Dependent Type Inference with Interpolants

We propose a novel type inference algorithm for a dependently-typed functional language. The novel features of our algorithm are: (i) it can iteratively refine dependent types with interpolants until the type inference succeeds or the program is found to be ill-typed, and (ii) in the latter case, it can generate a kind of counter-example as an explanation of why the program is ill-typed. We have implemented a prototype type inference system and tested it for several programs.