Advanced Functional Programming: Third International School, by Lex Augusteijn (auth.), S. Doaitse Swierstra, José N.

By Lex Augusteijn (auth.), S. Doaitse Swierstra, José N. Oliveira, Pedro R. Henriques (eds.)

This booklet originates from the 3rd summer season tuition on complex sensible Programming, held in Barga, Portugal, in September 1998. The lectures offered are detailed at person scholars and programming pros in addition to at small research teams and teachers who desire to turn into familiar with contemporary paintings within the speedily constructing quarter of sensible programming.
The booklet offers the next seven, conscientiously cross-reviewed chapters, written through major specialists within the box: Sorting Morphisms; general Programming: An creation; common software Transformation; Designing and imposing Combinator Languages; utilizing MetaML: A Staged Programming Language; Cayenne: A Language with based varieties; Haskell as an Automation Controller.

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Extra resources for Advanced Functional Programming: Third International School, AFP’98, Braga, Portugal, September 12-19, 1998, Revised Lectures

Sample text

There are several reasons for wanting to take the step from functions to relations. The most pressing is that specifications are relations between the input and the output, and our concern is with both specifications and implementations. Related to this is that termination properties of programs are typically established by appeal to a well-founded relation on the state space. We will not go into termination properties in these lecture notes but the use of well-founded relations will play an integral part in our discussion of one element of the correctness of a generic unification algorithm in chapter 4.

Datatypes having no type parameter also have a map combinator, but with no functional arguments! ) Functors Defined The idea that parameterised datatypes are structured repositories of information over which arbitrary functions can be mapped is captured by the concept of a functor. We first explain the concept informally for unary functors. Consider the world of typed functions. Functors are the structurerespecting functions for that world. So what is the structure involved? First, that world can be viewed as a directed graph, in which the nodes are types and the arcs are functions.

The first equality above should therefore only be applied to cases for which f •g is defined, and from now on we assume this as a tacit condition on such equations. It follows from the typing rule that then also the composition (F f) • (F g) is well-typed, so that is not needed as a condition. Now, in general, an n-ary functor F is a pair of mappings that maps an ntuple of types a0 , . . , an−1 to a type F a0 · · · an−1 and an n-tuple of functions f0 , . . , fn−1 to a function F f0 · · · fn−1 in such a way that typing, composition and identity are respected: :: ai → bi for i = 0, .

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