Abstract We show how higher kinded generic programming can be represented faithfully within a dependently typed programming system. This development has been implemented using the Oleg system. The present work can be seen as evidence for our thesis that extensions of type systems can be done by programming within a dependently typed language, using data as codes for types. 1.

Polymorphic regular types are tree-like datatypes generated by polynomial type expressions over a set of free variables and closed under least fixed point. The ‘equality types ’ of Core ML can be expressed in this form. Given such a type expression with free, this paper shows a way to represent the one-hole contexts for elements of within elements of, together with an operation which will plug an element of into the hole of such a context. One-hole contexts are given as inhabitants of a regular type, computed generically from the syntactic structure of by a mechanism better known as partial differentiation. The relevant notion of containment is shown to be appropriately characterized in terms of derivatives and plugging in. The technology is then exploited to give the one-hole contexts for sub-elements of recursive types in a manner similar to Huet’s ‘zippers’[Hue97]. 1

Abstract. In this paper we use the Epigram language to define the universe of regular tree types—closed under empty, unit, sum, product and least fixpoint. We then present a generic decision procedure for Epigram’s in-built equality at each type, taking a complementary approach to that of Benke, Dybjer and Jansson [7]. We also give a generic definition of map, taking our inspiration from Jansson and Jeuring [21]. Finally, we equip the regular universe with the partial derivative which can be interpreted functionally as Huet’s notion of ‘zipper’, as suggested by McBride in [27] and implemented (without the fixpoint case) in Generic Haskell by Hinze, Jeuring and Löh [18]. We aim to show through these examples that generic programming can be ordinary programming in a dependently typed language. 1

We exhibit the rationale behind the design of Epigram, a dependently typed programming language and interactive program development system, using refinements of a well known program—merge sort—as a running example. We discuss its relationship with other proposals to introduce aspects of dependent types into functional programming languages and sketch some topics for further work in this area. 1.

In these lecture notes we give an overview of recent research on the relationship

Abstract: An exercise assistant is a tool that supports students learning procedural skills, such as solving systems of linear equations, or rewriting a logic expression to disjunctive normal form. The domain reasoner is the component of an exercise assistant that deals with tasks that depend on the semantics of a particular domain, for example the rules that may be applied, or the procedure that should be followed when solving an exercise. An exercise assistant typically has multiple domain reasoners, and the behavior of each of these is, to a large extent, determined by the domain. Generic programming techniques claim to reduce code duplication, to make it easier to change the structure of data, and to provide implementations of many useful functions on most datatypes. There are many libraries for generic programming, all with different datatype support, expressiveness, and ease of use. While a lot of effort has been put into developing new libraries in the past few years, there are few examples of real-life applications of generic programming. In this paper we describe our experience with applying generic programming techniques to our domain reasoners implemented in Haskell. We have used the Uniplate, Multirec, and Regular generic programming libraries. We assess and compare the resulting generic domain reasoners with each other and with the initial, non-generic version, using the software quality factors of the ISO 9126 international standard.

Abstract: An exercise assistant is a tool that supports students learning procedural skills, such as solving systems of linear equations, or rewriting a logic expression to disjunctive normal form. The domain reasoner is the component of an exercise assistant that deals with tasks that depend on the semantics of a particular domain, for example the rules that may be applied, or the procedure that should be followed when solving an exercise. An exercise assistant typically has multiple domain reasoners, and the behavior of each of these is, to a large extent, determined by the domain. Generic programming techniques claim to reduce code duplication, to make it easier to change the structure of data, and to provide implementations of many useful functions on most datatypes. There are many libraries for generic programming, all with different datatype support, expressiveness and ease of use. While a lot of effort has been put into developing new libraries in the past few years, there are few examples of real-life applications of generic programming. In this paper we describe our experience with applying generic programming techniques to our domain reasoners implemented in Haskell. We have used the Uniplate, Multirec, and Regular generic programming libraries. We assess and compare the resulting generic domain reasoners with each other and with the initial, non-generic version, using the software quality factors of the ISO 9126 international standard.