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The Generic Haskell programming language allows functions to be defined by induction on the structure of data types. This gives rise to generic functions which can be applied to values of any conceivable data type. Compiling a Generic Haskell program amounts to generating a Haskell program in which all generic functions have been translated to ordinary… (More)
Consider the set U of real numbers q ≥ 1 for which only one sequence (c i) of integers 0 ≤ c i ≤ q satisfies the equality P ∞ i=1 c i q −i = 1. In this note we show that the set of algebraic numbers in U is dense in the closure U of U .
Let q > 1 be a real number and let m = m(q) be the largest integer smaller than q. It is well known that each number x ∈ Jq := [0, P ∞ i=1 mq −i ] can be written as x = P ∞ i=1 c i q −i with integer coefficients 0 ≤ c i < q. If q is a non-integer, then almost every x ∈ Jq has continuum many expansions of this form. In this note we consider some properties… (More)