This report discusses a system of recursive terms with n-ary sums and products,
and provides a semantic model (M-types) of these terms. It defines a language
of recursive coercions between these terms and an interpretation of coercions
as partial functions between M-types. In this model "axioms" such as the
associative, commutative, and distributive laws denote natural transformations
between polynomial functors. These laws give isomorphisms but are not
identities of M-types. An inference system is used to assign Curry-style types
(s-->t) to coercions, and we give conditions under which the interpretation of
such a coercion is a total function [| s |] --> [| t |]. Assuming the natural
transformations and leaf coercions that occur in a coercion c denote injective
(resp. surjective/bijective) maps, we show the same for c. We also show how to
invert formally a bijective coercion.
By: Charles M. Barton
Published in: RC21615 in 1999
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