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Monadic augment and generalised short cut fusion
 Journal of Functional Programming
, 2005
"... Monads are commonplace programming devices that are used to uniformly structure computations with effects such as state, exceptions, and I/O. This paper further develops the monadic programming paradigm by investigating the extent to which monadic computations can be optimised by using generalisatio ..."
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Cited by 16 (7 self)
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Monads are commonplace programming devices that are used to uniformly structure computations with effects such as state, exceptions, and I/O. This paper further develops the monadic programming paradigm by investigating the extent to which monadic computations can be optimised by using generalisations of short cut fusion to eliminate monadic structures whose sole purpose is to “glue together ” monadic program components. We make several contributions. First, we show that every inductive type has an associated build combinator and an associated short cut fusion rule. Second, we introduce the notion of an inductive monad to describe those monads that give rise to inductive types, and we give examples of such monads which are widely used in functional programming. Third, we generalise the standard augment combinators and cata/augment fusion rules for algebraic data types to types induced by inductive monads. This allows us to give the first cata/augment rules for some common data types, such as rose trees. Fourth, we demonstrate the practical applicability of our generalisations by providing Haskell implementations for all concepts and examples in the paper. Finally, we offer deep theoretical insights by showing that the augment combinators are monadic in nature, and thus that our cata/build and cata/augment rules are arguably the best generally applicable fusion rules obtainable.
Rewriting Haskell Strings
 In Practical Aspects of Declarative Languages 8th International Symposium, PADL 2007
, 2007
"... Abstract The Haskell String type is notoriously inefficient. We introduce a new data type, ByteString, based on lazy lists of byte arrays, combining the speed benefits of strict arrays with lazy evaluation. Equational transformations based on term rewriting are used to deforest intermediate ByteStri ..."
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Cited by 15 (6 self)
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Abstract The Haskell String type is notoriously inefficient. We introduce a new data type, ByteString, based on lazy lists of byte arrays, combining the speed benefits of strict arrays with lazy evaluation. Equational transformations based on term rewriting are used to deforest intermediate ByteStrings automatically. We describe novel fusion combinators with improved expressiveness and performance over previous functional array fusion strategies. A library for ByteStrings is implemented, providing a purely functional interface, which approaches the speed of lowlevel mutable arrays in C.
Declarative Program Transformation: a Deforestation casestudy
, 1999
"... Software engineering has to reconcile modularity with e ciency. One way to grapple with this dilemma is to automatically transform a modularspecied program into an ecientimplementable one. ..."
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Cited by 15 (2 self)
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Software engineering has to reconcile modularity with e ciency. One way to grapple with this dilemma is to automatically transform a modularspecied program into an ecientimplementable one.
The Impact of seq on Free TheoremsBased Program Transformations
 Fundamenta Informaticae
, 2006
"... Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, standard parametricity results — including socalled free theorems — fail for nonstrict ..."
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Cited by 14 (5 self)
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Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, standard parametricity results — including socalled free theorems — fail for nonstrict languages supporting a polymorphic strict evaluation primitive such as Haskell’s seq. A folk theorem maintains that such results hold for a subset of Haskell corresponding to a GirardReynolds calculus with fixpoints and algebraic datatypes even when seq is present provided the relations which appear in their derivations are required to be bottomreflecting and admissible. In this paper we show that this folklore is incorrect, but that parametricity results can be recovered in the presence of seq by restricting attention to leftclosed, total, and admissible relations instead. The key novelty of our approach is the asymmetry introduced by leftclosedness, which leads to “inequational” versions of standard parametricity results together with preconditions guaranteeing their validity even when seq is present. We use these results to derive criteria ensuring that both equational and inequational versions of short cut fusion and related program transformations based on free theorems hold in the presence of seq.
Constraints to Stop HigherOrder Deforestation
 In 24th ACM Symposium on Principles of Programming Languages
, 1997
"... Wadler's deforestation algorithm eliminates intermediate data structures from functional programs. To be suitable for inclusion in a compiler, it must terminate on all programs. Several techniques to ensure termination of deforestation on all firstorder programs are known, but a technique for ..."
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Cited by 13 (1 self)
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Wadler's deforestation algorithm eliminates intermediate data structures from functional programs. To be suitable for inclusion in a compiler, it must terminate on all programs. Several techniques to ensure termination of deforestation on all firstorder programs are known, but a technique for higherorder programs was only recently introduced by Hamilton, and elaborated and implemented in the Glasgow Haskell compiler by Marlow. We introduce a new technique for ensuring termination of deforestation on all higherorder programs that allows useful transformation steps prohibited in Hamilton's and Marlowe's techniques. 1 Introduction Lazy, higherorder, functional programming languages lend themselves to a certain style of programming which uses intermediate data structures [28]. Example 1 Consider the following program. letrec a = x; y:case x of [] ! y (h : t) ! h : a t y in u; v; w: a (a u v) w The term u; v; w:a (a u v) w appends the three lists u, v, and w. Appending u and v ...
Initial algebra semantics is enough
 Proceedings, Typed Lambda Calculus and Applications
, 2007
"... Abstract. Initial algebra semantics is a cornerstone of the theory of modern functional programming languages. For each inductive data type, it provides a fold combinator encapsulating structured recursion over data of that type, a Church encoding, a build combinator which constructs data of that ty ..."
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Cited by 10 (5 self)
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Abstract. Initial algebra semantics is a cornerstone of the theory of modern functional programming languages. For each inductive data type, it provides a fold combinator encapsulating structured recursion over data of that type, a Church encoding, a build combinator which constructs data of that type, and a fold/build rule which optimises modular programs by eliminating intermediate data of that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types. Specifically, the folds have been considered too weak to capture commonly occurring patterns of recursion, and no Church encodings, build combinators, or fold/build rules have been given for nested types. This paper overturns this conventional wisdom by solving all of these problems. 1
When is a function a fold or an unfold
 Coalgebraic Methods in Computer Science, number 44.1 in Electronic Notes in Theoretical Computer Science
, 2001
"... We give a necessary and sufficient condition for when a settheoretic function can be written using the recursion operator fold, and a dual condition for the recursion operator unfold. The conditions are simple, practically useful, and generic in the underlying datatype. 1 ..."
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Cited by 9 (3 self)
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We give a necessary and sufficient condition for when a settheoretic function can be written using the recursion operator fold, and a dual condition for the recursion operator unfold. The conditions are simple, practically useful, and generic in the underlying datatype. 1
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 ..."
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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.
Attribute Grammars and Folds: Generic Control Operators
, 1996
"... Generic control operators, such as fold, have been introduced in functional programming to increase the power and applicability of datastructurebased transformations. This is achieved by making the structure of the data more explicit in program specifications. We argue that this very important pro ..."
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Cited by 9 (5 self)
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Generic control operators, such as fold, have been introduced in functional programming to increase the power and applicability of datastructurebased transformations. This is achieved by making the structure of the data more explicit in program specifications. We argue that this very important property is one of the original concepts of attribute grammars. In this paper, we informally show the similarities between the fold formalism and attribute grammar specifications. We also compare their respective method to eliminate the intermediate data structures introduced by function composition (notion of deforestation or fusion): the normalization algorithm for programs expressed with folds and the descriptional composition of attribute grammars. Rather than identify the best way to achieve deforestation, the main goal of this paper is merely to intuitively present two programming paradigms to each other's supporting community and provide an unbiased account of their similarities and diff...