src/HOL/Bali/AxSound.thy
author wenzelm
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explicit checks stable_finished_theory/stable_command allow parallel asynchronous command transactions; tuned;
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(*  Title:      HOL/Bali/AxSound.thy
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    Author:     David von Oheimb and Norbert Schirmer
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*)
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header {* Soundness proof for Axiomatic semantics of Java expressions and 
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          statements
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       *}
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theory AxSound imports AxSem begin
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section "validity"
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definition
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  triple_valid2 :: "prog \<Rightarrow> nat \<Rightarrow> 'a triple \<Rightarrow> bool"  ("_\<Turnstile>_\<Colon>_"[61,0, 58] 57)
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  where
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    "G\<Turnstile>n\<Colon>t =
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      (case t of {P} t\<succ> {Q} \<Rightarrow>
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        \<forall>Y s Z. P Y s Z \<longrightarrow> (\<forall>L. s\<Colon>\<preceq>(G,L)
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          \<longrightarrow> (\<forall>T C A. (normal s \<longrightarrow> (\<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>t\<Colon>T \<and>
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            \<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>dom (locals (store s))\<guillemotright>t\<guillemotright>A)) \<longrightarrow>
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             (\<forall>Y' s'. G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (Y',s') \<longrightarrow> Q Y' s' Z \<and> s'\<Colon>\<preceq>(G,L)))))"
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text {* This definition differs from the ordinary  @{text triple_valid_def} 
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manly in the conclusion: We also ensures conformance of the result state. So
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we don't have to apply the type soundness lemma all the time during
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induction. This definition is only introduced for the soundness
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proof of the axiomatic semantics, in the end we will conclude to 
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the ordinary definition.
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*}
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definition
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  ax_valids2 :: "prog \<Rightarrow> 'a triples \<Rightarrow> 'a triples \<Rightarrow> bool"  ("_,_|\<Turnstile>\<Colon>_" [61,58,58] 57)
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  where "G,A|\<Turnstile>\<Colon>ts = (\<forall>n. (\<forall>t\<in>A. G\<Turnstile>n\<Colon>t) \<longrightarrow> (\<forall>t\<in>ts. G\<Turnstile>n\<Colon>t))"
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lemma triple_valid2_def2: "G\<Turnstile>n\<Colon>{P} t\<succ> {Q} =  
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 (\<forall>Y s Z. P Y s Z \<longrightarrow> (\<forall>Y' s'. G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (Y',s')\<longrightarrow>  
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  (\<forall>L. s\<Colon>\<preceq>(G,L) \<longrightarrow> (\<forall>T C A. (normal s \<longrightarrow> (\<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>t\<Colon>T \<and> 
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                            \<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>dom (locals (store s))\<guillemotright>t\<guillemotright>A)) \<longrightarrow>
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  Q Y' s' Z \<and> s'\<Colon>\<preceq>(G,L)))))"
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apply (unfold triple_valid2_def)
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apply (simp (no_asm) add: split_paired_All)
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apply blast
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done
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lemma triple_valid2_eq [rule_format (no_asm)]: 
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  "wf_prog G ==> triple_valid2 G = triple_valid G"
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apply (rule ext)
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apply (rule ext)
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apply (rule triple.induct)
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apply (simp (no_asm) add: triple_valid_def2 triple_valid2_def2)
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apply (rule iffI)
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apply  fast
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apply clarify
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apply (tactic "smp_tac 3 1")
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apply (case_tac "normal s")
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apply  clarsimp
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apply  (elim conjE impE)
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apply    blast
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apply    (tactic "smp_tac 2 1")
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apply    (drule evaln_eval)
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apply    (drule (1) eval_type_sound [THEN conjunct1],simp, assumption+)
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apply    simp
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apply    clarsimp
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done
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lemma ax_valids2_eq: "wf_prog G \<Longrightarrow> G,A|\<Turnstile>\<Colon>ts = G,A|\<Turnstile>ts"
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apply (unfold ax_valids_def ax_valids2_def)
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apply (force simp add: triple_valid2_eq)
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done
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lemma triple_valid2_Suc [rule_format (no_asm)]: "G\<Turnstile>Suc n\<Colon>t \<longrightarrow> G\<Turnstile>n\<Colon>t"
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apply (induct_tac "t")
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apply (subst triple_valid2_def2)
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apply (subst triple_valid2_def2)
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apply (fast intro: evaln_nonstrict_Suc)
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done
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lemma Methd_triple_valid2_0: "G\<Turnstile>0\<Colon>{Normal P} Methd C sig-\<succ> {Q}"
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by (auto elim!: evaln_elim_cases simp add: triple_valid2_def2)
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lemma Methd_triple_valid2_SucI: 
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"\<lbrakk>G\<Turnstile>n\<Colon>{Normal P} body G C sig-\<succ>{Q}\<rbrakk> 
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  \<Longrightarrow> G\<Turnstile>Suc n\<Colon>{Normal P} Methd C sig-\<succ> {Q}"
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apply (simp (no_asm_use) add: triple_valid2_def2)
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apply (intro strip, tactic "smp_tac 3 1", clarify)
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apply (erule wt_elim_cases, erule da_elim_cases, erule evaln_elim_cases)
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apply (unfold body_def Let_def)
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apply (clarsimp simp add: inj_term_simps)
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apply blast
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done
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lemma triples_valid2_Suc: 
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 "Ball ts (triple_valid2 G (Suc n)) \<Longrightarrow> Ball ts (triple_valid2 G n)"
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apply (fast intro: triple_valid2_Suc)
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done
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lemma "G|\<Turnstile>n:insert t A = (G\<Turnstile>n:t \<and> G|\<Turnstile>n:A)"
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oops
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section "soundness"
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lemma Methd_sound: 
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  assumes recursive: "G,A\<union>  {{P} Methd-\<succ> {Q} | ms}|\<Turnstile>\<Colon>{{P} body G-\<succ> {Q} | ms}"
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  shows "G,A|\<Turnstile>\<Colon>{{P} Methd-\<succ> {Q} | ms}"
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proof -
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  {
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    fix n
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    assume recursive: "\<And> n. \<forall>t\<in>(A \<union> {{P} Methd-\<succ> {Q} | ms}). G\<Turnstile>n\<Colon>t
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                              \<Longrightarrow>  \<forall>t\<in>{{P} body G-\<succ> {Q} | ms}.  G\<Turnstile>n\<Colon>t"
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    have "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t \<Longrightarrow> \<forall>t\<in>{{P} Methd-\<succ> {Q} | ms}.  G\<Turnstile>n\<Colon>t"
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    proof (induct n)
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      case 0
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      show "\<forall>t\<in>{{P} Methd-\<succ> {Q} | ms}.  G\<Turnstile>0\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   117
      proof -
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   118
        {
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   119
          fix C sig
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   120
          assume "(C,sig) \<in> ms" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   121
          have "G\<Turnstile>0\<Colon>{Normal (P C sig)} Methd C sig-\<succ> {Q C sig}"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   122
            by (rule Methd_triple_valid2_0)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   123
        }
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   124
        thus ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   125
          by (simp add: mtriples_def split_def)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   126
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   127
    next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   128
      case (Suc m)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   129
      note hyp = `\<forall>t\<in>A. G\<Turnstile>m\<Colon>t \<Longrightarrow> \<forall>t\<in>{{P} Methd-\<succ> {Q} | ms}.  G\<Turnstile>m\<Colon>t`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   130
      note prem = `\<forall>t\<in>A. G\<Turnstile>Suc m\<Colon>t`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   131
      show "\<forall>t\<in>{{P} Methd-\<succ> {Q} | ms}.  G\<Turnstile>Suc m\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   132
      proof -
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   133
        {
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   134
          fix C sig
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   135
          assume m: "(C,sig) \<in> ms" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   136
          have "G\<Turnstile>Suc m\<Colon>{Normal (P C sig)} Methd C sig-\<succ> {Q C sig}"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   137
          proof -
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   138
            from prem have prem_m: "\<forall>t\<in>A. G\<Turnstile>m\<Colon>t"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   139
              by (rule triples_valid2_Suc)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   140
            hence "\<forall>t\<in>{{P} Methd-\<succ> {Q} | ms}.  G\<Turnstile>m\<Colon>t"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   141
