Logic programming in the LF logical framework
Logical frameworks
Second-order unification and type inference for Church-style polymorphism
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Undecidability of Typability in the Lambda-Pi-Calculus
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Proof-Search in Intuitionistic Logic Based on Constraint Satisfaction
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
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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.