The Algebra of Programming

Bird, Richard; Moor, Oege de

doi:10.1007/978-3-642-61455-2_12

Cited by 207 publications

(212 citation statements)

References 7 publications

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“…Section 2 builds on many discussions with colleagues in and around the Datatype-Generic Programming project at Oxford and Nottingham. My views on origami programming in Section 3 are based on ideas from the Algebra of Programming ('Squiggol') community, and especially the work of: Roland Backhouse and Grant Malcolm [92,7,6]; Richard Bird and Oege de Moor [9,10]; Maarten Fokkinga, Erik Meijer and Ross Paterson [32,101]; Johan Jeuring, Patrik Jansson, Ralf Hinze and Andres Löh [68,69,57,60,91]; and John Hughes [66]. The analogy between design patterns and higher-order datatype-generic programs discussed in Section 4 elaborates on arguments developed in a course presented while on sabbatical at the University of Canterbury in New Zealand in early 2005, and explored further at tutorials at ECOOP [39] and OOPSLA [40] later that year; the contribution of participants at those venues and at less formal presentations of the same ideas is gratefully acknowledged.…”

Section: Discussionmentioning

confidence: 99%

“…There is a branch of the mathematics of program construction devoted to the relationship between the structure of programs and the structure of the data they manipulate [92,101,6,9,37]. We saw a glimpse of this field in Sections 2.3, 2.5 and 2.7, with the definitions of foldL, foldM and foldB respectively: the structure of each program reflects that of the datatype it traverses, for example in the number of clauses and the number and position of any recursive references.…”

Section: Origami Programmingmentioning

confidence: 99%

“…Among the various approaches to datatype-generic programming, one is what we have called elsewhere origami programming [38], and what others have variously called constructive algorithmics [12,123], Squiggol [93], bananas and lenses [101], the Bird-Meertens Formalism [122,52], and the algebra of programming [9], among other names. This is a style of functional (or relational) programming based on maps, folds, unfolds and other such higher-order structured recursion operators.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Origami Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Datatype-Generic Programming

Gibbons

2007

Datatype-Generic Programming

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“…However, for this potential to be realised, we must better understand how indexed types can be constructed. Moreover, since we want to ensure that all of the techniques developed for structured programming with and principled reasoning about inductive types -such as those championed in the Algebra of Programming [6] literature -are applicable to the resulting indexed types, we also want these types to be inductive. This paper therefore asks the following fundamental question:…”

Section: Introductionmentioning

confidence: 99%

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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“…In the latter domain, there has been a lot of research into systems that go beyond simply-typed polymorphism, see for example extensions of Haskell in the Glasgow Haskell Compiler (GHC) [12]. An important driving force for these developments has been the wish to support generic programming [2,1].…”

Section: Introductionmentioning

confidence: 99%

HOL2P - A System of Classical Higher Order Logic with Second Order Polymorphism

Völker

Lecture Notes in Computer Science

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Abstract. This paper introduces the logical system HOL2P that extends classical higher order logic (HOL) with type operator variables and universal types. HOL2P has explicit term operations for type abstraction and type application. The formation of type application terms t [ T ] is restricted to small types T that do not contain any universal types. This constraint ensures the existence of a set-theoretic model and thus consistency.The expressiveness of HOL2P allows category-theoretic concepts such as natural transformations and initial algebras to be applied at the level of polymorphic HOL functions. The parameterisation of terms with type operators adds genericity to theorems. Type variable quantification can also be expressed.A prototype of HOL2P has been implemented on top of HOL-Light. Type inference is semi-automatic, and some type annotations are necessary. Reasoning is supported by appropriate tactics. The implementation has been used to check some sample derivations.

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The Algebra of Programming

Cited by 207 publications

References 7 publications

Datatype-Generic Programming

Datatype-Generic Programming

When Is a Type Refinement an Inductive Type?

HOL2P - A System of Classical Higher Order Logic with Second Order Polymorphism

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