G. Hamilton. Higher order deforestation. In H. Kuchen and S.D. Swierstra, editors, Programming Languages: Implementation, Logics and Programs, LNCS 1140, pages 213--227, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....input list. 7. Conclusion This work comes from a large comparative study of various existing methods to perform deforestation and partial evaluation in various programming paradigm. Historically, we compared [3, 2, 1] the deforestation of attribute grammars [5, 6, 12] the Wadler deforestation [16, 13, 7] in functional programming, many works about folds [4, 9] and hylomorphisms [10, 15] In each of these formalisms, there were many interesting ideas. But they were sometimes restricted to one particular class of algorithms but sometimes more powerful than another method on the same class. However, ....

G. W. Hamilton. Higher order deforestation. In Herbert Kuchen and S. Doaitse Swierstra, editors, Int. Symp. on Progr. Languages, Implementations, Logics and Programs (PLILP'96), volume 1140 of Lect. Notes in Comp. Sci., pages 122--136, Aachen, September 1996. SpringerVerlag.

....program transformations [6, 4] Since 1990, di erent approaches have been developed in order to improve the eciency of deforestation transformations. Wadler s algorithm [29] based on Burstall and Darlington unfold fold strategy [1] has been improved and extended by several works [2, 12, 25, 27]. Another approach, the deforestation in calculational form [11, 26, 16, 28, 13] was based on algebraic notions. This latter aims at using categorial functors to capture both function and data type patterns of recursion [18] to guide the deforestation process. With a large degree of formalisms ....

G. W. Hamilton. Higher order deforestation. In Prog. Lang.: Impl., Logics and Programs (PLILP'96), LNCS # 1140, Aachen, September 1996. Springer-Verlag.

....have been developed by 2. 1 Program Specialisation by Partial Evaluation 14 Chin [Chi90, Chi91, Chi94] Hamilton [Ham93, HJ91, Ham91] Srensen [Sr94, Sr93] and Seidl [Sei96] Approaches to higher order deforestation problem include extending the rules of Wadler s deforestation [MW92, Mar96, Ham96] and adding a higher order removal transformation [Chi92] Deforestation provides no information propagation. The rule for evaluating a case statement by deforestation is shown below [Wad90] T [ case v of p 1 : t 1 j : j pn : t n ] case v of p 1 : T [ t 1 ] j : j pn : T [ t n ] ....

G. Hamilton. Higher order deforestation. In H. Kuchen and S.D. Swierstra, editors, Programming Languages: Implementation, Logics and Programs, LNCS 1140, pages 213--227, 1996.

....is identical to Chin s, in that it indicates the presence of an intermediate structure which will not be removed by the deforestation algorithm. Hamilton attempts only the theoretical study of his extended deforestation, without commenting on the practicalities. Some recent work by Hamilton [Ham95] gives a new deforestation algorithm for a higher order language, and gives a termination proof. Hamilton s work influenced the author in formulating the material presented in Chapter 2 (see Section 2.1) Srenson, Gluck and Jones [SGJ94] extended deforestation in order to be able to derive ....

....The algorithm presented in this chapter meets all three of these goals, but nevertheless has a number of shortcomings which will be addressed in the rest of this thesis. 2. 1 History The work presented in this chapter is inspired to some extent by Hamilton, whose recent work on deforestation [Ham95] provoked the author to re evaluate some old research in a new light. The deforestation algorithm given in this chapter had been discovered some time earlier, but had been dismissed as having no great advantages over the algorithm we had previously been using [MW92] Hamilton discovered a ....

G. W. Hamilton. Higher order deforestation. Technical Report 95-07, University of Keele, 1995.

....input list. 7. Conclusion This work comes from a large comparative study of various existing methods to perform deforestation and partial evaluation in various programming paradigm. Historically, we compared [3, 2, 1] the deforestation of attribute grammars [5, 6, 12] the Wadler deforestation [16, 13, 7] in functional programming, many works about folds [4, 9] and hylomorphisms [10, 15] In each of these formalisms, there were many interesting ideas. But they were sometimes restricted to one particular class of algorithms but sometimes more powerful than another method on the same class. However, ....

G. W. Hamilton. Higher order deforestation. In Herbert Kuchen and S. Doaitse Swierstra, editors, Int. Symp. on Progr. Languages, Implementations, Logics and Programs (PLILP'96), volume 1140 of Lect. Notes in Comp. Sci., pages 122--136, Aachen, September 1996. SpringerVerlag.

