It has been argued elsewhere that a logic programming language with function variables andλ-abstractions within terms makes a good meta-programming language, especially when an object-language contains notions of bound variables and scope. TheλProlog logic programming language and the related Elf and Isabelle systems provide meta-programs with both function variables andλ-abstractions by containing implementations of higher order unification. This paper presents a logic programming language, called Lλ, that also contains both function variables andλ-abstractions, although certain restrictions are placed on occurrences of function variables. As a result of these restrictions, an implementation of Lλdoes not need to implement full higher-order unification. Instead, an extension to first-order unification that respects bound variable names and scopes is all that is required. Such unification problems are shown to be decidable and to possess most general unifiers when unifiers exist. A unification algorithm and logic programming interpreter are described and proved correct. Several examples of using Lλas a meta-programming language are pre
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