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The Formal Reconstruction and Speedup Of The Linear Time Fragment Of Willard's Relational Calculus Subset
 In Bird and Meertens, editors, Algorithmic Languages and Calculi
, 1997
"... 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 runtime query per ..."
Abstract

Cited by 8 (4 self)
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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 runtime 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 unitspace data takes unit time. In this paper we use a settheoretic 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...
A Mechanized Hoare Logic of State Transitions
, 1993
"... this paper selfcontained, 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 nonti ..."
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Cited by 6 (0 self)
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this paper selfcontained, 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 nontimed 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 dataprocessing algorithms much easier by defining a Hoare logic on top of them. 1.3 Timed Hoare specifications