....program transformations [6, 4] Since 1990, different approaches have been developed in order to improve the efficiency of deforestation transformations. Wadler s algorithm [29] based on Burstall and Darlington unfold fold strategy [1] has been improved and extended by several works [2, 12, 25, 27]. Another approach, the deforestation in calculational form [11, 26, 16, 28, 13] was based on algebraic notions. This latter aims at using categorial functors to capture both function and data type patterns of recursion [18] to guide the deforestation process. With a large degree of formalisms or ....

G. W. Hamilton. Higher order deforestation. In Prog. Lang.: Impl., Logics and Programs (PLILP'96), LNCS # 1140, Aachen, September 1996. Springer-Verlag.

....with append 8 Conclusion This work comes from a large comparative study of various existing methods to perform deforestation and partial evaluation in various programming paradigm. Historically, we compared [3, 2, 1] the deforestation of attribute grammars [5, 6, 12] the Wadler deforestation [16, 13, 7] in functional programming, many works let fpfun2 = fun t38 ( fun t39 (match t38 with nil t39 cons t41 t42 ( cons t41) fpfun2 t42) t39) let f = fun t16 ( fun t17 ( fun t15 ( fpfun2 t16) append t17) t15) Figure 4: Better composition with append let revho ....

G. W. Hamilton. Higher order deforestation. In Herbert Kuchen and S. Doaitse Swierstra, editors, Int. Symp. on Progr. Languages, Implementations, Logics and Programs (PLILP'96), volume 1140 of Lect. Notes in Comp. Sci., pages 122-- 136, Aachen, September 1996. Springer-Verlag.

....section we introduce CBN unfolding both for our higher order language and for the first order fragment. For the first order fragment the unfolding mechanism is essentially the unfolding in Wadler s deforestation [Wad90] The higherorder unfolding is similar to the one higher order deforestation [Mar92, Ham94, San95]; we use a presentation similar to the one in [San95] We introduce the unfolding mechanism as a rewrite relation )n on Term Theta Term that generalizes the normal CBN rewrite semantics on closed terms; unknown (dynamic) values are represented by free variables. The sets Ctxt n and Redex n are ....

G. W. Hamilton. Higher Order Deforestation. Unpublished manuscript. 1994.

....into semantically equivalent first order programs, c.f. e.g. Nel91] The applicability of this method depends on how well the (first order) deforestation algorithm handles the first order translation of higher order constructs. Alternatively, Chin [Chi92a] Wadler and Marlow [Mar92] and Hamilton [Ham93] show how one can extend the deforestation algorithm to deal with higherorder features. With such a deforestation algorithm, any analysis which attempts to determine such properties as e.g. whether the algorithm terminates, must also take the higher order language features into account. Second, ....

....also be changed to other fold unfold transformation techniques, for instance Tupling [Chi93a] Chi93b] Also, the method could be extended to a more powerful language including general patterns or higher order functions. In the latter case, the work should be compared to [Chi92a] Mar92] and [Ham93]. 11.3 Conclusion We have described a means of ensuring termination of the deforestation algorithm which strictly extends (some) previous methods. We believe that extension of previous methods can be beaten by extensions of our method. Compared to previous methods, our means of ensuring ....

G. W. Hamilton. Higher Order Deforestation. Unpublished manuscript. 1991.

....execution by the run time system. Annotation functions similar to the ones shown in Sec. 2. 3 are considered in work on writing PGG s by hand [23, 59] Deforestation is well known and well investigated in the functional programming community because it is a powerful tool for program optimization [5,6,22,24,37,44,45, 54 56, 58, 63]. Symbolic composition is an important technique in the CERES compiler generator system [61] One of the key steps in CERES is the composition of a language definition considered as a compiler with a fixed compiler to a low level language. However, the technical details of this composition are ....

Geoffrey W. Hamilton. Higher order deforestation. In Kuchen and Swierstra [35], pages 213--227.

....of guaranteeing termination. Sands [44,46] and Nielsen and S rensen [40] give other formulations of higher order deforestation, but are concerned with other problems than ensuring termination. The first direct solution to the termination problem for higher order deforestation is due to Hamilton [24], who presents a blazed higher order deforestation algorithm and introduces a notion of higher order linear treelessness: i) no definition contains an application with a non variable argument; ii) no definition contains a case expression with a non variable case selector; iii) no definition nor ....

G. Hamilton. Higher order deforestation. In H. Kuchen and S.D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, volume 1140 of Lecture Notes in Computer Science, pages 213--227. SpringerVerlag, 1996.

....program transformations [6, 4] Since 1990, several different approaches have been developed in order to improve the efficiency of deforestation transformations. Wadler s algorithm [29] based on Burstall and Darlington unfold fold strategy [1] has been improved and extended by several works [2, 12, 25, 27]. Another approach, the deforestation in calculational form [11, 26, 16, 28, 13] was based on algebraic notions. This latter aims at using categorial functors to capture both function and data type patterns of recursion [18] to guide the deforestation process. With a large degree of formalisms or ....

