src/HOL/IMP/Procs_Stat_Vars_Dyn.thy
author nipkow
Mon, 04 Feb 2013 09:06:20 +0100
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theory Procs_Stat_Vars_Dyn imports Procs
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begin
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subsubsection "Static Scoping of Procedures, Dynamic of Variables"
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type_synonym penv = "(pname \<times> com) list"
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inductive
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  big_step :: "penv \<Rightarrow> com \<times> state \<Rightarrow> state \<Rightarrow> bool" ("_ \<turnstile> _ \<Rightarrow> _" [60,0,60] 55)
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where
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Skip:    "pe \<turnstile> (SKIP,s) \<Rightarrow> s" |
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Assign:  "pe \<turnstile> (x ::= a,s) \<Rightarrow> s(x := aval a s)" |
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Seq:     "\<lbrakk> pe \<turnstile> (c\<^isub>1,s\<^isub>1) \<Rightarrow> s\<^isub>2;  pe \<turnstile> (c\<^isub>2,s\<^isub>2) \<Rightarrow> s\<^isub>3 \<rbrakk> \<Longrightarrow>
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          pe \<turnstile> (c\<^isub>1;c\<^isub>2, s\<^isub>1) \<Rightarrow> s\<^isub>3" |
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IfTrue:  "\<lbrakk> bval b s;  pe \<turnstile> (c\<^isub>1,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
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         pe \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" |
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IfFalse: "\<lbrakk> \<not>bval b s;  pe \<turnstile> (c\<^isub>2,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
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         pe \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" |
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WhileFalse: "\<not>bval b s \<Longrightarrow> pe \<turnstile> (WHILE b DO c,s) \<Rightarrow> s" |
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WhileTrue:
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  "\<lbrakk> bval b s\<^isub>1;  pe \<turnstile> (c,s\<^isub>1) \<Rightarrow> s\<^isub>2;  pe \<turnstile> (WHILE b DO c, s\<^isub>2) \<Rightarrow> s\<^isub>3 \<rbrakk> \<Longrightarrow>
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   pe \<turnstile> (WHILE b DO c, s\<^isub>1) \<Rightarrow> s\<^isub>3" |
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Var: "pe \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> ({VAR x;; c}, s) \<Rightarrow> t(x := s x)" |
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Call1: "(p,c)#pe \<turnstile> (c, s) \<Rightarrow> t  \<Longrightarrow>  (p,c)#pe \<turnstile> (CALL p, s) \<Rightarrow> t" |
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Call2: "\<lbrakk> p' \<noteq> p;  pe \<turnstile> (CALL p, s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
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       (p',c)#pe \<turnstile> (CALL p, s) \<Rightarrow> t" |
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Proc: "(p,cp)#pe \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> ({PROC p = cp;; c}, s) \<Rightarrow> t"
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code_pred big_step .
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values "{map t [''x'', ''y''] |t. [] \<turnstile> (test_com, <>) \<Rightarrow> t}"
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end