              by (rule hyp)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   142
            with prem_m
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   143
            have "\<forall>t\<in>(A \<union> {{P} Methd-\<succ> {Q} | ms}). G\<Turnstile>m\<Colon>t"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   144
              by (simp add: ball_Un)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   145
            hence "\<forall>t\<in>{{P} body G-\<succ> {Q} | ms}.  G\<Turnstile>m\<Colon>t"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   146
              by (rule recursive)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   147
            with m have "G\<Turnstile>m\<Colon>{Normal (P C sig)} body G C sig-\<succ> {Q C sig}"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   148
              by (auto simp add: mtriples_def split_def)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   149
            thus ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   150
              by (rule Methd_triple_valid2_SucI)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   151
          qed
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   152
        }
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   153
        thus ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   154
          by (simp add: mtriples_def split_def)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   155
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   156
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   157
  }
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   158
  with recursive show ?thesis
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   159
    by (unfold ax_valids2_def) blast
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   160
qed
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   161
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   162
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   163
lemma valids2_inductI: "\<forall>s t n Y' s'. G\<turnstile>s\<midarrow>t\<succ>\<midarrow>n\<rightarrow> (Y',s') \<longrightarrow> t = c \<longrightarrow>    
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   164
  Ball A (triple_valid2 G n) \<longrightarrow> (\<forall>Y Z. P Y s Z \<longrightarrow>  
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   165
  (\<forall>L. s\<Colon>\<preceq>(G,L) \<longrightarrow> 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   166
    (\<forall>T C A. (normal s \<longrightarrow> (\<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>t\<Colon>T) \<and> 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   167
                            \<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>dom (locals (store s))\<guillemotright>t\<guillemotright>A) \<longrightarrow>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   168
    Q Y' s' Z \<and> s'\<Colon>\<preceq>(G, L)))) \<Longrightarrow>  
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   169
  G,A|\<Turnstile>\<Colon>{ {P} c\<succ> {Q}}"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   170
apply (simp (no_asm) add: ax_valids2_def triple_valid2_def2)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   171
apply clarsimp
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   172
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   173
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   174
lemma da_good_approx_evalnE [consumes 4]:
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   175
  assumes evaln: "G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v, s1)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   176
     and     wt: "\<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>t\<Colon>T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   177
     and     da: "\<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>t\<guillemotright> A"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   178
     and     wf: "wf_prog G"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   179
     and   elim: "\<lbrakk>normal s1 \<Longrightarrow> nrm A \<subseteq> dom (locals (store s1));
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   180
                  \<And> l. \<lbrakk>abrupt s1 = Some (Jump (Break l)); normal s0\<rbrakk>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   181
                        \<Longrightarrow> brk A l \<subseteq> dom (locals (store s1));
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   182
                   \<lbrakk>abrupt s1 = Some (Jump Ret);normal s0\<rbrakk>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   183
                   \<Longrightarrow>Result \<in> dom (locals (store s1))
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   184
                  \<rbrakk> \<Longrightarrow> P"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   185
  shows "P"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   186
proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   187
  from evaln have "G\<turnstile>s0 \<midarrow>t\<succ>\<rightarrow> (v, s1)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   188
    by (rule evaln_eval)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   189
  from this wt da wf elim show P
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   190
    by (rule da_good_approxE') iprover+
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   191
qed
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   192
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   193
lemma validI: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   194
   assumes I: "\<And> n s0 L accC T C v s1 Y Z.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   195
               \<lbrakk>\<forall>t\<in>A. G\<Turnstile>n\<Colon>t; s0\<Colon>\<preceq>(G,L); 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   196
               normal s0 \<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>T;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   197
               normal s0 \<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>t\<guillemotright>C;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   198
               G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s1); P Y s0 Z\<rbrakk> \<Longrightarrow> Q v s1 Z \<and> s1\<Colon>\<preceq>(G,L)" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   199
  shows "G,A|\<Turnstile>\<Colon>{ {P} t\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   200
apply (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   201
apply (intro allI impI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   202
apply (case_tac "normal s")
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   203
apply   clarsimp 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   204
apply   (rule I,(assumption|simp)+)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   205
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   206
apply   (rule I,auto)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   207
done
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   208
  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   209
24019
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23366
diff changeset
   210
declare [[simproc add: wt_expr wt_var wt_exprs wt_stmt]]
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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   211
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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   212
lemma valid_stmtI: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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   assumes I: "\<And> n s0 L accC C s1 Y Z.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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             \<lbrakk>\<forall>t\<in>A. G\<Turnstile>n\<Colon>t; s0\<Colon>\<preceq>(G,L); 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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   215
              normal s0\<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>c\<Colon>\<surd>;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
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   216
              normal s0\<Longrightarrow>\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>c\<rangle>\<^sub>s\<guillemotright>C;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
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   217
              G\<turnstile>s0 \<midarrow>c\<midarrow>n\<rightarrow> s1; P Y s0 Z\<rbrakk> \<Longrightarrow> Q \<diamondsuit> s1 Z \<and> s1\<Colon>\<preceq>(G,L)" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
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   218
  shows "G,A|\<Turnstile>\<Colon>{ {P} \<langle>c\<rangle>\<^sub>s\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   219
apply (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   220
apply (intro allI impI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   221
apply (case_tac "normal s")
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   222
apply   clarsimp 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   223
apply   (rule I,(assumption|simp)+)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   224
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   225
apply   (rule I,auto)
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   226
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   227
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   228
lemma valid_stmt_NormalI: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   229
   assumes I: "\<And> n s0 L accC C s1 Y Z.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   230
               \<lbrakk>\<forall>t\<in>A. G\<Turnstile>n\<Colon>t; s0\<Colon>\<preceq>(G,L); normal s0; \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>c\<Colon>\<surd>;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   231
               \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>c\<rangle>\<^sub>s\<guillemotright>C;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   232
               G\<turnstile>s0 \<midarrow>c\<midarrow>n\<rightarrow> s1; (Normal P) Y s0 Z\<rbrakk> \<Longrightarrow> Q \<diamondsuit> s1 Z \<and> s1\<Colon>\<preceq>(G,L)" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   233
  shows "G,A|\<Turnstile>\<Colon>{ {Normal P} \<langle>c\<rangle>\<^sub>s\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   234
apply (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   235
apply (intro allI impI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   236
apply (elim exE conjE)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   237
apply (rule I)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   238
by auto
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   239
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   240
lemma valid_var_NormalI: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   241
   assumes I: "\<And> n s0 L accC T C vf s1 Y Z.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   242
               \<lbrakk>\<forall>t\<in>A. G\<Turnstile>n\<Colon>t; s0\<Colon>\<preceq>(G,L); normal s0; 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   243
                \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>=T;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   244
                \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>t\<rangle>\<^sub>v\<guillemotright>C;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   245
                G\<turnstile>s0 \<midarrow>t=\<succ>vf\<midarrow>n\<rightarrow> s1; (Normal P) Y s0 Z\<rbrakk> 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   246
               \<Longrightarrow> Q (In2 vf) s1 Z \<and> s1\<Colon>\<preceq>(G,L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   247
   shows "G,A|\<Turnstile>\<Colon>{ {Normal P} \<langle>t\<rangle>\<^sub>v\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   248
apply (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   249
apply (intro allI impI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   250
apply (elim exE conjE)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   251
apply simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   252
apply (rule I)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   253
by auto
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   254
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   255
lemma valid_expr_NormalI: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   256
   assumes I: "\<And> n s0 L accC T C v s1 Y Z.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   257
