Type-inference based deforestation of functional programs

In lazy functional programming modularity is often achieved by using intermediate data structures to combine separate parts of a program. Each intermediate data structure is produced by one part and consumed by another one. Deforestation optimises a functional program by transformation into a program which does not produce such intermediate data structures. In this thesis we present a new method for deforestation, which combines a known method, short cut deforestation, with a new analysis that is based on type inference. Short cut deforestation eliminates an intermediate list by a single, local transformation. In return, short cut deforestation expects both producer and consumer of the intermediate list in a certain form. Whereas the required form of the consumer is generally considered desirable in a well-structured program anyway, the required form of the producer is only a crutch to enable deforestation. Hence only the list-producing functions of the standard libraries were defined in the desired form and short cut deforestation has been confined to compositions of these functions. Here, we present an algorithm which transforms an arbitrary producer into the required form. Starting from the observation that short cut deforestation is based on a parametricity theorem of the second-order typed λ-calculus, we show how the construction of the required form can be reduced to a type inference problem. Typability for the second-order typed λ-calculus is undecidable, but we only need to solve a partial type inference problem. For this problem we develop an algorithm based on the well-known Hindley-Milner type inference algorithm. The transformation of a producer often requires inlining of some function definitions. Type inference even indicates which function definitions need to be inlined. However, only limited inlining across module boundaries is practically feasible. Therefore, we extend the previously developed algorithm to split a function definition into a worker definition and a wrapper definition. We only need to inline the small wrapper definition, which transfers all information required for deforestation. The flexibility of type inference allows us to remove intermediate lists which original short cut deforestation cannot remove, even with hand-crafted producers. In contrast to most previous work on deforestation, we give a detailed proof of completeness and semantic correctness of our transformation.