Elf: a Language for Logic Deenition and Veriied Metaprogramming

We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for meta-programs such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf uniies logic deenition (in the style of LF, the Edinburgh Logical Framework) with logic programming (in the style of Prolog). It achieves this uniication by giving types an operational interpretation, much the same way that Prolog gives certain formulas (Horn-clauses) an operational interpretation. Novel features of Elf include: (1) the Elf search process automatically constructs terms that can represent object-logic proofs, and thus a program need not construct them explicitly, (2) the partial correct-ness of meta-programs with respect to a given logic can be expressed and proved in Elf itself, and (3) Elf exploits Elliott's uniication algorithm for a-calculus with dependent types.