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- Patricia Johann, Neil Ghani
- POPL
- 2008

GADTs are at the cutting edge of functional programming and becomemore widely used every day. Nevertheless, the semantic foundations underlying GADTs are not well understood. In this paper we solve this problem by showing that the standard theory of data types as carriers of initial algebras of functors can be extended from algebraic and nested data types… (More)

- Patricia Johann
- Higher-Order and Symbolic Computation
- 2002

Fusion is the process of improving the efficiency of modularly constructed programs by transforming them into monolithic equivalents. This paper defines a generalization of the standard build combinator which expresses uniform production of functorial contexts containing data of inductive types. It also proves correct a fusion rule which generalizes the… (More)

- Patricia Johann
- J. Funct. Program.
- 2003

- Robert Atkey, Patricia Johann, Neil Ghani
- FOSSACS
- 2011

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the Nindexed type of vectors refines lists by their lengths. Other data types may be refined in… (More)

- Robert Atkey, Patricia Johann, Neil Ghani
- Logical Methods in Computer Science
- 2012

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists by their lengths. Other data types may be refined in… (More)

- Patricia Johann, Janis Voigtländer
- POPL
- 2004

Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, the standard parametricity theorem fails for nonstrict languages supporting a polymorphic strict evaluation primitive like Haskell's <i>seq</i>.… (More)

- Neil Ghani, Patricia Johann
- J. Funct. Program.
- 2005

Monads are commonplace programming devices that are used to uniformly structure computations with effects such as state, exceptions, and I/O. This paper further develops the monadic programming paradigm by investigating the extent to which monadic computations can be optimised by using generalisations of short cut fusion to eliminate monadic structures… (More)

Abstract programming supports the separation of logical concerns from issues of control in program construction. While this separation of concerns leads to reduced code size and increased reusability of code, its main disadvantage is the computational overhead it incurs. Fusion techniques can be used to combine the reusability of abstract programs with the… (More)

- Daniel J. Dougherty, Patricia Johann
- J. Symb. Comput.
- 1990

A generalization of Paramodulation is deened and shown to lead to a complete E-uniication method for arbitrary equational theories E. The method is deened in terms of transformations on systems, building upon and reening results of Gallier and Snyder.