src/HOL/Bali/Evaln.thy
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(*  Title:      HOL/Bali/Evaln.thy
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    ID:         $Id$
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    Author:     David von Oheimb and Norbert Schirmer
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*)
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header {* Operational evaluation (big-step) semantics of Java expressions and 
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          statements
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*}
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theory Evaln imports TypeSafe begin
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text {*
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Variant of @{term eval} relation with counter for bounded recursive depth. 
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In principal @{term evaln} could replace @{term eval}.
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Validity of the axiomatic semantics builds on @{term evaln}. 
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For recursive method calls the axiomatic semantics rule assumes the method ok 
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to derive a proof for the body. To prove the method rule sound we need to 
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perform induction on the recursion depth. 
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For the completeness proof of the axiomatic semantics the notion of the most
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general formula is used. The most general formula right now builds on the 
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ordinary evaluation relation @{term eval}. 
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So sometimes we have to switch between @{term evaln} and @{term eval} and vice 
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versa. To make
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this switch easy @{term evaln} also does all the technical accessibility tests 
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@{term check_field_access} and @{term check_method_access} like @{term eval}. 
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If it would omit them @{term evaln} and @{term eval} would only be equivalent 
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for welltyped, and definitely assigned terms.
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*}
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inductive
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  evaln	:: "[prog, state, term, nat, vals, state] \<Rightarrow> bool"
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    ("_\<turnstile>_ \<midarrow>_\<succ>\<midarrow>_\<rightarrow> '(_, _')" [61,61,80,61,0,0] 60)
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  and evarn :: "[prog, state, var, vvar, nat, state] \<Rightarrow> bool"
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    ("_\<turnstile>_ \<midarrow>_=\<succ>_\<midarrow>_\<rightarrow> _" [61,61,90,61,61,61] 60)
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  and eval_n:: "[prog, state, expr, val, nat, state] \<Rightarrow> bool"
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    ("_\<turnstile>_ \<midarrow>_-\<succ>_\<midarrow>_\<rightarrow> _" [61,61,80,61,61,61] 60)
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  and evalsn :: "[prog, state, expr list, val  list, nat, state] \<Rightarrow> bool"
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    ("_\<turnstile>_ \<midarrow>_\<doteq>\<succ>_\<midarrow>_\<rightarrow> _" [61,61,61,61,61,61] 60)
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  and execn	:: "[prog, state, stmt, nat, state] \<Rightarrow> bool"
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    ("_\<turnstile>_ \<midarrow>_\<midarrow>_\<rightarrow> _"     [61,61,65,   61,61] 60)
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  for G :: prog
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where
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  "G\<turnstile>s \<midarrow>c     \<midarrow>n\<rightarrow>    s' \<equiv> G\<turnstile>s \<midarrow>In1r  c\<succ>\<midarrow>n\<rightarrow> (\<diamondsuit>    ,  s')"
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| "G\<turnstile>s \<midarrow>e-\<succ>v  \<midarrow>n\<rightarrow>    s' \<equiv> G\<turnstile>s \<midarrow>In1l e\<succ>\<midarrow>n\<rightarrow> (In1 v ,  s')"
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| "G\<turnstile>s \<midarrow>e=\<succ>vf \<midarrow>n\<rightarrow>    s' \<equiv> G\<turnstile>s \<midarrow>In2  e\<succ>\<midarrow>n\<rightarrow> (In2 vf,  s')"
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| "G\<turnstile>s \<midarrow>e\<doteq>\<succ>v  \<midarrow>n\<rightarrow>    s' \<equiv> G\<turnstile>s \<midarrow>In3  e\<succ>\<midarrow>n\<rightarrow> (In3 v ,  s')"
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--{* propagation of abrupt completion *}
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| Abrupt:   "G\<turnstile>(Some xc,s) \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (arbitrary3 t,(Some xc,s))"
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--{* evaluation of variables *}
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| LVar:	"G\<turnstile>Norm s \<midarrow>LVar vn=\<succ>lvar vn s\<midarrow>n\<rightarrow> Norm s"
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| FVar:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>Init statDeclC\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>e-\<succ>a\<midarrow>n\<rightarrow> s2;
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	  (v,s2') = fvar statDeclC stat fn a s2;
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          s3 = check_field_access G accC statDeclC fn stat a s2'\<rbrakk> \<Longrightarrow>
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	  G\<turnstile>Norm s0 \<midarrow>{accC,statDeclC,stat}e..fn=\<succ>v\<midarrow>n\<rightarrow> s3"
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| AVar:	"\<lbrakk>G\<turnstile> Norm s0 \<midarrow>e1-\<succ>a\<midarrow>n\<rightarrow> s1 ; G\<turnstile>s1 \<midarrow>e2-\<succ>i\<midarrow>n\<rightarrow> s2; 
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	  (v,s2') = avar G i a s2\<rbrakk> \<Longrightarrow>
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	              G\<turnstile>Norm s0 \<midarrow>e1.[e2]=\<succ>v\<midarrow>n\<rightarrow> s2'"
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--{* evaluation of expressions *}
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| NewC:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>Init C\<midarrow>n\<rightarrow> s1;
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	  G\<turnstile>     s1 \<midarrow>halloc (CInst C)\<succ>a\<rightarrow> s2\<rbrakk> \<Longrightarrow>
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	                          G\<turnstile>Norm s0 \<midarrow>NewC C-\<succ>Addr a\<midarrow>n\<rightarrow> s2"
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| NewA:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>init_comp_ty T\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>e-\<succ>i'\<midarrow>n\<rightarrow> s2; 
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	  G\<turnstile>abupd (check_neg i') s2 \<midarrow>halloc (Arr T (the_Intg i'))\<succ>a\<rightarrow> s3\<rbrakk> \<Longrightarrow>
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	                        G\<turnstile>Norm s0 \<midarrow>New T[e]-\<succ>Addr a\<midarrow>n\<rightarrow> s3"
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| Cast:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1;
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	  s2 = abupd (raise_if (\<not>G,snd s1\<turnstile>v fits T) ClassCast) s1\<rbrakk> \<Longrightarrow>
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			        G\<turnstile>Norm s0 \<midarrow>Cast T e-\<succ>v\<midarrow>n\<rightarrow> s2"
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| Inst:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1;
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	  b = (v\<noteq>Null \<and> G,store s1\<turnstile>v fits RefT T)\<rbrakk> \<Longrightarrow>
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			      G\<turnstile>Norm s0 \<midarrow>e InstOf T-\<succ>Bool b\<midarrow>n\<rightarrow> s1"
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| Lit:			   "G\<turnstile>Norm s \<midarrow>Lit v-\<succ>v\<midarrow>n\<rightarrow> Norm s"
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| UnOp: "\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1\<rbrakk> 
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         \<Longrightarrow> G\<turnstile>Norm s0 \<midarrow>UnOp unop e-\<succ>(eval_unop unop v)\<midarrow>n\<rightarrow> s1"
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| BinOp: "\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e1-\<succ>v1\<midarrow>n\<rightarrow> s1; 
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           G\<turnstile>s1 \<midarrow>(if need_second_arg binop v1 then (In1l e2) else (In1r Skip))
