Type theory is one of the most important tools in the design of higher-level programming
languages, such as ML. This book introduces and teaches its techniques by focusing on one …

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 …

In this paper, we reexamine the problem of general higher-order unification and develop an
approach based on the method of transformations on systems of terms which has its roots in …

We developed a procedure to enumerate complete sets of higher-order unifiers based on
work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by …

Historically, logic programming (LP) originated from first order logic (FOL). Two results of
FOL were crucial. The first is Skolem's theorem, according to which we can reformulate …

The higher order matching problem is the problem of determining whether a term is an
instance of another in the simply typed [lgr]-calculus, ie to solve the equation a= b where a …

A λ-language over a simple type structure is considered. Type B=(O→ O)→((O→ O)→(O→
O)) is called a binary word type because of the isomorphism between words over a binary …

Unification is a very general computational paradigm that plays an important role in many
different areas of symbolic computation. For example, unification plays a central role in …

In this paper is presented an algorithm for constructing natural deduction proofs in the
propositional intuitionistic and classical logics according to the analogy relating intuitionistic …

Abstract Zaionc, M., λ-Definability on free algebras, Annals of Pure and Applied Logic 51
(1991) 279-300. A λ-language over a simple type structure is considered. There is a natural …