Theory Procs_Stat_Vars_Stat

theory Procs_Stat_Vars_Stat
imports Procs
theory Procs_Stat_Vars_Stat imports Procs
begin

subsubsection "Static Scoping of Procedures and Variables"

type_synonym addr = nat
type_synonym venv = "vname => addr"
type_synonym store = "addr => val"
type_synonym penv = "(pname × com × venv) list"

fun venv :: "penv × venv × nat => venv" where
"venv(_,ve,_) = ve"

inductive
big_step :: "penv × venv × nat => com × store => store => bool"
("_ \<turnstile> _ => _" [60,0,60] 55)
where
Skip: "e \<turnstile> (SKIP,s) => s" |
Assign: "(pe,ve,f) \<turnstile> (x ::= a,s) => s(ve x := aval a (s o ve))" |
Seq: "[| e \<turnstile> (c1,s1) => s2; e \<turnstile> (c2,s2) => s3 |] ==>
e \<turnstile> (c1;;c2, s1) => s3"
|

IfTrue: "[| bval b (s o venv e); e \<turnstile> (c1,s) => t |] ==>
e \<turnstile> (IF b THEN c1 ELSE c2, s) => t"
|
IfFalse: "[| ¬bval b (s o venv e); e \<turnstile> (c2,s) => t |] ==>
e \<turnstile> (IF b THEN c1 ELSE c2, s) => t"
|

WhileFalse: "¬bval b (s o venv e) ==> e \<turnstile> (WHILE b DO c,s) => s" |
WhileTrue:
"[| bval b (s1 o venv e); e \<turnstile> (c,s1) => s2;
e \<turnstile> (WHILE b DO c, s2) => s3 |] ==>
e \<turnstile> (WHILE b DO c, s1) => s3"
|

Var: "(pe,ve(x:=f),f+1) \<turnstile> (c,s) => t ==>
(pe,ve,f) \<turnstile> ({VAR x; c}, s) => t"
|

Call1: "((p,c,ve)#pe,ve,f) \<turnstile> (c, s) => t ==>
((p,c,ve)#pe,ve',f) \<turnstile> (CALL p, s) => t"
|
Call2: "[| p' ≠ p; (pe,ve,f) \<turnstile> (CALL p, s) => t |] ==>
((p',c,ve')#pe,ve,f) \<turnstile> (CALL p, s) => t"
|

Proc: "((p,cp,ve)#pe,ve,f) \<turnstile> (c,s) => t
==> (pe,ve,f) \<turnstile> ({PROC p = cp; c}, s) => t"


code_pred big_step .


values "{map t [10,11] |t.
([], <''x'' := 10, ''y'' := 11>, 12)
\<turnstile> (test_com, <>) => t}"


end