Showing papers by "Lawrence C. Paulson published in 1986"
TL;DR: An interactive theorem prover, Isabelle, is under development, which has been used to prove theorems in Martin-Lof's constructive type theory and may have potential for logic programming.
Abstract: An interactive theorem prover, Isabelle, is under development. In lcf , each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause. Resolution gives both forwards and backwards proof, supporting a large class of logics. Isabelle has been used to prove theorems in Martin-Lof's constructive type theory. Quantifiers pose several difficulties: substitution, bound variables, Skolemization. Isabelle's representation of logical syntax is the typed λ-calculus, requiring higher-order unification. It may have potential for logic programming. Depth-first subgoaling along inference rules constitutes a higher-order PROLOG.
151 citations
TL;DR: In this article, a theory of well-founded relations over higher types is presented, including relations formed by inverse images, addition, multiplication, and exponentiation of other relations, and the constructions are given in detail to allow their use in theorem provers for Type Theory, such as PRL.
55 citations
TL;DR: In this article, Boyer and Moore have discussed a function that puts conditional expressions into normal form, and it is difficult to prove that this function terminates on all inputs, but three termination proofs are compared: (1) using a measure function, (2) in domain theory using LCF, (3) showing that its recursion relation, defined by the pattern of recursive calls, is wellfounded.
Abstract: Boyer and Moore have discussed a function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure function, (2) in domain theory using LCF, (3) showing that its recursion relation, defined by the pattern of recursive calls, is well-founded. The last two proofs are essentially the same though conducted in markedly different logical frameworks. An obviously total variant of the normalize function is presented as the ‘computational meaning’ of those two proofs.
24 citations