author  wenzelm 
Sat, 07 Apr 2012 16:41:59 +0200  
changeset 47389  e8552cba702d 
parent 46222  cb3f370e66e1 
child 51717  9e7d1c139569 
permissions  rwrr 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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header {* Definite Assignment *} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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16417  3 
theory DefiniteAssignment imports WellType begin 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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 {* Definite Assignment Analysis (cf. 16) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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The definite assignment analysis approximates the sets of local 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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variables that will be assigned at a certain point of evaluation, and ensures 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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that we will only read variables which previously were assigned. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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It should conform to the following idea: 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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If the evaluation of a term completes normally (no abruption (exception, 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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break, continue, return) appeared) , the set of local variables calculated 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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by the analysis is a subset of the 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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variables that were actually assigned during evaluation. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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16 
To get more precise information about the sets of assigned variables the 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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analysis includes the following optimisations: 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\begin{itemize} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\item Inside of a while loop we also take care of the variables assigned 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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before break statements, since the break causes the while loop to 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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continue normally. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\item For conditional statements we take care of constant conditions to 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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statically determine the path of evaluation. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\item Inside a distinct path of a conditional statements we know to which 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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boolean value the condition has evaluated to, and so can retrieve more 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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information about the variables assigned during evaluation of the 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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boolean condition. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\end{itemize} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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30 
Since in our model of Java the return values of methods are stored in a local 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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variable we also ensure that every path of (normal) evaluation will assign the 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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result variable, or in the sense of real Java every path ends up in and 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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return instruction. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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 covered yet: 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\begin{itemize} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\item analysis of definite unassigned 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\item special treatment of final fields 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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\end{itemize} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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*} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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section {* Correct nesting of jump statements *} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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 {* For definite assignment it becomes crucial, that jumps (break, 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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continue, return) are nested correctly i.e. a continue jump is nested in a 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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matching while statement, a break jump is nested in a proper label statement, 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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a class initialiser does not terminate abruptly with a return. With this we 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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can for example ensure that evaluation of an expression will never end up 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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with a jump, since no breaks, continues or returns are allowed in an 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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expression. *} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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37956  52 
primrec jumpNestingOkS :: "jump set \<Rightarrow> stmt \<Rightarrow> bool" 
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where 

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"jumpNestingOkS jmps (Skip) = True" 

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 "jumpNestingOkS jmps (Expr e) = True" 

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 "jumpNestingOkS jmps (j\<bullet> s) = jumpNestingOkS ({j} \<union> jmps) s" 

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 "jumpNestingOkS jmps (c1;;c2) = (jumpNestingOkS jmps c1 \<and> 

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jumpNestingOkS jmps c2)" 

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 "jumpNestingOkS jmps (If(e) c1 Else c2) = (jumpNestingOkS jmps c1 \<and> 

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jumpNestingOkS jmps c2)" 

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 "jumpNestingOkS jmps (l\<bullet> While(e) c) = jumpNestingOkS ({Cont l} \<union> jmps) c" 

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{* The label of the while loop only handles continue jumps. Breaks are only 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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handled by @{term Lab} *} 
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 "jumpNestingOkS jmps (Jmp j) = (j \<in> jmps)" 
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 "jumpNestingOkS jmps (Throw e) = True" 

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 "jumpNestingOkS jmps (Try c1 Catch(C vn) c2) = (jumpNestingOkS jmps c1 \<and> 

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jumpNestingOkS jmps c2)" 

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 "jumpNestingOkS jmps (c1 Finally c2) = (jumpNestingOkS jmps c1 \<and> 

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jumpNestingOkS jmps c2)" 

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 "jumpNestingOkS jmps (Init C) = True" 

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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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{* wellformedness of the program must enshure that for all initializers 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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jumpNestingOkS {} holds *} 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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{* Dummy analysis for intermediate smallstep term @{term FinA} *} 
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 "jumpNestingOkS jmps (FinA a c) = False" 
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definition jumpNestingOk :: "jump set \<Rightarrow> term \<Rightarrow> bool" where 
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"jumpNestingOk jmps t = (case t of 
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In1 se \<Rightarrow> (case se of 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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Inl e \<Rightarrow> True 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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 Inr s \<Rightarrow> jumpNestingOkS jmps s) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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 In2 v \<Rightarrow> True 
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 In3 es \<Rightarrow> True)" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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 jumpNestingOk_expr_simp [simp]: "jumpNestingOk jmps (In1l e) = True" 
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by (simp add: jumpNestingOk_def) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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 jumpNestingOk_expr_simp1 [simp]: "jumpNestingOk jmps \<langle>e::expr\<rangle> = True" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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by (simp add: inj_term_simps) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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 jumpNestingOk_stmt_simp [simp]: 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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"jumpNestingOk jmps (In1r s) = jumpNestingOkS jmps s" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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by (simp add: jumpNestingOk_def) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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94 

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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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95 
lemma jumpNestingOk_stmt_simp1 [simp]: 
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"jumpNestingOk jmps \<langle>s::stmt\<rangle> = jumpNestingOkS jmps s" 
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97 
by (simp add: inj_term_simps) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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98 

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lemma jumpNestingOk_var_simp [simp]: "jumpNestingOk jmps (In2 v) = True" 
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100 
by (simp add: jumpNestingOk_def) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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101 

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lemma jumpNestingOk_var_simp1 [simp]: "jumpNestingOk jmps \<langle>v::var\<rangle> = True" 
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103 
by (simp add: inj_term_simps) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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104 

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105 
lemma jumpNestingOk_expr_list_simp [simp]: "jumpNestingOk jmps (In3 es) = True" 
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106 
by (simp add: jumpNestingOk_def) 
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107 

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108 
lemma jumpNestingOk_expr_list_simp1 [simp]: 
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109 
"jumpNestingOk jmps \<langle>es::expr list\<rangle> = True" 
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110 
by (simp add: inj_term_simps) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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111 

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112 

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113 

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114 
section {* Calculation of assigned variables for boolean expressions*} 
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115 

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116 

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subsection {* Very restricted calculation fallback calculation *} 
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118 

37956  119 
primrec the_LVar_name :: "var \<Rightarrow> lname" 
120 
where "the_LVar_name (LVar n) = n" 

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37956  122 
primrec assignsE :: "expr \<Rightarrow> lname set" 
123 
and assignsV :: "var \<Rightarrow> lname set" 

124 
and assignsEs:: "expr list \<Rightarrow> lname set" 

125 
where 

126 
"assignsE (NewC c) = {}" 

127 
 "assignsE (NewA t e) = assignsE e" 

128 
 "assignsE (Cast t e) = assignsE e" 

129 
 "assignsE (e InstOf r) = assignsE e" 

130 
 "assignsE (Lit val) = {}" 

131 
 "assignsE (UnOp unop e) = assignsE e" 

132 
 "assignsE (BinOp binop e1 e2) = (if binop=CondAnd \<or> binop=CondOr 

133 
then (assignsE e1) 

134 
else (assignsE e1) \<union> (assignsE e2))" 

135 
 "assignsE (Super) = {}" 

136 
 "assignsE (Acc v) = assignsV v" 

137 
 "assignsE (v:=e) = (assignsV v) \<union> (assignsE e) \<union> 

138 
(if \<exists> n. v=(LVar n) then {the_LVar_name v} 

139 
else {})" 

140 
 "assignsE (b? e1 : e2) = (assignsE b) \<union> ((assignsE e1) \<inter> (assignsE e2))" 

141 
 "assignsE ({accC,statT,mode}objRef\<cdot>mn({pTs}args)) 

142 
= (assignsE objRef) \<union> (assignsEs args)" 

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143 
 {* Only dummy analysis for intermediate expressions 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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@{term Methd}, @{term Body}, @{term InsInitE} and @{term Callee} *} 
37956  145 
 "assignsE (Methd C sig) = {}" 
146 
 "assignsE (Body C s) = {}" 

147 
 "assignsE (InsInitE s e) = {}" 

148 
 "assignsE (Callee l e) = {}" 

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37956  150 
 "assignsV (LVar n) = {}" 
151 
 "assignsV ({accC,statDeclC,stat}objRef..fn) = assignsE objRef" 

152 
 "assignsV (e1.[e2]) = assignsE e1 \<union> assignsE e2" 

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153 

37956  154 
 "assignsEs [] = {}" 
155 
 "assignsEs (e#es) = assignsE e \<union> assignsEs es" 

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156 

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definition assigns :: "term \<Rightarrow> lname set" where 
37956  158 
"assigns t = (case t of 
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In1 se \<Rightarrow> (case se of 
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Inl e \<Rightarrow> assignsE e 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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161 
 Inr s \<Rightarrow> {}) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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162 
 In2 v \<Rightarrow> assignsV v 
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163 
 In3 es \<Rightarrow> assignsEs es)" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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164 

