Haskell Type Constraints Unleashed

The popular Glasgow Haskell Compiler extends the Haskell 98 type system with several powerful features, leading to an expressive language of type terms. In contrast, constraints over types have received much less attention, creating an imbalance in the expressivity of the type system. In this paper, we rectify the imbalance, transferring familiar type-level constructs, synonyms and families, to the language of constraints, providing a symmetrical set of features at the type-level and constraint-level. We introduce constraint synonyms and constraint families, and illustrate their increased expressivity for improving the utility of polymorphic EDSLs in Haskell, amongst other examples. We provide a discussion of the semantics of the new features relative to existing type system features and similar proposals, including details of terminatio

Maximal Sharing in the Lambda Calculus with Letrec

Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of 'maximal compactness' for

System F with type equality coercions

10.1145/1190315.1190324Proceedings of the TLDI 2007: 2007 ACM SIGPLAN International Workshop on Types in Languages Design and Implementation - Papers Presented at the Workshop53-6

With-Loop Scalarization: Merging Nested Array Operations

Abstract. Construction of complex array operations by composition of more basic ones allows for abstract and concise specifications of algorithms. Unfortunately, naïve compilation of such specifications leads to creation of many temporary arrays at runtime and, consequently, to poor performance characteristics. This paper elaborates on a new compiler optimization, named withloop-scalarization, which aims at eliminating temporary arrays in the context of nested array operations. It is based on with-loops, a versatile array comprehension construct used by the functional array language SaC both for specification as well as for internal representation of array operations. The impact of with-loop-scalarization on the runtime performance of compiled SaC code is demonstrated by several experiments involving support for arithmetic on arrays of complex numbers and the application kernel FT from the NAS benchmark suite.

First-class type classes

Abstract. Type Classes have met a large success in Haskell and Isabelle, as a solution for sharing notations by overloading and for specifying with abstract structures by quantification on contexts. However, both systems are limited by second-class implementations of these constructs, and these limitations are only overcomed by ad-hoc extensions to the respective systems. We propose an embedding of type classes into a dependent type theory that is first-class and supports some of the most popular extensions right away. The implementation is correspondingly cheap, general and integrates well inside the system, as we have experimented in Coq. We show how it can be used to help structured programming and proving by way of examples.