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theory Procs_Stat_Vars_Dyn imports Util 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 = "(name \<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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Semi: "\<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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(* FIXME: example state syntax *)
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values "{map t [''x'', ''y'', ''z''] |t.
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[] \<turnstile> (CALL ''p'', (%_. 0)(''x'' := 42, ''y'' := 43)) \<Rightarrow> t}"
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values "{map t [''x'', ''y'', ''z''] |t. [] \<turnstile> (test_com, (%_. 0) ) \<Rightarrow> t}"
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end
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