LambdaConf 2015 - Type Theory and its Meaning Explanations   Jon Sterling
Channel: Confreaks
Date: 2016-01-04

At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort arise naturally as enrichments of logical theories with further judgements, and contrast this with modern proof-theoretic type theories which interpret the judgements and proofs of logics, not their propositions and verifications. Expect the following questions to be answered: What is the difference between a judgement and a proposition? What is a meaning explanation? What is the difference between a proof and a verification? The so-called semantical approach to type theory is, in the speaker's view, more immediately philosophically acceptable than the modern syntactic one, and also provides a basis for a future where partiality and other effects may be treated naturally through refinement and behavioral typing, rather than by means of term-level monads and similar kludges.

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