Generic Programming with Dependent Types

Altenkirch, Thorsten; McBride, Conor; Morris, Peter D.

doi:10.1007/978-3-540-76786-2_4

Cited by 21 publications

(20 citation statements)

References 23 publications

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“…Subset types are also used heavily in the PVS theorem prover [24]. Our results extend the systematic code reuse delivered by generic programming [2,3,5]: in addition to generating new programs we can also generate new types from existing types. This area is being explored in Epigram [9], in which codes for data types can be represented within a predicative intensional system so that programs can generate new data types.…”

Section: Conclusion Applications Related and Future Worksupporting

confidence: 54%

When Is a Type Refinement an Inductive Type?

Atkey

Johann

Ghani

2011

Foundations of Software Science and Computational Structures

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Abstract. Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the Nindexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce purposespecific refinements on an ad hoc basis, developers must anticipate which refinements to include in libraries, and implementations often store redundant information about data and their refinements. This paper shows how to generically derive inductive characterisations of refinements of inductive types, and argues that these characterisations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. These characterisations also ensure that standard techniques for programming with and reasoning about inductive types are applicable to refinements, and that refinements can themselves be further refined.

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Section: Conclusion Applications Related and Future Worksupporting

confidence: 54%

When Is a Type Refinement an Inductive Type?

Atkey

Johann

Ghani

2011

Foundations of Software Science and Computational Structures

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“…Parts (3)(4)(5) and (8,9) of this process can be eased by existing Isabelle quotient/lifting/transfer packages [12,14].…”

Section: Automated Constructionsmentioning

confidence: 99%

“…Metatheorems of a common shape can be processed uniformly, which leads to better extensibility of packages. Metatheory-based constructions are a relatively recent idea even in dependent type theories that can engage in generic programming over type universes [3]. Application of these metatheories is usually not facilitated with automated isomorphic transfer and is thus left to idealistic users.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

“…where (e 1 + e 2 ) + e 3 = e 1 + (e 2 + e 3 ) and e 1 + e 2 = e 2 + e 3 and 0 + e = e and e + e = e and (e 1 · e 2 ) · e 3 = e 1 · (e 2 · e 3 ) and 1 · e = e and e · 1 = e and 0 · e = 0 and e 1 · (e 2 + e 3 ) = (e 1 · e 2 ) + (e 1 · e 3 ) and (1 + (e * · e)) + e * = e * and (1 + (e · e * )) + e * = e * and (e · e 1 ) + e 1 = e 1 −→ (e * · e 1 ) + e 1 = e 1 and (e 1 · e) + e 1 = e 1 −→ (e 1 · e * ) + e 1 = e 1 where we wrote infix + and × for Plus and Times and ·, postfix * for Star, and 0 and 1 for Zero and One. 5 The last two equations are conditional; they express the minimality of e * among the prefix points of λx.…”

Section: B4 Regular Expressionsmentioning

confidence: 99%

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Nonfree Datatypes in Isabelle/HOL

Schropp

Popescu

2013

Lecture Notes in Computer Science

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Abstract. Datatypes freely generated by their constructors are well supported in mainstream proof assistants. Algebraic specification languages offer more expressive datatypes on axiomatic means: nonfree datatypes generated from constructors modulo equations. We have implemented an Isabelle/HOL package for nonfree datatypes, without compromising foundations. The use of the package, and its nonfree iterator in particular, is illustrated with examples: bags, polynomials and λ-terms modulo α-equivalence. The many-sorted metatheory of nonfree datatypes is formalized as an ordinary Isabelle theory and is animated by the package into user-specified instances. HOL lacks a type of types, so we employ an ad hoc construction of a universe embedding the relevant parameter types.

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“…Parameterized datatypes are represented using indices as well; in this way we treat recursion and parameterization uniformly, allowing for flexible composition. Similarly to the universes of Altenkirch et al (2007), we include the fixed-point operator within the universe, which simplifies code reuse. To allow for easy encapsulation of user-defined datatypes, we encode datatype isomorphisms in the universe itself.…”

Section: Introductionmentioning

confidence: 99%

Generic programming with indexed functors

Löh¹,

Magalhães

2011

Proceedings of the Seventh ACM SIGPLAN Workshop on Generic Programming

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Much has been said and done about generic programming approaches in strongly-typed functional languages such as Haskell and Agda. Different approaches use different techniques and are better or worse suited for certain uses, depending on design decisions such as generic view, universe size and complexity, etc.We present a simple and intuitive yet powerful approach to generic programming in Agda using indexed functors. We show a universe incorporating fixed points that supports composition, indexing, and isomorphisms, and generalizes a number of previous approaches to generic programming with fixed points. Our indexed functors come with a map operation which obeys the functor laws, and associated recursion morphisms. Albeit expressive, the universe remains simple enough to allow defining standard recursion schemes as well as decidable equality. As for type-indexed datatypes, we show how to compute the type of one-hole contexts and define the generic zipper.

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Generic Programming with Dependent Types

Cited by 21 publications

References 23 publications

When Is a Type Refinement an Inductive Type?

When Is a Type Refinement an Inductive Type?

Nonfree Datatypes in Isabelle/HOL

Generic programming with indexed functors

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