Graduate Thesis Or Dissertation
 

Variational Typing and Its Applications

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/br86b6641

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  • The study of variational typing originated from the problem of type inference for variational programs, which encode numerous different but related plain programs. In this dissertation, I present a sound and complete type inference algorithm for inferring types of all plain programs encoded in variational programs. The proposed algorithm runs exponentially faster than the strategy of generating all plain programs and applying type inference to them separately. I also present an error-tolerant version of variational type inference to deliver better feedback in the presence of ill-typed plain programs. All presented algorithms require various kinds of variational unification. I prove that all these problems are decidable and unitary, and I develop sound and complete unification algorithms. The idea of variational typing has many applications. As one example, I present how variational typing can be employed to improve the diagnosis of type errors in functional programs, a problem that has been extensively studied.
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