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165 
lemma assigns_expr_simp [simp]: "assigns (In1l e) = assignsE e" 
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166 
by (simp add: assigns_def) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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167 

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168 
lemma assigns_expr_simp1 [simp]: "assigns (\<langle>e\<rangle>) = assignsE e" 
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169 
by (simp add: inj_term_simps) 
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170 

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171 
lemma assigns_stmt_simp [simp]: "assigns (In1r s) = {}" 
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172 
by (simp add: assigns_def) 
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173 

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174 
lemma assigns_stmt_simp1 [simp]: "assigns (\<langle>s::stmt\<rangle>) = {}" 
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175 
by (simp add: inj_term_simps) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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176 

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177 
lemma assigns_var_simp [simp]: "assigns (In2 v) = assignsV v" 
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178 
by (simp add: assigns_def) 
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179 

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180 
lemma assigns_var_simp1 [simp]: "assigns (\<langle>v\<rangle>) = assignsV v" 
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181 
by (simp add: inj_term_simps) 
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182 

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183 
lemma assigns_expr_list_simp [simp]: "assigns (In3 es) = assignsEs es" 
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184 
by (simp add: assigns_def) 
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185 

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186 
lemma assigns_expr_list_simp1 [simp]: "assigns (\<langle>es\<rangle>) = assignsEs es" 
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187 
by (simp add: inj_term_simps) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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188 

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189 
subsection "Analysis of constant expressions" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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190 

37956  191 
primrec constVal :: "expr \<Rightarrow> val option" 
192 
where 

193 
"constVal (NewC c) = None" 

194 
 "constVal (NewA t e) = None" 

195 
 "constVal (Cast t e) = None" 

196 
 "constVal (Inst e r) = None" 

197 
 "constVal (Lit val) = Some val" 

198 
 "constVal (UnOp unop e) = (case (constVal e) of 

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199 
None \<Rightarrow> None 
37956  200 
 Some v \<Rightarrow> Some (eval_unop unop v))" 
201 
 "constVal (BinOp binop e1 e2) = (case (constVal e1) of 

202 
None \<Rightarrow> None 

203 
 Some v1 \<Rightarrow> (case (constVal e2) of 

204 
None \<Rightarrow> None 

205 
 Some v2 \<Rightarrow> Some (eval_binop 

206 
binop v1 v2)))" 

207 
 "constVal (Super) = None" 

208 
 "constVal (Acc v) = None" 

209 
 "constVal (Ass v e) = None" 

210 
 "constVal (Cond b e1 e2) = (case (constVal b) of 

211 
None \<Rightarrow> None 

212 
 Some bv\<Rightarrow> (case the_Bool bv of 

213 
True \<Rightarrow> (case (constVal e2) of 

214 
None \<Rightarrow> None 

215 
 Some v \<Rightarrow> constVal e1) 

216 
 False\<Rightarrow> (case (constVal e1) of 

217 
None \<Rightarrow> None 

218 
 Some v \<Rightarrow> constVal e2)))" 

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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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219 
{* Note that @{text "constVal (Cond b e1 e2)"} is stricter as it could be. 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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220 
It requires that all tree expressions are constant even if we can decide 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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221 
which branch to choose, provided the constant value of @{term b} *} 
37956  222 
 "constVal (Call accC statT mode objRef mn pTs args) = None" 
223 
 "constVal (Methd C sig) = None" 

224 
 "constVal (Body C s) = None" 

225 
 "constVal (InsInitE s e) = None" 

226 
 "constVal (Callee l e) = None" 

13688
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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227 

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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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228 
lemma constVal_Some_induct [consumes 1, case_names Lit UnOp BinOp CondL CondR]: 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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229 
assumes const: "constVal e = Some v" and 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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230 
hyp_Lit: "\<And> v. P (Lit v)" and 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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231 
hyp_UnOp: "\<And> unop e'. P e' \<Longrightarrow> P (UnOp unop e')" and 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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232 
hyp_BinOp: "\<And> binop e1 e2. \<lbrakk>P e1; P e2\<rbrakk> \<Longrightarrow> P (BinOp binop e1 e2)" and 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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hyp_CondL: "\<And> b bv e1 e2. \<lbrakk>constVal b = Some bv; the_Bool bv; P b; P e1\<rbrakk> 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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234 
\<Longrightarrow> P (b? e1 : e2)" and 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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235 
hyp_CondR: "\<And> b bv e1 e2. \<lbrakk>constVal b = Some bv; \<not>the_Bool bv; P b; P e2\<rbrakk> 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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236 
\<Longrightarrow> P (b? e1 : e2)" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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237 
shows "P e" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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238 
proof  
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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239 
have "True" and "\<And> v. constVal e = Some v \<Longrightarrow> P e" and "True" and "True" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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240 
proof (induct "x::var" and e and "s::stmt" and "es::expr list") 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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241 
case Lit 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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242 
show ?case by (rule hyp_Lit) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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243 
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.
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244 
case UnOp 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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245 
thus ?case 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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246 
by (auto intro: hyp_UnOp) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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247 
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.
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248 
case BinOp 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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249 
thus ?case 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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250 
by (auto intro: hyp_BinOp) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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251 
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.
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252 
case (Cond b e1 e2) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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253 
then obtain v where v: "constVal (b ? e1 : e2) = Some v" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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254 
by blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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255 
then obtain bv where bv: "constVal b = Some bv" 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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256 
by simp 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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257 
show ?case 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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258 
proof (cases "the_Bool bv") 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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259 
case True 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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260 
with Cond show ?thesis using v bv 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
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261 
by (auto intro: hyp_CondL) 
13688
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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262 
next 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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263 
case False 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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264 
with Cond show ?thesis using v bv 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
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265 
by (auto intro: hyp_CondR) 
13688
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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266 
qed 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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267 
qed (simp_all) 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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268 
with const 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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269 
show ?thesis 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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270 
by blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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271 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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272 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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273 
lemma assignsE_const_simp: "constVal e = Some v \<Longrightarrow> assignsE e = {}" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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274 
by (induct rule: constVal_Some_induct) simp_all 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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275 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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276 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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277 
subsection {* Main analysis for boolean expressions *} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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278 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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279 
text {* Assigned local variables after evaluating the expression if it evaluates 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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280 
to a specific boolean value. If the expression cannot evaluate to a 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
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281 
@{term Boolean} value UNIV is returned. If we expect true/false the opposite 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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282 
constant false/true will also lead to UNIV. *} 
37956  283 
primrec assigns_if :: "bool \<Rightarrow> expr \<Rightarrow> lname set" 
284 
where 

285 
"assigns_if b (NewC c) = UNIV" {*can never evaluate to Boolean*} 

286 
 "assigns_if b (NewA t e) = UNIV" {*can never evaluate to Boolean*} 

287 
 "assigns_if b (Cast t e) = assigns_if b e" 

288 
 "assigns_if b (Inst e r) = assignsE e" {*Inst has type Boolean but 

289 
e is a reference type*} 

290 
 "assigns_if b (Lit val) = (if val=Bool b then {} else UNIV)" 

291 
 "assigns_if b (UnOp unop e) = (case constVal (UnOp unop e) of 

292 
None \<Rightarrow> (if unop = UNot 

293 
then assigns_if (\<not>b) e 

294 
else UNIV) 

295 
 Some v \<Rightarrow> (if v=Bool b 

296 
then {} 

297 
else UNIV))" 

298 
 "assigns_if b (BinOp binop e1 e2) 

299 
= (case constVal (BinOp binop e1 e2) of 

300 
None \<Rightarrow> (if binop=CondAnd then 

301 
(case b of 

302 
True \<Rightarrow> assigns_if True e1 \<union> assigns_if True e2 

303 
 False \<Rightarrow> assigns_if False e1 \<inter> 

304 
(assigns_if True e1 \<union> assigns_if False e2)) 

305 
else 

306 
(if binop=CondOr then 

307 
(case b of 

308 
True \<Rightarrow> assigns_if True e1 \<inter> 

309 
(assigns_if False e1 \<union> assigns_if True e2) 

310 
 False \<Rightarrow> assigns_if False e1 \<union> assigns_if False e2) 

311 
else assignsE e1 \<union> assignsE e2)) 

312 
 Some v \<Rightarrow> (if v=Bool b then {} else UNIV))" 

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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313 

37956  314 
 "assigns_if b (Super) = UNIV" {*can never evaluate to Boolean*} 
315 
 "assigns_if b (Acc v) = (assignsV v)" 

