Publisher Summary Equations and formulas occur frequently in mathematics, logic, and
computer science. This chapter reviews the main results concerning equations and the …

Interest is increasing in the transformational approach to programming and in mechanical
aids for supporting the program development process. Available aids range from simple …

The theory ZF implements Zermelo-Fraenkel set theory [23, 56] as an extension of FOL,
classical first-order logic. The theory includes a collection of derived natural deduction rules …

We describe motivation, design, use, and implementation of higher-order abstract syntax as
a central representation for programs, formulas, rules, and other syntactic objects in program …

We present a new method for characterizing the interpretive possibilities generated by
elliptical constructions in natural language. Unlike previous analyses, which postulate …

Abstract Miller, D., G. Nadathur, F. Pfenning and A. Scedrov, Uniform proofs as a foundation
for logic programming, Annals of Pure and Applied Logic 51 (1991) 125–157. A proof …

It has been argued elsewhere that a logic programming language with function variables
and λ-abstractions within terms makes a good meta-programming language, especially …

Abstract Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It
represents rules as propositions (not as functions) and builds proofs by combining rules …

ABSTgACT. Tree pattern matching is an interesting special problem which occurs as a
crucial step ma number of programmmg tasks, for instance, design of interpreters for …

XProlog is a logic programming language that extends Prolog by incorporating notions of
higher-order functions, A-terms, higher-order unification, polymorphic types, and …