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