A. Kuhnemann. Berechnungsstarken von Teilklassen primitiv-rekursiver Programmschemata. Ph.D thesis, Technical University of Dresden, 1997. In German.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the composition of fast reverses) which shortcut deforestation cannot do. This is due to the restriction to map style list producers and consumers. In fact, the laws for dmap show some interesting combinatorics. Recently, composition methods using results of attribute grammars have been proposed [4, 12, 13, 15] which allow transformations not possible by ordinary deforestation. The problem of accumulator composition studied in this note is a restricted instance of the more powerful composition of attribute grammars (or also tree transducers [6] 5, 7, 8] While our class is very limited compared to the ....

A. Kuhnemann. Berechnungsstarken von Teilklassen primitiv-rekursiver Programmschemata. Ph.D thesis, Technical University of Dresden, 1997. In German.

....are based on the concepts primitive recursion on trees and arbitrary tree walking . In [FV99] attributed tree transformations are characterized by restricted macro tree transformations. A comparison between the computational power of primitive recursive program schemes can also be found in [K uh97a]. For this purpose decomposition and composition results and pumping lemmata are developed and applied. We embed subclasses of the models for syntax directed semantics into the language of category theory (catamorphism, anamorphism, hylomorphism) and try to transfer results from one area to the ....

....programs using intermediate data structures into programs that do not (cf. Wad90] Tree transducers and (macro) attribute grammars can be seen as special functional programs and extensions of functional programs, respectively. Thus, also composition results for tree transducers (e.g. [EV85, KV94b, K uh97a]) and attribute grammars (e.g. Gan83, Gie88, K uh97a] can be used to remove intermediate data structures. In [K uh98] we describe a technique which uses composition results for attribute grammars in order to optimize functional programs. In this project, we want to compare deforestation like ....

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A. Kuhnemann. Berechnungsstarken von Teilklassen primitiv-rekursiver Programmschemata. PhD thesis, Technical University of Dresden, 1997. Shaker Verlag, Aachen.

....and the second one weakly single use , constructs a single new Macro Tree Transducer that implements the composition of the two original ones. We can give an a priori justi cation 1 of the feasibility of this aim by semantic reasoning with the help of other tree transduction classes [F ul81, K uh97] which are not covered in this thesis. Theorem 3.1 MAC nc ; MAC wsu = MAC 2 Proof: MAC nc ; MAC wsu TOP ; ATT su ; ATT (an analogue of Lemma 5.3 and Theorem 7.1 in [K uh98] TOP ; ATT (Lemma 6.4 in [K uh97] TOP ; MAC (cf. Fra82] MAC (Corollary 4.10 in [EV85] TOP ; Y IELD ....

....aim by semantic reasoning with the help of other tree transduction classes [F ul81, K uh97] which are not covered in this thesis. Theorem 3.1 MAC nc ; MAC wsu = MAC 2 Proof: MAC nc ; MAC wsu TOP ; ATT su ; ATT (an analogue of Lemma 5.3 and Theorem 7.1 in [K uh98] TOP ; ATT (Lemma 6. 4 in [K uh97] TOP ; MAC (cf. Fra82] MAC (Corollary 4.10 in [EV85] TOP ; Y IELD (Theorem 4.8 in [EV85] MAC nc ; MAC wsu (TOP MAC nc trivially; Lemma 6.10 in [K uh97] cf. EV85] The inclusion MAC nc ; MAC wsu MAC is also illustrated in Figure 3.1. 2 The same kind of semantic reasoning ....

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A. Kuhnemann. Berechnungsstarken von Teilklassen primitiv{rekursiver Programmschemata. PhD thesis, Dresden University of Technology, 1997. Shaker Verlag, Aachen.

....Functional World Transf. 6.8 and Observ. 6.15 Transf. 6.8 ) Transf. 7.1 P P P P P P P Pq Transf. 6.1 and Observ. 6.4 Figure 6: Transformation for the twofold composition of m rev . GG84, Gie88] and was presented in the framework of tree transducers in [K uh97] by generalizing the technique of [F ul81] Before giving the formal construction in Transformation 7.1, we informally explain it. For the att a we take the cartesian products S = S 1 S 2 ) I 1 I 2 ) and I = S 1 I 2 ) I 1 S 2 ) as sets of attributes. For every c 2 C (k) the rules in ....

....of listing every substitution pair , a compacter notation with constraints on substitution pairs is used here. 8 Note that in a strong sense a2 is not completely de ned to work on right hand sides of a1 , because the rules for outside attribute occurrences with respect to a1 are missing. In [K uh97] a more formal construction is given, which uses a modi ed att a 0 2 (similar to Section 4) Further, note that in a strong sense )a 2 ; is not de ned, because does not have the symbol root at its root. These two de ciencies are overcome by the substitution sub. 7.1 Composition of Restricted ....

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A. Kuhnemann. Berechnungsstarken von Teilklassen primitiv{rekursiver Programmschemata. PhD thesis, Dresden University of Technology, 1997. Shaker Verlag, Aachen.

....perform the optimization that we want to achieve here. In particular, classical deforestation fails due to its well known problem of not reaching accumulating parameters [Chi94] An approach that is applicable to our example is based on attribute grammars [Knu68] and was proposed independently in [K uh97, K uh98] and [CDPR98, CDPR99] The idea is to transform [CF82] the two functions (in our formalism represented by two restricted macro tree transducers) which we want to compose, into attribute grammars, respectively attributed tree transducers [F ul81] which are an abstraction of attribute ....

....rst of which is non copying and the second one weakly single use a single new mtt that implements the composition of the two original ones. We can give an a priori justi cation 3 of the feasibility of this aim by semantic reasoning with the help of other tree transduction classes [F ul81, K uh97] which are not covered in this paper. We only mention that ATT , Y IELD and ATT su denote the classes of attributed tree transductions, yield functions and tree transductions induced by single use attributed tree transducers, respectively. Theorem 3.1 MAC nc ; MAC wsu = MAC 2 Proof: MAC nc ; ....

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A. Kuhnemann. Berechnungsstarken von Teilklassen primitiv{rekursiver Programmschemata. PhD thesis, Dresden University of Technology, 1997. Shaker Verlag, Aachen.

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