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            \<succ>\<midarrow>n\<rightarrow> (In1 v2,s2)\<rbrakk> 
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         \<Longrightarrow> G\<turnstile>Norm s0 \<midarrow>BinOp binop e1 e2-\<succ>(eval_binop binop v1 v2)\<midarrow>n\<rightarrow> s2"
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| Super:		   "G\<turnstile>Norm s \<midarrow>Super-\<succ>val_this s\<midarrow>n\<rightarrow> Norm s"
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| Acc:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>va=\<succ>(v,f)\<midarrow>n\<rightarrow> s1\<rbrakk> \<Longrightarrow>
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	                          G\<turnstile>Norm s0 \<midarrow>Acc va-\<succ>v\<midarrow>n\<rightarrow> s1"
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| Ass:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>va=\<succ>(w,f)\<midarrow>n\<rightarrow> s1;
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          G\<turnstile>     s1 \<midarrow>e-\<succ>v     \<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow>
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				   G\<turnstile>Norm s0 \<midarrow>va:=e-\<succ>v\<midarrow>n\<rightarrow> assign f v s2"
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| Cond:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e0-\<succ>b\<midarrow>n\<rightarrow> s1;
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          G\<turnstile>     s1 \<midarrow>(if the_Bool b then e1 else e2)-\<succ>v\<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow>
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			    G\<turnstile>Norm s0 \<midarrow>e0 ? e1 : e2-\<succ>v\<midarrow>n\<rightarrow> s2"
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| Call:	
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  "\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>a'\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>args\<doteq>\<succ>vs\<midarrow>n\<rightarrow> s2;
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    D = invocation_declclass G mode (store s2) a' statT \<lparr>name=mn,parTs=pTs\<rparr>; 
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    s3=init_lvars G D \<lparr>name=mn,parTs=pTs\<rparr> mode a' vs s2;
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    s3' = check_method_access G accC statT mode \<lparr>name=mn,parTs=pTs\<rparr> a' s3;
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    G\<turnstile>s3'\<midarrow>Methd D \<lparr>name=mn,parTs=pTs\<rparr>-\<succ>v\<midarrow>n\<rightarrow> s4
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   \<rbrakk>
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   \<Longrightarrow> 
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    G\<turnstile>Norm s0 \<midarrow>{accC,statT,mode}e\<cdot>mn({pTs}args)-\<succ>v\<midarrow>n\<rightarrow> (restore_lvars s2 s4)"
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| Methd:"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>body G D sig-\<succ>v\<midarrow>n\<rightarrow> s1\<rbrakk> \<Longrightarrow>
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				G\<turnstile>Norm s0 \<midarrow>Methd D sig-\<succ>v\<midarrow>Suc n\<rightarrow> s1"
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| Body:	"\<lbrakk>G\<turnstile>Norm s0\<midarrow>Init D\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>c\<midarrow>n\<rightarrow> s2;
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          s3 = (if (\<exists> l. abrupt s2 = Some (Jump (Break l)) \<or>  
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                         abrupt s2 = Some (Jump (Cont l)))
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                  then abupd (\<lambda> x. Some (Error CrossMethodJump)) s2 
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                  else s2)\<rbrakk>\<Longrightarrow>
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         G\<turnstile>Norm s0 \<midarrow>Body D c
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          -\<succ>the (locals (store s2) Result)\<midarrow>n\<rightarrow>abupd (absorb Ret) s3"
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--{* evaluation of expression lists *}
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| Nil:
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				"G\<turnstile>Norm s0 \<midarrow>[]\<doteq>\<succ>[]\<midarrow>n\<rightarrow> Norm s0"
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| Cons:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e -\<succ> v \<midarrow>n\<rightarrow> s1;
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          G\<turnstile>     s1 \<midarrow>es\<doteq>\<succ>vs\<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow>
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			     G\<turnstile>Norm s0 \<midarrow>e#es\<doteq>\<succ>v#vs\<midarrow>n\<rightarrow> s2"
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--{* execution of statements *}
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| Skip:	 			    "G\<turnstile>Norm s \<midarrow>Skip\<midarrow>n\<rightarrow> Norm s"
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| Expr:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1\<rbrakk> \<Longrightarrow>
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				  G\<turnstile>Norm s0 \<midarrow>Expr e\<midarrow>n\<rightarrow> s1"
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| Lab:  "\<lbrakk>G\<turnstile>Norm s0 \<midarrow>c \<midarrow>n\<rightarrow> s1\<rbrakk> \<Longrightarrow>
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                             G\<turnstile>Norm s0 \<midarrow>l\<bullet> c\<midarrow>n\<rightarrow> abupd (absorb l) s1"
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| Comp:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>c1 \<midarrow>n\<rightarrow> s1;
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	  G\<turnstile>     s1 \<midarrow>c2 \<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow>
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				 G\<turnstile>Norm s0 \<midarrow>c1;; c2\<midarrow>n\<rightarrow> s2"
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| If:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>b\<midarrow>n\<rightarrow> s1;
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	  G\<turnstile>     s1\<midarrow>(if the_Bool b then c1 else c2)\<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow>
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		       G\<turnstile>Norm s0 \<midarrow>If(e) c1 Else c2 \<midarrow>n\<rightarrow> s2"
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| Loop:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>b\<midarrow>n\<rightarrow> s1;
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	  if the_Bool b 
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             then (G\<turnstile>s1 \<midarrow>c\<midarrow>n\<rightarrow> s2 \<and> 
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                   G\<turnstile>(abupd (absorb (Cont l)) s2) \<midarrow>l\<bullet> While(e) c\<midarrow>n\<rightarrow> s3)
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	     else s3 = s1\<rbrakk> \<Longrightarrow>
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			      G\<turnstile>Norm s0 \<midarrow>l\<bullet> While(e) c\<midarrow>n\<rightarrow> s3"
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| Jmp: "G\<turnstile>Norm s \<midarrow>Jmp j\<midarrow>n\<rightarrow> (Some (Jump j), s)"
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| Throw:"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>e-\<succ>a'\<midarrow>n\<rightarrow> s1\<rbrakk> \<Longrightarrow>
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				 G\<turnstile>Norm s0 \<midarrow>Throw e\<midarrow>n\<rightarrow> abupd (throw a') s1"
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| Try:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>c1\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>sxalloc\<rightarrow> s2;
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	  if G,s2\<turnstile>catch tn then G\<turnstile>new_xcpt_var vn s2 \<midarrow>c2\<midarrow>n\<rightarrow> s3 else s3 = s2\<rbrakk>
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          \<Longrightarrow>
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		  G\<turnstile>Norm s0 \<midarrow>Try c1 Catch(tn vn) c2\<midarrow>n\<rightarrow> s3"
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| Fin:	"\<lbrakk>G\<turnstile>Norm s0 \<midarrow>c1\<midarrow>n\<rightarrow> (x1,s1);
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	  G\<turnstile>Norm s1 \<midarrow>c2\<midarrow>n\<rightarrow> s2;
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          s3=(if (\<exists> err. x1=Some (Error err)) 
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              then (x1,s1) 
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              else abupd (abrupt_if (x1\<noteq>None) x1) s2)\<rbrakk> \<Longrightarrow>
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              G\<turnstile>Norm s0 \<midarrow>c1 Finally c2\<midarrow>n\<rightarrow> s3"