316 
 "assigns_if b (v := e) = (assignsE (Ass v e))" 

317 
 "assigns_if b (c? e1 : e2) = (assignsE c) \<union> 

318 
(case (constVal c) of 

319 
None \<Rightarrow> (assigns_if b e1) \<inter> 

320 
(assigns_if b e2) 

321 
 Some bv \<Rightarrow> (case the_Bool bv of 

322 
True \<Rightarrow> assigns_if b e1 

323 
 False \<Rightarrow> assigns_if b e2))" 

324 
 "assigns_if b ({accC,statT,mode}objRef\<cdot>mn({pTs}args)) 

325 
= assignsE ({accC,statT,mode}objRef\<cdot>mn({pTs}args)) " 

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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326 
 {* Only dummy analysis for intermediate expressions 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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327 
@{term Methd}, @{term Body}, @{term InsInitE} and @{term Callee} *} 
37956  328 
 "assigns_if b (Methd C sig) = {}" 
329 
 "assigns_if b (Body C s) = {}" 

330 
 "assigns_if b (InsInitE s e) = {}" 

331 
 "assigns_if b (Callee l e) = {}" 

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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332 

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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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333 
lemma assigns_if_const_b_simp: 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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334 
assumes boolConst: "constVal e = Some (Bool b)" (is "?Const b e") 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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335 
shows "assigns_if b e = {}" (is "?Ass b e") 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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336 
proof  
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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337 
have "True" and "\<And> b. ?Const b e \<Longrightarrow> ?Ass b e" and "True" and "True" 
18459  338 
proof (induct _ and e and _ and _ rule: var_expr_stmt.inducts) 
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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339 
case Lit 
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"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were 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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340 
thus ?case 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:
diff
changeset

341 
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:
diff
changeset

342 
case 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:
diff
changeset

343 
thus ?case 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:
diff
changeset

344 
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:
diff
changeset

345 
case (BinOp binop) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

346 
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:
diff
changeset

347 
by (cases binop) (simp_all) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

348 
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:
diff
changeset

349 
case (Cond c e1 e2 b) 
23350  350 
note hyp_c = `\<And> b. ?Const b c \<Longrightarrow> ?Ass b c` 
351 
note hyp_e1 = `\<And> b. ?Const b e1 \<Longrightarrow> ?Ass b e1` 

352 
note hyp_e2 = `\<And> b. ?Const b e2 \<Longrightarrow> ?Ass b e2` 

353 
note const = `constVal (c ? e1 : e2) = Some (Bool b)` 

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:
diff
changeset

354 
then obtain bv where bv: "constVal c = Some bv" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

355 
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:
diff
changeset

356 
hence emptyC: "assignsE c = {}" by (rule assignsE_const_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:
diff
changeset

357 
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:
diff
changeset

358 
proof (cases "the_Bool bv") 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

359 
case True 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

360 
with const bv 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

361 
have "?Const b e1" 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:
diff
changeset

362 
hence "?Ass b e1" by (rule hyp_e1) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

363 
with emptyC bv True 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

364 
show ?thesis 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

365 
by simp 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

366 
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:
diff
changeset

367 
case False 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

368 
with const bv 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

369 
have "?Const b e2" 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:
diff
changeset

370 
hence "?Ass b e2" by (rule hyp_e2) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

371 
with emptyC bv False 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

372 
show ?thesis 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

373 
by simp 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

374 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

375 
qed (simp_all) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

376 
with boolConst 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

377 
show ?thesis 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

378 
by blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

379 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

380 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

381 
lemma assigns_if_const_not_b_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:
diff
changeset

382 
assumes boolConst: "constVal e = Some (Bool b)" (is "?Const b e") 
18459  383 
shows "assigns_if (\<not>b) e = UNIV" (is "?Ass b e") 
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:
diff
changeset

384 
proof  
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

385 
have True and "\<And> b. ?Const b e \<Longrightarrow> ?Ass b e" and True and True 
18459  386 
proof (induct _ and e and _ and _ rule: var_expr_stmt.inducts) 
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:
diff
changeset

387 
case 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:
diff
changeset

388 
thus ?case 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:
diff
changeset

389 
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:
diff
changeset

390 
case 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:
diff
changeset

391 
thus ?case 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:
diff
changeset

392 
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:
diff
changeset

393 
case (BinOp binop) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

394 
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:
diff
changeset

395 
by (cases binop) (simp_all) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

396 
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:
diff
changeset

397 
case (Cond c e1 e2 b) 
23350  398 
note hyp_c = `\<And> b. ?Const b c \<Longrightarrow> ?Ass b c` 
399 
note hyp_e1 = `\<And> b. ?Const b e1 \<Longrightarrow> ?Ass b e1` 

400 
note hyp_e2 = `\<And> b. ?Const b e2 \<Longrightarrow> ?Ass b e2` 

401 
note const = `constVal (c ? e1 : e2) = Some (Bool b)` 

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:
diff
changeset

402 
then obtain bv where bv: "constVal c = Some bv" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

403 
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:
diff
changeset

404 
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:
diff
changeset

405 
proof (cases "the_Bool bv") 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

406 
case True 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

407 
with const bv 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

408 
have "?Const b e1" 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:
diff
changeset

409 
hence "?Ass b e1" by (rule hyp_e1) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

410 
with bv True 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

411 
show ?thesis 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

412 
by simp 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

413 
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:
diff
changeset

414 
case False 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

415 
with const bv 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

416 
have "?Const b e2" 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:
diff
changeset

417 
hence "?Ass b e2" by (rule hyp_e2) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

418 
with bv False 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

419 
show ?thesis 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

420 
by simp 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

421 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

422 
qed (simp_all) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

423 
with boolConst 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

424 
show ?thesis 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

425 
by blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

426 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

427 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

428 
subsection {* Lifting set operations to range of tables (map to a set) *} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

429 

37956  430 
definition 
431 
union_ts :: "('a,'b) tables \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables" ("_ \<Rightarrow>\<union> _" [67,67] 65) 

432 
where "A \<Rightarrow>\<union> B = (\<lambda> k. A k \<union> B k)" 

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:
diff
changeset

433 

37956  434 
definition 
435 
intersect_ts :: "('a,'b) tables \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables" ("_ \<Rightarrow>\<inter> _" [72,72] 71) 

436 
where "A \<Rightarrow>\<inter> B = (\<lambda>k. A k \<inter> B k)" 

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:
diff
changeset

437 

37956  438 
definition 
439 
all_union_ts :: "('a,'b) tables \<Rightarrow> 'b set \<Rightarrow> ('a,'b) tables" (infixl "\<Rightarrow>\<union>\<^sub>\<forall>" 40) 

440 
where "(A \<Rightarrow>\<union>\<^sub>\<forall> B) = (\<lambda> k. A k \<union> B)" 

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:
diff
changeset

441 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

442 
subsubsection {* Binary union of tables *} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

443 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

444 
lemma union_ts_iff [simp]: "(c \<in> (A \<Rightarrow>\<union> B) k) = (c \<in> A k \<or> c \<in> B k)" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

445 
by (unfold union_ts_def) blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

446 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

447 
lemma union_tsI1 [elim?]: "c \<in> A k \<Longrightarrow> c \<in> (A \<Rightarrow>\<union> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

448 
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:
diff
changeset

449 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

450 
lemma union_tsI2 [elim?]: "c \<in> B k \<Longrightarrow> c \<in> (A \<Rightarrow>\<union> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

451 
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:
diff
changeset

452 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

453 
lemma union_tsCI [intro!]: "(c \<notin> B k \<Longrightarrow> c \<in> A k) \<Longrightarrow> c \<in> (A \<Rightarrow>\<union> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

454 
by auto 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

455 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

456 
lemma union_tsE [elim!]: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

457 
"\<lbrakk>c \<in> (A \<Rightarrow>\<union> B) k; (c \<in> A k \<Longrightarrow> P); (c \<in> B k \<Longrightarrow> P)\<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:
diff
changeset

458 
by (unfold union_ts_def) blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

459 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

460 
subsubsection {* Binary intersection of tables *} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

461 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

462 
lemma intersect_ts_iff [simp]: "c \<in> (A \<Rightarrow>\<inter> B) k = (c \<in> A k \<and> c \<in> B k)" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

463 
by (unfold intersect_ts_def) blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

464 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

465 
lemma intersect_tsI [intro!]: "\<lbrakk>c \<in> A k; c \<in> B k\<rbrakk> \<Longrightarrow> c \<in> (A \<Rightarrow>\<inter> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

466 
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:
diff
changeset

467 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

468 
lemma intersect_tsD1: "c \<in> (A \<Rightarrow>\<inter> B) k \<Longrightarrow> c \<in> A k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

