Translating a Dependently-Typed Logic to First-Order Logic

DFOL is a logic that extends first-order logic with dependent types. We give a translation from DFOL to FOL formalized as an institution comorphism and show that it admits the model expansion property. This property together with the borrowing theorem implies the soundness of borrowing — a result that enables us to reason about entailment in DFOL by using automated tools for FOL. In addition, the translation permits us to deduce properties of DFOL such as completeness, compactness, and existence of free models from the corresponding properties of FOL, and to regard DFOL as a fragment of FOL. We give an example that shows how problems about DFOL can be solved by using the automated FOL prover Vampire. Future work will focus on the integration of the translation into the specification and translation tool HeTS.