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| Init:	"\<lbrakk>the (class G C) = c;
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	  if inited C (globs s0) then s3 = Norm s0
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	  else (G\<turnstile>Norm (init_class_obj G C s0)
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	          \<midarrow>(if C = Object then Skip else Init (super c))\<midarrow>n\<rightarrow> s1 \<and>
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	        G\<turnstile>set_lvars empty s1 \<midarrow>init c\<midarrow>n\<rightarrow> s2 \<and> 
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                s3 = restore_lvars s1 s2)\<rbrakk>
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          \<Longrightarrow>
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		 G\<turnstile>Norm s0 \<midarrow>Init C\<midarrow>n\<rightarrow> s3"
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   193
monos
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  if_bool_eq_conj
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declare split_if     [split del] split_if_asm     [split del]
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        option.split [split del] option.split_asm [split del]
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        not_None_eq [simp del] 
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        split_paired_All [simp del] split_paired_Ex [simp del]
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declaration {* K (Simplifier.map_ss (fn ss => ss delloop "split_all_tac")) *}
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inductive_cases evaln_cases: "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v, s')"
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inductive_cases evaln_elim_cases:
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	"G\<turnstile>(Some xc, s) \<midarrow>t                        \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r Skip                      \<succ>\<midarrow>n\<rightarrow> (x, s')"
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        "G\<turnstile>Norm s \<midarrow>In1r (Jmp j)                   \<succ>\<midarrow>n\<rightarrow> (x, s')"
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        "G\<turnstile>Norm s \<midarrow>In1r (l\<bullet> c)                    \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In3  ([])                      \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In3  (e#es)                    \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (Lit w)                   \<succ>\<midarrow>n\<rightarrow> (v, s')"
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        "G\<turnstile>Norm s \<midarrow>In1l (UnOp unop e)             \<succ>\<midarrow>n\<rightarrow> (v, s')"
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        "G\<turnstile>Norm s \<midarrow>In1l (BinOp binop e1 e2)       \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In2  (LVar vn)                 \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (Cast T e)                \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (e InstOf T)              \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (Super)                   \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (Acc va)                  \<succ>\<midarrow>n\<rightarrow> (v, s')"
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   220
	"G\<turnstile>Norm s \<midarrow>In1r (Expr e)                  \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r (c1;; c2)                 \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (Methd C sig)             \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (Body D c)                \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (e0 ? e1 : e2)            \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r (If(e) c1 Else c2)        \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r (l\<bullet> While(e) c)           \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r (c1 Finally c2)           \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r (Throw e)                 \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In1l (NewC C)                  \<succ>\<midarrow>n\<rightarrow> (v, s')"
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   230
	"G\<turnstile>Norm s \<midarrow>In1l (New T[e])                \<succ>\<midarrow>n\<rightarrow> (v, s')"
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   231
	"G\<turnstile>Norm s \<midarrow>In1l (Ass va e)                \<succ>\<midarrow>n\<rightarrow> (v, s')"
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	"G\<turnstile>Norm s \<midarrow>In1r (Try c1 Catch(tn vn) c2)  \<succ>\<midarrow>n\<rightarrow> (x, s')"
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	"G\<turnstile>Norm s \<midarrow>In2  ({accC,statDeclC,stat}e..fn) \<succ>\<midarrow>n\<rightarrow> (v, s')"
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   234
	"G\<turnstile>Norm s \<midarrow>In2  (e1.[e2])                 \<succ>\<midarrow>n\<rightarrow> (v, s')"
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   235
	"G\<turnstile>Norm s \<midarrow>In1l ({accC,statT,mode}e\<cdot>mn({pT}p)) \<succ>\<midarrow>n\<rightarrow> (v, s')"
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   236
	"G\<turnstile>Norm s \<midarrow>In1r (Init C)                  \<succ>\<midarrow>n\<rightarrow> (x, s')"
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        "G\<turnstile>Norm s \<midarrow>In1r (Init C)                  \<succ>\<midarrow>n\<rightarrow> (x, s')"
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declare split_if     [split] split_if_asm     [split] 
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        option.split [split] option.split_asm [split]
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a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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        not_None_eq [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.
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        split_paired_All [simp] split_paired_Ex [simp]
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declaration {* K (Simplifier.map_ss (fn ss => ss addloop ("split_all_tac", split_all_tac))) *}
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lemma evaln_Inj_elim: "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (w,s') \<Longrightarrow> case t of In1 ec \<Rightarrow>  
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  (case ec of Inl e \<Rightarrow> (\<exists>v. w = In1 v) | Inr c \<Rightarrow> w = \<diamondsuit>)  
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  | In2 e \<Rightarrow> (\<exists>v. w = In2 v) | In3 e \<Rightarrow> (\<exists>v. w = In3 v)"
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apply (erule evaln_cases , auto)
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apply (induct_tac "t")
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apply   (induct_tac "a")
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apply auto
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done
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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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text {* The following simplification procedures set up the proper injections of
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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   255
 terms and their corresponding values in the evaluation relation:
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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 E.g. an expression 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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 (injection @{term In1l} into terms) always evaluates to ordinary values 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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 (injection @{term In1} into generalised values @{term vals}). 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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*}
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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lemma evaln_expr_eq: "G\<turnstile>s \<midarrow>In1l t\<succ>\<midarrow>n\<rightarrow> (w, s') = (\<exists>v. w=In1 v \<and> G\<turnstile>s \<midarrow>t-\<succ>v \<midarrow>n\<rightarrow> s')"
89275a3ed7be Adapted to new inductive definition package.
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  by (auto, frule evaln_Inj_elim, auto)
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   263
89275a3ed7be Adapted to new inductive definition package.
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lemma evaln_var_eq: "G\<turnstile>s \<midarrow>In2 t\<succ>\<midarrow>n\<rightarrow> (w, s') = (\<exists>vf. w=In2 vf \<and> G\<turnstile>s \<midarrow>t=\<succ>vf\<midarrow>n\<rightarrow> s')"
89275a3ed7be Adapted to new inductive definition package.
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  by (auto, frule evaln_Inj_elim, auto)
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   266
89275a3ed7be Adapted to new inductive definition package.
