Titlebook: Extensional Constructs in Intensional Type Theory; Martin Hofmann Book 1997 Springer-Verlag London Limited 1997 calculus.decidability.equa

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https://doi.org/10.1007/978-3-642-60302-0In this chapter we fix a particular syntax for a dependently typed calculus and define an abstract notion of model as well as a general interpretation function mapping syntactical objects to entities in a model. This interpretation function is shown to be sound with respect to the syntax.

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Continuous Asymmetric Hydrogenation,In this chapter we study models for quotient types and the related constructs of functional and propositional extensionality. The general method is to construct models in which types are interpreted as types together with partial equivalence relations. Propositional equality at some type is then the associated partial equivalence relation.

投射

That Soluble Specific Substance,We have compared extensional and intensional formulations of type theory and argued for the need for adding “extensional constructs” to the latter. These extensional constructs have been justified using syntactic models based on pure intensional type theory.

Canopy

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Extensionality and quotient types,In this chapter we study models for quotient types and the related constructs of functional and propositional extensionality. The general method is to construct models in which types are interpreted as types together with partial equivalence relations. Propositional equality at some type is then the associated partial equivalence relation.

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https://doi.org/10.1007/978-981-10-2510-5onal equality identified. The first property is undecidability of this theory; in view of the information loss in the equality reflection rule an obvious thing, which is nevertheless not completely trivial to prove (Section 3.2.2). The second property is the conservativity of extensional type theory

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https://doi.org/10.1007/978-3-319-53515-9ly provides these concepts, but also relates two approaches to program development in Martin-L?f type theory [88] or the Extended Calculus of Constructions (ECC) [68]. Under the first one specifications and types are freely mixed using .-types. This methodology underpins a project for development of