Species and functors and types, oh my!

Yorgey, Brent A.

doi:10.1145/2088456.1863542

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…In the species library (decribed in [Yorgey 2010]) there is a method enumerate : Enumerable f ⇒ [a] → [f a] which takes a (list representation of) an object a to all f a-structures obtained by the S 0 map. The key to comparing this with our paper is to represent the objects as finite enumerations N n → a instead of as lists [a].…”

Section: Generating (Typed) Lambda Termsmentioning

confidence: 99%

Feat

Duregård

Jansson

Wang

2012

Proceedings of the 2012 Haskell Symposium

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In mathematics, an enumeration of a set S is a bijective function from (an initial segment of) the natural numbers to S. We define "functional enumerations" as efficiently computable such bijections. This paper describes a theory of functional enumeration and provides an algebra of enumerations closed under sums, products, guarded recursion and bijections. We partition each enumerated set into numbered, finite subsets.We provide a generic enumeration such that the number of each part corresponds to the size of its values (measured in the number of constructors). We implement our ideas in a Haskell library called testing-feat, and make the source code freely available. Feat provides efficient "random access" to enumerated values. The primary application is property-based testing, where it is used to define both random sampling (for example QuickCheck generators) and exhaustive enumeration (in the style of SmallCheck). We claim that functional enumeration is the best option for automatically generating test cases from large groups of mutually recursive syntax tree types. As a case study we use Feat to test the prettyprinter of the Template Haskell library (uncovering several bugs).

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Section: Generating (Typed) Lambda Termsmentioning

confidence: 99%

Feat

Duregård

Jansson

Wang

2012

Proceedings of the 2012 Haskell Symposium

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Bag Equivalence via a Proof-Relevant Membership Relation

Danielsson

2012

Interactive Theorem Proving

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Abstract. Two lists are bag equivalent if they are permutations of each other, i.e. if they contain the same elements, with the same multiplicity, but perhaps not in the same order. This paper describes how one can define bag equivalence as the presence of bijections between sets of membership proofs. This definition has some desirable properties:-Many bag equivalences can be proved using a flexible form of equational reasoning. -The definition generalises easily to arbitrary unary containers, including types with infinite values, such as streams. -By using a slight variation of the definition one gets set equivalence instead, i.e. equality up to order and multiplicity. Other variations give the subset and subbag preorders. -The definition works well in mechanised proofs.

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Species and functors and types, oh my!

Cited by 2 publications

References 17 publications

Feat

Feat

Bag Equivalence via a Proof-Relevant Membership Relation

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