Ph.D. Interim Report: Mathematical Studies of Infinite Computation

Polymorphic stream functions operate on the structure of streams, infinite lists of elements, without inspection of the contained data. We prove that a simple system for specifying recursive stream functions, consisting of equations using only stream constructors and destructors and recursive calls, is already enough to define all computable polymorphic stream functions. Requiring an entirely different approach, we prove this holds true even for purely unary equations not even mutually recursive, yielding an elegant model of Turing-completeness in a severely restricted environment.