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25
TypeIndexed Data Types
 SCIENCE OF COMPUTER PROGRAMMING
, 2004
"... A polytypic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of polytypic functions are the functions that can be derived in Haskell, such as show , read , and ` '. More advanced examples are functions for digital searching, ..."
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Cited by 61 (23 self)
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A polytypic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of polytypic functions are the functions that can be derived in Haskell, such as show , read , and ` '. More advanced examples are functions for digital searching, pattern matching, unification, rewriting, and structure editing. For each of these problems, we not only have to define polytypic functionality, but also a typeindexed data type: a data type that is constructed in a generic way from an argument data type. For example, in the case of digital searching we have to define a search tree type by induction on the structure of the type of search keys. This paper shows how to define typeindexed data types, discusses several examples of typeindexed data types, and shows how to specialize typeindexed data types. The approach has been implemented in Generic Haskell, a generic programming extension of the functional language Haskell.
Towards Merging Recursion and Comonads
, 2000
"... Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold op ..."
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Cited by 9 (2 self)
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Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold operator on the product comonad. Both versions capture functions that require extra arguments for their computation and are related with the notion of strong datatype. 1 Introduction One of the main features of recursive operators derivable from datatype definitions is that they impose a structure upon programs which can be exploited for program transformation. Recursive operators structure functional programs according to the data structures they traverse or generate and come equipped with a battery of algebraic laws, also derivable from type definitions, which are used in program calculations [24, 11, 5, 15]. Some of these laws, the socalled fusion laws, are particularly interesting in p...
Modular Tree Automata
"... Abstract. Tree automata are traditionally used to study properties of tree languages and tree transformations. In this paper, we consider tree automata as the basis for modular and extensible recursion schemes. We show, using wellknown techniques, how to derive from standard tree automata highly mo ..."
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Cited by 7 (6 self)
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Abstract. Tree automata are traditionally used to study properties of tree languages and tree transformations. In this paper, we consider tree automata as the basis for modular and extensible recursion schemes. We show, using wellknown techniques, how to derive from standard tree automata highly modular recursion schemes. Functions that are defined in terms of these recursion schemes can be combined, reused and transformed in many ways. This flexibility facilitates the specification of complex transformations in a concise manner, which is illustrated with a number of examples. 1
An Analytical Method For Parallelization Of Recursive Functions
, 2001
"... Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult ..."
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Cited by 7 (0 self)
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Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult tasks. In this paper, we propose an analytical approach to transforming recursive functions on general recursive data structures into compositions of parallel skeletons. Using static slicing, we have defined a classification of subexpressions based on their dataparallelism. Then, skeletonbased parallel programs are generated from the classification. To extend the scope of parallelization, we have adopted more general parallel skeletons which do not require the associativity of argument functions. In this way, our analytical method can parallelize recursive functions with complex data flows. Keywords: data parallelism, parallelization, functional languages, parallel skeletons, data flow analysis, static slice 1.
Programming macro tree transducers
 In WGP ’13
, 2013
"... A tree transducer is a set of mutually recursive functions transforming an input tree into an output tree. Macro tree transducers extend this recursion scheme by allowing each function to be defined in terms of an arbitrary number of accumulation parameters. In this paper, we show how macro tree tra ..."
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Cited by 5 (5 self)
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A tree transducer is a set of mutually recursive functions transforming an input tree into an output tree. Macro tree transducers extend this recursion scheme by allowing each function to be defined in terms of an arbitrary number of accumulation parameters. In this paper, we show how macro tree transducers can be concisely represented in Haskell, and demonstrate the benefits of utilising such an approach with a number of examples. In particular, tree transducers afford a modular programming style as they can be easily composed and manipulated. Our Haskell representation generalises the original definition of (macro) tree transducers, abolishing a restriction on finite state spaces. However, as we demonstrate, this generalisation does not affect compositionality.
Streaming RepresentationChangers
 LNCS
, 2004
"... Unfolds generate data structures, and folds consume them. ..."
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Cited by 3 (0 self)
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Unfolds generate data structures, and folds consume them.
Unifying structured recursion schemes
 in International Conference on Functional Programming. ACM
"... Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent su ..."
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Cited by 3 (3 self)
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Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent such unifications are the ‘recursion schemes from comonads ’ of Uustalu, Vene and Pardo, and our own ‘adjoint folds’. Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads. The proof of this claim involves standard constructions in category theory that are nevertheless not well known in functional programming: EilenbergMoore categories and bialgebras.