Categorical univalence of a universe does not entail function extensionality, as shown by polynomial models of type theory that refute the latter while satisfying the former.
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Proposes constraint-based type inference for type-directed synthesis of polymorphic code and GADTs, implemented in the Scythe live programming tool for Haskell.
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Univalence without function extensionality
Categorical univalence of a universe does not entail function extensionality, as shown by polynomial models of type theory that refute the latter while satisfying the former.
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Constraint-Based Type-Directed Program Synthesis
Proposes constraint-based type inference for type-directed synthesis of polymorphic code and GADTs, implemented in the Scythe live programming tool for Haskell.