469 
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:
diff
changeset

470 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

471 
lemma intersect_tsD2: "c \<in> (A \<Rightarrow>\<inter> B) k \<Longrightarrow> c \<in> B k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

472 
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:
diff
changeset

473 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

474 
lemma intersect_tsE [elim!]: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

475 
"\<lbrakk>c \<in> (A \<Rightarrow>\<inter> B) k; \<lbrakk>c \<in> A k; c \<in> B k\<rbrakk> \<Longrightarrow> P\<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:
diff
changeset

476 
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:
diff
changeset

477 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

478 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

479 
subsubsection {* AllUnion of tables and set *} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

480 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

481 
lemma all_union_ts_iff [simp]: "(c \<in> (A \<Rightarrow>\<union>\<^sub>\<forall> B) k) = (c \<in> A k \<or> c \<in> 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:
diff
changeset

482 
by (unfold all_union_ts_def) blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

483 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

484 
lemma all_union_tsI1 [elim?]: "c \<in> A k \<Longrightarrow> c \<in> (A \<Rightarrow>\<union>\<^sub>\<forall> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

485 
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:
diff
changeset

486 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

487 
lemma all_union_tsI2 [elim?]: "c \<in> B \<Longrightarrow> c \<in> (A \<Rightarrow>\<union>\<^sub>\<forall> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

488 
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:
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:
diff
changeset

490 
lemma all_union_tsCI [intro!]: "(c \<notin> B \<Longrightarrow> c \<in> A k) \<Longrightarrow> c \<in> (A \<Rightarrow>\<union>\<^sub>\<forall> B) k" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

491 
by auto 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

492 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

493 
lemma all_union_tsE [elim!]: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

494 
"\<lbrakk>c \<in> (A \<Rightarrow>\<union>\<^sub>\<forall> B) k; (c \<in> A k \<Longrightarrow> P); (c \<in> B \<Longrightarrow> P)\<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:
diff
changeset

495 
by (unfold all_union_ts_def) blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

496 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

497 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

498 
section "The rules of definite assignment" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

499 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

500 

41778  501 
type_synonym breakass = "(label, lname) tables" 
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:
diff
changeset

502 
{* Mapping from a break label, to the set of variables that will be assigned 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

503 
if the evaluation terminates with this break *} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

504 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

505 
record assigned = 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

506 
nrm :: "lname set" {* Definetly assigned variables 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

507 
for normal completion*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

508 
brk :: "breakass" {* Definetly assigned variables for 
14030  509 
abrupt completion with a break *} 
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:
diff
changeset

510 

37956  511 
definition 
512 
rmlab :: "'a \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables" 

513 
where "rmlab k A = (\<lambda>x. if x=k then UNIV else A x)" 

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:
diff
changeset

514 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

515 
(* 
37956  516 
definition 
517 
setbrk :: "breakass \<Rightarrow> assigned \<Rightarrow> breakass set" where 

518 
"setbrk b A = {b} \<union> {a a. a\<in> brk A \<and> lab a \<noteq> lab b}" 

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:
diff
changeset

519 
*) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

520 

37956  521 
definition 
522 
range_inter_ts :: "('a,'b) tables \<Rightarrow> 'b set" ("\<Rightarrow>\<Inter>_" 80) 

523 
where "\<Rightarrow>\<Inter>A = {x x. \<forall> k. x \<in> A k}" 

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:
diff
changeset

524 

21765  525 
text {* 
526 
In @{text "E\<turnstile> B \<guillemotright>t\<guillemotright> A"}, 

527 
@{text B} denotes the ''assigned'' variables before evaluating term @{text t}, 

528 
whereas @{text A} denotes the ''assigned'' variables after evaluating term @{text t}. 

529 
The environment @{term E} is only needed for the conditional @{text "_ ? _ : _"}. 

530 
The definite assignment rules refer to the typing rules here to 

531 
distinguish boolean and other expressions. 

532 
*} 

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:
diff
changeset

533 

23747  534 
inductive 
21765  535 
da :: "env \<Rightarrow> lname set \<Rightarrow> term \<Rightarrow> assigned \<Rightarrow> bool" ("_\<turnstile> _ \<guillemotright>_\<guillemotright> _" [65,65,65,65] 71) 
536 
where 

537 
Skip: "Env\<turnstile> B \<guillemotright>\<langle>Skip\<rangle>\<guillemotright> \<lparr>nrm=B,brk=\<lambda> l. UNIV\<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:
diff
changeset

538 

21765  539 
 Expr: "Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> A 
540 
\<Longrightarrow> 

541 
Env\<turnstile> B \<guillemotright>\<langle>Expr e\<rangle>\<guillemotright> A" 

542 
 Lab: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>c\<rangle>\<guillemotright> C; nrm A = nrm C \<inter> (brk C) l; brk A = rmlab l (brk C)\<rbrakk> 

543 
\<Longrightarrow> 

544 
Env\<turnstile> B \<guillemotright>\<langle>Break l\<bullet> c\<rangle>\<guillemotright> A" 

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:
diff
changeset

545 

21765  546 
 Comp: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>c1\<rangle>\<guillemotright> C1; Env\<turnstile> nrm C1 \<guillemotright>\<langle>c2\<rangle>\<guillemotright> C2; 
547 
nrm A = nrm C2; brk A = (brk C1) \<Rightarrow>\<inter> (brk C2)\<rbrakk> 

548 
\<Longrightarrow> 

549 
Env\<turnstile> B \<guillemotright>\<langle>c1;; c2\<rangle>\<guillemotright> A" 

550 

551 
 If: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> E; 

552 
Env\<turnstile> (B \<union> assigns_if True e) \<guillemotright>\<langle>c1\<rangle>\<guillemotright> C1; 

553 
Env\<turnstile> (B \<union> assigns_if False e) \<guillemotright>\<langle>c2\<rangle>\<guillemotright> C2; 

554 
nrm A = nrm C1 \<inter> nrm C2; 

555 
brk A = brk C1 \<Rightarrow>\<inter> brk C2 \<rbrakk> 

556 
\<Longrightarrow> 

557 
Env\<turnstile> B \<guillemotright>\<langle>If(e) c1 Else c2\<rangle>\<guillemotright> A" 

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:
diff
changeset

558 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

559 
{* Note that @{term E} is not further used, because we take the specialized 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

560 
sets that also consider if the expression evaluates to true or false. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

561 
Inside of @{term e} there is no {\tt break} or {\tt finally}, so the break 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

562 
map of @{term E} will be the trivial one. So 
21765  563 
@{term "Env\<turnstile>B \<guillemotright>\<langle>e\<rangle>\<guillemotright> E"} is just used to ensure the definite assignment in 
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:
diff
changeset

564 
expression @{term e}. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

565 
Notice the implicit analysis of a constant boolean expression @{term e} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

566 
in this rule. For example, if @{term e} is constantly @{term True} 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:
diff
changeset

567 
@{term "assigns_if False e = UNIV"} and therefor @{term "nrm C2=UNIV"}. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

568 
So finally @{term "nrm A = nrm C1"}. For the break maps this trick 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

569 
workd too, because the trival break map will map all labels to 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

570 
@{term UNIV}. In the example, if no break occurs in @{term c2} the break 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

571 
maps will trivially map to @{term UNIV} and if a break occurs it will map 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

572 
to @{term UNIV} too, because @{term "assigns_if False e = UNIV"}. So 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

573 
in the intersection of the break maps the path @{term c2} will have no 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

574 
contribution. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

575 
*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

576 

21765  577 
 Loop: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> E; 
578 
Env\<turnstile> (B \<union> assigns_if True e) \<guillemotright>\<langle>c\<rangle>\<guillemotright> C; 

579 
nrm A = nrm C \<inter> (B \<union> assigns_if False e); 

580 
brk A = brk C\<rbrakk> 

581 
\<Longrightarrow> 

582 
Env\<turnstile> B \<guillemotright>\<langle>l\<bullet> While(e) c\<rangle>\<guillemotright> A" 

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:
diff
changeset

583 
{* The @{text Loop} rule resembles some of the ideas of the @{text If} rule. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

584 
For the @{term "nrm A"} the set @{term "B \<union> assigns_if False e"} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

585 
will be @{term UNIV} if the condition is constantly true. To normally exit 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

586 
the while loop, we must consider the body @{term c} to be completed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

587 
normally (@{term "nrm C"}) or with a break. But in this model, 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

588 
the label @{term l} of the 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:
diff
changeset

589 
only handles continue labels, not break labels. The break label will be 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

590 
handled by an enclosing @{term Lab} statement. So we don't have to 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

