Verifikation reaktiver Systeme - Universität Kaiserslautern

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UNDISCH_TAC ‘‘is_gcd m (SUC (m’ * 2)) (gcd m (SUC (m’ * 2)))‘‘ THEN
REWRITE_TAC[is_gcd_def] THEN
ARW_TAC[]
] );
val BGCD_ODD_EVEN = store_thm("BGCD_ODD_EVEN",
‘‘!x y. ODD x /\ EVEN y ==> (gcd x y = gcd x (y DIV 2))‘‘,
ONCE_REWRITE_TAC[GCD_SYM] THEN
ARW_TAC[BGCD_EVEN_ODD] );
val BGCD_ODD_ODD0 = store_thm("BGCD_ODD_ODD0",
‘‘!x y. ODD x /\ ODD y /\ (x=y) ==> (gcd x y = x)‘‘,
REPEAT STRIP_TAC THEN
ARW_TAC[GCD_REF] );
val BGCD_ODD_ODD1 = store_thm("BGCD_ODD_ODD1",
‘‘!x y. ODD x /\ ODD y /\ y (gcd x y = gcd (x-y) y)‘‘,
REPEAT STRIP_TAC THEN
ASSUME_TAC (SPEC ‘‘x-y‘‘ (SPEC ‘‘y:num‘‘ GCD_ADD_L)) THEN
UNDISCH_TAC ‘‘gcd (y + (x - y)) y = gcd y (x - y)‘‘ THEN
ONCE_REWRITE_TAC[ADD_SYM] THEN
ASSUME_TAC (UNDISCH_ALL (prove(‘‘y < x ==> ybool, out:num->bool) =
!t. out t = ~inp t‘;
val MUX_def = Define ‘MUX(sw:num->bool,in1:num->num,in2:num->num,out:num->num) =
!t. out t = if sw t then in1 t else in2 t‘;
val OR_def = Define ‘OR(in1:num->bool,in2:num->bool,out:num->bool) =
!t. out t = (in1 t) \/ (in2 t)‘;
val AND_def = Define ‘AND(in1:num->bool,in2:num->bool,out:num->bool) =
!t. out t = (in1 t) /\ (in2 t)‘;
val COUNTER_def = Define ‘COUNTER(inp:num->bool,out:num->num) =
!t. out t = if (t=0) then 0 else
if (inp t) then (out(t-1)+1) else out(t-1)‘;
val REG_def = Define ‘REG(inp:num->num,out:num->num,init:num) =
!t. out t = if (t=0) then init else inp (t-1)‘;
val SHIFT_def = Define ‘SHIFT(inp:num->num, out:num->num) =
!t. out t = (inp t) DIV 2‘;