G. W. Hamilton. Higher order deforestation. In Prog. Lang.: Impl., Logics and Programs (PLILP'96), LNCS # 1140, Aachen, September 1996. Springer-Verlag.

....have been found for them and will be exposed in a technical paper. This work comes from our large comparative study of various existing methods of similar program transformations. Historically, we compared [5, 4, 3] the deforestation of attribute grammars [7, 8, 15] the Wadler deforestation [21, 18, 10] in functional programming, many works about folds [6, 12] and hylomorphisms [13, 19] In each of these formalisms, there were many interesting ideas. In this context, equationnal semantics have been especially designed to gather all of them in an homogeneous way. The key of our approach is to ....

G. W. Hamilton. Higher order deforestation. In Herbert Kuchen and S. Doaitse Swierstra, editors, Int. Symp. on Progr. Languages, Implementations, Logics and Programs (PLILP'96), volume 1140 of Lect. Notes in Comp. Sci., pages 122--136, Aachen, September 1996. SpringerVerlag.

....the Hindley Milner type system, but a more efficient and transparent approach is desirable. The first formulation of deforestation applicable directly to higher order programs is due to Marlow and Wadler [33] who leave open the question of guaranteeing termination. This was addressed by Hamilton [22], who gives a formulation of the higher order deforestation algorithm applicable to annotated programs and introduces a notion of higherorder treelessness. He then proves that deforestation of any Hindley Milner typable program terminates, if all parts of the program violating the higher order ....

....or decomposes uniquely into a context e and redex r with t j ehri. Stating that t j ehri does not mean that t has any brackets t is a term. However, e is a context containing an occurrence of hi, and replacing this occurrence of hi by r yields t. In the following definition, inspired by [22], the clauses are mutually exclusive and together exhaustive. The essence of the rules is that, in every step, deforestation decomposes t into e and r such that t j ehri, unfolds r one step yielding r 0 , and continues with ehr 0 i. Definition 5 (Deforestation) letrec d1 ; dn in ....

[Article contains additional citation context not shown here]

G. Hamilton. Higher order deforestation. In H. Kuchen and S.D. Swierstra, editors, Programming Languages: Implementations, Logics and Programs, volume 1140 of Lecture Notes in Computer Science, pages 213--227. Springer-Verlag, 1996.

....treeless form could be generalised to allow more intermediate structures to be removed. This is exactly what has been achieved in this paper. Further work is desirable in two directions. Firstly, only first order expressions have been considered in this paper, but other work has been done in [ 6 ] to extend the deforestation algorithm to higher order functions. The treeless form defined in [ 6 ] is similar to that defined in [ 14 ] so it could be further extended in a similar way to that described in this paper. Secondly, further practical experience of the extensions described in this ....

....exactly what has been achieved in this paper. Further work is desirable in two directions. Firstly, only first order expressions have been considered in this paper, but other work has been done in [ 6 ] to extend the deforestation algorithm to higher order functions. The treeless form defined in [ 6 ] is similar to that defined in [ 14 ] so it could be further extended in a similar way to that described in this paper. Secondly, further practical experience of the extensions described in this paper as compared to the original deforestation algorithm are required in order to be able to assess ....

G.W. Hamilton. Higher order deforestation. Technical Report TR 95-07, Dept. of Computer Science, Keele University, 1995.

No context found.

G. Hamilton. Higher order deforestation. In H. Kuchen and S.D. Swierstra, editors, Programming Languages: Implementation, Logics and Programs, LNCS 1140, pages 213--227, 1996.

No context found.

G. W. Hamilton. Higher order deforestation. In Herbert Kuchen and S. Doaitse Swierstra, editors, Int. Symp. on Progr. Languages, Implementations, Logics and Programs (PLILP'96), volume 1140 of Lect. Notes in Comp. Sci., pages 122-- 136, Aachen, September 1996. Springer-Verlag.

No context found.

G. W. Hamilton. Higher order deforestation. In Prog. Lang.: Impl., Logics and Programs (PLILP'96), LNCS # 1140, Aachen, September 1996. Springer-Verlag.

No context found.

G. W. Hamilton. Higher Order Deforestation. In H. Kuchen and S. Doaitse Swierstra, editors, Proceedings of the 8th International Symposium on Programming Languages: Implementations, Logics and Programs (PLILP), number 1140 in Lecture Notes in Computer Science, pages 213227. SpringerVerlag, 1996.

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