591 
handle the breaks specially. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

592 
*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

593 

21765  594 
 Jmp: "\<lbrakk>jump=Ret \<longrightarrow> Result \<in> B; 
595 
nrm A = UNIV; 

596 
brk A = (case jump of 

597 
Break l \<Rightarrow> \<lambda> k. if k=l then B else UNIV 

598 
 Cont l \<Rightarrow> \<lambda> k. UNIV 

599 
 Ret \<Rightarrow> \<lambda> k. UNIV)\<rbrakk> 

600 
\<Longrightarrow> 

601 
Env\<turnstile> B \<guillemotright>\<langle>Jmp jump\<rangle>\<guillemotright> A" 

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:
diff
changeset

602 
{* In case of a break to label @{term l} the corresponding break set is all 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

603 
variables assigned before the break. The assigned variables for normal 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

604 
completion of the @{term Jmp} is @{term UNIV}, because the statement will 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

605 
never complete normally. For continue and return the break map is the 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

606 
trivial one. In case of a return we enshure that the result value is 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

607 
assigned. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

608 
*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

609 

21765  610 
 Throw: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> E; nrm A = UNIV; brk A = (\<lambda> l. UNIV)\<rbrakk> 
611 
\<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>Throw e\<rangle>\<guillemotright> A" 

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:
diff
changeset

612 

21765  613 
 Try: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>c1\<rangle>\<guillemotright> C1; 
614 
Env\<lparr>lcl := lcl Env(VName vn\<mapsto>Class C)\<rparr>\<turnstile> (B \<union> {VName vn}) \<guillemotright>\<langle>c2\<rangle>\<guillemotright> C2; 

615 
nrm A = nrm C1 \<inter> nrm C2; 

616 
brk A = brk C1 \<Rightarrow>\<inter> brk C2\<rbrakk> 

617 
\<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>Try c1 Catch(C vn) c2\<rangle>\<guillemotright> A" 

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:
diff
changeset

618 

21765  619 
 Fin: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>c1\<rangle>\<guillemotright> C1; 
620 
Env\<turnstile> B \<guillemotright>\<langle>c2\<rangle>\<guillemotright> C2; 

621 
nrm A = nrm C1 \<union> nrm C2; 

622 
brk A = ((brk C1) \<Rightarrow>\<union>\<^sub>\<forall> (nrm C2)) \<Rightarrow>\<inter> (brk C2)\<rbrakk> 

623 
\<Longrightarrow> 

624 
Env\<turnstile> B \<guillemotright>\<langle>c1 Finally c2\<rangle>\<guillemotright> A" 

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:
diff
changeset

625 
{* The set of assigned variables before execution @{term c2} are the same 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

626 
as before execution @{term c1}, because @{term c1} could throw an exception 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

627 
and so we can't guarantee that any variable will be assigned in @{term c1}. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

628 
The @{text Finally} statement completes 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

629 
normally if both @{term c1} and @{term c2} complete normally. If @{term c1} 
14030  630 
completes abruptly with a break, then @{term c2} also will be executed 
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:
diff
changeset

631 
and may terminate normally or with a break. The overall break map then is 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

632 
the intersection of the maps of both paths. If @{term c2} terminates 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

633 
normally we have to extend all break sets in @{term "brk C1"} with 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

634 
@{term "nrm C2"} (@{text "\<Rightarrow>\<union>\<^sub>\<forall>"}). If @{term c2} exits with a break this 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

635 
break will appear in the overall result state. We don't know if 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

636 
@{term c1} completed normally or abruptly (maybe with an exception not only 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

637 
a break) so @{term c1} has no contribution to the break map following this 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

638 
path. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

639 
*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

640 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

641 
{* Evaluation of expressions and the break sets of definite assignment: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

642 
Thinking of a Java expression we assume that we can never 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:
diff
changeset

643 
a break statement inside of a expression. So for all expressions the 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

644 
break sets could be set to the trivial one: @{term "\<lambda> l. UNIV"}. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

645 
But we can't 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

646 
trivially proof, that evaluating an expression will never result in a 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

647 
break, allthough Java expressions allready syntactically don't allow 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

648 
nested stetements in them. The reason are the nested class initialzation 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

649 
statements which are inserted by the evaluation rules. So to proof the 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

650 
absence of a break we need to ensure, that the initialization statements 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

651 
will never end up in a break. In a wellfromed initialization statement, 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

652 
of course, were breaks are nested correctly inside of @{term 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:
diff
changeset

653 
or @{term Loop} statements evaluation of the whole initialization 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

654 
statement will never result in a break, because this break will be 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

655 
handled inside of the statement. But for simplicity we haven't added 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

656 
the analysis of the correct nesting of breaks in the typing judgments 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

657 
right now. So we have decided to adjust the rules of definite assignment 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

658 
to fit to these circumstances. If an initialization is involved during 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

659 
evaluation of the expression (evaluation rules @{text FVar}, @{text 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:
diff
changeset

660 
and @{text NewA} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

661 
*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

662 

21765  663 
 Init: "Env\<turnstile> B \<guillemotright>\<langle>Init C\<rangle>\<guillemotright> \<lparr>nrm=B,brk=\<lambda> l. UNIV\<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:
diff
changeset

664 
{* Wellformedness of a program will ensure, that every static initialiser 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

665 
is definetly assigned and the jumps are nested correctly. The case here 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

666 
for @{term Init} is just for convenience, to get a proper precondition 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

667 
for the induction hypothesis in various proofs, so that we don't have to 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

668 
expand the initialisation on every point where it is triggerred by the 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

669 
evaluation rules. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

670 
*} 
21765  671 
 NewC: "Env\<turnstile> B \<guillemotright>\<langle>NewC C\<rangle>\<guillemotright> \<lparr>nrm=B,brk=\<lambda> l. UNIV\<rparr>" 
672 

673 
 NewA: "Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> A 

674 
\<Longrightarrow> 

675 
Env\<turnstile> B \<guillemotright>\<langle>New T[e]\<rangle>\<guillemotright> A" 

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:
diff
changeset

676 

21765  677 
 Cast: "Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> A 
678 
\<Longrightarrow> 

679 
Env\<turnstile> B \<guillemotright>\<langle>Cast T e\<rangle>\<guillemotright> A" 

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:
diff
changeset

680 

21765  681 
 Inst: "Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> A 
682 
\<Longrightarrow> 

683 
Env\<turnstile> B \<guillemotright>\<langle>e InstOf T\<rangle>\<guillemotright> A" 

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:
diff
changeset

684 

21765  685 
 Lit: "Env\<turnstile> B \<guillemotright>\<langle>Lit v\<rangle>\<guillemotright> \<lparr>nrm=B,brk=\<lambda> l. UNIV\<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:
diff
changeset

686 

21765  687 
 UnOp: "Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> A 
688 
\<Longrightarrow> 

689 
Env\<turnstile> B \<guillemotright>\<langle>UnOp unop e\<rangle>\<guillemotright> A" 

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:
diff
changeset

690 

21765  691 
 CondAnd: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e1\<rangle>\<guillemotright> E1; Env\<turnstile> (B \<union> assigns_if True e1) \<guillemotright>\<langle>e2\<rangle>\<guillemotright> E2; 
692 
nrm A = B \<union> (assigns_if True (BinOp CondAnd e1 e2) \<inter> 

693 
assigns_if False (BinOp CondAnd e1 e2)); 

694 
brk A = (\<lambda> l. UNIV) \<rbrakk> 

695 
\<Longrightarrow> 

696 
Env\<turnstile> B \<guillemotright>\<langle>BinOp CondAnd e1 e2\<rangle>\<guillemotright> A" 

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:
diff
changeset

697 

21765  698 
 CondOr: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e1\<rangle>\<guillemotright> E1; Env\<turnstile> (B \<union> assigns_if False e1) \<guillemotright>\<langle>e2\<rangle>\<guillemotright> E2; 
699 
nrm A = B \<union> (assigns_if True (BinOp CondOr e1 e2) \<inter> 

700 
assigns_if False (BinOp CondOr e1 e2)); 

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:
diff
changeset

701 
brk A = (\<lambda> l. UNIV) \<rbrakk> 
21765  702 
\<Longrightarrow> 
703 
Env\<turnstile> B \<guillemotright>\<langle>BinOp CondOr e1 e2\<rangle>\<guillemotright> A" 

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:
diff
changeset

704 

21765  705 
 BinOp: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e1\<rangle>\<guillemotright> E1; Env\<turnstile> nrm E1 \<guillemotright>\<langle>e2\<rangle>\<guillemotright> A; 
706 
binop \<noteq> CondAnd; binop \<noteq> CondOr\<rbrakk> 

