PolyP extends a functional language (a subset of Haskell) with a construct for defining polytypic functions by induction on the structure of user-defined datatypes. Programs in the extended language are translated to Haskell. PolyLib contains powerful structured recursion operators like catamorphisms, maps and traversals, as well as polytypic versions of a number of standard functions from functional programming: sum, length, zip, (==), (6), etc. Both the specification of the library and a PolyP implementation are presented.

The (exact) pattern matching problem can be informally specified as follows: given a pattern and a text, find all occurrences of the pattern in the text. The pattern and the text may both be lists, or they may both be trees, or they may both be multi-dimensional arrays, etc. This paper describes a general pattern-matching algorithm for all datatypes definable as an initial object in a category of F -algebras, where F is a regular functor. This class of datatypes includes mutual recursive datatypes and lots of different kinds of trees. The algorithm is a generalisation of the Knuth, Morris, Pratt like pattern-matching algorithm on trees first described by Hoffmann and O'Donnell. 1 Introduction Most editors provide a search function that takes a string of symbols and returns the first position in the text being edited at which this string of symbols occurs. The string of symbols is called a pattern, and the algorithm that detects the position at which a pattern occurs is called a (exa...