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

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 …

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 …

We develop a theory of abstract syntax with variable binding. To every binding signature we
associate a category of models consisting of variable sets endowed with compatible algebra …

We have built the first family of tagless interpretations for a higher-order typed object
language in a typed metalanguage (Haskell or ML) that require no dependent types …

The Fraenkel-Mostowski permutation model of set theory with atoms (FM-sets) can serve as
the semantic basis of meta-logics for specifying and reasoning about formal systems …

Formal systems that describe computations over syntactic structures occur frequently in
computer science. Logic programming provides a natural framework for encoding and …

Unification problems are identified with conjunctions of equations between simply typed λ-
terms where free variables in the equations can be universally or existentially quantified …

This thesis presents and studies a unifying theory of dependent types ECC-Extended
Calculus of Constructions. ECC integrates Coquand-Huet's (impredicative) calculus of …