src/HOL/IMP/Procs_Stat_Vars_Stat.thy
author bulwahn
Fri Oct 21 11:17:14 2011 +0200 (2011-10-21)
changeset 45231 d85a2fdc586c
parent 45212 e87feee00a4c
child 47818 151d137f1095
permissions -rw-r--r--
replacing code_inline by code_unfold, removing obsolete code_unfold, code_inline del now that the ancient code generator is removed
     1 theory Procs_Stat_Vars_Stat imports Procs
     2 begin
     3 
     4 subsubsection "Static Scoping of Procedures and Variables"
     5 
     6 type_synonym addr = nat
     7 type_synonym venv = "vname \<Rightarrow> addr"
     8 type_synonym store = "addr \<Rightarrow> val"
     9 type_synonym penv = "(pname \<times> com \<times> venv) list"
    10 
    11 fun venv :: "penv \<times> venv \<times> nat \<Rightarrow> venv" where
    12 "venv(_,ve,_) = ve"
    13 
    14 inductive
    15   big_step :: "penv \<times> venv \<times> nat \<Rightarrow> com \<times> store \<Rightarrow> store \<Rightarrow> bool"
    16   ("_ \<turnstile> _ \<Rightarrow> _" [60,0,60] 55)
    17 where
    18 Skip:    "e \<turnstile> (SKIP,s) \<Rightarrow> s" |
    19 Assign:  "(pe,ve,f) \<turnstile> (x ::= a,s) \<Rightarrow> s(ve x := aval a (s o ve))" |
    20 Semi:    "\<lbrakk> e \<turnstile> (c\<^isub>1,s\<^isub>1) \<Rightarrow> s\<^isub>2;  e \<turnstile> (c\<^isub>2,s\<^isub>2) \<Rightarrow> s\<^isub>3 \<rbrakk> \<Longrightarrow>
    21           e \<turnstile> (c\<^isub>1;c\<^isub>2, s\<^isub>1) \<Rightarrow> s\<^isub>3" |
    22 
    23 IfTrue:  "\<lbrakk> bval b (s \<circ> venv e);  e \<turnstile> (c\<^isub>1,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
    24          e \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" |
    25 IfFalse: "\<lbrakk> \<not>bval b (s \<circ> venv e);  e \<turnstile> (c\<^isub>2,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
    26          e \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" |
    27 
    28 WhileFalse: "\<not>bval b (s \<circ> venv e) \<Longrightarrow> e \<turnstile> (WHILE b DO c,s) \<Rightarrow> s" |
    29 WhileTrue:
    30   "\<lbrakk> bval b (s\<^isub>1 \<circ> venv e);  e \<turnstile> (c,s\<^isub>1) \<Rightarrow> s\<^isub>2;
    31      e \<turnstile> (WHILE b DO c, s\<^isub>2) \<Rightarrow> s\<^isub>3 \<rbrakk> \<Longrightarrow>
    32    e \<turnstile> (WHILE b DO c, s\<^isub>1) \<Rightarrow> s\<^isub>3" |
    33 
    34 Var: "(pe,ve(x:=f),f+1) \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>
    35       (pe,ve,f) \<turnstile> ({VAR x;; c}, s) \<Rightarrow> t(f := s f)" |
    36 
    37 Call1: "((p,c,ve)#pe,ve,f) \<turnstile> (c, s) \<Rightarrow> t  \<Longrightarrow>
    38         ((p,c,ve)#pe,ve',f) \<turnstile> (CALL p, s) \<Rightarrow> t" |
    39 Call2: "\<lbrakk> p' \<noteq> p;  (pe,ve,f) \<turnstile> (CALL p, s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
    40        ((p',c,ve')#pe,ve,f) \<turnstile> (CALL p, s) \<Rightarrow> t" |
    41 
    42 Proc: "((p,cp,ve)#pe,ve,f) \<turnstile> (c,s) \<Rightarrow> t
    43       \<Longrightarrow>  (pe,ve,f) \<turnstile> ({PROC p = cp;; c}, s) \<Rightarrow> t"
    44 
    45 code_pred big_step .
    46 
    47 
    48 values "{map t [0,1] |t. ([], <>, 0) \<turnstile> (CALL ''p'', nth [42, 43]) \<Rightarrow> t}"
    49 
    50 values "{map t [0, 1, 2] |t.
    51   ([], <''x'' := 0, ''y'' := 1,''z'' := 2>, 0)
    52   \<turnstile> (test_com, <>) \<Rightarrow> t}"
    53 
    54 end