Deforestation optimises a functional program by transforming it into another one that does not create certain intermediate data structures. Short cut deforestation is a deforestation method which is based on a single, local transformation rule. In return, short cut deforestation expects both producer and consumer of the intermediate structure in a certain form. Warm fusion was proposed to automatically transform functions into this form. Unfortunately, it is costly and hard to implement. Starting from the fact that short cut deforestation is based on a parametricity theorem of the second-order typed λ-calculus, we show how the required form of a list producer can be derived through the use of type inference. Typability for the second-order typed λ-calculus is undecidable. However, we present a linear-time algorithm that solves a partial type inference problem and that, together with controlled inlining and polymorphic type instantiation, suffices for deforestation. The resulting new sho...

Generic control operators, such as fold, have been introduced in functional programming to increase the power and applicability of data-structure-based transformations. This is achieved by making the structure of the data more explicit in program specifications. We argue that this very important property is one of the original concepts of attribute grammars. In this paper, we informally show the similarities between the fold formalism and attribute grammar specifications. We also compare their respective method to eliminate the intermediate data structures introduced by function composition (notion of deforestation or fusion): the normalization algorithm for programs expressed with folds and the descriptional composition of attribute grammars. Rather than identify the best way to achieve deforestation, the main goal of this paper is merely to intuitively present two programming paradigms to each other's supporting community and provide an unbiased account of their similarities and diff...

Abstract Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equality functions, unifiers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of user-defined datatypes. This thesis introduces polytypic functions, shows how to construct and reason about polytypic functions and describes the implementation of the polytypic programming system PolyP. PolyP extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions. Programs in the extended language are translated to Haskell.