707 
\<Longrightarrow> 

708 
Env\<turnstile> B \<guillemotright>\<langle>BinOp binop e1 e2\<rangle>\<guillemotright> A" 

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:
diff
changeset

709 

21765  710 
 Super: "This \<in> B 
711 
\<Longrightarrow> 

712 
Env\<turnstile> B \<guillemotright>\<langle>Super\<rangle>\<guillemotright> \<lparr>nrm=B,brk=\<lambda> l. UNIV\<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:
diff
changeset

713 

21765  714 
 AccLVar: "\<lbrakk>vn \<in> B; 
715 
nrm A = B; brk A = (\<lambda> k. UNIV)\<rbrakk> 

716 
\<Longrightarrow> 

717 
Env\<turnstile> B \<guillemotright>\<langle>Acc (LVar vn)\<rangle>\<guillemotright> A" 

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:
diff
changeset

718 
{* To properly access a local variable we have to test the definite 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

719 
assignment here. The variable must occur in the set @{term 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:
diff
changeset

720 
*} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

721 

21765  722 
 Acc: "\<lbrakk>\<forall> vn. v \<noteq> LVar vn; 
723 
Env\<turnstile> B \<guillemotright>\<langle>v\<rangle>\<guillemotright> A\<rbrakk> 

724 
\<Longrightarrow> 

725 
Env\<turnstile> B \<guillemotright>\<langle>Acc v\<rangle>\<guillemotright> A" 

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:
diff
changeset

726 

21765  727 
 AssLVar: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> E; nrm A = nrm E \<union> {vn}; brk A = brk E\<rbrakk> 
728 
\<Longrightarrow> 

729 
Env\<turnstile> B \<guillemotright>\<langle>(LVar vn) := e\<rangle>\<guillemotright> A" 

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:
diff
changeset

730 

21765  731 
 Ass: "\<lbrakk>\<forall> vn. v \<noteq> LVar vn; Env\<turnstile> B \<guillemotright>\<langle>v\<rangle>\<guillemotright> V; Env\<turnstile> nrm V \<guillemotright>\<langle>e\<rangle>\<guillemotright> A\<rbrakk> 
732 
\<Longrightarrow> 

733 
Env\<turnstile> B \<guillemotright>\<langle>v := e\<rangle>\<guillemotright> A" 

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:
diff
changeset

734 

21765  735 
 CondBool: "\<lbrakk>Env\<turnstile>(c ? e1 : e2)\<Colon>(PrimT Boolean); 
736 
Env\<turnstile> B \<guillemotright>\<langle>c\<rangle>\<guillemotright> C; 

737 
Env\<turnstile> (B \<union> assigns_if True c) \<guillemotright>\<langle>e1\<rangle>\<guillemotright> E1; 

738 
Env\<turnstile> (B \<union> assigns_if False c) \<guillemotright>\<langle>e2\<rangle>\<guillemotright> E2; 

739 
nrm A = B \<union> (assigns_if True (c ? e1 : e2) \<inter> 

740 
assigns_if False (c ? e1 : e2)); 

741 
brk A = (\<lambda> l. UNIV)\<rbrakk> 

742 
\<Longrightarrow> 

743 
Env\<turnstile> B \<guillemotright>\<langle>c ? e1 : e2\<rangle>\<guillemotright> A" 

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:
diff
changeset

744 

21765  745 
 Cond: "\<lbrakk>\<not> Env\<turnstile>(c ? e1 : e2)\<Colon>(PrimT Boolean); 
746 
Env\<turnstile> B \<guillemotright>\<langle>c\<rangle>\<guillemotright> C; 

747 
Env\<turnstile> (B \<union> assigns_if True c) \<guillemotright>\<langle>e1\<rangle>\<guillemotright> E1; 

748 
Env\<turnstile> (B \<union> assigns_if False c) \<guillemotright>\<langle>e2\<rangle>\<guillemotright> E2; 

749 
nrm A = nrm E1 \<inter> nrm E2; brk A = (\<lambda> l. UNIV)\<rbrakk> 

750 
\<Longrightarrow> 

751 
Env\<turnstile> B \<guillemotright>\<langle>c ? e1 : e2\<rangle>\<guillemotright> A" 

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:
diff
changeset

752 

21765  753 
 Call: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> E; Env\<turnstile> nrm E \<guillemotright>\<langle>args\<rangle>\<guillemotright> A\<rbrakk> 
754 
\<Longrightarrow> 

755 
Env\<turnstile> B \<guillemotright>\<langle>{accC,statT,mode}e\<cdot>mn({pTs}args)\<rangle>\<guillemotright> A" 

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:
diff
changeset

756 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

757 
 {* The interplay of @{term Call}, @{term Methd} and @{term Body}: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

758 
Why rules for @{term Methd} and @{term Body} at all? Note that a 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

759 
Java source program will not include bare @{term Methd} or @{term Body} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

760 
terms. These terms are just introduced during evaluation. So definite 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

761 
assignment of @{term Call} does not consider @{term Methd} or 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

762 
@{term Body} at all. So for definite assignment alone we could omit the 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

763 
rules for @{term Methd} and @{term Body}. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

764 
But since evaluation of the method invocation is 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

765 
split up into three rules we must ensure that we have enough information 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

766 
about the call even in the @{term Body} term to make sure that we can 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

767 
proof type safety. Also we must be able transport this information 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

768 
from @{term Call} to @{term Methd} and then further to @{term Body} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

769 
during evaluation to establish the definite assignment of @{term 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:
diff
changeset

770 
during evaluation of @{term Call}, and of @{term Body} during evaluation 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

771 
of @{term Methd}. This is necessary since definite assignment will be 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

772 
a precondition for each induction hypothesis coming out of the evaluation 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

773 
rules, and therefor we have to establish the definite assignment of the 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

774 
subevaluation during the typesafety proof. Note that welltypedness is 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

775 
also a precondition for typesafety and so we can omit some assertion 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

776 
that are already ensured by welltypedness. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

777 
*} 
21765  778 
 Methd: "\<lbrakk>methd (prg Env) D sig = Some m; 
779 
Env\<turnstile> B \<guillemotright>\<langle>Body (declclass m) (stmt (mbody (mthd m)))\<rangle>\<guillemotright> A 

780 
\<rbrakk> 

781 
\<Longrightarrow> 

782 
Env\<turnstile> B \<guillemotright>\<langle>Methd D sig\<rangle>\<guillemotright> A" 

783 

784 
 Body: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>c\<rangle>\<guillemotright> C; jumpNestingOkS {Ret} c; Result \<in> nrm C; 

785 
nrm A = B; brk A = (\<lambda> l. UNIV)\<rbrakk> 

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:
diff
changeset

786 
\<Longrightarrow> 
21765  787 
Env\<turnstile> B \<guillemotright>\<langle>Body D c\<rangle>\<guillemotright> A" 
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:
diff
changeset

788 
 {* Note that @{term A} is not correlated to @{term C}. If the body 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

789 
statement returns abruptly with return, evaluation of @{term Body} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

790 
will absorb this return and complete normally. So we cannot trivially 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

791 
get the assigned variables of the body statement since it has not 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

792 
completed normally or with a break. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

793 
If the body completes normally we guarantee that the result variable 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

794 
is set with this rule. But if the body completes abruptly with a return 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

795 
we can't guarantee that the result variable is set here, since 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

796 
definite assignment only talks about normal completion and breaks. So 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

797 
for a return the @{term Jump} rule ensures that the result variable is 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

798 
set and then this information must be carried over to the @{term Body} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

799 
rule by the conformance predicate of the state. 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

800 
*} 
21765  801 
 LVar: "Env\<turnstile> B \<guillemotright>\<langle>LVar vn\<rangle>\<guillemotright> \<lparr>nrm=B, brk=\<lambda> l. UNIV\<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:
diff
changeset

802 

21765  803 
 FVar: "Env\<turnstile> B \<guillemotright>\<langle>e\<rangle>\<guillemotright> A 
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:
diff
changeset

804 
\<Longrightarrow> 
21765  805 
Env\<turnstile> B \<guillemotright>\<langle>{accC,statDeclC,stat}e..fn\<rangle>\<guillemotright> A" 
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:
diff
changeset

806 

21765  807 
 AVar: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e1\<rangle>\<guillemotright> E1; Env\<turnstile> nrm E1 \<guillemotright>\<langle>e2\<rangle>\<guillemotright> A\<rbrakk> 
808 
\<Longrightarrow> 

809 
Env\<turnstile> B \<guillemotright>\<langle>e1.[e2]\<rangle>\<guillemotright> A" 

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:
diff
changeset

810 

21765  811 
 Nil: "Env\<turnstile> B \<guillemotright>\<langle>[]::expr list\<rangle>\<guillemotright> \<lparr>nrm=B, brk=\<lambda> l. UNIV\<rparr>" 
812 

