Patrik Jansson. Polytypism and Polytypic Unification. Master's thesis, Chalmers University of Technology and University of Goteborg, 1995. WwW file:// ftp.cs.chalmers.se/pub/users/patrikj/papers/masters/thesis.ps.Z .  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... was polytypically unified by de Moor in [5] Several further examples of polytypic calculations can be found in Bird and de Moor [3] The most impressive polytypic algorithms today are those developed by Jeuring and his group, such as Jeuring s polytypic pattern matching algorithm [21] Jansson [17] presents a polytypic unification algorithm (see also Jansson and Jeuring [19] Although not derived calculationally, these algorithms provide strong evidence of the potential of polytypic definitions. Huisman [16] defines a polytypic function unparser rather like polytypic flatten but with ....

Patrik Jansson. Polytypism and Polytypic Unification. Master's thesis, Chalmers University of Technology and University of Goteborg, 1995. WwW file:// ftp.cs.chalmers.se/pub/users/patrikj/papers/masters/thesis.ps.Z .

....to be used in it. The functions in these classes are easily written as polytypic functions. Implementing Squiggol s [28, 30, 31, 33] general purpose datatype independent functions such as cata, map, zip, para etc. Implementing general purpose, datatype independent programs for unification [14, 15], pattern matching [20] data compression [21] etc. 1.4 Writing polytypic programs There exist various ways to implement polytypic programs. Three possibilities are: using a universal datatype; using higher order polymorphism and constructor classes; using a special syntactic ....

.... Polytypic functions for specific problems, such as the maximum segment sum problem and the pattern matching problem were first given by Bird et al. 3] and Jeuring [20] Special purpose polytypic functions such as the generalised version of function length and the operator ( can be found in [30, 34, 35, 40, 14]. Jay [18] has developed an alternative theory for polytypic functions, in which values are represented by their structure and their contents. Type systems for languages with constructs for writing polytypic functions have been developed by Jay [17] Ruehr [38, 39] Sheard and Nelson [41] and ....

P. Jansson. Polytypism and polytypic unification. Master's thesis, Chalmers University of Technology and University of Goteborg, 1995.

....of non mutual recursive, regular datatypes with one type argument. Multiple type arguments can be encoded in a single sum type, but we are working on a more elegant treatment of multiple type arguments. One of PolyP s predecessors (a preprocessor that generated instances of polytypic functions [11]) could handle mutual recursive datatypes, and we hope to port this part of the predecessor to PolyP in the near future. In the future PolyP will be able to handle mutual recursive datatypes with an arbitrary number of type arguments and in which function spaces may occur. 1.4 Background and ....

....may occur. 1.4 Background and related work Polytypic functions are standard in the Squiggol community, see [24, 26, 27] Generating instances for specific polytypic functions, such as ( map, cata, hylo, etc. for a given type, is rather simple and has been demonstrated by several authors [3, 8, 11, 13, 31]. Given a number of predefined polytypic functions many others can be defined, and amongst others Jay et al. s type system [2, 13] and Jones type system based on qualified types and higher order polymorphism [18, 20] can be used to type check expressions in a language with predefined polytypic ....

P. Jansson. Polytypism and polytypic unification. Master's thesis, Chalmers University of Technology and University of Goteborg, 1995.

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