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

The unification problem and several variants are presented. Various algorithms and data
structures are discussed. Research on unification arising in several areas of computer …

We present the Calculus of Constructions, a higher-order formalism for constructive proofs in
natural deduction style. Every proof is a X-expression, typed with propositions of the …

The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is
based on a general treatment of syntax, rules, and proofs by means of a typed λ-calculus …

We hope to accomplish four things by writing this book. Our rst goal is to o er a tutorial on the
new mathematical ideas which underlie our research. In doing so we have tried to provide …

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 …

Dependent type theories [ML72] have a long history of being used for theorem proving. One
aspect of type theory which makes it very powerful as a proof language is that it mixes …

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 …

The unification problem in f'mst-order predicate calculus is described in general terms as the
solution of a system of equations, and a nondeterministic algorithm is given. A new …

This paper introduces corpus-guided top-down synthesis as a mechanism for synthesizing
library functions that capture common functionality from a corpus of programs in a domain …