Build, Augment and Destroy, Universally

Ghani, Neil; Uustalu, Tarmo; Vene, Varmo

doi:10.1007/978-3-540-30477-7_22

Cited by 17 publications

(47 citation statements)

References 29 publications

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“…In this section we first recall the derivation of initial algebra packages for inductive types from [Ghani et al (2003)], and then recap the well-known categorical ideas which underlie it. In the next section we show how to instantiate these same ideas in our higherorder setting to derive initial algebra packages for GADTs.…”

Section: Semantic Foundations Of Initial Algebra Packagesmentioning

confidence: 99%

“…It is well known [Ghani et al (2005), Ghani et al (2003), Takano & Meijer (1995)] that every inductive type has an associated initial algebra package. If f is a Haskell functor, then the associated inductive type M f and its associated fold and build combinators can be implemented generically in Haskell by…”

Section: Initial Algebra Packages For Inductive Typesmentioning

confidence: 99%

“…This situation was rectified in [Ghani et al (2003)], where the standard initial algebra semantics was extended to support not only fold combinators for inductive types, but also Church encodings and build combinators for them. Indeed, [Ghani et al (2003)] considers the initial F -algebra to be not only the initial object of the category of F -algebras, but also the limit of the forgetful functor from the category of F -algebras to the underlying category C as well.…”

Section: Church Encodings Builds and Fold/build Fusion Rulesmentioning

confidence: 99%

“…Indeed, [Ghani et al (2003)] considers the initial F -algebra to be not only the initial object of the category of F -algebras, but also the limit of the forgetful functor from the category of F -algebras to the underlying category C as well. We now summarize this result and its consequences, which we later apply to derive our combinators for GADTs.…”

Section: Church Encodings Builds and Fold/build Fusion Rulesmentioning

confidence: 99%

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Foundations for structured programming with GADTs

Johann

Ghani

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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GADTs are at the cutting edge of functional programming and be-come 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 well-known and widely-used 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 met theoretical artifact. The main technical ideas underlying our approach are (i) to modify the notion of a higher-order functor so that GADTs can be seen as carriers of initial algebras of higher-order functors, and (ii) to use left Kan extensions to trade arbitrary GADTs for simpler-but-equivalent ones for which initial algebra semantics can be derived.

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Section: Semantic Foundations Of Initial Algebra Packagesmentioning

confidence: 99%

Section: Initial Algebra Packages For Inductive Typesmentioning

confidence: 99%

Section: Church Encodings Builds and Fold/build Fusion Rulesmentioning

confidence: 99%

Section: Church Encodings Builds and Fold/build Fusion Rulesmentioning

confidence: 99%

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Foundations for structured programming with GADTs

Johann

Ghani

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…Folds are not the only program structure that reflects data structure, although they are often given unfair emphasis [48]; we outline unfolds and builds too, which are two kinds of dual (producing structured data rather than consuming it), and maps, which are special cases of these operators, and some simple combinations of all of these. There are many other datatype-generic patterns of computation that we might also have considered: paramorphisms [98], apomorphisms [130], histomorphisms and futumorphisms [127], metamorphisms [42], dynamorphisms [78], destroy [36], and so on.…”

Section: Origami Programmingmentioning

confidence: 99%

Datatype-Generic Programming

Gibbons

2007

Datatype-Generic Programming

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Abstract. Generic programming aims to increase the flexibility of programming languages, by expanding the possibilities for parametrization -ideally, without also expanding the possibilities for uncaught errors. The term means different things to different people: parametric polymorphism, data abstraction, meta-programming, and so on. We use it to mean polytypism, that is, parametrization by the shape of data structures rather than their contents. To avoid confusion with other uses, we have coined the qualified term datatype-generic programming for this purpose. In these lecture notes, we expand on the definition of datatype-generic programming, and present some examples of datatypegeneric programs. We also explore the connection with design patterns in object-oriented programming; in particular, we argue that certain design patterns are just higher-order datatype-generic programs.

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Faster Coroutine Pipelines: A Reconstruction

Pieters

Schrijvers

2018

Lecture Notes in Computer Science

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Spivey has recently presented a novel functional representation that supports the efficient composition, or merging, of coroutine pipelines for processing streams of data. This representation was inspired by Shivers and Might's three-continuation approach and is shown to be equivalent to a simple yet inefficient executable specification. Unfortunately, neither Shivers and Might's original work nor the equivalence proof sheds much light on the underlying principles allowing the derivation of this efficient representation from its specification. This paper gives the missing insight by reconstructing a systematic derivation in terms of known transformation steps from the simple specification to the efficient representation. This derivation sheds light on the limitations of the representation and on its applicability to other settings. In particular, it has enabled us to obtain a similar representation for pipes featuring two-way communication, similar to the Haskell pipes library. Our benchmarks confirm that this two-way representation retains the same improved performance characteristics.

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Build, Augment and Destroy, Universally

Cited by 17 publications

References 29 publications

Foundations for structured programming with GADTs

Foundations for structured programming with GADTs

Datatype-Generic Programming

Faster Coroutine Pipelines: A Reconstruction

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