Verifikation reaktiver Systeme - Universität Kaiserslautern

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val SUB_def = Define ‘SUB(in1:num->num,in2:num->num,out:num->num) =
!t. out t = (in1 t - in2 t)‘;
val LESS_def = Define ‘LESS(in1:num->num,in2:num->num,out:num->bool) =
!t. out t = (in1 t < in2 t)‘;
val LSB_def = Define ‘LSB(inp:num->num,out:num->bool) =
!t. out t = ((inp t) MOD 2 = 1)‘;
val BGCD_IMP_def = Define ‘BGCD_IMP
(initX:num, initY:num,
regX:num->num, regY:num->num, regK:num->num) =
? inX, inY, regXshift, regYshift, oddX, oddY, regXcor, regYcor,
evenX, evenY, evenXY, oddXY, oddXYy, oddXYx,
subX, subY, subXY, subYX.
REG(inX,regX,initX) /\ REG(inY,regY,initY) /\
SHIFT(regX,regXshift) /\ SHIFT(regY,regYshift) /\
LSB(regX,oddX) /\ LSB(regY,oddY) /\
MUX(oddX,regX,regXshift,regXcor) /\ MUX(oddY,regY,regYshift,regYcor) /\
NOT(oddX,evenX) /\ NOT(oddY,evenY) /\
AND(evenX,evenY,evenXY)/\
COUNTER(evenXY,regK)/\
AND(oddX, oddY, oddXY) /\
LESS(regXcor,regYcor,oddXYx) /\ LESS(regYcor,regXcor,oddXYy) /\
AND(oddXY,oddXYx,subX) /\ AND(oddXY,oddXYy,subY) /\
SUB(regXcor,regYcor,subXY) /\ SUB(regYcor,regXcor,subYX) /\
MUX(subX,regXcor,subXY,inX) /\ MUX(subY,regYcor,subYX,inY)‘;
A.2 fractionScript
(*==========================================================================*)
(* Theory of fractions. (Jens Brandt) *)
(* *)
(* The fractions are pairs of integers. Denominator of fractions is always *)
(* positive. *)
(* *)
(* February 2004 *)
(* *)
(*==========================================================================*)
open HolKernel boolLib Parse bossLib;
(* interactive mode
app load ["integerTheory","intLib","ringLib",
"integerRingTheory","integerRingLib"];
*)
open
arithmeticTheory ringTheory ringLib
integerTheory intLib integerRingTheory integerRingLib;
val _ = new_theory "fraction";