Polytypic Functional Programming

Structural polymorphism is a generic programming technique known within the functional programming community under the names of polytypic or datatype-generic programming. In this thesis we show that such a technique conflicts with the principle of data abstraction and propose a solution for reconciliation. More concretely, we show that popular polytypic extensions of the functional programming language Haskell, namely, Generic Haskell and Scrap your Boilerplate have their genericity limited by data abstraction. We propose an extension to the Generic Haskell language where the ‘structure’ in ‘structural polymorphism’ is defined around the concept of interface and not the representation of a type. More precisely, polytypic functions capture families of polymorphic functions in one single template definition. Instances of a polytypic function for specific algebraic types can be generated automatically by a compiler following the definitional structure of the types. However, the definitional structure of an abstract type is, for maintainability reasons, logically hidden and, sometimes, even physically unavailable (e.g., precompiled libraries). Even if the representation is known, the semantic gap between an abstract type and its representation type makes automatic generation difficult, if not impossible. Furthermore, if it were possible it would nevertheless be impractical: the code generated from the definitional structure of the internal representation is rendered obsolete when the representation changes. The purpose of an abstract type is to minimise the impact of representation changes on client code. Data abstraction is upheld by client code, whether polytypic or not, when it works with abstract types through their public interfaces. Fortunately, interfaces can provide enough description of ‘structure’ to guide the automatic construction of two polytypic functions that extract and insert data from abstract types to concrete types and vice versa. Polytypic functions can be defined in this setting in terms of polytypic insertion, polytypic extraction, and ordinary polytypic functions on concrete types. We propose the extension of the Generic Haskell language with mechanisms that enable programmers to supply the necessary information. The scheme relies on another proposed extension to support polytypic programming with type-class constrained types, which we show are not supported by Generic Haskell.