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Polynomial Polymorphism
 Proceedings of the Eighteenth Australasian Computer Science Conference: Glenelg, South Australia 13 February
, 1995
"... Inductive types, such as lists and trees, have a uniform semantic description, both of the types themselves and the folding algorithms that construct homomorphisms out of them. Though implementations have been able to give a uniform description of the types, this has not been true of folding, since ..."
Abstract

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Inductive types, such as lists and trees, have a uniform semantic description, both of the types themselves and the folding algorithms that construct homomorphisms out of them. Though implementations have been able to give a uniform description of the types, this has not been true of folding, since there has not been a uniform mechanism for finding the subexpressions (the sublists or subtrees, etc.) to which recursion applies. Polynomial types overcome this problem by distinguishing the indeterminate of the polynomial (on which the recursion occurs) from its coefficients. Further, this uniformity is recognised by the type system, which is able to treat fld as a (shape) polymorphic constant of the calculus. These ideas have been implemented in a language P2. Key words types, polynomials, polymorphism, folding, shape, P2. 1 Introduction The use of initial algebras to describe inductive data types, such as lists and trees, produces a uniform method for describing a large class of ...