| author | wenzelm |
| Sun, 02 Nov 2014 17:58:35 +0100 | |
| changeset 58886 | 8a6cac7c7247 |
| parent 42463 | f270e3e18be5 |
| child 61361 | 8b5f00202e1a |
| permissions | -rw-r--r-- |
| 42150 | 1 |
(* Title: HOL/MicroJava/DFA/Typing_Framework.thy |
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Author: Tobias Nipkow |
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Copyright 2000 TUM |
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*) |
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section {* Typing and Dataflow Analysis Framework *}
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theory Typing_Framework |
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imports Listn |
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begin |
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text {*
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The relationship between dataflow analysis and a welltyped-instruction predicate. |
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*} |
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type_synonym 's step_type = "nat \<Rightarrow> 's \<Rightarrow> (nat \<times> 's) list" |
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definition stable :: "'s ord \<Rightarrow> 's step_type \<Rightarrow> 's list \<Rightarrow> nat \<Rightarrow> bool" where |
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"stable r step ss p == !(q,s'):set(step p (ss!p)). s' <=_r ss!q" |
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definition stables :: "'s ord \<Rightarrow> 's step_type \<Rightarrow> 's list \<Rightarrow> bool" where |
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"stables r step ss == !p<size ss. stable r step ss p" |
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definition wt_step :: |
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"'s ord \<Rightarrow> 's \<Rightarrow> 's step_type \<Rightarrow> 's list \<Rightarrow> bool" where |
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"wt_step r T step ts == |
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!p<size(ts). ts!p ~= T & stable r step ts p" |
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definition is_bcv :: "'s ord \<Rightarrow> 's \<Rightarrow> 's step_type |
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\<Rightarrow> nat \<Rightarrow> 's set \<Rightarrow> ('s list \<Rightarrow> 's list) \<Rightarrow> bool" where
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"is_bcv r T step n A bcv == !ss : list n A. |
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(!p<n. (bcv ss)!p ~= T) = |
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(? ts: list n A. ss <=[r] ts & wt_step r T step ts)" |
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end |