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Journals ACM SIGACT News Volume 33 Issue 4

Chapter 2 is on simply typed lambda calculus. The simply typed lambda calculus is the syntactic basis of Church ™s formulation of higher-order logic. The chapter supplies necessary information on type symbols, terms, conversions and reductions, normal forms, and substitutions. After building background in chapter 1, and 2; the chapter 3 introduces Clausal Theory of Types. The outcome of the chapter 3 is higher order Skolem-Herbrand-Godel theorem for the CTT. Chapter 4 presents details related to the higher-order equational uni cation. Major forms and their complexities down to the rst-order cases are presented. Higher order equational uni ability uses a de nition of higher-order rewriting. Soundness and completeness results for higher-order equational uni cation procedures are given. Higher-order resolution with built-in higher-order equational theories for the Clausal Theory of Types formulas is de ned. Also, higher-order uni cation and matching, second-order monadic uni cation, and rst-order equational uni cation are discussed. Chapter 5 is on higher-order equational logic programming. The chapter discusses the role of CTT as a programming language. It provides a method for testing the unsatis ability of CTT formulas. It de nes CTT horn clauses, and shows that they meet the programming language criteria of

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Discrete mathematical problems with medical applications DIMACS volume 55

Venkatasubramanian, Suresh
ACM SIGACT News , Volume 33 (4)
Association for Computing Machinery – Dec 1, 2002

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