In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being … Zobacz więcej The terms "predicative" and "impredicative" were introduced by Russell (1907), though the meaning has changed a little since then. Solomon Feferman provides a historical review of … Zobacz więcej • Gödel, Escher, Bach • Impredicative polymorphism • Logicism • Richard's paradox Zobacz więcej Witryna15 lis 2014 · CoC distinguishes between the impredicative type of predicates (\(\star\), small types), a predicative hierarchy of types of types (\(\square _{i}\), large types), and the type of all large types. As in other PTS, from \(\Pi\) constructor it is possible to derive the usual logical operators. CoC also has void type and 1 type, and it is easy to ...

Sets in Types, Types in Sets - Springer

Witryna21 sty 2015 · There are several more exotic flavours of polymorphism that are implemented in some extensions to Haskell, e.g. rank-N types and impredicative types. There are some kinds of polymorphism that Haskell doesn't support, or at least not natively, e.g. inclusion polymorphism and subtyping, common in OO languages, … Witrynaof impredicative type systems, since it makes it possible to interpret universes, intersection types and subtyping in the same framework. But the most interesting feature of the model is that the inhabitants of impredicative types are not interpreted in a syntactical way, but by the points of an arbitrary coherence space, provided it is a … can i tickle my dog

lo.logic - Impredicativity - MathOverflow

Witryna1 sty 2012 · This type can be tested by following the manual for testing Π-types and I-types over the type N. 5 Impredicative Type Theory We have explained how the meaning explanations for intuitionistic type theory are about testing judgements by running programs interactively, that is, by generating input, and observing results. Witrynasynthetic guarded domain theory, BI-hyperdoctrine, impredicative polymorphism, recursive types 1 Introduction State of the art program logics such as Iris [30] and the Veri ed Software Toolchain [1] typically combine two design decisions: the basic sorts of the logic are generated by the raw, untyped terms of the programming Witryna29 mar 2015 · 6 Type : Type is inconsistent. Impredicative Set with excluded middle implies proof irrelevance, so impredicative Set with proof relevance, e.g. true <> false, refutes excluded middle, which intuitionism isn't supposed to do. Therefore we leave impredicativity in Prop and the rest of the type hierarchy gives us predicativity. By the … can i throw out empty paint cans