S applies a function to successive members of a list, producing a list. The machine w i l l stop at address 4. In calculation, t h e properties of objects a r e de- termined by a c t u a l observation. The Proofchecker accom- plished t h e t r a n s l a t i o n from an input proof t o a rigorous proof through t h e use of macro-steps, which bear the same r e l a t i o n t o rigorous proof s t e p s t h a t macro-bstructions in a computer macro- assembly language bear t o machine i n s t r u c t i o n s i n t h a t language. Stated in precise English, and using a recursive definition without making use of division , the remainder when the dividend Y is divided by the divisor X, is determined as follows: i If Y equals X, the remainder is 0 ; otherwise, ii If Y is less than X, the remainder is Y; otherwise, iii The remainder is the same as the remainder we would get if the result of Y minus X were divided by the divisor X.
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