rm arith2.adv

/bin/umodem arith2.adv STOP

{ comments are enclosed by curly-braces;
  no nested comments are allowed  }

{remonter }
Compute(Z) => U(Z);
Compute(S x) => S (Compute x);
S(U x) => U (S x);

{ addition

  these rules work when the arguments are numerals
  but not for all arbitrary expressions

}


{Compute(Add Z y) => Compute(y);
Compute(Add (S x) y) => S (Compute(Add x y));}

Compute (Add x y) => Add (Compute x) y;
Add (U x) y => Add x (Compute y);
Add Z (U y) => (U y);
Add (S x) (U y) =>  S (Add x (U y)); 

{Add x (U y) => U (Add x y) --- inutile !!!}


{ define multiplication (Mult) here }


Compute(Mult x y) => Mult (Compute x) y;
Mult (U x) y => Mult x (Compute y);
Mult (S x) (U y) => Add y (Compute(Mult x y));
Mult Z (U y) => U Z;



{ when all other computation is done }


U x => x;
. { end of rules }

STOP

advise run arith2.adv arith.tests

advise arith arith2.adv