               \<lbrakk>\<forall>t\<in>A. G\<Turnstile>n\<Colon>t; s0\<Colon>\<preceq>(G,L); normal s0; 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   258
                \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>-T;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   259
                \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>t\<rangle>\<^sub>e\<guillemotright>C;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   260
                G\<turnstile>s0 \<midarrow>t-\<succ>v\<midarrow>n\<rightarrow> s1; (Normal P) Y s0 Z\<rbrakk> 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   261
               \<Longrightarrow> Q (In1 v) s1 Z \<and> s1\<Colon>\<preceq>(G,L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   262
   shows "G,A|\<Turnstile>\<Colon>{ {Normal P} \<langle>t\<rangle>\<^sub>e\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   263
apply (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   264
apply (intro allI impI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   265
apply (elim exE conjE)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   266
apply simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   267
apply (rule I)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   268
by auto
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   269
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   270
lemma valid_expr_list_NormalI: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   271
   assumes I: "\<And> n s0 L accC T C vs s1 Y Z.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   272
               \<lbrakk>\<forall>t\<in>A. G\<Turnstile>n\<Colon>t; s0\<Colon>\<preceq>(G,L); normal s0; 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   273
                \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>\<doteq>T;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   274
                \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>t\<rangle>\<^sub>l\<guillemotright>C;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   275
                G\<turnstile>s0 \<midarrow>t\<doteq>\<succ>vs\<midarrow>n\<rightarrow> s1; (Normal P) Y s0 Z\<rbrakk> 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   276
                \<Longrightarrow> Q (In3 vs) s1 Z \<and> s1\<Colon>\<preceq>(G,L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   277
   shows "G,A|\<Turnstile>\<Colon>{ {Normal P} \<langle>t\<rangle>\<^sub>l\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   278
apply (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   279
apply (intro allI impI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   280
apply (elim exE conjE)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   281
apply simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   282
apply (rule I)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   283
by auto
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   284
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   285
lemma validE [consumes 5]: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   286
  assumes valid: "G,A|\<Turnstile>\<Colon>{ {P} t\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   287
   and    P: "P Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   288
   and    valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   289
   and    conf: "s0\<Colon>\<preceq>(G,L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   290
   and    eval: "G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s1)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   291
   and    wt: "normal s0 \<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   292
   and    da: "normal s0 \<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>t\<guillemotright>C"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   293
   and    elim: "\<lbrakk>Q v s1 Z; s1\<Colon>\<preceq>(G,L)\<rbrakk> \<Longrightarrow> concl" 
26888
9942cd184c48 remobed obsolete keyword concl;
wenzelm
parents: 24727
diff changeset
   294
  shows concl
41529
ba60efa2fd08 eliminated global prems;
wenzelm
parents: 37956
diff changeset
   295
using assms
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   296
by (simp add: ax_valids2_def triple_valid2_def2) fast
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   297
(* why consumes 5?. If I want to apply this lemma in a context wgere
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   298
   \<not> normal s0 holds,
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   299
   I can chain "\<not> normal s0" as fact number 6 and apply the rule with
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   300
   cases. Auto will then solve premise 6 and 7.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   301
*)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   302
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   303
lemma all_empty: "(!x. P) = P"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   304
by simp
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   305
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12859
diff changeset
   306
corollary evaln_type_sound:
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   307
  assumes evaln: "G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s1)" and
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   308
             wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>T" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   309
             da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0)) \<guillemotright>t\<guillemotright> A" and
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   310
        conf_s0: "s0\<Colon>\<preceq>(G,L)" and
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   311
             wf: "wf_prog G"                         
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   312
  shows "s1\<Colon>\<preceq>(G,L) \<and>  (normal s1 \<longrightarrow> G,L,store s1\<turnstile>t\<succ>v\<Colon>\<preceq>T) \<and> 
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12859
diff changeset
   313
         (error_free s0 = error_free s1)"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12859
diff changeset
   314
proof -
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   315
  from evaln have "G\<turnstile>s0 \<midarrow>t\<succ>\<rightarrow> (v,s1)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   316
    by (rule evaln_eval)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   317
  from this wt da wf conf_s0 show ?thesis
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   318
    by (rule eval_type_sound)
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12859
diff changeset
   319
qed
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12859
diff changeset
   320
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   321
corollary dom_locals_evaln_mono_elim [consumes 1]: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   322
  assumes   
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   323
  evaln: "G\<turnstile> s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s1)" and
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   324
    hyps: "\<lbrakk>dom (locals (store s0)) \<subseteq> dom (locals (store s1));
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   325
           \<And> vv s val. \<lbrakk>v=In2 vv; normal s1\<rbrakk> 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   326
                        \<Longrightarrow> dom (locals (store s)) 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   327
                             \<subseteq> dom (locals (store ((snd vv) val s)))\<rbrakk> \<Longrightarrow> P"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   328
 shows "P"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   329
proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   330
  from evaln have "G\<turnstile> s0 \<midarrow>t\<succ>\<rightarrow> (v,s1)" by (rule evaln_eval)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   331
  from this hyps show ?thesis
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   332
    by (rule dom_locals_eval_mono_elim) iprover+
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   333
qed
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   334
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   335
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   336
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   337
lemma evaln_no_abrupt: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   338
   "\<And>s s'. \<lbrakk>G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (w,s'); normal s'\<rbrakk> \<Longrightarrow> normal s"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   339
by (erule evaln_cases,auto)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   340
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   341
declare inj_term_simps [simp]
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   342
lemma ax_sound2: 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   343
  assumes    wf: "wf_prog G" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   344
    and   deriv: "G,A|\<turnstile>ts"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   345
  shows "G,A|\<Turnstile>\<Colon>ts"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   346
using deriv
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   347
proof (induct)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   348
  case (empty A)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   349
  show ?case
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   350
    by (simp add: ax_valids2_def triple_valid2_def2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   351
next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   352
  case (insert A t ts)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   353
  note valid_t = `G,A|\<Turnstile>\<Colon>{t}`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   354
  moreover
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   355
  note valid_ts = `G,A|\<Turnstile>\<Colon>ts`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   356
  {
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   357
    fix n assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   358
    have "G\<Turnstile>n\<Colon>t" and "\<forall>t\<in>ts. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   359
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   360
      from valid_A valid_t show "G\<Turnstile>n\<Colon>t"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   361
        by (simp add: ax_valids2_def)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   362
    next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   363
      from valid_A valid_ts show "\<forall>t\<in>ts. G\<Turnstile>n\<Colon>t"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   364
        by (unfold ax_valids2_def) blast
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   365
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   366
    hence "\<forall>t'\<in>insert t ts. G\<Turnstile>n\<Colon>t'"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   367
      by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   368
  }
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   369
  thus ?case
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   370
    by (unfold ax_valids2_def) blast
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   371
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   372
  case (asm ts A)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   373
  from `ts \<subseteq> A`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   374
  show "G,A|\<Turnstile>\<Colon>ts"
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   375
    by (auto simp add: ax_valids2_def triple_valid2_def)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   376
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   377
  case (weaken A ts' ts)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   378
  note `G,A|\<Turnstile>\<Colon>ts'`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   379
  moreover note `ts \<subseteq> ts'`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   380
  ultimately show "G,A|\<Turnstile>\<Colon>ts"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   381
    by (unfold ax_valids2_def triple_valid2_def) blast
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   382
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   383
  case (conseq P A t Q)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   384
  note con = `\<forall>Y s Z. P Y s Z \<longrightarrow> 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   385
              (\<exists>P' Q'.