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lemma evaln_exprs_eq: "G\<turnstile>s \<midarrow>In3 t\<succ>\<midarrow>n\<rightarrow> (w, s') = (\<exists>vs. w=In3 vs \<and> G\<turnstile>s \<midarrow>t\<doteq>\<succ>vs\<midarrow>n\<rightarrow> s')"
89275a3ed7be Adapted to new inductive definition package.
berghofe
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   268
  by (auto, frule evaln_Inj_elim, auto)
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   269
89275a3ed7be Adapted to new inductive definition package.
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lemma evaln_stmt_eq: "G\<turnstile>s \<midarrow>In1r t\<succ>\<midarrow>n\<rightarrow> (w, s') = (w=\<diamondsuit> \<and> G\<turnstile>s \<midarrow>t \<midarrow>n\<rightarrow> s')"
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  by (auto, frule evaln_Inj_elim, auto, frule evaln_Inj_elim, auto)
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simproc_setup evaln_expr ("G\<turnstile>s \<midarrow>In1l t\<succ>\<midarrow>n\<rightarrow> (w, s')") = {*
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  fn _ => fn _ => fn ct =>
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    (case Thm.term_of ct of
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      (_ $ _ $ _ $ _ $ _ $ (Const _ $ _) $ _) => NONE
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    | _ => SOME (mk_meta_eq @{thm evaln_expr_eq})) *}
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67bde7cfcf10 tuned ML/simproc declarations;
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simproc_setup evaln_var ("G\<turnstile>s \<midarrow>In2 t\<succ>\<midarrow>n\<rightarrow> (w, s')") = {*
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  fn _ => fn _ => fn ct =>
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    (case Thm.term_of ct of
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      (_ $ _ $ _ $ _ $ _ $ (Const _ $ _) $ _) => NONE
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    | _ => SOME (mk_meta_eq @{thm evaln_var_eq})) *}
12854
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24019
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simproc_setup evaln_exprs ("G\<turnstile>s \<midarrow>In3 t\<succ>\<midarrow>n\<rightarrow> (w, s')") = {*
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   286
  fn _ => fn _ => fn ct =>
67bde7cfcf10 tuned ML/simproc declarations;
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   287
    (case Thm.term_of ct of
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   288
      (_ $ _ $ _ $ _ $ _ $ (Const _ $ _) $ _) => NONE
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    | _ => SOME (mk_meta_eq @{thm evaln_exprs_eq})) *}
12854
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simproc_setup evaln_stmt ("G\<turnstile>s \<midarrow>In1r t\<succ>\<midarrow>n\<rightarrow> (w, s')") = {*
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   292
  fn _ => fn _ => fn ct =>
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   293
    (case Thm.term_of ct of
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   294
      (_ $ _ $ _ $ _ $ _ $ (Const _ $ _) $ _) => NONE
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   295
    | _ => SOME (mk_meta_eq @{thm evaln_stmt_eq})) *}
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   296
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ML_setup {* bind_thms ("evaln_AbruptIs", sum3_instantiate @{thm evaln.Abrupt}) *}
12854
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declare evaln_AbruptIs [intro!]
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lemma evaln_Callee: "G\<turnstile>Norm s\<midarrow>In1l (Callee l e)\<succ>\<midarrow>n\<rightarrow> (v,s') = False"
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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   301
proof -
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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   302
  { fix s t v s'
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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   303
    assume eval: "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s')" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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         normal: "normal s" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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   305
         callee: "t=In1l (Callee l e)"
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   306
    then have "False" by induct auto
13337
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   307
  }
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   308
  then show ?thesis
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   309
    by (cases s') fastsimp 
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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   310
qed
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   311
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
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   312
lemma evaln_InsInitE: "G\<turnstile>Norm s\<midarrow>In1l (InsInitE c e)\<succ>\<midarrow>n\<rightarrow> (v,s') = False"
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   313
proof -
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   314
  { fix s t v s'
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   315
    assume eval: "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s')" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   316
         normal: "normal s" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   317
         callee: "t=In1l (InsInitE c e)"
21765
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berghofe
parents: 18249
diff changeset
   318
    then have "False" by induct auto
13337
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   319
  }
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   320
  then show ?thesis
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   321
    by (cases s') fastsimp
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   322
qed
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   323
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   324
lemma evaln_InsInitV: "G\<turnstile>Norm s\<midarrow>In2 (InsInitV c w)\<succ>\<midarrow>n\<rightarrow> (v,s') = False"
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   325
proof -
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   326
  { fix s t v s'
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
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diff changeset
   327
    assume eval: "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s')" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   328
         normal: "normal s" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   329
         callee: "t=In2 (InsInitV c w)"
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   330
    then have "False" by induct auto
13337
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   331
  }  
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   332
  then show ?thesis
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   333
    by (cases s') fastsimp
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   334
qed
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   335
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   336
lemma evaln_FinA: "G\<turnstile>Norm s\<midarrow>In1r (FinA a c)\<succ>\<midarrow>n\<rightarrow> (v,s') = False"
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   337
proof -
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   338
  { fix s t v s'
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   339
    assume eval: "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s')" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   340
         normal: "normal s" and
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   341
         callee: "t=In1r (FinA a c)"
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   342
    then have "False" by induct auto
13337
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   343
  } 
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   344
  then show ?thesis
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   345
    by (cases s') fastsimp
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   346
qed
f75dfc606ac7 Added unary and binary operations like (+,-,<, ...); Added smallstep semantics (no proofs about it yet).
