In this paper, we discuss a lightweight approach to eliminate the overhead due to implicit type arguments during higher-order unification of dependently-typed terms. First, we show that some implicit type information is uniquely determined, and can therefore be safely skipped during higher-order unification. Second, we discuss its impact in practice during type reconstruction and during proof s...

A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full rst-order predicate calculus. It di ers from Prolog in its use of uni cation with the occurs check for soundness, depthrst iterative-deepening search instead of unbounded depthrst search to make the search strategy complete, and the model elimination reduction rule that is added to Prolog inference...

A uniquely converging (UC) property for a possibly nonlinear term rewriting system (TRS) is investigated. UC, which is an intermediate property between conventional Church-Rosser (CR) and uniquely normalizing (UN), is newly proposed in connection with the consistency of continuous semantics. Continuous semantics is de ned by constructing free-continuous algebra which is required in algebraic sp...