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Stream Fusion. From Lists to Streams to Nothing at All
 ICFP’07
, 2007
"... This paper presents an automatic deforestation system, stream fusion, based on equational transformations, that fuses a wider range of functions than existing shortcut fusion systems. In particular, stream fusion is able to fuse zips, left folds and functions over nested lists, including list compr ..."
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Cited by 68 (8 self)
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This paper presents an automatic deforestation system, stream fusion, based on equational transformations, that fuses a wider range of functions than existing shortcut fusion systems. In particular, stream fusion is able to fuse zips, left folds and functions over nested lists, including list comprehensions. A distinguishing feature of the framework is its simplicity: by transforming list functions to expose their structure, intermediate values are eliminated by general purpose compiler optimisations. We have reimplemented the Haskell standard List library on top of our framework, providing stream fusion for Haskell lists. By allowing a wider range of functions to fuse, we see an increase in the number of occurrences of fusion in typical Haskell programs. We present benchmarks documenting time and space improvements.
Deriving Structural Hylomorphisms From Recursive Definitions
 In ACM SIGPLAN International Conference on Functional Programming
, 1996
"... this paper, we propose an algorithm which can automatically turn all practical recursive definitions into structural hylomorphisms making program fusion be easily applied. 1 Introduction ..."
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Cited by 52 (17 self)
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this paper, we propose an algorithm which can automatically turn all practical recursive definitions into structural hylomorphisms making program fusion be easily applied. 1 Introduction
Tupling Calculation Eliminates Multiple Data Traversals
 In ACM SIGPLAN International Conference on Functional Programming
, 1997
"... Tupling is a wellknown transformation tactic to obtain new efficient recursive functions by grouping some recursive functions into a tuple. It may be applied to eliminate multiple traversals over the common data structure. The major difficulty in tupling transformation is to find what functions are ..."
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Cited by 38 (20 self)
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Tupling is a wellknown transformation tactic to obtain new efficient recursive functions by grouping some recursive functions into a tuple. It may be applied to eliminate multiple traversals over the common data structure. The major difficulty in tupling transformation is to find what functions are to be tupled and how to transform the tupled function into an efficient one. Previous approaches to tupling transformation are essentially based on fold/unfold transformation. Though general, they suffer from the high cost of keeping track of function calls to avoid infinite unfolding, which prevents them from being used in a compiler. To remedy this situation, we propose a new method to expose recursive structures in recursive definitions and show how this structural information can be explored for calculating out efficient programs by means of tupling. Our new tupling calculation algorithm can eliminate most of multiple data traversals and is easy to be implemented. 1 Introduction Tupli...
A Calculational Fusion System HYLO
, 1997
"... Fusion, one of the most useful transformation tactics for deriving efficient programs, is the process whereby separate pieces of programs are fused into a single one, leading to an efficient program with no intermediate data structures produced. In this paper, we report our ongoing investigation on ..."
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Cited by 35 (10 self)
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Fusion, one of the most useful transformation tactics for deriving efficient programs, is the process whereby separate pieces of programs are fused into a single one, leading to an efficient program with no intermediate data structures produced. In this paper, we report our ongoing investigation on the design and implementation of an automatic transformation system HYLO which performs fusion transformation in a more systematic and more general way than any other systems. The distinguished point of our system is its calculational feature based on simple application of transformation laws rather than traditional searchbased transformation.
Functional Programming with Graphs
 2ND ACM SIGPLAN INT. CONF. ON FUNCTIONAL PROGRAMMING
, 1997
"... Graph algorithms expressed in functional languages often suffer from their inherited imperative, statebased style. In particular, this impedes formal program manipulation. We show how to model persistent graphs in functional languages by graph constructors. This provides a decompositional view of g ..."
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Cited by 35 (12 self)
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Graph algorithms expressed in functional languages often suffer from their inherited imperative, statebased style. In particular, this impedes formal program manipulation. We show how to model persistent graphs in functional languages by graph constructors. This provides a decompositional view of graphs which is very close to that of data types and leads to a "more functional" formulation of graph algorithms. Graph constructors enable the definition of general fold operations for graphs. We present a promotion theorem for one of these folds that allows program fusion and the elimination of intermediate results. Fusion is not restricted to the elimination of treelike structures, and we prove another theorem that facilitates the elimination of intermediate graphs. We describe an MLimplementation of persistent graphs which efficiently supports the presented fold operators. For example, depthfirstsearch expressed by a fold over a functional graph has the same complexity as the corresp...