schirmer
parents: 12937
diff changeset
   347
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   348
lemma evaln_abrupt_lemma: "G\<turnstile>s \<midarrow>e\<succ>\<midarrow>n\<rightarrow> (v,s') \<Longrightarrow> 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   349
 fst s = Some xc \<longrightarrow> s' = s \<and> v = arbitrary3 e"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   350
apply (erule evaln_cases , auto)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   351
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   352
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   353
lemma evaln_abrupt: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   354
 "\<And>s'. G\<turnstile>(Some xc,s) \<midarrow>e\<succ>\<midarrow>n\<rightarrow> (w,s') = (s' = (Some xc,s) \<and>  
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   355
  w=arbitrary3 e \<and> G\<turnstile>(Some xc,s) \<midarrow>e\<succ>\<midarrow>n\<rightarrow> (arbitrary3 e,(Some xc,s)))"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   356
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   357
apply (frule evaln_abrupt_lemma, auto)+
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   358
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   359
24019
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   360
simproc_setup evaln_abrupt ("G\<turnstile>(Some xc,s) \<midarrow>e\<succ>\<midarrow>n\<rightarrow> (w,s')") = {*
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   361
  fn _ => fn _ => fn ct =>
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   362
    (case Thm.term_of ct of
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   363
      (_ $ _ $ _ $ _ $ _ $ _ $ (Const ("Pair",_) $ (Const ("Datatype.option.Some",_) $ _)$ _))
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   364
        => NONE
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   365
    | _ => SOME (mk_meta_eq @{thm evaln_abrupt}))
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   366
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   367
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   368
lemma evaln_LitI: "G\<turnstile>s \<midarrow>Lit v-\<succ>(if normal s then v else arbitrary)\<midarrow>n\<rightarrow> s"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   369
apply (case_tac "s", case_tac "a = None")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   370
by (auto intro!: evaln.Lit)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   371
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   372
lemma CondI: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   373
 "\<And>s1. \<lbrakk>G\<turnstile>s \<midarrow>e-\<succ>b\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>(if the_Bool b then e1 else e2)-\<succ>v\<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow> 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   374
  G\<turnstile>s \<midarrow>e ? e1 : e2-\<succ>(if normal s1 then v else arbitrary)\<midarrow>n\<rightarrow> s2"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   375
apply (case_tac "s", case_tac "a = None")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   376
by (auto intro!: evaln.Cond)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   377
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   378
lemma evaln_SkipI [intro!]: "G\<turnstile>s \<midarrow>Skip\<midarrow>n\<rightarrow> s"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   379
apply (case_tac "s", case_tac "a = None")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   380
by (auto intro!: evaln.Skip)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   381
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   382
lemma evaln_ExprI: "G\<turnstile>s \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s' \<Longrightarrow> G\<turnstile>s \<midarrow>Expr e\<midarrow>n\<rightarrow> s'"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   383
apply (case_tac "s", case_tac "a = None")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   384
by (auto intro!: evaln.Expr)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   385
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   386
lemma evaln_CompI: "\<lbrakk>G\<turnstile>s \<midarrow>c1\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>c2\<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow> G\<turnstile>s \<midarrow>c1;; c2\<midarrow>n\<rightarrow> s2"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   387
apply (case_tac "s", case_tac "a = None")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   388
by (auto intro!: evaln.Comp)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   389
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   390
lemma evaln_IfI: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   391
 "\<lbrakk>G\<turnstile>s \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1; G\<turnstile>s1 \<midarrow>(if the_Bool v then c1 else c2)\<midarrow>n\<rightarrow> s2\<rbrakk> \<Longrightarrow> 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   392
  G\<turnstile>s \<midarrow>If(e) c1 Else c2\<midarrow>n\<rightarrow> s2"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   393
apply (case_tac "s", case_tac "a = None")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   394
by (auto intro!: evaln.If)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   395
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   396
lemma evaln_SkipD [dest!]: "G\<turnstile>s \<midarrow>Skip\<midarrow>n\<rightarrow> s' \<Longrightarrow> s' = s" 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   397
by (erule evaln_cases, auto)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   398
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   399
lemma evaln_Skip_eq [simp]: "G\<turnstile>s \<midarrow>Skip\<midarrow>n\<rightarrow> s' = (s = s')"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   400
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   401
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   402
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
   403
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   404
13384
a34e38154413 Added conditional and (&&) and or (||).
schirmer
parents: 13337
diff changeset
   405
a34e38154413 Added conditional and (&&) and or (||).
schirmer
parents: 13337
diff changeset
   406
section {* evaln implies 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
   407
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   408
lemma 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
   409
  assumes evaln: "G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,s1)" 
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   410
  shows "G\<turnstile>s0 \<midarrow>t\<succ>\<rightarrow> (v,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
   411
using evaln 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
proof (induct)
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   413
  case (Loop s0 e n b s1 c s2 l s3)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   414
  note `G\<turnstile>Norm s0 \<midarrow>e-\<succ>b\<rightarrow> 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
   415
  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
   416
  have "if the_Bool b
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   417
        then (G\<turnstile>s1 \<midarrow>c\<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
   418
             G\<turnstile>abupd (absorb (Cont l)) s2 \<midarrow>l\<bullet> While(e) c\<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
   419
        else s3 = 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
   420
    using Loop.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
   421
  ultimately show ?case by (rule eval.Loop)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   422
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   423
  case (Try s0 c1 n s1 s2 C vn c2 s3)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   424
  note `G\<turnstile>Norm s0 \<midarrow>c1\<rightarrow> 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
   425
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   426
  note `G\<turnstile>s1 \<midarrow>sxalloc\<rightarrow> s2`
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
   427
  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
   428
  have "if G,s2\<turnstile>catch C then G\<turnstile>new_xcpt_var vn s2 \<midarrow>c2\<rightarrow> s3 else s3 = 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
   429
    using Try.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
   430
  ultimately show ?case by (rule eval.Try)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   432
  case (Init C c s0 s3 n s1 s2)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   433
  note `the (class G C) = 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
   434
  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
   435
  have "if inited C (globs 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
   436
           then s3 = Norm 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
   437
           else G\<turnstile>Norm ((init_class_obj G C) 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
   438
                  \<midarrow>(if C = Object then Skip else Init (super c))\<rightarrow> 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
   439
                G\<turnstile>(set_lvars empty) s1 \<midarrow>init c\<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
   440
                s3 = (set_lvars (locals (store s1))) 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
   441
    using Init.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
   442
  ultimately show ?case by (rule eval.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
   443
qed (rule eval.intros,(assumption+ | assumption?))+
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   444
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   445
lemma Suc_le_D_lemma: "\<lbrakk>Suc n <= m'; (\<And>m. n <= m \<Longrightarrow> P (Suc m)) \<rbrakk> \<Longrightarrow> P m'"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   446
apply (frule Suc_le_D)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   447
apply fast
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   448
done
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   449
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   450
lemma evaln_nonstrict [rule_format (no_asm), elim]: 
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   451
  "G\<turnstile>s \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (w, s') \<Longrightarrow> \<forall>m. n\<le>m \<longrightarrow> G\<turnstile>s \<midarrow>t\<succ>\<midarrow>m\<rightarrow> (w, s')"
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   452
apply (erule evaln.induct)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   453
apply (tactic {* ALLGOALS (EVERY'[strip_tac, TRY o etac (thm "Suc_le_D_lemma"),
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   454
  REPEAT o smp_tac 1, 
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   455
  resolve_tac (thms "evaln.intros") THEN_ALL_NEW TRY o atac]) *})
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   456
