Higher-Order Catamorphisms as Bases for Program Structuring and Design Recovery

Abstract

Catamorphisms ("foldr" on lists, but generally applicable to any regular recursive datatype) are not just useful but are an effective basis for a recursion-pattern-based discipline of program design. A new presentation for catamorphisms makes it clear how they provide functional semantics for symbolic datatypes, with the capacity to expose significant variations in program design. A further development of the new presentation exploits the higherorder capabilities of functional languages. This is the key enabler for a comprehensive replacement of symbolic data and their interpreters, either implicit or explicit, with direct functional representations. These extensions, of the applicability of catamorphisms and of their presentations, make them even more attractive as bases for program structuring and design, and likewise as targets for software reverse engineering and design recovery. KEY WORDS Software design and development; Programming Tools and languages; Functional programming; Recursion pattern. 2 Catamorphisms are Useful Catamorphisms represent a general, indeed generic recursion pattern on regular recursive datatypes. The design of programs is improved by expressing their recursive components as explicit instantiations of these general patterns.

Denotational trace: a category-theoretic solution to the practical problems of software execution tracing

“…Bailes and Brough have shown how these recursion patterns can be used as the basis for a simplified, sub-recursive style of programming [BB13], and with Kemp, that this can therefore provide a useful basis for program structuring as well as recovery of designs from source code [BBK12]. Because category theory applies well to describing abstract type system structures, it has therefore also been used as a basis for generic (polytypic) programming [BJJM99,Hin12].…”