(* Title: HOL/IMPP/Natural.thy
ID: $Id$
Author: David von Oheimb (based on a theory by Tobias Nipkow et al), TUM
Copyright 1999 TUM
Natural semantics of commands
*)
Natural = Com +
(** Execution of commands **)
consts evalc :: "(com * state * state) set"
"@evalc":: [com,state, state] => bool ("<_,_>/ -c-> _" [0,0, 51] 51)
evaln :: "(com * state * nat * state) set"
"@evaln":: [com,state,nat,state] => bool ("<_,_>/ -_-> _" [0,0,0,51] 51)
translations "<c,s> -c-> s'" == "(c,s, s') : evalc"
"<c,s> -n-> s'" == "(c,s,n,s') : evaln"
consts
newlocs :: locals
setlocs :: state => locals => state
getlocs :: state => locals
update :: state => vname => val => state ("_/[_/::=/_]" [900,0,0] 900)
syntax (* IN Natural.thy *)
loc :: state => locals ("_<_>" [75,0] 75)
translations
"s<X>" == "getlocs s X"
inductive evalc
intrs
Skip "<SKIP,s> -c-> s"
Assign "<X :== a,s> -c-> s[X::=a s]"
Local "<c, s0[Loc Y::= a s0]> -c-> s1 ==>
<LOCAL Y := a IN c, s0> -c-> s1[Loc Y::=s0<Y>]"
Semi "[| <c0,s0> -c-> s1; <c1,s1> -c-> s2 |] ==>
<c0;; c1, s0> -c-> s2"
IfTrue "[| b s; <c0,s> -c-> s1 |] ==>
<IF b THEN c0 ELSE c1, s> -c-> s1"
IfFalse "[| ~b s; <c1,s> -c-> s1 |] ==>
<IF b THEN c0 ELSE c1, s> -c-> s1"
WhileFalse "~b s ==> <WHILE b DO c,s> -c-> s"
WhileTrue "[| b s0; <c,s0> -c-> s1; <WHILE b DO c, s1> -c-> s2 |] ==>
<WHILE b DO c, s0> -c-> s2"
Body "<the (body pn), s0> -c-> s1 ==>
<BODY pn, s0> -c-> s1"
Call "<BODY pn, (setlocs s0 newlocs)[Loc Arg::=a s0]> -c-> s1 ==>
<X:=CALL pn(a), s0> -c-> (setlocs s1 (getlocs s0))
[X::=s1<Res>]"
inductive evaln
intrs
Skip "<SKIP,s> -n-> s"
Assign "<X :== a,s> -n-> s[X::=a s]"
Local "<c, s0[Loc Y::= a s0]> -n-> s1 ==>
<LOCAL Y := a IN c, s0> -n-> s1[Loc Y::=s0<Y>]"
Semi "[| <c0,s0> -n-> s1; <c1,s1> -n-> s2 |] ==>
<c0;; c1, s0> -n-> s2"
IfTrue "[| b s; <c0,s> -n-> s1 |] ==>
<IF b THEN c0 ELSE c1, s> -n-> s1"
IfFalse "[| ~b s; <c1,s> -n-> s1 |] ==>
<IF b THEN c0 ELSE c1, s> -n-> s1"
WhileFalse "~b s ==> <WHILE b DO c,s> -n-> s"
WhileTrue "[| b s0; <c,s0> -n-> s1; <WHILE b DO c, s1> -n-> s2 |] ==>
<WHILE b DO c, s0> -n-> s2"
Body "<the (body pn), s0> - n-> s1 ==>
<BODY pn, s0> -Suc n-> s1"
Call "<BODY pn, (setlocs s0 newlocs)[Loc Arg::=a s0]> -n-> s1 ==>
<X:=CALL pn(a), s0> -n-> (setlocs s1 (getlocs s0))
[X::=s1<Res>]"
end