(* 3 subgoals *)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   457
apply (auto split del: split_if)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   458
done
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   459
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   460
lemmas evaln_nonstrict_Suc = evaln_nonstrict [OF _ le_refl [THEN le_SucI]]
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   461
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   462
lemma evaln_max2: "\<lbrakk>G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>n1\<rightarrow> (w1, s1'); G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>n2\<rightarrow> (w2, s2')\<rbrakk> \<Longrightarrow> 
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   463
             G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>max n1 n2\<rightarrow> (w1, s1') \<and> G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>max n1 n2\<rightarrow> (w2, s2')"
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
by (fast intro: le_maxI1 le_maxI2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
corollary evaln_max2E [consumes 2]:
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   467
  "\<lbrakk>G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>n1\<rightarrow> (w1, s1'); G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>n2\<rightarrow> (w2, s2'); 
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   468
    \<lbrakk>G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>max n1 n2\<rightarrow> (w1, s1');G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>max n1 n2\<rightarrow> (w2, s2') \<rbrakk> \<Longrightarrow> P \<rbrakk> \<Longrightarrow> 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
   469
by (drule (1) evaln_max2) 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
   470
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   471
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   472
lemma evaln_max3: 
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   473
"\<lbrakk>G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>n1\<rightarrow> (w1, s1'); G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>n2\<rightarrow> (w2, s2'); G\<turnstile>s3 \<midarrow>t3\<succ>\<midarrow>n3\<rightarrow> (w3, s3')\<rbrakk> \<Longrightarrow>
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   474
 G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>max (max n1 n2) n3\<rightarrow> (w1, s1') \<and>
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   475
 G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>max (max n1 n2) n3\<rightarrow> (w2, s2') \<and> 
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   476
 G\<turnstile>s3 \<midarrow>t3\<succ>\<midarrow>max (max n1 n2) n3\<rightarrow> (w3, s3')"
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   477
apply (drule (1) evaln_max2, erule thin_rl)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   478
apply (fast intro!: le_maxI1 le_maxI2)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   479
done
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   480
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
   481
corollary evaln_max3E: 
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   482
"\<lbrakk>G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>n1\<rightarrow> (w1, s1'); G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>n2\<rightarrow> (w2, s2'); G\<turnstile>s3 \<midarrow>t3\<succ>\<midarrow>n3\<rightarrow> (w3, s3');
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   483
   \<lbrakk>G\<turnstile>s1 \<midarrow>t1\<succ>\<midarrow>max (max n1 n2) n3\<rightarrow> (w1, s1');
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   484
    G\<turnstile>s2 \<midarrow>t2\<succ>\<midarrow>max (max n1 n2) n3\<rightarrow> (w2, s2'); 
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   485
    G\<turnstile>s3 \<midarrow>t3\<succ>\<midarrow>max (max n1 n2) n3\<rightarrow> (w3, s3')
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
   486
   \<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
   487
  \<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
   488
by (drule (2) evaln_max3) 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
   489
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   490
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   491
lemma le_max3I1: "(n2::nat) \<le> max n1 (max n2 n3)"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   492
proof -
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   493
  have "n2 \<le> max n2 n3"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   494
    by (rule le_maxI1)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   495
  also
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   496
  have "max n2 n3 \<le> max n1 (max n2 n3)"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   497
    by (rule le_maxI2)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   498
  finally
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   499
  show ?thesis .
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   500
qed
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   501
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   502
lemma le_max3I2: "(n3::nat) \<le> max n1 (max n2 n3)"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   503
proof -
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   504
  have "n3 \<le> max n2 n3"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   505
    by (rule le_maxI2)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   506
  also
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   507
  have "max n2 n3 \<le> max n1 (max n2 n3)"
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   508
    by (rule le_maxI2)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   509
  finally
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   510
  show ?thesis .
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   511
qed
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   512
24019
67bde7cfcf10 tuned ML/simproc declarations;
wenzelm
parents: 23747
diff changeset
   513
declare [[simproc del: 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.
schirmer
parents: 13601
diff changeset
   514
13384
a34e38154413 Added conditional and (&&) and or (||).
schirmer
parents: 13337
diff changeset
   515
section {* eval implies evaln *}
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   516
lemma eval_evaln: 
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
  assumes eval: "G\<turnstile>s0 \<midarrow>t\<succ>\<rightarrow> (v,s1)"
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12925
diff changeset
   518
  shows  "\<exists>n. G\<turnstile>s0 \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (v,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
   519
using 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
   520
proof (induct)
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   521
  case (Abrupt xc s 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
   522
  obtain n where
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   523
    "G\<turnstile>(Some xc, s) \<midarrow>t\<succ>\<midarrow>n\<rightarrow> (arbitrary3 t, (Some xc, s))"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   524
    by (iprover intro: evaln.Abrupt)
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
   525
  then 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
   526
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
   527
  case 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
   528
  show ?case by (blast intro: evaln.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
   529
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   530
  case (Expr s0 e v 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
   531
  then obtain n 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
   532
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   533
    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
   534
  then have "G\<turnstile>Norm s0 \<midarrow>Expr e\<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
   535
    by (rule evaln.Expr) 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   536
  then 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
   537
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   538
  case (Lab s0 c s1 l)
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
   539
  then obtain n 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
   540
    "G\<turnstile>Norm s0 \<midarrow>c\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   541
    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
   542
  then have "G\<turnstile>Norm s0 \<midarrow>l\<bullet> c\<midarrow>n\<rightarrow> abupd (absorb l) 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
   543
    by (rule evaln.Lab)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   545
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   546
  case (Comp s0 c1 s1 c2 s2)
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
   547
  then obtain n1 n2 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
   548
    "G\<turnstile>Norm s0 \<midarrow>c1\<midarrow>n1\<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
   549
    "G\<turnstile>s1 \<midarrow>c2\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   550
    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
   551
  then have "G\<turnstile>Norm s0 \<midarrow>c1;; c2\<midarrow>max n1 n2\<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
   552
    by (blast intro: evaln.Comp dest: evaln_max2 )
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   553
  then 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
   554
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   555
  case (If s0 e b s1 c1 c2 s2)
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
   556
  then obtain n1 n2 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
   557
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>b\<midarrow>n1\<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
   558
    "G\<turnstile>s1 \<midarrow>(if the_Bool b then c1 else c2)\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   559
    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
   560
  then have "G\<turnstile>Norm s0 \<midarrow>If(e) c1 Else c2\<midarrow>max n1 n2\<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
   561
    by (blast intro: evaln.If dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   562
  then 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
   563
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   564
  case (Loop s0 e b s1 c s2 l s3)
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
   565
  from Loop.hyps obtain n1 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
   566
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>b\<midarrow>n1\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   567
    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
   568
  moreover from Loop.hyps obtain n2 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
   569
    "if the_Bool b 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
