| author | Cezary Kaliszyk <kaliszyk@in.tum.de> |
| Fri, 19 Aug 2011 12:49:38 +0900 (2011-08-19) | |
| changeset 2998 | f0fab367453a |
| parent 2984 | 1b39ba5db2c1 |
| child 3089 | 9bcf02a6eea9 |
| permissions | -rw-r--r-- |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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1 |
header {* The Call-by-Value Lambda Calculus *}
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theory Lt |
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imports "../../Nominal2" |
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begin |
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5635a968fd3f
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5 |
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5635a968fd3f
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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atom_decl name |
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7 |
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5635a968fd3f
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nominal_datatype lt = |
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5635a968fd3f
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Var name ("_~" [150] 149)
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| Lam x::"name" t::"lt" binds x in t |
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| App lt lt (infixl "$" 100) |
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5635a968fd3f
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nominal_primrec |
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subst :: "lt \<Rightarrow> name \<Rightarrow> lt \<Rightarrow> lt" ("_ [_ ::= _]" [90, 90, 90] 90)
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where |
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"(Var x)[y ::= s] = (if x = y then s else (Var x))" |
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| "(App t1 t2)[y ::= s] = App (t1[y ::= s]) (t2[y ::= s])" |
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| "atom x \<sharp> (y, s) \<Longrightarrow> (Lam x t)[y ::= s] = Lam x (t[y ::= s])" |
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unfolding eqvt_def subst_graph_def |
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apply (rule, perm_simp, rule) |
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apply(rule TrueI) |
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apply(auto simp add: lt.distinct lt.eq_iff) |
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apply(rule_tac y="a" and c="(aa, b)" in lt.strong_exhaust) |
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apply blast |
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f0fab367453a
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apply(simp_all add: fresh_star_def fresh_Pair_elim) |
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apply blast |
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f0fab367453a
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apply (erule_tac c="(ya,sa)" in Abs_lst1_fcb2) |
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apply(simp_all add: Abs_fresh_iff) |
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f0fab367453a
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apply(simp add: fresh_star_def fresh_Pair) |
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f0fab367453a
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apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)+ |
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done |
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update to 'termination (eqvt)'.
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termination (eqvt) by lexicographic_order |
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5635a968fd3f
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lemma forget[simp]: |
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shows "atom x \<sharp> M \<Longrightarrow> M[x ::= s] = M" |
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parents:
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by (nominal_induct M avoiding: x s rule: lt.strong_induct) |
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5635a968fd3f
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Cezary Kaliszyk <kaliszyk@in.tum.de>
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(auto simp add: lt.fresh fresh_at_base) |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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parents:
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lemma [simp]: "supp (M[x ::= V]) <= (supp(M) - {atom x}) Un (supp V)"
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parents:
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by (nominal_induct M avoiding: x V rule: lt.strong_induct) |
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5635a968fd3f
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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(auto simp add: lt.supp supp_at_base, blast, blast) |
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5635a968fd3f
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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2998
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Use same constructor names as Lambda, remove copies of FCB, remove [eqvt].
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2984
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nominal_primrec |
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parents:
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isValue:: "lt => bool" |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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where |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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"isValue (Var x) = True" |
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| "isValue (Lam y N) = True" |
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| "isValue (A $ B) = False" |
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5635a968fd3f
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unfolding eqvt_def isValue_graph_def |
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5635a968fd3f
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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by (perm_simp, auto) |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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(erule lt.exhaust, auto) |
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5635a968fd3f
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parents:
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termination (eqvt) |
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1b39ba5db2c1
update to 'termination (eqvt)'.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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by (relation "measure size") (simp_all) |
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5635a968fd3f
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inductive |
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parents:
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eval :: "[lt, lt] \<Rightarrow> bool" (" _ \<longrightarrow>\<^isub>\<beta> _" [80,80] 80)
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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where |
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2998
f0fab367453a
Use same constructor names as Lambda, remove copies of FCB, remove [eqvt].