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   386
                  (G,A\<turnstile>{P'} t\<succ> {Q'} \<and> G,A|\<Turnstile>\<Colon>{ {P'} t\<succ> {Q'} }) \<and>
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   387
                  (\<forall>Y' s'. (\<forall>Y Z'. P' Y s Z' \<longrightarrow> Q' Y' s' Z') \<longrightarrow> Q Y' s' Z))`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   388
  show "G,A|\<Turnstile>\<Colon>{ {P} t\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   389
  proof (rule validI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   390
    fix n s0 L accC T C v s1 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   391
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   392
    assume conf: "s0\<Colon>\<preceq>(G,L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   393
    assume wt: "normal s0 \<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>t\<Colon>T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   394
    assume da: "normal s0 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   395
                 \<Longrightarrow> \<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0)) \<guillemotright>t\<guillemotright> C"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   396
    assume eval: "G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v, s1)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   397
    assume P: "P Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   398
    show "Q v s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   399
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   400
      from valid_A conf wt da eval P con
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   401
      have "Q v s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   402
        apply (simp add: ax_valids2_def triple_valid2_def2)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   403
        apply (tactic "smp_tac 3 1")
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   404
        apply clarify
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   405
        apply (tactic "smp_tac 1 1")
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   406
        apply (erule allE,erule allE, erule mp)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   407
        apply (intro strip)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   408
        apply (tactic "smp_tac 3 1")
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   409
        apply (tactic "smp_tac 2 1")
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   410
        apply (tactic "smp_tac 1 1")
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   411
        by blast
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   412
      moreover have "s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   413
      proof (cases "normal s0")
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   414
        case True
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   415
        from eval wt [OF True] da [OF True] conf wf 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   416
        show ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   417
          by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   418
      next
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   419
        case False
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   420
        with eval have "s1=s0"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   421
          by auto
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   422
        with conf show ?thesis by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   423
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   424
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   425
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   426
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   427
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   428
  case (hazard A P t Q)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   429
  show "G,A|\<Turnstile>\<Colon>{ {P \<and>. Not \<circ> type_ok G t} t\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   430
    by (simp add: ax_valids2_def triple_valid2_def2 type_ok_def) fast
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   431
next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   432
  case (Abrupt A P t)
28524
644b62cf678f arbitrary is undefined
haftmann
parents: 26888
diff changeset
   433
  show "G,A|\<Turnstile>\<Colon>{ {P\<leftarrow>undefined3 t \<and>. Not \<circ> normal} t\<succ> {P} }"
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   434
  proof (rule validI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   435
    fix n s0 L accC T C v s1 Y Z 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   436
    assume conf_s0: "s0\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   437
    assume eval: "G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v, s1)"
28524
644b62cf678f arbitrary is undefined
haftmann
parents: 26888
diff changeset
   438
    assume "(P\<leftarrow>undefined3 t \<and>. Not \<circ> normal) Y s0 Z"
644b62cf678f arbitrary is undefined
haftmann
parents: 26888
diff changeset
   439
    then obtain P: "P (undefined3 t) s0 Z" and abrupt_s0: "\<not> normal s0"
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   440
      by simp
28524
644b62cf678f arbitrary is undefined
haftmann
parents: 26888
diff changeset
   441
    from eval abrupt_s0 obtain "s1=s0" and "v=undefined3 t"
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   442
      by auto
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   443
    with P conf_s0
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   444
    show "P v s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   445
      by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   446
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   447
next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   448
  case (LVar A P vn)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   449
  show "G,A|\<Turnstile>\<Colon>{ {Normal (\<lambda>s.. P\<leftarrow>In2 (lvar vn s))} LVar vn=\<succ> {P} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   450
  proof (rule valid_var_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   451
    fix n s0 L accC T C vf s1 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   452
    assume conf_s0: "s0\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   453
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   454
    assume wt: "\<lparr>prg = G, cls = accC, lcl = L\<rparr>\<turnstile>LVar vn\<Colon>=T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   455
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>LVar vn\<rangle>\<^sub>v\<guillemotright> C"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   456
    assume eval: "G\<turnstile>s0 \<midarrow>LVar vn=\<succ>vf\<midarrow>n\<rightarrow> s1" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   457
    assume P: "(Normal (\<lambda>s.. P\<leftarrow>In2 (lvar vn s))) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   458
    show "P (In2 vf) s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   459
    proof 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   460
      from eval normal_s0 obtain "s1=s0" "vf=lvar vn (store s0)"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   461
        by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   462
      with P show "P (In2 vf) s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   463
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   464
    next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   465
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   466
      show "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   467
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   468
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   469
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   470
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   471
  case (FVar A P statDeclC Q e stat fn R accC)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   472
  note valid_init = `G,A|\<Turnstile>\<Colon>{ {Normal P} .Init statDeclC. {Q} }`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   473
  note valid_e = `G,A|\<Turnstile>\<Colon>{ {Q} e-\<succ> {\<lambda>Val:a:. fvar statDeclC stat fn a ..; R} }`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   474
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} {accC,statDeclC,stat}e..fn=\<succ> {R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   475
  proof (rule valid_var_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   476
    fix n s0 L accC' T V vf s3 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   477
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   478
    assume conf_s0:  "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   479
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   480
    assume wt: "\<lparr>prg=G,cls=accC',lcl=L\<rparr>\<turnstile>{accC,statDeclC,stat}e..fn\<Colon>=T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   481
    assume da: "\<lparr>prg=G,cls=accC',lcl=L\<rparr>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   482
                  \<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>{accC,statDeclC,stat}e..fn\<rangle>\<^sub>v\<guillemotright> V"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   483
    assume eval: "G\<turnstile>s0 \<midarrow>{accC,statDeclC,stat}e..fn=\<succ>vf\<midarrow>n\<rightarrow> s3"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   484
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   485
    show "R \<lfloor>vf\<rfloor>\<^sub>v s3 Z \<and> s3\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   486
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   487
      from wt obtain statC f where
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   488
        wt_e: "\<lparr>prg=G, cls=accC, lcl=L\<rparr>\<turnstile>e\<Colon>-Class statC" and
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   489
        accfield: "accfield G accC statC fn = Some (statDeclC,f)" and
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   490
        eq_accC: "accC=accC'" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   491
        stat: "stat=is_static f" and
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   492
        T: "T=(type f)"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   493
        by (cases) (auto simp add: member_is_static_simp)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   494
      from da eq_accC
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   495
      have da_e: "\<lparr>prg=G, cls=accC, lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> V"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   496
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   497
      from eval obtain a s1 s2 s2' where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   498
        eval_init: "G\<turnstile>s0 \<midarrow>Init statDeclC\<midarrow>n\<rightarrow> s1" and 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   499
        eval_e: "G\<turnstile>s1 \<midarrow>e-\<succ>a\<midarrow>n\<rightarrow> s2" and 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   500
        fvar: "(vf,s2')=fvar statDeclC stat fn a s2" and
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   501
        s3: "s3 = check_field_access G accC statDeclC fn stat a s2'"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   502
        using normal_s0 by (fastforce elim: evaln_elim_cases) 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   503
      have wt_init: "\<lparr>prg=G, cls=accC, lcl=L\<rparr>\<turnstile>(Init statDeclC)\<Colon>\<surd>"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   504
      proof -
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   505
        from wf wt_e 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   506
        have iscls_statC: "is_class G statC"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   507
          by (auto dest: ty_expr_is_type type_is_class)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   508
        with wf accfield 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   509
        have iscls_statDeclC: "is_class G statDeclC"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   510
          by (auto dest!: accfield_fields dest: fields_declC)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   511
        thus ?thesis by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   512
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   513
      obtain I where 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   514
        da_init: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   515
                    \<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>Init statDeclC\<rangle>\<^sub>s\<guillemotright> I"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   516
        by (auto intro: da_Init [simplified] assigned.select_convs)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   517
      from valid_init P valid_A conf_s0 eval_init wt_init da_init
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   518
      obtain Q: "Q \<diamondsuit> s1 Z" and conf_s1: "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   519
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   520
      obtain 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   521
        R: "R \<lfloor>vf\<rfloor>\<^sub>v s2' Z" and 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   522
        conf_s2: "s2\<Colon>\<preceq>(G, L)" and
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   523
        conf_a: "normal s2 \<longrightarrow> G,store s2\<turnstile>a\<Colon>\<preceq>Class statC"
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   524
      proof (cases "normal s1")
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   525
        case True
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   526
        obtain V' where 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   527
          da_e':
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   528
          "\<lparr>prg=G,cls=accC,lcl=L\<rparr> \<turnstile>dom (locals (store s1))\<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> V'"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   529
        proof -
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   530
          from eval_init 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   531
          have "(dom (locals (store s0))) \<subseteq> (dom (locals (store s1)))"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   532
            by (rule dom_locals_evaln_mono_elim)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   533
          with da_e show thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   534
            by (rule da_weakenE) (rule that)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   535
        qed
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   536
        with valid_e Q valid_A conf_s1 eval_e wt_e
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   537
        obtain "R \<lfloor>vf\<rfloor>\<^sub>v s2' Z" and "s2\<Colon>\<preceq>(G, L)"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   538
          by (rule validE) (simp add: fvar [symmetric])
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   539
        moreover
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   540
        from eval_e wt_e da_e' conf_s1 wf
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   541
        have "normal s2 \<longrightarrow> G,store s2\<turnstile>a\<Colon>\<preceq>Class statC"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   542
          by (rule evaln_type_sound [elim_format]) simp
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   543
        ultimately show ?thesis ..