Generic Program Transformation
 Proc. 3rd International Summer School on Advanced Functional Programming, LNCS 1608
, 1998
"... ion versus efficiency For concreteness, let us first examine a number of examples of the type of optimisation that we wish to capture, and the kind of programs on which they operate. This will give us a specific aim when developing the machinery for automating the process, and a yardstick for evalu ..."
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Cited by 32 (5 self)
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ion versus efficiency For concreteness, let us first examine a number of examples of the type of optimisation that we wish to capture, and the kind of programs on which they operate. This will give us a specific aim when developing the machinery for automating the process, and a yardstick for evaluating our results. 2.1 Minimum depth of a tree Consider the data type of leaf labelled binary trees: dataBtreea = Leaf a j Bin (Btree a)(Btree a) The minimum depth of such a tree is returned by the function mindepth :: Btree a ! Int : mindepth (Leaf a) = 0 mindepth (Bin s t) = min (mindepth s)(mindepth t) + 1 This program is clear, but rather inefficient. It traverses the whole tree, regardless of leaves that may occur at a small depth. A better program would keep track of the `minimum depth so far', and never explore subtrees beyond that current best solution. One possible implementation of that idea is mindepth t = md t 01 md (Leaf a)d m = mindm md (Bin s t)d m = if d 0 m then m...
Type Inference Builds a Short Cut to Deforestation
, 1999
"... Deforestation optimises a functional program by transforming it into another one that does not create certain intermediate data structures. Short cut deforestation is a deforestation method which is based on a single, local transformation rule. In return, short cut deforestation expects both produce ..."
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Cited by 26 (2 self)
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Deforestation optimises a functional program by transforming it into another one that does not create certain intermediate data structures. Short cut deforestation is a deforestation method which is based on a single, local transformation rule. In return, short cut deforestation expects both producer and consumer of the intermediate structure in a certain form. Warm fusion was proposed to automatically transform functions into this form. Unfortunately, it is costly and hard to implement. Starting from the fact that short cut deforestation is based on a parametricity theorem of the secondorder typed λcalculus, we show how the required form of a list producer can be derived through the use of type inference. Typability for the secondorder typed λcalculus is undecidable. However, we present a lineartime algorithm that solves a partial type inference problem and that, together with controlled inlining and polymorphic type instantiation, suffices for deforestation. The resulting new sho...
The Worker/Wrapper Transformation
 Journal of Functional Programming
, 2009
"... The worker/wrapper transformation is a technique for changing the type of a computation, usually with the aim of improving its performance. It has been used by compiler writers for many years, but the technique is little known in the wider functional programming community, and has never been describ ..."
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Cited by 26 (14 self)
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The worker/wrapper transformation is a technique for changing the type of a computation, usually with the aim of improving its performance. It has been used by compiler writers for many years, but the technique is little known in the wider functional programming community, and has never been described precisely. In this article we explain, formalise and explore the generality of the worker/wrapper transformation. We also provide a systematic recipe for its use as an equational reasoning technique for improving the performance of programs, and illustrate the power of this recipe using a range of examples. 1
Fold and Unfold for Program Semantics
 In Proc. 3rd ACM SIGPLAN International Conference on Functional Programming
, 1998
"... In this paper we explain how recursion operators can be used to structure and reason about program semantics within a functional language. In particular, we show how the recursion operator fold can be used to structure denotational semantics, how the dual recursion operator unfold can be used to str ..."
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Cited by 25 (4 self)
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In this paper we explain how recursion operators can be used to structure and reason about program semantics within a functional language. In particular, we show how the recursion operator fold can be used to structure denotational semantics, how the dual recursion operator unfold can be used to structure operational semantics, and how algebraic properties of these operators can be used to reason about program semantics. The techniques are explained with the aid of two main examples, the first concerning arithmetic expressions, and the second concerning Milner's concurrent language CCS. The aim of the paper is to give functional programmers new insights into recursion operators, program semantics, and the relationships between them. 1 Introduction Many computations are naturally expressed as recursive programs defined in terms of themselves, and properties proved of such programs using some form of inductive argument. Not surprisingly, many programs will have a similar recursive stru...