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System F with type equality coercions
, 2007
"... We introduce System FC, which extends System F with support for nonsyntactic type equality. There are two main extensions: (i) explicit witnesses for type equalities, and (ii) open, nonparametric type functions, given meaning by toplevel equality axioms. Unlike System F, FC is expressive enough to ..."
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Cited by 75 (25 self)
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We introduce System FC, which extends System F with support for nonsyntactic type equality. There are two main extensions: (i) explicit witnesses for type equalities, and (ii) open, nonparametric type functions, given meaning by toplevel equality axioms. Unlike System F, FC is expressive enough to serve as a target for several different sourcelanguage features, including Haskell’s newtype, generalised algebraic data types, associated types, functional dependencies, and perhaps more besides.
A framework for extended algebraic data types
 In Proc. of FLOPS’06, volume 3945 of LNCS
, 2006
"... 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 exten ..."
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Cited by 22 (9 self)
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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
Foundations for structured programming with GADTs
 Conference record of the ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2008
"... GADTs are at the cutting edge of functional programming and become more 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 fun ..."
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Cited by 22 (4 self)
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GADTs are at the cutting edge of functional programming and become more 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 to GADTs. We then use this observation to derive an initial algebra semantics for GADTs, thus ensuring that all of the accumulated knowledge about initial algebras can be brought to bear on them. Next, we use our initial algebra semantics for GADTs to derive expressive and principled tools — analogous to the wellknown and widelyused ones for algebraic and nested data types — for reasoning about, programming with, and improving the performance of programs involving, GADTs; we christen such a collection of tools for a GADT an initial algebra package. Along the way, we give a constructive demonstration that every GADT can be reduced to one which uses only the equality GADT and existential quantification. Although other such reductions exist in the literature, ours is entirely local, is independent of any particular syntactic presentation of GADTs, and can be implemented in the host language, rather than existing solely as a metatheoretical artifact. The main technical ideas underlying our approach are (i) to modify the notion of a higherorder functor so that GADTs can be seen as carriers of initial algebras of higherorder functors, and (ii) to use left Kan extensions to trade arbitrary GADTs for simplerbutequivalent ones for which initial algebra semantics can be derived.