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   544
      next
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   545
        case False
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   546
        with valid_e Q valid_A conf_s1 eval_e
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   547
        obtain  "R \<lfloor>vf\<rfloor>\<^sub>v s2' Z" and "s2\<Colon>\<preceq>(G, L)"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   548
          by (cases rule: validE) (simp add: fvar [symmetric])+
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   549
        moreover from False eval_e have "\<not> normal s2"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   550
          by auto
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   551
        hence "normal s2 \<longrightarrow> G,store s2\<turnstile>a\<Colon>\<preceq>Class statC"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   552
          by auto
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   553
        ultimately show ?thesis ..
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   554
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   555
      from accfield wt_e eval_init eval_e conf_s2 conf_a fvar stat s3 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   556
      have eq_s3_s2': "s3=s2'"  
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   557
        using normal_s0 by (auto dest!: error_free_field_access evaln_eval)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   558
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   559
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   560
      have "s3\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   561
        by (rule evaln_type_sound [elim_format]) simp
23366
a1e61b5c000f tuned proofs: avoid implicit prems;
wenzelm
parents: 23350
diff changeset
   562
      ultimately show ?thesis using Q R by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   563
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   564
  qed
13690
ac335b2f4a39 Inserted some extra paragraphs in large proofs to make tex run...
schirmer
parents: 13688
diff changeset
   565
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   566
  case (AVar A P e1 Q e2 R)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   567
  note valid_e1 = `G,A|\<Turnstile>\<Colon>{ {Normal P} e1-\<succ> {Q} }`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   568
  have valid_e2: "\<And> a. G,A|\<Turnstile>\<Colon>{ {Q\<leftarrow>In1 a} e2-\<succ> {\<lambda>Val:i:. avar G i a ..; R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   569
    using AVar.hyps by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   570
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} e1.[e2]=\<succ> {R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   571
  proof (rule valid_var_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   572
    fix n s0 L accC T V vf s2' Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   573
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   574
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   575
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   576
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e1.[e2]\<Colon>=T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   577
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   578
                  \<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>e1.[e2]\<rangle>\<^sub>v\<guillemotright> V"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   579
    assume eval: "G\<turnstile>s0 \<midarrow>e1.[e2]=\<succ>vf\<midarrow>n\<rightarrow> s2'"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   580
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   581
    show "R \<lfloor>vf\<rfloor>\<^sub>v s2' Z \<and> s2'\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   582
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   583
      from wt obtain 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   584
        wt_e1: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e1\<Colon>-T.[]" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   585
        wt_e2: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e2\<Colon>-PrimT Integer" 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   586
        by (rule wt_elim_cases) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   587
      from da obtain E1 where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   588
        da_e1: "\<lparr>prg=G,cls=accC,lcl=L\<rparr> \<turnstile>dom (locals (store s0))\<guillemotright>\<langle>e1\<rangle>\<^sub>e\<guillemotright> E1" and
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   589
        da_e2: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> nrm E1 \<guillemotright>\<langle>e2\<rangle>\<^sub>e\<guillemotright> V"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   590
        by (rule da_elim_cases) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   591
      from eval obtain s1 a i s2 where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   592
        eval_e1: "G\<turnstile>s0 \<midarrow>e1-\<succ>a\<midarrow>n\<rightarrow> s1" and
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   593
        eval_e2: "G\<turnstile>s1 \<midarrow>e2-\<succ>i\<midarrow>n\<rightarrow> s2" and
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   594
        avar: "avar G i a s2 =(vf, s2')"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   595
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   596
      from valid_e1 P valid_A conf_s0 eval_e1 wt_e1 da_e1
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   597
      obtain Q: "Q \<lfloor>a\<rfloor>\<^sub>e s1 Z" and conf_s1: "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   598
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   599
      from Q have Q': "\<And> v. (Q\<leftarrow>In1 a) v s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   600
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   601
      have "R \<lfloor>vf\<rfloor>\<^sub>v s2' Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   602
      proof (cases "normal s1")
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   603
        case True
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   604
        obtain V' where 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   605
          "\<lparr>prg=G,cls=accC,lcl=L\<rparr> \<turnstile>dom (locals (store s1))\<guillemotright>\<langle>e2\<rangle>\<^sub>e\<guillemotright> V'"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   606
        proof -
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   607
          from eval_e1  wt_e1 da_e1 wf True
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   608
          have "nrm E1 \<subseteq> dom (locals (store s1))"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   609
            by (cases rule: da_good_approx_evalnE) iprover
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   610
          with da_e2 show thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   611
            by (rule da_weakenE) (rule that)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   612
        qed
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   613
        with valid_e2 Q' valid_A conf_s1 eval_e2 wt_e2 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   614
        show ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   615
          by (rule validE) (simp add: avar)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   616
      next
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   617
        case False
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   618
        with valid_e2 Q' valid_A conf_s1 eval_e2
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   619
        show ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   620
          by (cases rule: validE) (simp add: avar)+
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   621
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   622
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   623
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   624
      have "s2'\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   625
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   626
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   627
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   628
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   629
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   630
  case (NewC A P C Q)
23366
a1e61b5c000f tuned proofs: avoid implicit prems;
wenzelm
parents: 23350
diff changeset
   631
  note valid_init = `G,A|\<Turnstile>\<Colon>{ {Normal P} .Init C. {Alloc G (CInst C) Q} }`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   632
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} NewC C-\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   633
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   634
    fix n s0 L accC T E v s2 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   635
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   636
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   637
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   638
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>NewC C\<Colon>-T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   639
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   640
                  \<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>NewC C\<rangle>\<^sub>e\<guillemotright> E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   641
    assume eval: "G\<turnstile>s0 \<midarrow>NewC C-\<succ>v\<midarrow>n\<rightarrow> s2"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   642
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   643
    show "Q \<lfloor>v\<rfloor>\<^sub>e s2 Z \<and> s2\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   644
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   645
      from wt obtain is_cls_C: "is_class G C" 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   646
        by (rule wt_elim_cases) (auto dest: is_acc_classD)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   647
      hence wt_init: "\<lparr>prg=G, cls=accC, lcl=L\<rparr>\<turnstile>Init C\<Colon>\<surd>" 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   648
        by auto
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   649
      obtain I where 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   650
        da_init: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>Init C\<rangle>\<^sub>s\<guillemotright> I"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   651
        by (auto intro: da_Init [simplified] assigned.select_convs)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   652
      from eval obtain s1 a where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   653
        eval_init: "G\<turnstile>s0 \<midarrow>Init C\<midarrow>n\<rightarrow> s1" and 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   654
        alloc: "G\<turnstile>s1 \<midarrow>halloc CInst C\<succ>a\<rightarrow> s2" and
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   655
        v: "v=Addr a"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   656
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   657
      from valid_init P valid_A conf_s0 eval_init wt_init da_init
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   658
      obtain "(Alloc G (CInst C) Q) \<diamondsuit> s1 Z" 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   659
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   660
      with alloc v have "Q \<lfloor>v\<rfloor>\<^sub>e s2 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   661
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   662
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   663
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   664
      have "s2\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   665
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   666
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   667
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   668
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   669
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   670
