src/HOL/IMP/Procs_Dyn_Vars_Dyn.thy
author paulson
Wed, 24 Feb 2021 18:41:39 +0000
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theory Procs_Dyn_Vars_Dyn imports Procs
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begin
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subsubsection "Dynamic Scoping of Procedures and Variables"
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type_synonym penv = "pname \<Rightarrow> com"
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inductive
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  big_step :: "penv \<Rightarrow> com \<times> state \<Rightarrow> state \<Rightarrow> bool" ("_ \<turnstile> _ \<Rightarrow> _" [60,0,60] 55)
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where
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Skip:    "pe \<turnstile> (SKIP,s) \<Rightarrow> s" |
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Assign:  "pe \<turnstile> (x ::= a,s) \<Rightarrow> s(x := aval a s)" |
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Seq:     "\<lbrakk> pe \<turnstile> (c\<^sub>1,s\<^sub>1) \<Rightarrow> s\<^sub>2;  pe \<turnstile> (c\<^sub>2,s\<^sub>2) \<Rightarrow> s\<^sub>3 \<rbrakk> \<Longrightarrow>
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          pe \<turnstile> (c\<^sub>1;;c\<^sub>2, s\<^sub>1) \<Rightarrow> s\<^sub>3" |
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IfTrue:  "\<lbrakk> bval b s;  pe \<turnstile> (c\<^sub>1,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
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         pe \<turnstile> (IF b THEN c\<^sub>1 ELSE c\<^sub>2, s) \<Rightarrow> t" |
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IfFalse: "\<lbrakk> \<not>bval b s;  pe \<turnstile> (c\<^sub>2,s) \<Rightarrow> t \<rbrakk> \<Longrightarrow>
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         pe \<turnstile> (IF b THEN c\<^sub>1 ELSE c\<^sub>2, s) \<Rightarrow> t" |
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WhileFalse: "\<not>bval b s \<Longrightarrow> pe \<turnstile> (WHILE b DO c,s) \<Rightarrow> s" |
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WhileTrue:
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  "\<lbrakk> bval b s\<^sub>1;  pe \<turnstile> (c,s\<^sub>1) \<Rightarrow> s\<^sub>2;  pe \<turnstile> (WHILE b DO c, s\<^sub>2) \<Rightarrow> s\<^sub>3 \<rbrakk> \<Longrightarrow>
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   pe \<turnstile> (WHILE b DO c, s\<^sub>1) \<Rightarrow> s\<^sub>3" |
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Var: "pe \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> ({VAR x; c}, s) \<Rightarrow> t(x := s x)" |
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Call: "pe \<turnstile> (pe p, s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> (CALL p, s) \<Rightarrow> t" |
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Proc: "pe(p := cp) \<turnstile> (c,s) \<Rightarrow> t  \<Longrightarrow>  pe \<turnstile> ({PROC p = cp; c}, s) \<Rightarrow> t"
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code_pred big_step .
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values "{map t [''x'',''y''] |t. (\<lambda>p. SKIP) \<turnstile> (test_com, <>) \<Rightarrow> t}"
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end