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

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 not increased in any context. This paper investigates improvements an untyped call-by-need lambdacalculus 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 the improvement theory of Moran and Sands. We also prove that several different length measures used for improvement in the call-by-need calculus of Moran and Sands and our calculus are equivalent.