--- a/IMP/Com.thy Fri Jan 19 12:49:36 1996 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,112 +0,0 @@
-(* Title: HOL/IMP/Com.thy
- ID: $Id$
- Author: Heiko Loetzbeyer & Robert Sandner, TUM
- Copyright 1994 TUM
-
-Arithmetic expressions, Boolean expressions, Commands
-
-And their Operational semantics
-*)
-
-Com = Arith +
-
-(** Arithmetic expressions **)
-types loc
- state = "loc => nat"
- n2n = "nat => nat"
- n2n2n = "nat => nat => nat"
-
-arities loc :: term
-
-datatype
- aexp = N (nat)
- | X (loc)
- | Op1 (n2n, aexp)
- | Op2 (n2n2n, aexp, aexp)
-
-(** Evaluation of arithmetic expressions **)
-consts evala :: "(aexp*state*nat)set"
- "@evala" :: "[aexp,state,nat] => bool" ("<_,_>/ -a-> _" [0,0,50] 50)
-translations
- "<ae,sig> -a-> n" == "<ae,sig,n> : evala"
-inductive "evala"
- intrs
- N "<N(n),s> -a-> n"
- X "<X(x),s> -a-> s(x)"
- Op1 "<e,s> -a-> n ==> <Op1(f,e),s> -a-> f(n)"
- Op2 "[| <e0,s> -a-> n0; <e1,s> -a-> n1 |]
- ==> <Op2(f,e0,e1),s> -a-> f(n0,n1)"
-
-types n2n2b = "[nat,nat] => bool"
-
-(** Boolean expressions **)
-
-datatype
- bexp = true
- | false
- | ROp (n2n2b, aexp, aexp)
- | noti (bexp)
- | andi (bexp,bexp) (infixl 60)
- | ori (bexp,bexp) (infixl 60)
-
-(** Evaluation of boolean expressions **)
-consts evalb :: "(bexp*state*bool)set"
- "@evalb" :: "[bexp,state,bool] => bool" ("<_,_>/ -b-> _" [0,0,50] 50)
-
-translations
- "<be,sig> -b-> b" == "<be,sig,b> : evalb"
-
-inductive "evalb"
- intrs (*avoid clash with ML constructors true, false*)
- tru "<true,s> -b-> True"
- fls "<false,s> -b-> False"
- ROp "[| <a0,s> -a-> n0; <a1,s> -a-> n1 |]
- ==> <ROp(f,a0,a1),s> -b-> f(n0,n1)"
- noti "<b,s> -b-> w ==> <noti(b),s> -b-> (~w)"
- andi "[| <b0,s> -b-> w0; <b1,s> -b-> w1 |]
- ==> <b0 andi b1,s> -b-> (w0 & w1)"
- ori "[| <b0,s> -b-> w0; <b1,s> -b-> w1 |]
- ==> <b0 ori b1,s> -b-> (w0 | w1)"
-
-(** Commands **)
-
-datatype
- com = skip
- | ":=" (loc,aexp) (infixl 60)
- | semic (com,com) ("_; _" [60, 60] 10)
- | whileC (bexp,com) ("while _ do _" 60)
- | ifC (bexp, com, com) ("ifc _ then _ else _" 60)
-
-(** Execution of commands **)
-consts evalc :: "(com*state*state)set"
- "@evalc" :: "[com,state,state] => bool" ("<_,_>/ -c-> _" [0,0,50] 50)
- "assign" :: "[state,nat,loc] => state" ("_[_'/_]" [95,0,0] 95)
-
-translations
- "<ce,sig> -c-> s" == "<ce,sig,s> : evalc"
-
-rules
- assign_def "s[m/x] == (%y. if(y=x,m,s(y)))"
-
-inductive "evalc"
- intrs
- skip "<skip,s> -c-> s"
-
- assign "<a,s> -a-> m ==> <x := a,s> -c-> s[m/x]"
-
- semi "[| <c0,s> -c-> s2; <c1,s2> -c-> s1 |]
- ==> <c0 ; c1, s> -c-> s1"
-
- ifcTrue "[| <b,s> -b-> True; <c0,s> -c-> s1 |]
- ==> <ifc b then c0 else c1, s> -c-> s1"
-
- ifcFalse "[| <b,s> -b-> False; <c1,s> -c-> s1 |]
- ==> <ifc b then c0 else c1, s> -c-> s1"
-
- whileFalse "<b, s> -b-> False ==> <while b do c,s> -c-> s"
-
- whileTrue "[| <b,s> -b-> True; <c,s> -c-> s2;
- <while b do c, s2> -c-> s1 |]
- ==> <while b do c, s> -c-> s1 "
-
-end