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parents:
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evbeta: "\<lbrakk>atom x\<sharp>V; isValue V\<rbrakk> \<Longrightarrow> ((Lam x M) $ V) \<longrightarrow>\<^isub>\<beta> (M[x ::= V])" |
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parents:
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| ev1: "\<lbrakk>isValue V; M \<longrightarrow>\<^isub>\<beta> M' \<rbrakk> \<Longrightarrow> (V $ M) \<longrightarrow>\<^isub>\<beta> (V $ M')" |
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parents:
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| ev2: "M \<longrightarrow>\<^isub>\<beta> M' \<Longrightarrow> (M $ N) \<longrightarrow>\<^isub>\<beta> (M' $ N)" |
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parents:
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parents:
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equivariance eval |
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parents:
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nominal_inductive eval |
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done |
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parents:
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68 |
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5635a968fd3f
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parents:
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(*lemmas [simp] = lt.supp(2)*) |
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parents:
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lemma closedev1: assumes "s \<longrightarrow>\<^isub>\<beta> t" |
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parents:
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shows "supp t <= supp s" |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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using assms |
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parents:
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by (induct, auto simp add: lt.supp) |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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75 |
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5635a968fd3f
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parents:
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parents:
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lemma [simp]: "~ ((Lam x M) \<longrightarrow>\<^isub>\<beta> N)" |
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parents:
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by (rule, erule eval.cases, simp_all) |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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79 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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lemma [simp]: assumes "M \<longrightarrow>\<^isub>\<beta> N" shows "~ isValue M" |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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81 |
using assms |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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82 |
by (cases, auto) |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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83 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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84 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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85 |
inductive |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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86 |
eval_star :: "[lt, lt] \<Rightarrow> bool" (" _ \<longrightarrow>\<^isub>\<beta>\<^sup>* _" [80,80] 80)
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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87 |
where |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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88 |
evs1: "M \<longrightarrow>\<^isub>\<beta>\<^sup>* M" |
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5635a968fd3f
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89 |
| evs2: "\<lbrakk>M \<longrightarrow>\<^isub>\<beta> M'; M' \<longrightarrow>\<^isub>\<beta>\<^sup>* M'' \<rbrakk> \<Longrightarrow> M \<longrightarrow>\<^isub>\<beta>\<^sup>* M''" |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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90 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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91 |
lemma eval_evs: assumes *: "M \<longrightarrow>\<^isub>\<beta> M'" shows "M \<longrightarrow>\<^isub>\<beta>\<^sup>* M'" |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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92 |
by (rule evs2, rule *, rule evs1) |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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93 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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94 |
lemma eval_trans[trans]: |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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95 |
assumes "M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M2" |
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parents:
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96 |
and "M2 \<longrightarrow>\<^isub>\<beta>\<^sup>* M3" |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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97 |
shows "M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M3" |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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98 |
using assms |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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99 |
by (induct, auto intro: evs2) |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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100 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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101 |
lemma evs3[rule_format]: assumes "M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M2" |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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102 |
shows "M2 \<longrightarrow>\<^isub>\<beta> M3 \<longrightarrow> M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M3" |
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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103 |
using assms |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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104 |
by (induct, auto intro: eval_evs evs2) |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
105 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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106 |
equivariance eval_star |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
107 |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
108 |
lemma evbeta': |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
109 |
fixes x :: name |
|
2998
f0fab367453a
Use same constructor names as Lambda, remove copies of FCB, remove [eqvt].
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2984
diff
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110 |
assumes "isValue V" and "atom x\<sharp>V" and "N = (M[x ::= V])" |
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f0fab367453a
Use same constructor names as Lambda, remove copies of FCB, remove [eqvt].
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2984
diff
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|
111 |
shows "((Lam x M) $ V) \<longrightarrow>\<^isub>\<beta>\<^sup>* N" |
|
2861
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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112 |
using assms by simp (rule evs2, rule evbeta, simp_all add: evs1) |
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parents:
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113 |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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114 |
end |
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5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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|
115 |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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parents:
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|
116 |
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Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
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117 |