813 
 Cons: "\<lbrakk>Env\<turnstile> B \<guillemotright>\<langle>e::expr\<rangle>\<guillemotright> E; Env\<turnstile> nrm E \<guillemotright>\<langle>es\<rangle>\<guillemotright> A\<rbrakk> 

814 
\<Longrightarrow> 

815 
Env\<turnstile> B \<guillemotright>\<langle>e#es\<rangle>\<guillemotright> A" 

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:
diff
changeset

816 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

817 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

818 
declare inj_term_sym_simps [simp] 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

819 
declare assigns_if.simps [simp del] 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

820 
declare split_paired_All [simp del] split_paired_Ex [simp del] 
24019  821 
declaration {* K (Simplifier.map_ss (fn ss => ss delloop "split_all_tac")) *} 
822 

23747  823 
inductive_cases da_elim_cases [cases set]: 
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:
diff
changeset

824 
"Env\<turnstile> B \<guillemotright>\<langle>Skip\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

825 
"Env\<turnstile> B \<guillemotright>In1r Skip\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

826 
"Env\<turnstile> B \<guillemotright>\<langle>Expr e\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

827 
"Env\<turnstile> B \<guillemotright>In1r (Expr e)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

828 
"Env\<turnstile> B \<guillemotright>\<langle>l\<bullet> c\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

829 
"Env\<turnstile> B \<guillemotright>In1r (l\<bullet> c)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

830 
"Env\<turnstile> B \<guillemotright>\<langle>c1;; c2\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

831 
"Env\<turnstile> B \<guillemotright>In1r (c1;; c2)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

832 
"Env\<turnstile> B \<guillemotright>\<langle>If(e) c1 Else c2\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

833 
"Env\<turnstile> B \<guillemotright>In1r (If(e) c1 Else c2)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

834 
"Env\<turnstile> B \<guillemotright>\<langle>l\<bullet> While(e) c\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

835 
"Env\<turnstile> B \<guillemotright>In1r (l\<bullet> While(e) c)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

836 
"Env\<turnstile> B \<guillemotright>\<langle>Jmp jump\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

837 
"Env\<turnstile> B \<guillemotright>In1r (Jmp jump)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

838 
"Env\<turnstile> B \<guillemotright>\<langle>Throw e\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

839 
"Env\<turnstile> B \<guillemotright>In1r (Throw e)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

840 
"Env\<turnstile> B \<guillemotright>\<langle>Try c1 Catch(C vn) c2\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

841 
"Env\<turnstile> B \<guillemotright>In1r (Try c1 Catch(C vn) c2)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

842 
"Env\<turnstile> B \<guillemotright>\<langle>c1 Finally c2\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

843 
"Env\<turnstile> B \<guillemotright>In1r (c1 Finally c2)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

844 
"Env\<turnstile> B \<guillemotright>\<langle>Init C\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

845 
"Env\<turnstile> B \<guillemotright>In1r (Init C)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

846 
"Env\<turnstile> B \<guillemotright>\<langle>NewC C\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

847 
"Env\<turnstile> B \<guillemotright>In1l (NewC C)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

848 
"Env\<turnstile> B \<guillemotright>\<langle>New T[e]\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

849 
"Env\<turnstile> B \<guillemotright>In1l (New T[e])\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

850 
"Env\<turnstile> B \<guillemotright>\<langle>Cast T e\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

851 
"Env\<turnstile> B \<guillemotright>In1l (Cast T e)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

852 
"Env\<turnstile> B \<guillemotright>\<langle>e InstOf T\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

853 
"Env\<turnstile> B \<guillemotright>In1l (e InstOf T)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

854 
"Env\<turnstile> B \<guillemotright>\<langle>Lit v\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

855 
"Env\<turnstile> B \<guillemotright>In1l (Lit v)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

856 
"Env\<turnstile> B \<guillemotright>\<langle>UnOp unop e\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

857 
"Env\<turnstile> B \<guillemotright>In1l (UnOp unop e)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

858 
"Env\<turnstile> B \<guillemotright>\<langle>BinOp binop e1 e2\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

859 
"Env\<turnstile> B \<guillemotright>In1l (BinOp binop e1 e2)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

860 
"Env\<turnstile> B \<guillemotright>\<langle>Super\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

861 
"Env\<turnstile> B \<guillemotright>In1l (Super)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

862 
"Env\<turnstile> B \<guillemotright>\<langle>Acc v\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

863 
"Env\<turnstile> B \<guillemotright>In1l (Acc v)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

864 
"Env\<turnstile> B \<guillemotright>\<langle>v := e\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

865 
"Env\<turnstile> B \<guillemotright>In1l (v := e)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

866 
"Env\<turnstile> B \<guillemotright>\<langle>c ? e1 : e2\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

867 
"Env\<turnstile> B \<guillemotright>In1l (c ? e1 : e2)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

868 
"Env\<turnstile> B \<guillemotright>\<langle>{accC,statT,mode}e\<cdot>mn({pTs}args)\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

869 
"Env\<turnstile> B \<guillemotright>In1l ({accC,statT,mode}e\<cdot>mn({pTs}args))\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

870 
"Env\<turnstile> B \<guillemotright>\<langle>Methd C sig\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

871 
"Env\<turnstile> B \<guillemotright>In1l (Methd C sig)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

872 
"Env\<turnstile> B \<guillemotright>\<langle>Body D c\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

873 
"Env\<turnstile> B \<guillemotright>In1l (Body D c)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

874 
"Env\<turnstile> B \<guillemotright>\<langle>LVar vn\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

875 
"Env\<turnstile> B \<guillemotright>In2 (LVar vn)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

876 
"Env\<turnstile> B \<guillemotright>\<langle>{accC,statDeclC,stat}e..fn\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

877 
"Env\<turnstile> B \<guillemotright>In2 ({accC,statDeclC,stat}e..fn)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

878 
"Env\<turnstile> B \<guillemotright>\<langle>e1.[e2]\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

879 
"Env\<turnstile> B \<guillemotright>In2 (e1.[e2])\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

880 
"Env\<turnstile> B \<guillemotright>\<langle>[]::expr list\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

881 
"Env\<turnstile> B \<guillemotright>In3 ([]::expr list)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

882 
"Env\<turnstile> B \<guillemotright>\<langle>e#es\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

883 
"Env\<turnstile> B \<guillemotright>In3 (e#es)\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

884 
declare inj_term_sym_simps [simp del] 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

885 
declare assigns_if.simps [simp] 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

886 
declare split_paired_All [simp] split_paired_Ex [simp] 
24019  887 
declaration {* K (Simplifier.map_ss (fn ss => ss addloop ("split_all_tac", split_all_tac))) *} 
888 

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:
diff
changeset

889 
(* To be able to eliminate both the versions with the overloaded brackets: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

890 
(B \<guillemotright>\<langle>Skip\<rangle>\<guillemotright> A) and with the explicit constructor (B \<guillemotright>In1r Skip\<guillemotright> A), 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

891 
every rule appears in both versions 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

892 
*) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

893 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

894 
lemma da_Skip: "A = \<lparr>nrm=B,brk=\<lambda> l. UNIV\<rparr> \<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>Skip\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

895 
by (auto intro: da.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:
diff
changeset

896 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

897 
lemma da_NewC: "A = \<lparr>nrm=B,brk=\<lambda> l. UNIV\<rparr> \<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>NewC C\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

898 
by (auto intro: da.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:
diff
changeset

899 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

900 
lemma da_Lit: "A = \<lparr>nrm=B,brk=\<lambda> l. UNIV\<rparr> \<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>Lit v\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

901 
by (auto intro: da.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:
diff
changeset

902 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

903 
lemma da_Super: "\<lbrakk>This \<in> B;A = \<lparr>nrm=B,brk=\<lambda> l. UNIV\<rparr>\<rbrakk> \<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>Super\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

904 
by (auto intro: da.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:
diff
changeset

905 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

906 
lemma da_Init: "A = \<lparr>nrm=B,brk=\<lambda> l. UNIV\<rparr> \<Longrightarrow> Env\<turnstile> B \<guillemotright>\<langle>Init C\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

907 
by (auto intro: da.Init) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

908 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

909 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

910 
(* 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

911 
For boolean expressions: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

912 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

913 
The following holds: "assignsE e \<subseteq> assigns_if True e \<inter> assigns_if False e" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

914 
but not vice versa: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

915 
"assigns_if True e \<inter> assigns_if False e \<subseteq> assignsE e" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