        then (G\<turnstile>s1 \<midarrow>c\<midarrow>n2\<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
   571
              G\<turnstile>(abupd (absorb (Cont l)) s2)\<midarrow>l\<bullet> While(e) c\<midarrow>n2\<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
   572
	else s3 = s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   573
    by simp (iprover intro: evaln_nonstrict le_maxI1 le_maxI2)
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
   574
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>l\<bullet> While(e) c\<midarrow>max n1 n2\<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
   576
    apply -
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
    apply (rule evaln.Loop)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   578
    apply   (iprover intro: evaln_nonstrict intro: le_maxI1)
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   579
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
   580
    apply   (auto intro: evaln_nonstrict intro: le_maxI2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
    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
   582
  then 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
   583
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   584
  case (Jmp s j)
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
  have "G\<turnstile>Norm s \<midarrow>Jmp j\<midarrow>n\<rightarrow> (Some (Jump j), 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
   586
    by (rule evaln.Jmp)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   588
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   589
  case (Throw s0 e a 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
   590
  then obtain n 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
   591
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>a\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   592
    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
   593
  then have "G\<turnstile>Norm s0 \<midarrow>Throw e\<midarrow>n\<rightarrow> abupd (throw a) 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
   594
    by (rule evaln.Throw)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   595
  then 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
   596
next 
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   597
  case (Try s0 c1 s1 s2 catchC vn c2 s3)
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
   598
  from Try.hyps obtain n1 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
   599
    "G\<turnstile>Norm s0 \<midarrow>c1\<midarrow>n1\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   600
    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
   601
  moreover 
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   602
  note sxalloc = `G\<turnstile>s1 \<midarrow>sxalloc\<rightarrow> s2`
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
   603
  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
   604
  from Try.hyps obtain n2 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
   605
    "if G,s2\<turnstile>catch catchC then G\<turnstile>new_xcpt_var vn s2 \<midarrow>c2\<midarrow>n2\<rightarrow> s3 else s3 = 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
   606
    by fastsimp 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   607
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   608
  have "G\<turnstile>Norm s0 \<midarrow>Try c1 Catch(catchC vn) c2\<midarrow>max n1 n2\<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
   609
    by (auto intro!: evaln.Try le_maxI1 le_maxI2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   610
  then 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
   611
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   612
  case (Fin s0 c1 x1 s1 c2 s2 s3)
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
   613
  from Fin obtain n1 n2 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
   614
    "G\<turnstile>Norm s0 \<midarrow>c1\<midarrow>n1\<rightarrow> (x1, 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
   615
    "G\<turnstile>Norm s1 \<midarrow>c2\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   616
    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
   617
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   618
  note s3 = `s3 = (if \<exists>err. x1 = Some (Error err) 
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   619
                   then (x1, s1)
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   620
                   else abupd (abrupt_if (x1 \<noteq> None) x1) s2)`
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
  ultimately 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
    "G\<turnstile>Norm s0 \<midarrow>c1 Finally c2\<midarrow>max n1 n2\<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
   624
    by (blast intro: evaln.Fin dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   625
  then 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
   626
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   627
  case (Init C c s0 s3 s1 s2)
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   628
  note cls = `the (class G C) = 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
   629
  moreover from Init.hyps obtain n where
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   630
      "if inited C (globs s0) then s3 = Norm s0
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   631
       else (G\<turnstile>Norm (init_class_obj G C s0)
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   632
	      \<midarrow>(if C = Object then Skip else Init (super c))\<midarrow>n\<rightarrow> s1 \<and>
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   633
	           G\<turnstile>set_lvars empty s1 \<midarrow>init c\<midarrow>n\<rightarrow> s2 \<and> 
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   634
                   s3 = restore_lvars s1 s2)"
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
   635
    by (auto intro: evaln_nonstrict le_maxI1 le_maxI2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  ultimately have "G\<turnstile>Norm s0 \<midarrow>Init C\<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
   637
    by (rule evaln.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
   638
  then 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
   639
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   640
  case (NewC s0 C s1 a s2)
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
   641
  then obtain n 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
   642
    "G\<turnstile>Norm s0 \<midarrow>Init C\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   643
    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
   644
  with NewC 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>NewC C-\<succ>Addr a\<midarrow>n\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   646
    by (iprover intro: evaln.NewC)
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
  then 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
   648
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   649
  case (NewA s0 T s1 e i s2 a s3)
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
   650
  then obtain n1 n2 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
   651
    "G\<turnstile>Norm s0 \<midarrow>init_comp_ty T\<midarrow>n1\<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
   652
    "G\<turnstile>s1 \<midarrow>e-\<succ>i\<midarrow>n2\<rightarrow> s2"      
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   653
    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
   654
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   655
  note `G\<turnstile>abupd (check_neg i) s2 \<midarrow>halloc Arr T (the_Intg i)\<succ>a\<rightarrow> s3`
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
   656
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>New T[e]-\<succ>Addr a\<midarrow>max n1 n2\<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
   658
    by (blast intro: evaln.NewA dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   659
  then 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
   660
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   661
  case (Cast s0 e v s1 s2 castT)
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
  then obtain n 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
   663
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   664
    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
   665
  moreover 
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   666
  note `s2 = abupd (raise_if (\<not> G,snd s1\<turnstile>v fits castT) ClassCast) 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
   667
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>Cast castT 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
   669
    by (rule evaln.Cast)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   670
  then 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
   671
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   672
  case (Inst s0 e v s1 b 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
   673
  then obtain n 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
   674
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   675
    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
   676
  moreover 
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   677
  note `b = (v \<noteq> Null \<and> G,snd s1\<turnstile>v fits RefT 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
   678
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>e InstOf T-\<succ>Bool b\<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
   680
    by (rule evaln.Inst)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   682
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
   683
  case (Lit s 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
   684
  have "G\<turnstile>Norm s \<midarrow>Lit v-\<succ>v\<midarrow>n\<rightarrow> Norm 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
   685
    by (rule evaln.Lit)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   687
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   688
  case (UnOp s0 e v s1 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
   689
  then obtain n 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
   690
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   691
    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
   692
  hence "G\<turnstile>Norm s0 \<midarrow>UnOp unop e-\<succ>eval_unop unop 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
   693
    by (rule evaln.UnOp)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   694
  then 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
   695
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   696
  case (BinOp s0 e1 v1 s1 binop e2 v2 s2)
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
   697
  then obtain n1 n2 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
   698
    "G\<turnstile>Norm s0 \<midarrow>e1-\<succ>v1\<midarrow>n1\<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
   699
    "G\<turnstile>s1 \<midarrow>(if need_second_arg binop v1 then In1l e2
13384
a34e38154413 Added conditional and (&&) and or (||).
