Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik
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57 [V3]
We explore space improvements in LRP, a polymorphically typed call-by-need functional core language. A relaxed space measure is chosen for the maximal size usage during an evaluation. It Abstracts from the details of the implementation via abstract machines, but it takes garbage collection into account and thus can be seen as a realistic approximation of space usage. The results are: a context lemma for space improving translations and for space equivalences; all but one reduction rule of the calculus are shown to be space improvements, and the exceptional one, the copy-rule, is shown to increase space only moderately.
Several further program transformations are shown to be space improvements or space equivalences, in particular the translation into machine expressions is a space equivalence. These results are a step Forward in making predictions about the change in runtime space behavior of optimizing transformations in callbyneed functional languages.
57 [V2]
We explore space improvements in LRP, a polymorphically typed call-by-need functional core language. A relaxed space measure is chosen for the maximal size usage during an evaluation. It Abstracts from the details of the implementation via abstract machines, but it takes garbage collection into account and thus can be seen as a realistic approximation of space usage. The results are: a context lemma for space improving translations and for space equivalences; all but one reduction rule of the calculus are shown to be space improvements, and the exceptional one, the copy-rule, is shown to increase space only moderately.
Several further program transformations are shown to be space improvements or space equivalences, in particular the translation into machine expressions is a space equivalence. These results are a step Forward in making predictions about the change in runtime space behavior of optimizing transformations in callbyneed functional languages.
57
We explore space improvements in LRP, a polymorphically typed call-by-need functional core language. A relaxed space measure is chosen for the maximal size usage during an evaluation. It Abstracts from the details of the implementation via abstract machines, but it takes garbage collection into account and thus can be seen as a realistic approximation of space usage. The results are: a context lemma for space improving translations and for space equivalences; all but one reduction rule of the calculus are shown to be space improvements, and the exceptional one, the copy-rule, is shown to increase space only moderately.
Several further program transformations are shown to be space improvements or space equivalences, in particular the translation into machine expressions is a space equivalence. These results are a step Forward in making predictions about the change in runtime space behavior of optimizing transformations in callbyneed functional languages.
56 [version 3.0]
The calculus LRP is a polymorphically typed call-by-need lambda calculus extended by data constructors, case-expressions, seq-expressions and type abstraction and type application. This report is devoted to the extension LRPw of LRP by scoped sharing decorations. The extension cannot be properly encoded into LRP if improvements are defined w.r.t. the number of lbeta, case, and seq-reductions, which makes it necessary to reconsider the claims and proofs of properties. We show correctness of improvement properties of reduction and transformation rules and also of computation rules for decorations in the extended calculus LRPw. We conjecture that conservativity of the embedding of LRP in LRPw holds.
56 [version 2.0]
The calculus LRP is a polymorphically typed call-by-need lambda calculus extended by data constructors, case-expressions, seq-expressions and type abstraction and type application. This report is devoted to the extension LRPw of LRP by scoped sharing decorations. The extension cannot be properly encoded into LRP if improvements are defined w.r.t. the number of lbeta, case, and seq-reductions, which makes it necessary to reconsider the claims and proofs of properties. We show correctness of improvement properties of reduction and transformation rules and also of computation rules for decorations in the extended calculus LRPw. We conjecture that conservativity of the embedding of LRP in LRPw holds.
56 [version 1.0]
This report documents the extension LRPw of LRP by sharing decorations. We show correctness of improvement properties of reduction and transformation rules and also of computation rules for decorations in the extended calculus LRPw. We conjecture that conservativity of the embedding of LRP in LRPw holds.
55 [version 3.0]
An improvement is a correct program transformation that optimizes the program, where the criterion is that the number of computation steps until a value is obtained is decreased. This paper investigates improvements in both { an untyped and a polymorphically typed { call-by-need lambda-calculus with letrec, case, constructors and seq. Besides showing that several local optimizations are improvements, the main result of the paper is a proof that common subexpression elimination is correct and an improvement, which proves a conjecture and thus closes a gap in Moran and Sands' improvement theory. We also prove that several different length measures used for improvement in Moran and Sands' call-by-need calculus and our calculus are equivalent.
55 [version 2.0]
An improvement is a correct program transformation that optimizes the program, where the criterion is that the number of computation steps until a value is obtained is decreased. This paper investigates improvements in both { an untyped and a polymorphically typed { call-by-need lambda-calculus with letrec, case, constructors and seq. Besides showing that several local optimizations are improvements, the main result of the paper is a proof that common subexpression elimination is correct and an improvement, which proves a conjecture and thus closes a gap in Moran and Sands' improvement theory. We also prove that several different length measures used for improvement in Moran and Sands' call-by-need calculus and our calculus are equivalent.
55 [version 1.0]
An improvement is a correct program transformation that optimizes the program, where the criterion is that the number of computation steps until a value is obtained is decreased. This paper investigates improvements in both { an untyped and a polymorphically typed { call-by-need lambda-calculus with letrec, case, constructors and seq. Besides showing that several local optimizations are improvements, the main result of the paper is a proof that common subexpression elimination is correct and an improvement, which proves a conjecture and thus closes a gap in Moran and Sands' improvement theory. We also prove that several different length measures used for improvement in Moran and Sands' call-by-need calculus and our calculus are equivalent.
54
Motivated by the question whether sound and expressive applicative similarities for program calculi with should-convergence exist, this paper investigates expressive applicative similarities for the untyped call-by-value lambda-calculus extended with McCarthy's ambiguous choice operator amb. Soundness of the applicative similarities w.r.t. contextual equivalence based on may-and should-convergence is proved by adapting Howe's method to should-convergence. As usual for nondeterministic calculi, similarity is not complete w.r.t. contextual equivalence which requires a rather complex counter example as a witness. Also the call-by-value lambda-calculus with the weaker nondeterministic construct erratic choice is analyzed and sound applicative similarities are provided. This justifies the expectation that also for more expressive and call-by-need higher-order calculi there are sound and powerful similarities for should-convergence.