Phantom types are data types with type constraints associated with dierent cases. Examples of phantom types include typed type representations and typed higher-order abstract syntax trees. These types can be used to support typed generic functions, dynamic typing, and staged compilation in higher-order, statically typed languages such as Haskell or Standard ML. In our system, type constraints can be equations between type constructors as well as type functions of higher-order kinds. We prove type soundness and decidability for a Haskell-like language extended by phantom types.

Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. Generic programs often embody non-traditional kinds of polymorphism. Generic Haskell is an extension of Haskell [38] that supports the construction of generic programs. Generic Haskell adds to Haskell the notion of structural polymorphism, the ability to define a function (or a type) by induction on the structure of types. Such a function is generic in the sense that it works not only for a specific type but for a whole class of types. Typical examples include equality, parsing and pretty printing, serialising, ordering, hashing, and so on. The lecture notes on Generic Haskell are organized into two parts. This first part motivates the need for genericity, describes the basic constructs of Generic Haskell, puts Generic Haskell into perspective, and highlights the underlying theory. The second part entitled “Generic Haskell: applications ” delves deeper into the language discussing three non-trivial applications of Generic Haskell: generic dictionaries, compressing XML documents, and a generic version of the zipper data type. The first part is organized as follows. Section 1 provides some background discussing type systems in general and the type system of Haskell in particular. Furthermore, it motivates the basic constructs of Generic Haskell. Section 2 takes a closer look at generic definitions and shows how to define some popular generic functions. Section 3 highlights the theory underlying Generic Haskell and discusses its implementation. Section 4 concludes. 1

This paper explores a new point in the design space of formal reasoning systems - part programming language, part logical framework. The system is built on a programming language where the user expresses equality constraints between types and the type checker then enforces these constraints. This simple extension to the type system allows the programmer to describe properties of his program in the types of witness objects which can be thought of as concrete evidence that the program has the property desired. These techniques and two other rich typing mechanisms, rank-N polymorphism and extensible kinds, create a powerful new programming idiom for writing programs whose types enforce semantic properties. A language with these features is both a practical programming language and a logic. This marriage between two previously separate entities increases the probability that users will apply formal methods to their programming designs. This kind of synthesis creates the foundations for the languages of the future.

We introduce System FC, which extends System F with support for non-syntactic type equality. There are two main extensions: (i) explicit witnesses for type equalities, and (ii) open, non-parametric type functions, given meaning by toplevel equality axioms. Unlike System F, FC is expressive enough to serve as a target for several different source-language features, including Haskell’s newtype, generalised algebraic data types, associated types, functional dependencies, and perhaps more besides.

A heterogeneous collection is a datatype that is capable of storing data of different types, while providing operations for look-up, update, iteration, and others. There are various kinds of heterogeneous collections, differing in representation, invariants, and access operations. We describe HLIST — a Haskell library for strongly typed heterogeneous collections including extensible records. We illustrate HLIST’s benefits in the context of type-safe database access in Haskell. The HLIST library relies on common extensions of Haskell 98. Our exploration raises interesting issues regarding Haskell’s type system, in particular, avoidance of overlapping instances, and reification of type equality and type unification.

Abstract. There are a number of extended forms of algebraic data types such as type classes with existential types and generalized algebraic data types. Such extensions are highly useful but their interaction has not been studied formally so far. Here, we present a unifying framework for these extensions. We show that the combination of type classes and generalized algebraic data types allows us to express a number of interesting properties which are desired by programmers. We support type checking based on a novel constraint solver. Our results show that our system is practical and greatly extends the expressive power of languages such as Haskell and ML. 1

A type-indexed function is a function that is defined for each member of some family of types. Haskell's type class mechanism provides collections of open type-indexed functions, in which the indexing family can be extended by defining a new type class instance but the collection of functions is fixed. The purpose of this paper is to present TypeCase: a design pattern that allows the definition of closed type-indexed functions, in which the index family is fixed but the collection of functions is extensible. It is inspired by Cheney and Hinze's work on lightweight approaches to generic programming. We generalise their techniques as a design pattern. Furthermore, we show that type-indexed functions with typeindexed types, and consequently generic functions with generic types, can also be encoded in a lightweight manner, thereby overcoming one of the main limitations of the lightweight approaches.

A session type is an abstraction of a set of sequences of heterogeneous values sent and received over a communication channel. Session types can be used for specifying stream-based Internet protocols.

Abstract. A generic function is defined by induction on the structure of types. The structure of a data type can be defined in several ways. For example, in PolyP a pattern functor gives the structure of a data type viewed as a fixed point, and in Generic Haskell a structural representation type gives an isomorphic type view of a data type in terms of sums of products. Depending on this generic view on the structure of data types, some generic functions are easier, more difficult, or even impossible to define. Furthermore, the efficiency of some generic functions can be improved by choosing a different view. This paper introduces generic views on data types and shows why they are useful. Furthermore, it shows how generic views have been added to Generic Haskell, an extension of the functional programming language Haskell that supports the construction of generic functions. The separation between inductive definitions on type structure and generic views allows us to combine many approaches to generic programming in a single framework. 1

We study HMG(X), an extension of the constraint-based type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (first-class) phantom types, and equality qualified types, and are closely related to inductive types. Their characteristic property is to allow every branch of a case construct to be typechecked under different assumptions about the type variables in scope. We prove that HMG(X) is sound and that, provided recursive definitions carry a type annotation, type inference can be reduced to constraint solving. Constraint solving is decidable, at least for some instances of X, but prohibitively expensive. Effective type inference for guarded algebraic data types is left as an issue for future research.