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Type Checking with Open Type Functions

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by Tom Schrijvers , Simon Peyton Jones , Manuel Chakravarty , Martin Sulzmann
Citations:28 - 14 self
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BibTeX

@MISC{Schrijvers_typechecking,
    author = {Tom Schrijvers and Simon Peyton Jones and Manuel Chakravarty and Martin Sulzmann},
    title = {Type Checking with Open Type Functions},
    year = {}
}

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Abstract

We report on an extension of Haskell with open type-level functions and equality constraints that unifies earlier work on GADTs, functional dependencies, and associated types. The contribution of the paper is that we identify and characterise the key technical challenge of entailment checking; and we give a novel, decidable, sound, and complete algorithm to solve it, together with some practically-important variants. Our system is implemented in GHC, and is already in active use.

Citations

213 Monad transformers and modular interpreters - Liang, Hudak, et al. - 1995
138 Type classes with functional dependencies - Jones - 2000
129 Simple unification-based type inference for GADTs - Jones, Vytiniotis, et al. - 2006
115 Guarded recursive datatype constructors - Xi, Chen, et al. - 2003
76 Combining programming with theorem proving - Chen, Xi - 2005
57 System F with type equality coercions - Sulzmann, Chakravarty, et al. - 2007
30 Shostak’s Congruence Closure as Completion, in: H - Kapur - 1997
29 Proof-Producing Congruence Closure - Nieuwenhuis, Oliveras - 2005
27 A completion-based method for mixed universal and rigid E-unification - Beckert - 1994
27 On the algorithmic unsolvability of the word problem in group theory - Novikov - 1955
23 A formulation of dependent ML with explicit equality proofs - Licata, Harper - 2005
22 A framework for extended algebraic data types - Sulzmann, Wazny, et al. - 2006
19 A constraint-based approach to guarded algebraic data types - Simonet, Pottier - 2007
18 Understanding functional dependencies via Constraint Handling Rules - Sulzmann, Duck, et al. - 2007
15 Epigram reloaded: a standalone typechecker for ETT - Chapman, Altenkirch, et al. - 2007
15 Thiemann.Functional logic overloading - Gasbichler, Neubauer, et al. - 2000
12 Proof lengths for equational completion - Plaisted, Sattler-Klein - 1996
12 Foundations for structured programming with GADTs - Johann, Ghani - 2008
12 Type inference for gadts via herbrand constraint abduction - Sulzmann, Schrijvers, et al. - 2006
4 One vote for type families in Haskell - Guillemette, Monnier - 2009
2 and Ashish Tiwari. Abstract congruence closure and specializations - Bachmair - 2000
2 Restoring confluence of functional dependencies via type families - Schrijvers, Sulzmann
2 Type-level computation using narrowing in Omega - Press
2 Rigid -unification revisited - Tiwari, Bachmair, et al. - 2000
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