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38
Polytypic Programming With Ease
, 1999
"... A functional polytypic program is one that is parameterised by datatype. Since polytypic functions are defined by induction on types rather than by induction on values they typically operate on a higher level of abstraction than their monotypic counterparts. However, polytypic programming is not nec ..."
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Cited by 13 (5 self)
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A functional polytypic program is one that is parameterised by datatype. Since polytypic functions are defined by induction on types rather than by induction on values they typically operate on a higher level of abstraction than their monotypic counterparts. However, polytypic programming is not necessarily more complicated than conventional programming. We show that a polytypic function is uniquely defined by its action on constant functors, projection functors, sums, and products. This information is sufficient to specialize a polytypic function to arbitrary polymorphic datatypes, including mutually recursive datatypes and nested datatypes. The key idea is to use infinite trees as index sets for polytypic functions and to interpret datatypes as algebraic trees. This approach appears both to be simpler, more general, and more efficient than previous ones which are based on the initial algebra semantics of datatypes. Polytypic functions enjoy polytypic properties. We show that wellkno...
Typesafe Functional Strategies
 In Draft proc. of SFP'00, St
, 2000
"... We demonstrate how the concept of strategies originating from term rewriting can be introduced in a typed, functional setting. We provide a model of strategies based on a further generalisation of updatable, monadic, generalised fold algebras. We show how strategies can be used as a structuring devi ..."
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Cited by 12 (6 self)
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We demonstrate how the concept of strategies originating from term rewriting can be introduced in a typed, functional setting. We provide a model of strategies based on a further generalisation of updatable, monadic, generalised fold algebras. We show how strategies can be used as a structuring device for functional programming. 1
Universal regular path queries
 HigherOrder and Symbolic Computation
, 2003
"... Given are a directed edgelabelled graph G with a distinguished node n0, and a regular expression P which may contain variables. We wish to compute all substitutions φ (of symbols for variables), together with all nodes n such that all paths n0 → n are in φ(P). We derive an algorithm for this proble ..."
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Cited by 12 (1 self)
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Given are a directed edgelabelled graph G with a distinguished node n0, and a regular expression P which may contain variables. We wish to compute all substitutions φ (of symbols for variables), together with all nodes n such that all paths n0 → n are in φ(P). We derive an algorithm for this problem using relational algebra, and show how it may be implemented in Prolog. The motivation for the problem derives from a declarative framework for specifying compiler optimisations. 1 Bob Paige and IFIP WG 2.1 Bob Paige was a longstanding member of IFIP Working Group 2.1 on Algorithmic Languages and Calculi. In recent years, the main aim of this group has been to investigate the derivation of algorithms from specifications by program transformation. Already in the mideighties, Bob was way ahead of the pack: instead of applying transformational techniques to wellworn examples, he was applying his theories of program transformation to new problems, and discovering new algorithms [16, 48, 52]. The secret of his success lay partly in his insistence on the study of general algorithm design strategies (in particular
Scala for generic programmers
 ACM SIGPLAN Workshop on Generic Programming
, 2008
"... Datatypegeneric programming involves parametrization by the shape of data, in the form of type constructors such as ‘list of’. Most approaches to datatypegeneric programming are developed in the lazy functional programming language Haskell. We argue that the functional objectoriented language Sca ..."
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Cited by 10 (2 self)
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Datatypegeneric programming involves parametrization by the shape of data, in the form of type constructors such as ‘list of’. Most approaches to datatypegeneric programming are developed in the lazy functional programming language Haskell. We argue that the functional objectoriented language Scala is in many ways a better setting. Not only does Scala provide equivalents of all the necessary functional programming features (such parametric polymorphism, higherorder functions, higherkinded type operations, and type and constructorclasses), but it also provides the most useful features of objectoriented languages (such as subtyping, overriding, traditional single inheritance, and multiple inheritance in the form of traits). We show how this combination of features benefits datatypegeneric programming, using three different approaches as illustrations.
Promotional Transformation on Monadic Programs
, 1995
"... this paper, we propose a new theory on monadic catamorphism bymoving Fokkinga's assumption on the monad to the condition of a map between monadic algebras so that our theory is valid for arbitrary monads including, for example, the state monad that is not allowed in Fokkinga's theory. Our theory cov ..."
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Cited by 9 (0 self)
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this paper, we propose a new theory on monadic catamorphism bymoving Fokkinga's assumption on the monad to the condition of a map between monadic algebras so that our theory is valid for arbitrary monads including, for example, the state monad that is not allowed in Fokkinga's theory. Our theory covers Fokkinga's as a special case. Moreover, Meijer and Jeuring's informal transformation rules of monadic programs in their case study is actually an instance of our general promotion theorem.
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...
Reasoning About Effects: Seeing the Wood Through the Trees (Extended Version)
"... Pure functional languages such as Haskell support programming with impure effects by exploiting mathematical notions such as monads, applicative functors, and arrows. However, in contrast to the wealth of research on the use of these notions to write effectful programs, there has been comparatively ..."
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Cited by 8 (0 self)
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Pure functional languages such as Haskell support programming with impure effects by exploiting mathematical notions such as monads, applicative functors, and arrows. However, in contrast to the wealth of research on the use of these notions to write effectful programs, there has been comparatively little progress on reasoning about the resulting programs. In this article we focus on this problem, using a simple but instructive example concerned with relabelling binary trees. 1
Functional polytypic programming  use and implementation
, 1997
"... Abstract Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern match ..."
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Cited by 5 (2 self)
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Abstract Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equality functions, unifiers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of userdefined datatypes. This thesis introduces polytypic functions, shows how to construct and reason about polytypic functions and describes the implementation of the polytypic programming system PolyP. PolyP extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions. Programs in the extended language are translated to Haskell.
Monadic Corecursion  Definition, Fusion Laws, and Applications
 Electronic Notes in Theoretical Computer Science
, 1998
"... This paper investigates corecursive definitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational effect modeled by a monad. We introduce a functional, called monadic anamorphism, that cap ..."
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Cited by 5 (1 self)
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This paper investigates corecursive definitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational effect modeled by a monad. We introduce a functional, called monadic anamorphism, that captures definitions of this kind. We also explore another class of monadic recursive functions, corresponding to the composition of a monadic anamorphism followed by (the lifting of) a function defined by structural recursion on the data structure that the monadic anamorphism generates. Such kind of functions are captured by socalled monadic hylomorphism. We present transformation laws for these monadic functionals. Two nontrivial applications are also described.
A Calculational Approach to Strong Datatypes
 Department of Informatics, University of Oslo
, 1997
"... This paper describes calculational properties of fold, a recursive functional on inductive types that extends the standard catamorphism [MFP91] to global parameters. As described by Cockett and Spencer [CS91] fold is definable for those inductive types that are strong in the sense of being given by ..."
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Cited by 5 (2 self)
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This paper describes calculational properties of fold, a recursive functional on inductive types that extends the standard catamorphism [MFP91] to global parameters. As described by Cockett and Spencer [CS91] fold is definable for those inductive types that are strong in the sense of being given by an algebra that happens to be initial with parameters. The laws for fold are presented in two groups. The first one corresponds to standard laws for catamorphisms now adapted to folds when these are regarded as catamorphisms in a category of socalled Xactions (for X an object of parameters). The second group contains laws that describe the combination of folds and the interaction between folds and catamorphisms. 1 Introduction In programming semantics, a recursive type is understood as a solution of a recursive type equation. Least fixpoints of covariant recursive type equations correspond to the socalled inductive types which contain only finite elements, like natural numbers, lists o...