<p> The Haskell programming language uses type classes to deal with overloading. Functions are overloaded by defining some types to be instances of a class. A meaningful instance should satisfy the invariants of the class.</p> <p> In this thesis we present one method to validate the type instances of classes informally, and another one to verify them in a formal way.</p> <p> The first method uses QuickCheck, which is an automatic testing tool for Haskell programs. We introduce how to specify the properties of type classes in QuickCheck by some examples, and I also present testing for Haskell standard types and classes.</p> <p> The second method I adopted uses the theorem prover Isabelle/HOL. To facilitate the usage of Isabelle/HOL for Haskell programmers, I define a set of translation rules from Haskell programs to Isabelle/HOL, and design a simple automatic translating tool based on those rules. Logical differences between Haskell and Isabelle/HOL need to be considered in the translation. For example Isabelle/HOL is not suitable to describe the semantics of lazy evaluation and of Haskell functions that are non-terminating. I also prove some type instances to illustrate how the properties are verified in Isabelle/HOL.</p> / Thesis / Master of Applied Science (MASc)

In this thesis we address a long-term maintainability problem in Haskell type class system. In particular we study a possibility of backward-compatible changes in existing class hierarchies. In the first part of the thesis we give a brief overview of the language. The following part summarizes current proposed solutions to the problem and analyzes their properties. Based on this analysis we derive our own language extension proposal. In the penultimate chapter we present several possible applications of the language extension and compare the extension to other solutions. As a part of the thesis we also give a proof-of-concept implementation of the extension for the GHC compiler, which is briefly described in the last part of this thesis. Powered by TCPDF (www.tcpdf.org)

The intricate concepts of ad-hoc polymorphism and overloading permeate the field of programming languages despite their somewhat nebulous definitions. With the perspective afforded by the state of the art, object-oriented Fortress programming language, this thesis presents a contemporary account of ad-hoc polymorphism and overloading in theory and in practice. Common language constructs are reinterpreted with a new emphasis on overloading as a key facility. Furthermore, concrete problems with overloading in Fortress, encountered during the author's experience in the development of the language, are presented with an emphasis on the ad hoc nature of their solutions. / text

La modularité est un enjeu important en programmation, surtout quand on l’enrichit avec des preuves, comme dans les langages avec des types dépendants. Typer est un tel langage, et afin d’augmenter sa modularité et de lui ajouter un moyen de faire la surcharge d’opérateurs, on s’inspire d’Agda et Coq et on l’étend avec les arguments instances, qui généralisent les classes de types de Haskell. Un aspect qui distingue notre conception est que comme Typer généralise les définitions, la généralisation des contraintes de classe est grandement facilitée. Pour pouvoir faire les preuves de lois de classes, on doit également ajouter l’élimination dépendante des types inductifs au langage, dont certains aspects sont en retour facilités par les arguments instances. Sur la base de ces deux fonctionnalités, on offre également une solution au problème de la cécité booléenne, tel que décrit par Harper. / Modularity is an important concern for software development, especially when the latter is enriched with proofs in a language with dependent types. Typer is such a language, and in order to increase its modularity, and also provide a way to overload operators, we take inspiration from Agda and Coq and extend it with instance arguments, a generalization of Haskell’s type classes. An aspect that sets our design apart is that since Typer generalizes definitions, it greatly simplifies the generalization of class constraints. In order to allow writing proofs for class laws, we must also implement the dependent elimination of inductive types. In return, instance arguments facilitate some details of dependent elimination. Using both features, we suggest a solution to the problem of Boolean Blindness.