  case (NewA A P T Q e R)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   671
  note valid_init = `G,A|\<Turnstile>\<Colon>{ {Normal P} .init_comp_ty T. {Q} }`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   672
  note valid_e = `G,A|\<Turnstile>\<Colon>{ {Q} e-\<succ> {\<lambda>Val:i:. abupd (check_neg i) .; 
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   673
                                            Alloc G (Arr T (the_Intg i)) R}}`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   674
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} New T[e]-\<succ> {R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   675
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   676
    fix n s0 L accC arrT E v s3 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   677
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   678
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   679
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   680
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>New T[e]\<Colon>-arrT"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   681
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0)) \<guillemotright>\<langle>New T[e]\<rangle>\<^sub>e\<guillemotright> E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   682
    assume eval: "G\<turnstile>s0 \<midarrow>New T[e]-\<succ>v\<midarrow>n\<rightarrow> s3"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   683
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   684
    show "R \<lfloor>v\<rfloor>\<^sub>e s3 Z \<and> s3\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   685
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   686
      from wt obtain
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   687
        wt_init: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>init_comp_ty T\<Colon>\<surd>" and 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   688
        wt_e: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e\<Colon>-PrimT Integer" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   689
        by (rule wt_elim_cases) (auto intro: wt_init_comp_ty )
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   690
      from da obtain
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   691
        da_e:"\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> E"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   692
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   693
      from eval obtain s1 i s2 a where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   694
        eval_init: "G\<turnstile>s0 \<midarrow>init_comp_ty T\<midarrow>n\<rightarrow> s1" and 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   695
        eval_e: "G\<turnstile>s1 \<midarrow>e-\<succ>i\<midarrow>n\<rightarrow> s2" and
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   696
        alloc: "G\<turnstile>abupd (check_neg i) s2 \<midarrow>halloc Arr T (the_Intg i)\<succ>a\<rightarrow> s3" and
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   697
        v: "v=Addr a"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   698
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   699
      obtain I where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   700
        da_init:
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   701
        "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0)) \<guillemotright>\<langle>init_comp_ty T\<rangle>\<^sub>s\<guillemotright> I"
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   702
      proof (cases "\<exists>C. T = Class C")
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   703
        case True
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   704
        thus ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   705
          by - (rule that, (auto intro: da_Init [simplified] 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   706
                                        assigned.select_convs
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   707
                              simp add: init_comp_ty_def))
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   708
         (* simplified: to rewrite \<langle>Init C\<rangle> to In1r (Init C) *)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   709
      next
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   710
        case False
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   711
        thus ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   712
          by - (rule that, (auto intro: da_Skip [simplified] 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   713
                                      assigned.select_convs
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   714
                           simp add: init_comp_ty_def))
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   715
         (* simplified: to rewrite \<langle>Skip\<rangle> to In1r (Skip) *)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   716
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   717
      with valid_init P valid_A conf_s0 eval_init wt_init 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   718
      obtain Q: "Q \<diamondsuit> s1 Z" and conf_s1: "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   719
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   720
      obtain E' where
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   721
       "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s1)) \<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> E'"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   722
      proof -
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   723
        from eval_init 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   724
        have "dom (locals (store s0)) \<subseteq> dom (locals (store s1))"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   725
          by (rule dom_locals_evaln_mono_elim)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   726
        with da_e show thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   727
          by (rule da_weakenE) (rule that)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   728
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   729
      with valid_e Q valid_A conf_s1 eval_e wt_e
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   730
      have "(\<lambda>Val:i:. abupd (check_neg i) .; 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   731
                      Alloc G (Arr T (the_Intg i)) R) \<lfloor>i\<rfloor>\<^sub>e s2 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   732
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   733
      with alloc v have "R \<lfloor>v\<rfloor>\<^sub>e s3 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   734
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   735
      moreover 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   736
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   737
      have "s3\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   738
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   739
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   740
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   741
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   742
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   743
  case (Cast A P e T Q)
23366
a1e61b5c000f tuned proofs: avoid implicit prems;
wenzelm
parents: 23350
diff changeset
   744
  note valid_e = `G,A|\<Turnstile>\<Colon>{ {Normal P} e-\<succ> 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   745
                 {\<lambda>Val:v:. \<lambda>s.. abupd (raise_if (\<not> G,s\<turnstile>v fits T) ClassCast) .;
23366
a1e61b5c000f tuned proofs: avoid implicit prems;
wenzelm
parents: 23350
diff changeset
   746
                  Q\<leftarrow>In1 v} }`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   747
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} Cast T e-\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   748
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   749
    fix n s0 L accC castT E v s2 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   750
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   751
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   752
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   753
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>Cast T e\<Colon>-castT"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   754
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0)) \<guillemotright>\<langle>Cast T e\<rangle>\<^sub>e\<guillemotright> E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   755
    assume eval: "G\<turnstile>s0 \<midarrow>Cast T e-\<succ>v\<midarrow>n\<rightarrow> s2"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   756
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   757
    show "Q \<lfloor>v\<rfloor>\<^sub>e s2 Z \<and> s2\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   758
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   759
      from wt obtain eT where 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   760
        wt_e: "\<lparr>prg = G, cls = accC, lcl = L\<rparr>\<turnstile>e\<Colon>-eT" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   761
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   762
      from da obtain
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   763
        da_e: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> E"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   764
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   765
      from eval obtain s1 where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   766
        eval_e: "G\<turnstile>s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   767
        s2: "s2 = abupd (raise_if (\<not> G,snd s1\<turnstile>v fits T) ClassCast) s1"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   768
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   769
      from valid_e P valid_A conf_s0 eval_e wt_e da_e
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   770
      have "(\<lambda>Val:v:. \<lambda>s.. abupd (raise_if (\<not> G,s\<turnstile>v fits T) ClassCast) .;
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   771
                  Q\<leftarrow>In1 v) \<lfloor>v\<rfloor>\<^sub>e s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   772
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   773
      with s2 have "Q \<lfloor>v\<rfloor>\<^sub>e s2 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   774
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   775
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   776
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   777
      have "s2\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   778
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   779
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   780
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   781
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   782
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   783
  case (Inst A P e Q T)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   784
  assume valid_e: "G,A|\<Turnstile>\<Colon>{ {Normal P} e-\<succ>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   785
               {\<lambda>Val:v:. \<lambda>s.. Q\<leftarrow>In1 (Bool (v \<noteq> Null \<and> G,s\<turnstile>v fits RefT T))} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   786
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} e InstOf T-\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   787
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   788
    fix n s0 L accC instT E v s1 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   789
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   790
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   791
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   792
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e InstOf T\<Colon>-instT"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   793
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>e InstOf T\<rangle>\<^sub>e\<guillemotright> E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   794
