in ty
1f3c01345c9e Reordered examples in Test.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents: 1396
diff changeset
   759
1312
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   760
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   761
b0eae8c93314 added some more examples from Peter Sewell's bestiary
Christian Urban <urbanc@in.tum.de>
parents: 1304
diff changeset
   762
b0eae8c93314 added some more examples from Peter Sewell's bestiary
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(* example 9 from Peter Sewell's bestiary *)
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(* run out of steam at the moment *)
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fc8f5897b00a first attempt to make sense out of the core-haskell definition
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end
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