916 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

917 
Example: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

918 
e = ((x < 5)  (y = true)) && (y = true) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

919 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

920 
= ( a  b ) && c 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

921 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

922 
assigns_if True a = {} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

923 
assigns_if False a = {} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

924 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

925 
assigns_if True b = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

926 
assigns_if False b = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

927 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

928 
assigns_if True c = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

929 
assigns_if False c = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

930 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

931 
assigns_if True (a  b) = assigns_if True a \<inter> 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

932 
(assigns_if False a \<union> assigns_if True 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:
diff
changeset

933 
= {} \<inter> ({} \<union> {y}) = {} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

934 
assigns_if False (a  b) = assigns_if False a \<union> assigns_if False 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:
diff
changeset

935 
= {} \<union> {y} = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

936 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

937 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

938 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

939 
assigns_ifE True e = assigns_if True (a  b) \<union> assigns_if True c 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

940 
= {} \<union> {y} = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

941 
assigns_ifE False e = assigns_if False (a  b) \<inter> 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

942 
(assigns_if True (a  b) \<union> assigns_if False c) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

943 
= {y} \<inter> ({} \<union> {y}) = {y} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

944 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

945 
assignsE e = {} 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

946 
*) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

947 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

948 
lemma assignsE_subseteq_assigns_ifs: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

949 
assumes boolEx: "E\<turnstile>e\<Colon>PrimT Boolean" (is "?Boolean e") 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

950 
shows "assignsE e \<subseteq> assigns_if True e \<inter> assigns_if False e" (is "?Incl e") 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

951 
proof  
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

952 
have True and "?Boolean e \<Longrightarrow> ?Incl e" and True and True 
18459  953 
proof (induct _ and e and _ and _ rule: var_expr_stmt.inducts) 
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:
diff
changeset

954 
case (Cast T e) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

955 
have "E\<turnstile>e\<Colon> (PrimT Boolean)" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

956 
proof  
23350  957 
from `E\<turnstile>(Cast T e)\<Colon> (PrimT Boolean)` 
958 
obtain Te where "E\<turnstile>e\<Colon>Te" 

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:
diff
changeset

959 
"prg E\<turnstile>Te\<preceq>? PrimT Boolean" 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

960 
by cases simp 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

961 
thus ?thesis 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

962 
by  (drule cast_Boolean2,simp) 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

963 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

964 
with Cast.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:
diff
changeset

965 
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:
diff
changeset

966 
by simp 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

967 
next 
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:
diff
changeset

968 
case (Lit val) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

969 
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:
diff
changeset

970 
by  (erule wt_elim_cases, cases "val", auto simp add: empty_dt_def) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

971 
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:
diff
changeset

972 
case (UnOp unop e) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

973 
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:
diff
changeset

974 
by  (erule wt_elim_cases,cases unop, 
44890
22f665a2e91c
new fastforce replacing fastsimp  less confusing name
nipkow
parents:
44045
diff
changeset

975 
(fastforce simp add: assignsE_const_simp)+) 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

976 
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:
diff
changeset

977 
case (BinOp binop e1 e2) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

978 
from BinOp.prems obtain e1T e2T 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

979 
where "E\<turnstile>e1\<Colon>e1T" and "E\<turnstile>e2\<Colon>e2T" and "wt_binop (prg E) binop e1T e2T" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

980 
and "(binop_type binop) = Boolean" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

981 
by (elim wt_elim_cases) 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:
diff
changeset

982 
with BinOp.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:
diff
changeset

983 
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:
diff
changeset

984 
by  (cases binop, auto simp add: assignsE_const_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:
diff
changeset

985 
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:
diff
changeset

986 
case (Cond c e1 e2) 
23350  987 
note hyp_c = `?Boolean c \<Longrightarrow> ?Incl c` 
988 
note hyp_e1 = `?Boolean e1 \<Longrightarrow> ?Incl e1` 

989 
note hyp_e2 = `?Boolean e2 \<Longrightarrow> ?Incl e2` 

990 
note wt = `E\<turnstile>(c ? e1 : e2)\<Colon>PrimT Boolean` 

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:
diff
changeset

991 
then obtain 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

992 
boolean_c: "E\<turnstile>c\<Colon>PrimT Boolean" 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:
diff
changeset

993 
boolean_e1: "E\<turnstile>e1\<Colon>PrimT Boolean" 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:
diff
changeset

994 
boolean_e2: "E\<turnstile>e2\<Colon>PrimT Boolean" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

995 
by (elim wt_elim_cases) (auto dest: widen_Boolean2) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

996 
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:
diff
changeset

997 
proof (cases "constVal c") 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

998 
case None 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

999 
with boolean_e1 boolean_e2 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1000 
show ?thesis 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

1001 
using hyp_e1 hyp_e2 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

1002 
by (auto) 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1003 
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:
diff
changeset

1004 
case (Some bv) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1005 
show ?thesis 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1006 
proof (cases "the_Bool bv") 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

1007 
case True 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

1008 
with Some show ?thesis using hyp_e1 boolean_e1 by auto 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1009 
next 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

1010 
case False 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
24019
diff
changeset

1011 
with Some show ?thesis using hyp_e2 boolean_e2 by auto 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1012 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1013 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1014 
qed simp_all 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1015 
with boolEx 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1016 
show ?thesis 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1017 
by blast 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1018 
qed 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1019 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1020 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1021 
(* Trick: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1022 
If you have a rule with the abstract term injections: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1023 
e.g: da.Skip "B \<guillemotright>\<langle>Skip\<rangle>\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1024 
and the current goal state as an concrete injection: 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1025 
e.g: "B \<guillemotright>In1r Skip\<guillemotright> A" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1026 
you can convert the rule by: da.Skip [simplified] 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1027 
if inj_term_simps is in the simpset 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1028 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1029 
*) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1030 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1031 
lemma rmlab_same_label [simp]: "(rmlab l A) l = UNIV" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1032 
by (simp add: rmlab_def) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1033 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1034 
lemma rmlab_same_label1 [simp]: "l=l' \<Longrightarrow> (rmlab l A) l' = UNIV" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1035 
by (simp add: rmlab_def) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1036 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1037 
lemma rmlab_other_label [simp]: "l\<noteq>l'\<Longrightarrow> (rmlab l A) l' = A l'" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1038 
by (auto simp add: rmlab_def) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1039 

46222  1040 
lemma range_inter_ts_subseteq [intro]: "\<forall> k. A k \<subseteq> B k \<Longrightarrow> \<Rightarrow>\<Inter>A \<subseteq> \<Rightarrow>\<Inter>B" 
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:
diff
changeset

1041 
by (auto simp add: range_inter_ts_def) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1042 

46222  1043 
lemma range_inter_ts_subseteq': "\<forall> k. A k \<subseteq> B k \<Longrightarrow> x \<in> \<Rightarrow>\<Inter>A \<Longrightarrow> x \<in> \<Rightarrow>\<Inter>B" 
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:
diff
changeset

1044 
by (auto simp add: range_inter_ts_def) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1045 

a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1046 
lemma da_monotone: 
23350  1047 
assumes da: "Env\<turnstile> B \<guillemotright>t\<guillemotright> A" and 
1048 
"B \<subseteq> B'" and 

1049 
da': "Env\<turnstile> B' \<guillemotright>t\<guillemotright> A'" 

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:
diff
changeset

1050 
shows "(nrm A \<subseteq> nrm A') \<and> (\<forall> l. (brk A l \<subseteq> brk A' l))" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1051 
proof  
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1052 
from da 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1053 
show "\<And> B' A'. \<lbrakk>Env\<turnstile> B' \<guillemotright>t\<guillemotright> A'; B \<subseteq> B'\<rbrakk> 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1054 
\<Longrightarrow> (nrm A \<subseteq> nrm A') \<and> (\<forall> l. (brk A l \<subseteq> brk A' l))" 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1055 
(is "PROP ?Hyp Env B t A") 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1056 
proof (induct) 
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1057 
case Skip 
44045
2814ff2a6e3e
infrastructure for attaching names to hypothesis in cases; realised via the same tag mechanism as case names
nipkow
parents:
41778
diff
changeset

1058 
then show ?case by cases simp 
13688
a0b16d42d489
"Definite Assignment Analysis" included, with proof of correctness. Large adjustments of type safety proof and soundness proof of the axiomatic semantics were necessary. Completeness proof of the loop rule of the axiomatic semantic was altered. So the additional polymorphic variants of some rules could be removed.
schirmer
parents:
diff
changeset

1059 
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:
diff
changeset

1060 
case 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:
diff
changeset

1061 
from Expr.prems Expr.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:
diff
changeset

1062 
show ?case by cases simp 