    assume eval: "G\<turnstile>s0 \<midarrow>e InstOf T-\<succ>v\<midarrow>n\<rightarrow> s1"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   795
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   796
    show "Q \<lfloor>v\<rfloor>\<^sub>e s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   797
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   798
      from wt obtain eT where 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   799
        wt_e: "\<lparr>prg = G, cls = accC, lcl = L\<rparr>\<turnstile>e\<Colon>-eT" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   800
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   801
      from da obtain
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   802
        da_e: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> E"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   803
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   804
      from eval obtain a where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   805
        eval_e: "G\<turnstile>s0 \<midarrow>e-\<succ>a\<midarrow>n\<rightarrow> s1" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   806
        v: "v = Bool (a \<noteq> Null \<and> G,store s1\<turnstile>a fits RefT T)"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   807
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   808
      from valid_e P valid_A conf_s0 eval_e wt_e da_e
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   809
      have "(\<lambda>Val:v:. \<lambda>s.. Q\<leftarrow>In1 (Bool (v \<noteq> Null \<and> G,s\<turnstile>v fits RefT T))) 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   810
              \<lfloor>a\<rfloor>\<^sub>e s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   811
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   812
      with v have "Q \<lfloor>v\<rfloor>\<^sub>e s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   813
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   814
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   815
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   816
      have "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   817
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   818
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   819
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   820
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   821
next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   822
  case (Lit A P v)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   823
  show "G,A|\<Turnstile>\<Colon>{ {Normal (P\<leftarrow>In1 v)} Lit v-\<succ> {P} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   824
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   825
    fix n L s0 s1 v'  Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   826
    assume conf_s0: "s0\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   827
    assume normal_s0: " normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   828
    assume eval: "G\<turnstile>s0 \<midarrow>Lit v-\<succ>v'\<midarrow>n\<rightarrow> s1"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   829
    assume P: "(Normal (P\<leftarrow>In1 v)) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   830
    show "P \<lfloor>v'\<rfloor>\<^sub>e s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   831
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   832
      from eval have "s1=s0" and  "v'=v"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   833
        using normal_s0 by (auto elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   834
      with P conf_s0 show ?thesis by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   835
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   836
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   837
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   838
  case (UnOp A P e Q unop)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   839
  assume valid_e: "G,A|\<Turnstile>\<Colon>{ {Normal P}e-\<succ>{\<lambda>Val:v:. Q\<leftarrow>In1 (eval_unop unop v)} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   840
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} UnOp unop e-\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   841
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   842
    fix n s0 L accC T E v s1 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   843
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   844
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   845
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   846
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>UnOp unop e\<Colon>-T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   847
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>UnOp unop e\<rangle>\<^sub>e\<guillemotright>E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   848
    assume eval: "G\<turnstile>s0 \<midarrow>UnOp unop e-\<succ>v\<midarrow>n\<rightarrow> s1"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   849
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   850
    show "Q \<lfloor>v\<rfloor>\<^sub>e s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   851
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   852
      from wt obtain eT where 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   853
        wt_e: "\<lparr>prg = G, cls = accC, lcl = L\<rparr>\<turnstile>e\<Colon>-eT" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   854
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   855
      from da obtain
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   856
        da_e: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>e\<rangle>\<^sub>e\<guillemotright> E"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   857
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   858
      from eval obtain ve where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   859
        eval_e: "G\<turnstile>s0 \<midarrow>e-\<succ>ve\<midarrow>n\<rightarrow> s1" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   860
        v: "v = eval_unop unop ve"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   861
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   862
      from valid_e P valid_A conf_s0 eval_e wt_e da_e
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   863
      have "(\<lambda>Val:v:. Q\<leftarrow>In1 (eval_unop unop v)) \<lfloor>ve\<rfloor>\<^sub>e s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   864
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   865
      with v have "Q \<lfloor>v\<rfloor>\<^sub>e s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   866
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   867
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   868
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   869
      have "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   870
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   871
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   872
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   873
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   874
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   875
  case (BinOp A P e1 Q binop e2 R)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   876
  assume valid_e1: "G,A|\<Turnstile>\<Colon>{ {Normal P} e1-\<succ> {Q} }" 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   877
  have valid_e2: "\<And> v1.  G,A|\<Turnstile>\<Colon>{ {Q\<leftarrow>In1 v1}
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   878
              (if need_second_arg binop v1 then In1l e2 else In1r Skip)\<succ>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   879
              {\<lambda>Val:v2:. R\<leftarrow>In1 (eval_binop binop v1 v2)} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   880
    using BinOp.hyps by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   881
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} BinOp binop e1 e2-\<succ> {R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   882
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   883
    fix n s0 L accC T E v s2 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   884
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   885
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   886
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   887
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>BinOp binop e1 e2\<Colon>-T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   888
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   889
                  \<turnstile>dom (locals (store s0)) \<guillemotright>\<langle>BinOp binop e1 e2\<rangle>\<^sub>e\<guillemotright> E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   890
    assume eval: "G\<turnstile>s0 \<midarrow>BinOp binop e1 e2-\<succ>v\<midarrow>n\<rightarrow> s2"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   891
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   892
    show "R \<lfloor>v\<rfloor>\<^sub>e s2 Z \<and> s2\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   893
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   894
      from wt obtain e1T e2T where
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   895
        wt_e1: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e1\<Colon>-e1T" and
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   896
        wt_e2: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e2\<Colon>-e2T" and
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   897
        wt_binop: "wt_binop G binop e1T e2T" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   898
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   899
      have wt_Skip: "\<lparr>prg = G, cls = accC, lcl = L\<rparr>\<turnstile>Skip\<Colon>\<surd>"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   900
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   901
      (*
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   902
      obtain S where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   903
        daSkip: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   904
                   \<turnstile> dom (locals (store s1)) \<guillemotright>In1r Skip\<guillemotright> S"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   905
        by (auto intro: da_Skip [simplified] assigned.select_convs) *)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   906
      from da obtain E1 where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   907
        da_e1: "\<lparr>prg=G,cls=accC,lcl=L\<rparr> \<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>e1\<rangle>\<^sub>e\<guillemotright> E1"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   908
        by cases simp+
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   909
      from eval obtain v1 s1 v2 where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   910
        eval_e1: "G\<turnstile>s0 \<midarrow>e1-\<succ>v1\<midarrow>n\<rightarrow> s1" and
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   911
        eval_e2: "G\<turnstile>s1 \<midarrow>(if need_second_arg binop v1 then \<langle>e2\<rangle>\<^sub>e else \<langle>Skip\<rangle>\<^sub>s)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   912
                        \<succ>\<midarrow>n\<rightarrow> (\<lfloor>v2\<rfloor>\<^sub>e, s2)" and
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   913
        v: "v=eval_binop binop v1 v2"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   914
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   915
      from valid_e1 P valid_A conf_s0 eval_e1 wt_e1 da_e1
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   916
      obtain Q: "Q \<lfloor>v1\<rfloor>\<^sub>e s1 Z" and conf_s1: "s1\<Colon>\<preceq>(G,L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   917
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   918
      from Q have Q': "\<And> v. (Q\<leftarrow>In1 v1) v s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   919
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   920
      have "(\<lambda>Val:v2:. R\<leftarrow>In1 (eval_binop binop v1 v2)) \<lfloor>v2\<rfloor>\<^sub>e s2 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   921
      proof (cases "normal s1")
