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82
Deforestation: Transforming programs to eliminate trees
 Theoretical Computer Science
, 1990
"... An algorithm that transforms programs to eliminate intermediate trees is presented. The algorithm applies to any term containing only functions with definitions in a given syntactic form, and is suitable for incorporation in an optimising compiler. Intermediate listsand, more generally, interm ..."
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Cited by 402 (5 self)
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An algorithm that transforms programs to eliminate intermediate trees is presented. The algorithm applies to any term containing only functions with definitions in a given syntactic form, and is suitable for incorporation in an optimising compiler. Intermediate listsand, more generally, intermediate treesare both the basis and the bane of a certain style of programming in functional languages. For example, to compute the sum of the squares of the numbers from 1 to n, one could write the following program: sum (map square (upto 1 n)) (1) A key feature of this style is the use of functions (upto, map, sum) to encapsulate common patterns of computation ("consider the numbers from 1 to n ", "apply a function to each element", "sum a collection of elements"). Intermediate lists are the basis of this stylethey are the glue that holds the functions together. In this case, the list [1; 2; : : : ; n] connects upto to map, and the list [1; 4; : : : ; n 2 ] connects map to sum. B...
How to Make AdHoc Polymorphism Less Ad Hoc
, 1988
"... This paper presents type classes, a new approach to adhoc polymorphism. Type classes permit overloading of arithmetic operators such as multiplication, and generalise the "eqtype variables" of Standard ML. Type classes extend the Hindley/Milner polymorphic type system, and provide a new approach to ..."
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Cited by 347 (3 self)
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This paper presents type classes, a new approach to adhoc polymorphism. Type classes permit overloading of arithmetic operators such as multiplication, and generalise the "eqtype variables" of Standard ML. Type classes extend the Hindley/Milner polymorphic type system, and provide a new approach to issues that arise in objectoriented programming, bounded type quantification, and abstract data types. This paper provides an informal introduction to type classes, and defines them formally by means of type inference rules. 1 Introduction Strachey chose the adjectives adhoc and parametric to distinguish two varieties of polymorphism [Str67]. Adhoc polymorphism occurs when a function is defined over several different types, acting in a different way for each type. A typical example is overloaded multiplication: the same symbol may be used to denote multiplication of integers (as in 3*3) and multiplication of floating point values (as in 3.14*3.14). Parametric polymorphism occurs wh...
Theorems for free!
 FUNCTIONAL PROGRAMMING LANGUAGES AND COMPUTER ARCHITECTURE
, 1989
"... From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus. ..."
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Cited by 330 (6 self)
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From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.
Report on the programming language Haskell: A nonstrict, purely functional language
 ACM SIGPLAN Notices
, 1992
"... ..."
Linear Types Can Change the World!
 PROGRAMMING CONCEPTS AND METHODS
, 1990
"... The linear logic of J.Y. Girard suggests a new type system for functional languages, one which supports operations that "change the world". Values belonging to a linear type must be used exactly once: like the world, they cannot be duplicated or destroyed. Such values require no reference counti ..."
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Cited by 135 (9 self)
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The linear logic of J.Y. Girard suggests a new type system for functional languages, one which supports operations that "change the world". Values belonging to a linear type must be used exactly once: like the world, they cannot be duplicated or destroyed. Such values require no reference counting or garbage collection, and safely admit destructive array update. Linear types extend Schmidt's notion of single threading; provide an alternative to Hudak and Bloss' update analysis; and offer a practical complement to Lafont and Holmström's elegant linear languages.
Type classes in Haskell
 ACM Transactions on Programming Languages and Systems
, 1996
"... This paper de nes a set of type inference rules for resolving overloading introduced by type classes. Programs including type classes are transformed into ones which may be typed by the HindleyMilner inference rules. In contrast to other work on type classes, the rules presented here relate directl ..."
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Cited by 124 (5 self)
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This paper de nes a set of type inference rules for resolving overloading introduced by type classes. Programs including type classes are transformed into ones which may be typed by the HindleyMilner inference rules. In contrast to other work on type classes, the rules presented here relate directly to user programs. An innovative aspect of this work is the use of secondorder lambda calculus to record type information in the program. 1.
Complete restrictions of the intersection type discipline
 Theoretical Computer Science
, 1992
"... In this paper the intersection type discipline as defined in [Barendregt et al. ’83] is studied. We will present two different and independent complete restrictions of the intersection type discipline. The first restricted system, the strict type assignment system, is presented in section two. Its m ..."
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Cited by 103 (40 self)
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In this paper the intersection type discipline as defined in [Barendregt et al. ’83] is studied. We will present two different and independent complete restrictions of the intersection type discipline. The first restricted system, the strict type assignment system, is presented in section two. Its major feature is the absence of the derivation rule (≤) and it is based on a set of strict types. We will show that these together give rise to a strict filter lambda model that is essentially different from the one presented in [Barendregt et al. ’83]. We will show that the strict type assignment system is the nucleus of the full system, i.e. for every derivation in the intersection type discipline there is a derivation in which (≤) is used only at the very end. Finally we will prove that strict type assignment is complete for inference semantics. The second restricted system is presented in section three. Its major feature is the absence of the type ω. We will show that this system gives rise to a filter λImodel and that type assignment without ω is complete for the λIcalculus. Finally we will prove that a lambda term is typeable in this system if and only if it is strongly normalizable.
Is there a use for linear logic?
, 1991
"... Past attempts to apply Girard's linear logic have either had a clear relation to the theory (Lafont, Holmstrom, Abramsky) or a clear practical value (Guzm'an and Hudak, Wadler), but not both. This paper defines a sequence of languages based on linear logic that span the gap between theory and practi ..."
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Cited by 89 (7 self)
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Past attempts to apply Girard's linear logic have either had a clear relation to the theory (Lafont, Holmstrom, Abramsky) or a clear practical value (Guzm'an and Hudak, Wadler), but not both. This paper defines a sequence of languages based on linear logic that span the gap between theory and practice. Type reconstruction in a linear type system can derive information about sharing. An approach to linear type reconstruction based on use types is presented. Applications to the array update problem are considered.
Once Upon a Type
 In Functional Programming Languages and Computer Architecture
, 1995
"... A number of useful optimisations are enabled if we can determine when a value is accessed at most once. We extend the HindleyMilner type system with uses, yielding a typeinference based program analysis which determines when values are accessed at most once. Our analysis can handle higherorder fun ..."
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Cited by 81 (2 self)
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A number of useful optimisations are enabled if we can determine when a value is accessed at most once. We extend the HindleyMilner type system with uses, yielding a typeinference based program analysis which determines when values are accessed at most once. Our analysis can handle higherorder functions and data structures, and admits principal types for terms. Unlike previous analyses, we prove our analysis sound with respect to callbyneed reduction. Callbyname reduction does not provide an accurate model of how often a value is used during lazy evaluation, since it duplicates work which would actually be shared in a real implementation. Our type system can easily be modified to analyse usage in a callbyvalue language. 1 Introduction This paper describes a method for determining when a value is used at most once. Our method is based on a simple modification of the HindleyMilner type system. Each type is labelled to indicate whether the corresponding value is used at most onc...
A syntax for linear logic
 Presented at Conference on Mathematical Foundations of Programming Language Semantics
, 1993
"... Abstract. This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An app ..."
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Cited by 72 (5 self)
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Abstract. This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An application to the array update problem is briefly discussed. 1