src/CCL/ex/Nat.thy
changeset 1149 5750eba8820d
parent 0 a5a9c433f639
child 1474 3f7d67927fe2
equal deleted inserted replaced
1148:e125fc7a1183 1149:5750eba8820d
    19 
    19 
    20   not_def     "not(b) == if b then false else true"
    20   not_def     "not(b) == if b then false else true"
    21 
    21 
    22   add_def     "a #+ b == nrec(a,b,%x g.succ(g))"
    22   add_def     "a #+ b == nrec(a,b,%x g.succ(g))"
    23   mult_def    "a #* b == nrec(a,zero,%x g.b #+ g)"
    23   mult_def    "a #* b == nrec(a,zero,%x g.b #+ g)"
    24   sub_def     "a #- b == letrec sub x y be ncase(y,x,%yy.ncase(x,zero,%xx.sub(xx,yy))) \
    24   sub_def     "a #- b == letrec sub x y be ncase(y,x,%yy.ncase(x,zero,%xx.sub(xx,yy))) 
    25 \                        in sub(a,b)"
    25                         in sub(a,b)"
    26   le_def     "a #<= b == letrec le x y be ncase(x,true,%xx.ncase(y,false,%yy.le(xx,yy))) \
    26   le_def     "a #<= b == letrec le x y be ncase(x,true,%xx.ncase(y,false,%yy.le(xx,yy))) 
    27 \                        in le(a,b)"
    27                         in le(a,b)"
    28   lt_def     "a #< b == not(b #<= a)"
    28   lt_def     "a #< b == not(b #<= a)"
    29 
    29 
    30   div_def    "a ## b == letrec div x y be if x #< y then zero else succ(div(x#-y,y)) \
    30   div_def    "a ## b == letrec div x y be if x #< y then zero else succ(div(x#-y,y)) 
    31 \                       in div(a,b)"
    31                        in div(a,b)"
    32   ack_def    
    32   ack_def    
    33   "ackermann(a,b) == letrec ack n m be ncase(n,succ(m),%x. \
    33   "ackermann(a,b) == letrec ack n m be ncase(n,succ(m),%x. 
    34 \                          ncase(m,ack(x,succ(zero)),%y.ack(x,ack(succ(x),y))))\
    34                           ncase(m,ack(x,succ(zero)),%y.ack(x,ack(succ(x),y))))
    35 \                    in ack(a,b)"
    35                     in ack(a,b)"
    36 
    36 
    37 end
    37 end
    38 
    38