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definition. A fundamental distinction is extensional vs intensional type theory. In extensional type theory, definitional (i.e., computational) equality...

science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as...

given type theory's semantics of equality, that is, whether the type theory is intensional or extensional. In 1934, Haskell Curry noticed that the types used...

science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to...

In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands...

functorial in extensional type theories (see #Properties). In intensional type theories, such functions are not truly functors, because the universe type is not...

(X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional set. Setoids are studied...

The blood type personality theory is a pseudoscientific belief prevalent in Japan which states that a person's blood group system is predictive of a person's...

set theory at the turn of the 20th century, like Russell's paradox. This third aim motivated the adoption of the theory of types in PM. The theory of types...

In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements...

computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system...

c):C({\mathsf {sup}}(a,f))}{{\mathsf {elim}}(w,h):C(w)}}} In extensional type theories, W-types (resp. M-types) can be defined up to isomorphism as initial algebras...

organist English Touring Theatre Euler tour technique, in graph theory Extensional type theory, in logic Endotracheal tube, in respiratory medicine Epithelioid...

following system is Mendelson's (1997, 289–293) ST type theory. ST is equivalent with Russell's ramified theory plus the Axiom of reducibility. The domain of...

The type theory was initially created to avoid paradoxes in a variety of formal logics and rewrite systems. Later, type theory referred to a class of formal...

In type theory, the identity type represents the concept of equality. It is also known as propositional equality to differentiate it from "judgemental...

valuation of extension over intension. See for example extension, and the extensional devices. Enumerative definition Extensional definition Extensional logic...

whereas rheometers that apply extensional stress or extensional strain are extensional rheometers. Rotational or shear type rheometers are usually designed...

the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved...

theory, the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and...