Hash-consing is a technique to share values that are structurally equal. Beyond the obvious advantage of saving memory blocks, hash-consing may also be used to speed up fundamental operations and data structures by several orders of magnitude when sharing is maximal. This paper introduces an OCAML hash-consing library that encapsulates hash-consed terms in an abstract datatype, thus safely ensuring maximal sharing. This library is also parameterized by an equality that allows the user to identify terms according to an arbitrary equivalence relation. D.2.3 [Software engineer-

We propose to add sets and maps to Standard ML. Our implementation uses hash-tries to code them, yields fast general-purpose set-theoretic operations, and is based on a run-time where all equal objects are shared. We present evidence that this systematic use of hash-consing, and the use of hash-tries to code sets, provide good performance. 1 Introduction Sets have been an adequate foundation for mathematics for nearly a century, and are also an important conceptual medium in computer science. Modern specification languages like VDM [18] and Z [30] are based on sets. But few programming languages provide general-purpose sets and maps: although they could be adequate for prototyping, it is feared that they would be too slow for real applications. We have designed and implemented an extension of Standard ML [17], called HimML 1 [12] providing fast general (polymorphic) set-theoretic data-structures, and a comprehensive set of efficient operations on them. After mentioning related work...

. We present a new automated proof method for first-order classical logic, aimed at limiting the combinatorial explosion of the search. It is non-clausal, based on BDDs (binary decision diagrams) and on new strategies that control the size and traversal of the search space by controlling the amount of information, in Shannon's sense, gained at each step of the proof. Our prover does not search blindly for a proof, but thinks a lot to decide of a course of action. Practical results show that this pays off. 1 Introduction We present a complete refutation method for first-order classical logic that aims at controlling the growth and at guiding the traversal of the search space intelligently. Our starting point is [10], which proves that finding whether a given proposition in this logic is obvious, for several different reasonable definitions of non-obviousness, is \Sigma p 2 -complete. This not only means that proving is hard, but also that any complete proof method is built on, or hid...

We present a new approach to classical first-order theorem proving, and derive a method from it, which can handle formulas for which the textual representation is no help in guiding the proof. Inspired by Prawitz's method, it is close in spirit to Bibel's connection method. However, the strategy we use is different: at each stage in the search for a proof, the prover minimizes the branching factor, and thus the loss of information. We show experimental results on classical test problems, and analyse them. We show that the parameters of the method are measures of the degree of difficulty of the theorem to prove. This leads us to justify future improvements. 1 Introduction Both the connection method [4] or the method of general matings [2] rely on the textual form of the given formula to guide the search, but what happens when the syntax does not help? Indeed, although the syntax of human-entered formulas is likely to guide the proof effectively, it is not the case for computer-generate...