Towards Observational Type Theory
نویسندگان
چکیده
Observational Type Theory (OTT) combines beneficial aspects of Intensional and Extensional Type Theory (ITT/ETT). It separates definitional equality, decidable as in ITT, and a substitutive propositional equality, capturing extensional equality of functions, as in ETT. Moreover, canonicity holds: any closed term is definitionally reducible to a canonical value. Building on previous work by each author, this article reports substantial progress in the form of a simplified theory with a straightforward syntactic presentation, which we have implemented. As well as simplifying reasoning about functions, OTT offers potential foundational benefits, e.g. it gives rise to a closed type theory encoding inductive datatypes.
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