Type Inference for First-Order Logic

Abstract

Although type inference for dependent types is in general undecidable, people experience that the algorithms for type inference in Elf programming language stop in common cases. The present paper is a partial explanation of this behaviour. It shows that for a wide range of terms — terms that correspond to first-order logic proofs — the formalism of dependent types gives decidable type inference. We remark also that imposing that the context and the type of a judgement are first-order is not sufficient for obtaining decidability.KeywordsType VariableDependent TypeType InferenceConstant SymbolLambda CalculusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.