Improvements in a functional core language with call-by-need operational semantics

Abstract

Abstract. 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.

An Environment for Analyzing Space Optimizations in Call-by-Need Functional Languages

“…The first expression has four separate occurrences of a (long) list, whereas the second expression shares the lists, where list varies in length in the experiments. The results are consistent with the claim that common subexpression elimination (cse) is a time improvement [14], and show that (cse) and an increase of sharing in general may increase the (maximal) space usage. In neither direction the example is a space improvement, which shows that (cse) is not a space improvement.…”

“…For measuring the space-behavior of s, we use the maximum size occurring in an nogc-reduction sequence to a WHNF: This measure is very strict and especially appropriate if the available space is limited. A transformation is a time improvement [14,13] if it never increases the rln-reduction length, and a transformation is a space improvement if it never increases the space consumption. These relations are precongruences.…”

“…The used abstract machine is defined in [14,13] and is based on the abstract machine Mark 1 by Peter Sestoft (see [17]), which was designed for call-by-need evaluation. The machine is extended in a straightforward way to handle seq-expressions, where a seq-expression evaluates the first argument to a value and then returns the second argument.…”

“…time usage (the number of reduction steps), is e.g. [9,10,11] for call-by-name and [8,15,13,14] for call-by-need. There seem to be only a few studies on space improvements, by Gustavsson and Sands [4,5,3].…”