src/HOL/IMP/Procs_Stat_Vars_Dyn.thy
author huffman
Thu Aug 11 09:11:15 2011 -0700 (2011-08-11)
changeset 44165 d26a45f3c835
parent 43158 686fa0a0696e
child 44177 b4b5cbca2519
permissions -rw-r--r--
remove lemma stupid_ext
     1 theory Procs_Stat_Vars_Dyn imports Util Procs
     2 begin
     3 
     4 subsubsection "Static Scoping of Procedures, Dynamic of Variables"
     5 
     6 type_synonym penv = "(name \<times> com) list"
     7 
     8 inductive
     9   big_step :: "penv \<Rightarrow> com \<times> state \<Rightarrow> state \<Rightarrow> bool" ("_ \<turnstile> _ \<Rightarrow> _" [60,0,60] 55)
    10 where
    11 Skip:    "pe \<turnstile> (SKIP,s) \<Rightarrow> s" |
    12 Assign:  "pe \<turnstile> (x ::= a,s) \<Rightarrow> s(x := aval a s)" |
    13 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>
    14           pe \<turnstile> (c\<^isub>1;c\<^isub>2, s\<^isub>1) \<Rightarrow> s\<^isub>3" |
    15 
    16 IfTrue:  "\<lbrakk> bval b s;  pe \<turnstile> (c\<^isub>1,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
    17          pe \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" |
    18 IfFalse: "\<lbrakk> \<not>bval b s;  pe \<turnstile> (c\<^isub>2,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
    19          pe \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" |
    20 
    21 WhileFalse: "\<not>bval b s \<Longrightarrow> pe \<turnstile> (WHILE b DO c,s) \<Rightarrow> s" |
    22 WhileTrue:
    23   "\<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>
    24    pe \<turnstile> (WHILE b DO c, s\<^isub>1) \<Rightarrow> s\<^isub>3" |
    25 
    26 Var: "pe \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> ({VAR x;; c}, s) \<Rightarrow> t(x := s x)" |
    27 
    28 Call1: "(p,c)#pe \<turnstile> (c, s) \<Rightarrow> t  \<Longrightarrow>  (p,c)#pe \<turnstile> (CALL p, s) \<Rightarrow> t" |
    29 Call2: "\<lbrakk> p' \<noteq> p;  pe \<turnstile> (CALL p, s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
    30        (p',c)#pe \<turnstile> (CALL p, s) \<Rightarrow> t" |
    31 
    32 Proc: "(p,cp)#pe \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> ({PROC p = cp;; c}, s) \<Rightarrow> t"
    33 
    34 code_pred big_step .
    35 
    36 
    37 (* FIXME: example state syntax *)
    38 values "{map t [''x'', ''y'', ''z''] |t. 
    39             [] \<turnstile> (CALL ''p'', (%_. 0)(''x'' := 42, ''y'' := 43)) \<Rightarrow> t}"
    40 
    41 values "{map t [''x'', ''y'', ''z''] |t. [] \<turnstile> (test_com, (%_. 0) ) \<Rightarrow> t}"
    42 
    43 end