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1 theory Procs_Stat_Vars_Stat imports Util Procs |
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2 begin |
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3 |
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4 subsubsection "Static Scoping of Procedures and Variables" |
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5 |
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6 type_synonym addr = nat |
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7 type_synonym venv = "name \<Rightarrow> addr" |
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8 type_synonym store = "addr \<Rightarrow> val" |
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9 type_synonym penv = "(name \<times> com \<times> venv) list" |
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10 |
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11 fun venv :: "penv \<times> venv \<times> nat \<Rightarrow> venv" where |
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12 "venv(_,ve,_) = ve" |
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13 |
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14 inductive |
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15 big_step :: "penv \<times> venv \<times> nat \<Rightarrow> com \<times> store \<Rightarrow> store \<Rightarrow> bool" |
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16 ("_ \<turnstile> _ \<Rightarrow> _" [60,0,60] 55) |
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17 where |
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18 Skip: "e \<turnstile> (SKIP,s) \<Rightarrow> s" | |
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19 Assign: "(pe,ve,f) \<turnstile> (x ::= a,s) \<Rightarrow> s(ve x := aval a (s o ve))" | |
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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> |
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21 e \<turnstile> (c\<^isub>1;c\<^isub>2, s\<^isub>1) \<Rightarrow> s\<^isub>3" | |
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22 |
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23 IfTrue: "\<lbrakk> bval b (s \<circ> venv e); e \<turnstile> (c\<^isub>1,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow> |
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24 e \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" | |
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25 IfFalse: "\<lbrakk> \<not>bval b (s \<circ> venv e); e \<turnstile> (c\<^isub>2,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow> |
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26 e \<turnstile> (IF b THEN c\<^isub>1 ELSE c\<^isub>2, s) \<Rightarrow> t" | |
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27 |
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28 WhileFalse: "\<not>bval b (s \<circ> venv e) \<Longrightarrow> e \<turnstile> (WHILE b DO c,s) \<Rightarrow> s" | |
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29 WhileTrue: |
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30 "\<lbrakk> bval b (s\<^isub>1 \<circ> venv e); e \<turnstile> (c,s\<^isub>1) \<Rightarrow> s\<^isub>2; |
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31 e \<turnstile> (WHILE b DO c, s\<^isub>2) \<Rightarrow> s\<^isub>3 \<rbrakk> \<Longrightarrow> |
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32 e \<turnstile> (WHILE b DO c, s\<^isub>1) \<Rightarrow> s\<^isub>3" | |
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33 |
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34 Var: "(pe,ve(x:=f),f+1) \<turnstile> (c,s) \<Rightarrow> t \<Longrightarrow> |
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35 (pe,ve,f) \<turnstile> ({VAR x;; c}, s) \<Rightarrow> t(f := s f)" | |
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36 |
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37 Call1: "((p,c,ve)#pe,ve,f) \<turnstile> (c, s) \<Rightarrow> t \<Longrightarrow> |
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38 ((p,c,ve)#pe,ve',f) \<turnstile> (CALL p, s) \<Rightarrow> t" | |
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39 Call2: "\<lbrakk> p' \<noteq> p; (pe,ve,f) \<turnstile> (CALL p, s) \<Rightarrow> t \<rbrakk> \<Longrightarrow> |
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40 ((p',c,ve')#pe,ve,f) \<turnstile> (CALL p, s) \<Rightarrow> t" | |
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41 |
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42 Proc: "((p,cp,ve)#pe,ve,f) \<turnstile> (c,s) \<Rightarrow> t |
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43 \<Longrightarrow> (pe,ve,f) \<turnstile> ({PROC p = cp;; c}, s) \<Rightarrow> t" |
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44 |
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45 code_pred big_step . |
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46 |
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47 values "{map t [0,1] |t. ([], \<lambda>n. 0, 0) \<turnstile> (CALL ''p'', nth [42, 43]) \<Rightarrow> t}" |
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48 |
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49 (* FIXME: syntax *) |
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50 values "{map t [0, 1, 2] |t. ([], (\<lambda>_. 3)(''x'' := 0, ''y'' := 1,''z'' := 2), 0) \<turnstile> (test_com, (%_. 0)) \<Rightarrow> t}" |
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51 |
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52 |
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53 end |