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   922
        case True
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   923
        from eval_e1 wt_e1 da_e1 conf_s0 wf
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   924
        have conf_v1: "G,store s1\<turnstile>v1\<Colon>\<preceq>e1T" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   925
          by (rule evaln_type_sound [elim_format]) (insert True,simp)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   926
        from eval_e1 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   927
        have "G\<turnstile>s0 \<midarrow>e1-\<succ>v1\<rightarrow> s1"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   928
          by (rule evaln_eval)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   929
        from da wt_e1 wt_e2 wt_binop conf_s0 True this conf_v1 wf
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   930
        obtain E2 where
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   931
          da_e2: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile> dom (locals (store s1)) 
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   932
                   \<guillemotright>(if need_second_arg binop v1 then \<langle>e2\<rangle>\<^sub>e else \<langle>Skip\<rangle>\<^sub>s)\<guillemotright> E2"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   933
          by (rule da_e2_BinOp [elim_format]) iprover
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   934
        from wt_e2 wt_Skip obtain T2 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   935
          where "\<lparr>prg=G,cls=accC,lcl=L\<rparr>
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   936
                  \<turnstile>(if need_second_arg binop v1 then \<langle>e2\<rangle>\<^sub>e else \<langle>Skip\<rangle>\<^sub>s)\<Colon>T2"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   937
          by (cases "need_second_arg binop v1") auto
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   938
        note ve=validE [OF valid_e2,OF  Q' valid_A conf_s1 eval_e2 this da_e2]
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   939
        (* chaining Q', without extra OF causes unification error *)
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   940
        thus ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   941
          by (rule ve)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   942
      next
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   943
        case False
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   944
        note ve=validE [OF valid_e2,OF Q' valid_A conf_s1 eval_e2]
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   945
        with False show ?thesis
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   946
          by iprover
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   947
      qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   948
      with v have "R \<lfloor>v\<rfloor>\<^sub>e s2 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   949
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   950
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   951
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   952
      have "s2\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   953
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   954
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   955
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   956
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   957
next
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   958
  case (Super A P)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   959
  show "G,A|\<Turnstile>\<Colon>{ {Normal (\<lambda>s.. P\<leftarrow>In1 (val_this s))} Super-\<succ> {P} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   960
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   961
    fix n L s0 s1 v  Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   962
    assume conf_s0: "s0\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   963
    assume normal_s0: " normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   964
    assume eval: "G\<turnstile>s0 \<midarrow>Super-\<succ>v\<midarrow>n\<rightarrow> s1"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   965
    assume P: "(Normal (\<lambda>s.. P\<leftarrow>In1 (val_this s))) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   966
    show "P \<lfloor>v\<rfloor>\<^sub>e s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   967
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   968
      from eval have "s1=s0" and  "v=val_this (store s0)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   969
        using normal_s0 by (auto elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   970
      with P conf_s0 show ?thesis by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   971
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   972
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   973
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   974
  case (Acc A P var Q)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
   975
  note valid_var = `G,A|\<Turnstile>\<Colon>{ {Normal P} var=\<succ> {\<lambda>Var:(v, f):. Q\<leftarrow>In1 v} }`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   976
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} Acc var-\<succ> {Q} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   977
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   978
    fix n s0 L accC T E v s1 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   979
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   980
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   981
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   982
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>Acc var\<Colon>-T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   983
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>Acc var\<rangle>\<^sub>e\<guillemotright>E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   984
    assume eval: "G\<turnstile>s0 \<midarrow>Acc var-\<succ>v\<midarrow>n\<rightarrow> s1"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   985
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   986
    show "Q \<lfloor>v\<rfloor>\<^sub>e s1 Z \<and> s1\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   987
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   988
      from wt obtain 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   989
        wt_var: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>var\<Colon>=T" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   990
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   991
      from da obtain V where 
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   992
        da_var: "\<lparr>prg=G,cls=accC,lcl=L\<rparr> \<turnstile> dom (locals (store s0)) \<guillemotright>\<langle>var\<rangle>\<^sub>v\<guillemotright> V"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   993
        by (cases "\<exists> n. var=LVar n") (insert da.LVar,auto elim!: da_elim_cases)
46714
a7ca72710dfe tuned proofs;
wenzelm
parents: 44890
diff changeset
   994
      from eval obtain upd where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   995
        eval_var: "G\<turnstile>s0 \<midarrow>var=\<succ>(v, upd)\<midarrow>n\<rightarrow> s1"
44890
22f665a2e91c new fastforce replacing fastsimp - less confusing name
nipkow
parents: 41529
diff changeset
   996
        using normal_s0 by (fastforce elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   997
      from valid_var P valid_A conf_s0 eval_var wt_var da_var
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   998
      have "(\<lambda>Var:(v, f):. Q\<leftarrow>In1 v) \<lfloor>(v, upd)\<rfloor>\<^sub>v s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
   999
        by (rule validE)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1000
      then have "Q \<lfloor>v\<rfloor>\<^sub>e s1 Z"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1001
        by simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1002
      moreover
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1003
      from eval wt da conf_s0 wf
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1004
      have "s1\<Colon>\<preceq>(G, L)"
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1005
        by (rule evaln_type_sound [elim_format]) simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1006
      ultimately show ?thesis ..
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1007
    qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1008
  qed
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1009
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
  1010
  case (Ass A P var Q e R)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 21765
diff changeset
  1011
  note valid_var = `G,A|\<Turnstile>\<Colon>{ {Normal P} var=\<succ> {Q} }`
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1012
  have valid_e: "\<And> vf. 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1013
                  G,A|\<Turnstile>\<Colon>{ {Q\<leftarrow>In2 vf} e-\<succ> {\<lambda>Val:v:. assign (snd vf) v .; R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1014
    using Ass.hyps by simp
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1015
  show "G,A|\<Turnstile>\<Colon>{ {Normal P} var:=e-\<succ> {R} }"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1016
  proof (rule valid_expr_NormalI)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1017
    fix n s0 L accC T E v s3 Y Z
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1018
    assume valid_A: "\<forall>t\<in>A. G\<Turnstile>n\<Colon>t"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1019
    assume conf_s0: "s0\<Colon>\<preceq>(G,L)"  
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1020
    assume normal_s0: "normal s0"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1021
    assume wt: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>var:=e\<Colon>-T"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1022
    assume da: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>dom (locals (store s0))\<guillemotright>\<langle>var:=e\<rangle>\<^sub>e\<guillemotright>E"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1023
    assume eval: "G\<turnstile>s0 \<midarrow>var:=e-\<succ>v\<midarrow>n\<rightarrow> s3"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1024
    assume P: "(Normal P) Y s0 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1025
    show "R \<lfloor>v\<rfloor>\<^sub>e s3 Z \<and> s3\<Colon>\<preceq>(G, L)"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1026
    proof -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1027
      from wt obtain varT  where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1028
        wt_var: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>var\<Colon>=varT" and
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1029
        wt_e: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>\<turnstile>e\<Colon>-T" 
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1030
        by cases simp
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1031
      from eval obtain w upd s1 s2 where
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1032
        eval_var: "G\<turnstile>s0 \<midarrow>var=\<succ>(w, upd)\<midarrow>n\<rightarrow> s1" and
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1033
        eval_e: "G\<turnstile>s1 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s2" and
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1034
        s3: "s3=assign upd v s2"
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1035
        using normal_s0 by (auto elim: evaln_elim_cases)
13688
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1036
      have "R \<lfloor>v\<rfloor>\<^sub>e s3 Z"
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
  1037
      proof (cases "\<exists> vn. var = LVar vn")
32960
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1038
        case False
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1039
        with da obtain V where
69916a850301 eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents: 28524
diff changeset
  1040
          da_var: "\<lparr>prg=G,cls=accC,lcl=L\<rparr>