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 …

We consider typed λ-calculi with pairing over the algebra W of words over {0, 1}, with a
destructor and discriminator function. We show that the poly-time functions are precisely the …

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 usage of sorts in rst-order automated deduction has brought greater conciseness of
representation and a considerable gain in e ciency by reducing the search spaces involved …

Safety is a syntactic condition of higher-order grammars that constrains occurrences of
variables in the production rules according to their type-theoretic order. In this paper, we …

As a contribution to ongoing research on computing over general algebraic structures, we
consider subrecurrence over free algebras. Since the natural sub-recursive classification of …

We present grammatical (or equational) descriptions of the set of normal inhabitants {M| Γ⊢
M: A, Minβ-normal form} of a given typeAunder a given basisΓ, both for the standard simple …

The history of building automated theorem provers for higher-order logic is almost as old as
the field of deduction systems itself. The first successful attempts to mechanize and …

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 …

We study a pumping lemma for the word/tree languages generated by higher-order
grammars. Pumping lemmas are known up to order-2 word languages (ie, for …