Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 2 / d / Solution

Use infinite coefficient lazy lists:

zero, one :: Num a => [a]
zero = 0 : zero
one  = 1 : zero

For ordinary numeric coefficients such as Rational, zero == zero does not terminate, while zero == one is False. The former comparison never finds a differing coefficient or reaches two empty lists; the latter rejects the unequal first coefficients immediately. Equality of denoted formal power series is mathematical equality of all coefficients, whereas this executable list comparison is a potentially nonterminating procedure.