We demonstrate how several programming language concepts and methods can be used economically to obtain an improved solution to a difficult algorithmic problem. The problem is to compile a subset RCS of Relational Calculus defined by Willard (1978) in a novel way so that efficient run-time query performance is guaranteed. Willard gives an algorithm to compile each query q belonging to RCS so that it executes in O(n log d n+o) steps and O(n) space, where n and o are respectively the input and output set sizes, and d is a parameter associated with the syntax of query q. Willard's time bounds are based on the assumption that hashing unit-space data takes unit time. In this paper we use a set-theoretic complexity measure and formal transformational techniques to reconstruct the linear time fragment of RCS in a simplified way. In doing this, we show how complexity can be determined by language abstraction and algebraic reasoning without resorting to low level counting arguments. This ap...

this paper self-contained, a simplified version of the theory is outlined in 1.7. The general idea of mechanising Hoare logics by generating verification conditions and then feeding them to a theorem prover is standard [3, 5, 13]. The particular approach used here was originally developed for non-timed Hoare logics [4]. Verification conditions are described in 1.6. The main contribution of this paper is to make the use of STAs for reasoning about data-processing algorithms much easier by defining a Hoare logic on top of them. 1.3 Timed Hoare specifications