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