schirmer
parents: 13337
diff changeset
   700
               else In1r Skip)\<succ>\<midarrow>n2\<rightarrow> (In1 v2, s2)"    
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   701
    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
   702
  hence "G\<turnstile>Norm s0 \<midarrow>BinOp binop e1 e2-\<succ>(eval_binop binop v1 v2)\<midarrow>max n1 n2
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   703
          \<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
   704
    by (blast intro!: evaln.BinOp dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   705
  then 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
   706
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
   707
  case (Super 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
   708
  have "G\<turnstile>Norm s \<midarrow>Super-\<succ>val_this s\<midarrow>n\<rightarrow> Norm 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
   709
    by (rule evaln.Super)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   710
  then 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
   711
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   712
  case (Acc s0 va v f 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
   713
  then obtain n 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
   714
    "G\<turnstile>Norm s0 \<midarrow>va=\<succ>(v, f)\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   715
    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
   716
  then
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>Acc va-\<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
   718
    by (rule evaln.Acc)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   719
  then 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
   720
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   721
  case (Ass s0 var w f s1 e v s2)
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
   722
  then obtain n1 n2 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
   723
    "G\<turnstile>Norm s0 \<midarrow>var=\<succ>(w, f)\<midarrow>n1\<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
   724
    "G\<turnstile>s1 \<midarrow>e-\<succ>v\<midarrow>n2\<rightarrow> s2"      
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   725
    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
   726
  then
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   727
  have "G\<turnstile>Norm s0 \<midarrow>var:=e-\<succ>v\<midarrow>max n1 n2\<rightarrow> assign f v 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
   728
    by (blast intro: evaln.Ass dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   730
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   731
  case (Cond s0 e0 b s1 e1 e2 v s2)
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
   732
  then obtain n1 n2 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
   733
    "G\<turnstile>Norm s0 \<midarrow>e0-\<succ>b\<midarrow>n1\<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
   734
    "G\<turnstile>s1 \<midarrow>(if the_Bool b then e1 else e2)-\<succ>v\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   735
    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
   736
  then
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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 "G\<turnstile>Norm s0 \<midarrow>e0 ? e1 : e2-\<succ>v\<midarrow>max n1 n2\<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
   738
    by (blast intro: evaln.Cond dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   740
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   741
  case (Call s0 e a' s1 args vs s2 invDeclC mode statT mn pTs' s3 s3' accC' v s4)
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
   742
  then obtain n1 n2 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
   743
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>a'\<midarrow>n1\<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
   744
    "G\<turnstile>s1 \<midarrow>args\<doteq>\<succ>vs\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   745
    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
   746
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   747
  note `invDeclC = invocation_declclass G mode (store s2) a' statT 
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   748
                       \<lparr>name=mn,parTs=pTs'\<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
   749
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   750
  note `s3 = init_lvars G invDeclC \<lparr>name=mn,parTs=pTs'\<rparr> mode a' vs s2`
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
   751
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   752
  note `s3'=check_method_access G accC' statT mode \<lparr>name=mn,parTs=pTs'\<rparr> a' s3`
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
   753
  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
   754
  from Call.hyps
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  obtain m 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
   756
    "G\<turnstile>s3' \<midarrow>Methd invDeclC \<lparr>name=mn, parTs=pTs'\<rparr>-\<succ>v\<midarrow>m\<rightarrow> s4"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   757
    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
   758
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>{accC',statT,mode}e\<cdot>mn( {pTs'}args)-\<succ>v\<midarrow>max n1 (max n2 m)\<rightarrow> 
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   760
            (set_lvars (locals (store s2))) s4"
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
   761
    by (auto intro!: evaln.Call le_maxI1 le_max3I1 le_max3I2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  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
   763
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   764
  case (Methd s0 D sig v 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
   765
  then obtain n 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
   766
    "G\<turnstile>Norm s0 \<midarrow>body G D sig-\<succ>v\<midarrow>n\<rightarrow> s1"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   767
    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
   768
  then have "G\<turnstile>Norm s0 \<midarrow>Methd D sig-\<succ>v\<midarrow>Suc 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
   769
    by (rule evaln.Methd)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   771
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   772
  case (Body s0 D s1 c s2 s3)
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
  from Body.hyps obtain n1 n2 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
   774
    evaln_init: "G\<turnstile>Norm s0 \<midarrow>Init D\<midarrow>n1\<rightarrow> 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
   775
    evaln_c: "G\<turnstile>s1 \<midarrow>c\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   776
    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
   777
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   778
  note `s3 = (if \<exists>l. fst s2 = Some (Jump (Break l)) \<or> 
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
                     fst s2 = Some (Jump (Cont l))
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   780
              then abupd (\<lambda>x. Some (Error CrossMethodJump)) s2 
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   781
              else s2)`
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
   782
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents: 13601
diff changeset
   783
  have
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   784
     "G\<turnstile>Norm s0 \<midarrow>Body D c-\<succ>the (locals (store s2) Result)\<midarrow>max n1 n2
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
   785
       \<rightarrow> abupd (absorb Ret) s3"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   786
    by (iprover intro: evaln.Body dest: evaln_max2)
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
   787
  then 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
   788
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
   789
  case (LVar s 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
   790
  obtain n 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
   791
    "G\<turnstile>Norm s \<midarrow>LVar vn=\<succ>lvar vn s\<midarrow>n\<rightarrow> Norm s"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   792
    by (iprover intro: evaln.LVar)
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
   793
  then 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
   794
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   795
  case (FVar s0 statDeclC s1 e a s2 v s2' stat fn s3 accC)
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
   796
  then obtain n1 n2 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
   797
    "G\<turnstile>Norm s0 \<midarrow>Init statDeclC\<midarrow>n1\<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
   798
    "G\<turnstile>s1 \<midarrow>e-\<succ>a\<midarrow>n2\<rightarrow> s2"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   799
    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
   800
  moreover
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   801
  note `s3 = check_field_access G accC statDeclC fn stat a s2'`
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   802
    and `(v, s2') = fvar statDeclC stat fn a s2`
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
   803
  ultimately
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>{accC,statDeclC,stat}e..fn=\<succ>v\<midarrow>max n1 n2\<rightarrow> s3"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   805
    by (iprover intro: evaln.FVar dest: evaln_max2)
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
  then 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
   807
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   808
  case (AVar s0 e1 a s1 e2 i s2 v s2')
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
   809
  then obtain n1 n2 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
   810
    "G\<turnstile>Norm s0 \<midarrow>e1-\<succ>a\<midarrow>n1\<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
   811
    "G\<turnstile>s1 \<midarrow>e2-\<succ>i\<midarrow>n2\<rightarrow> s2"      
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   812
    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
   813
  moreover 
23350
50c5b0912a0c tuned proofs: avoid implicit prems;
wenzelm
parents: 22218
diff changeset
   814
  note `(v, s2') = avar G i a s2`
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
   815
  ultimately 
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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 "G\<turnstile>Norm s0 \<midarrow>e1.[e2]=\<succ>v\<midarrow>max n1 n2\<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
   817
    by (blast intro!: evaln.AVar dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then 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
   819
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
   820
  case (Nil s0)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   821
  show ?case by (iprover intro: evaln.Nil)
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
   822
next
21765
89275a3ed7be Adapted to new inductive definition package.
berghofe
parents: 18249
diff changeset
   823
  case (Cons s0 e v s1 es vs s2)
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
   824
  then obtain n1 n2 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
   825
    "G\<turnstile>Norm s0 \<midarrow>e-\<succ>v\<midarrow>n1\<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
   826
    "G\<turnstile>s1 \<midarrow>es\<doteq>\<succ>vs\<midarrow>n2\<rightarrow> s2"      
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 16417
diff changeset
   827
    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
   828
  then
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  have "G\<turnstile>Norm s0 \<midarrow>e # es\<doteq>\<succ>v # vs\<midarrow>max n1 n2\<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
   830
    by (blast intro!: evaln.Cons dest: evaln_max2)
a0b16d42d489 "Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the 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
  then show ?case ..
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
   832
qed
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
   833
       
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   834
end