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Programming with bananas, lenses, envelopes and barbed wire
 In FPCA
, 1991
"... We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example Functions in Bird and Wadler's "Introdu ..."
Abstract

Cited by 302 (11 self)
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We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example Functions in Bird and Wadler's "Introduction to Functional Programming " can be expressed using these operators. 1
Program Calculation Properties of Continuous Algebras
, 1991
"... Defining data types as initial algebras, or dually as final coalgebras, is beneficial, if not indispensible, for an algebraic calculus for program construction, in view of the nice equational properties that then become available. It is not hard to render finite lists as an initial algebra and, ..."
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Cited by 19 (0 self)
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Defining data types as initial algebras, or dually as final coalgebras, is beneficial, if not indispensible, for an algebraic calculus for program construction, in view of the nice equational properties that then become available. It is not hard to render finite lists as an initial algebra and, dually, infinite lists as a final coalgebra. However, this would mean that there are two distinct data types for lists, and then a program that is applicable to both finite and infinite lists is not possible, and arbitrary recursive definitions are not allowed. We prove the existence of algebras that are both initial in one category of algebras and final in the closely related category of coalgebras, and for which arbitrary (continuous) fixed point definitions ("recursion") do have a solution. Thus there is a single data type that comprises both the finite and the infinite lists. The price to be paid, however, is that partiality (of functions and values) is unavoidable.