Disciplined, efficient, generalised folds for nested datatypes

Martin, Clare; Gibbons, Jeremy; Bayley, Ian

doi:10.1007/s00165-003-0013-6

Cited by 25 publications

(21 citation statements)

References 11 publications

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“…In particular, map functions and relators are missing and can be difficult to add. c) Other Work: The pioneering work of Bird and his collaborators on nonuniform datatypes [7], [8], [9] has been extended into several directions, including structures for efficient functional programming [23], [24], [30], datatypes with references [16], as well as work directly relevant for DTT proof assistants: reduction to W-types and container types [1], typed term rewriting frameworks for total programming [2], [3], [31], intensional-DTT induction [32]. Our current contribution was concerned with bootstrapping nonuniform datatypes in HOL on a sound and compositional basis.…”

Section: )mentioning

confidence: 99%

Foundational nonuniform (Co)datatypes for higher-order logic

Blanchette

Meier²,

Popescu³

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Abstract-Nonuniform (or "nested" or "heterogeneous") datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)recusion and (co)induction principles based on a weak variant of parametricity.

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Section: )mentioning

confidence: 99%

Foundational nonuniform (Co)datatypes for higher-order logic

Blanchette

Meier²,

Popescu³

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…However, the use of nested datatypes, complicates the definition of the generic combinators. Folds for cyclic stream and tree structures require higher-ranked types [32] (as usual for nested datatypes [5,25]) and they suggest that in a datatype-generic version one-hole contexts [1] are also needed, adding extra complexity to the approach.…”

Section: Related Workmentioning

confidence: 99%

Functional programming with structured graphs

Oliveira

Cook

2012

SIGPLAN Not.

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This paper presents a new functional programming model for graph structures called structured graphs. Structured graphs extend conventional algebraic datatypes with explicit definition and manipulation of cycles and/or sharing, and offer a practical and convenient way to program graphs in functional programming languages like Haskell. The representation of sharing and cycles (edges) employs recursive binders and uses an encoding inspired by parametric higher-order abstract syntax. Unlike traditional approaches based on mutable references or node/edge lists, well-formedness of the graph structure is ensured statically and reasoning can be done with standard functional programming techniques. Since the binding structure is generic, we can define many useful generic combinators for manipulating structured graphs. We give applications and show how to reason about structured graphs.

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“…However, truly nested datatypes are not accepted as inductive definitions in the theorem prover Coq [23] since they are considered to violate the condition of strict positivity [6, Section 14.1.2.1]. This is certainly accepted due to the fact that there are not yet type-theoretical formulations of the reasoning principles for the proposed means of structured programming for these datatypes [8,12,17].…”

Section: Definitionmentioning

confidence: 99%

“…For nested datatypes, there are the "hofunctors" [8,17]. Generic Haskell [14,16] goes further up the hierarchy and allows all finite kinds.…”

Section: Future Work and Conclusionmentioning

confidence: 99%

A Datastructure for Iterated Powers

Matthes

2006

Lecture Notes in Computer Science

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Abstract. Bushes are considered as the first example of a truly nested datatype, i. e., a family of datatypes indexed over all types where a constructor argument not only calls this family with a changing index but even with an index that involves the family itself. For the time being, no induction principles for these datatypes are known. However, the author has introduced with Abel and Uustalu (TCS 333(1-2), pp. 2005) iteration schemes that guarantee to define only terminating functions on those datatypes. The article uses a generalization of Bushes to n-fold self-application and shows how to define elements of these types that have a number of data entries that is obtained by iterated raising to the power of n. Moreover, the data entries are just all the n-branching trees up to a certain height. The real question is how to extract this list of trees from that complicated data structure and to prove this extraction correct. Here, we use the "refined conventional iteration" from the cited article for the extraction and describe a verification that has been formally verified inside Coq with its predicative notion of set.

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Disciplined, efficient, generalised folds for nested datatypes

Cited by 25 publications

References 11 publications

Foundational nonuniform (Co)datatypes for higher-order logic

Foundational nonuniform (Co)datatypes for higher-order logic

Functional programming with structured graphs

A Datastructure for Iterated Powers

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