definition

**natural deduction** metalanguage, practical foundations

**type theory** (dependent, intensional, observational type theory, homotopy type theory)

**computational trinitarianism** = **propositions as types** +**programs as proofs** +**relation type theory/category theory**

There are good reasons why the theorems should all be easy and the definitions hard. (Michael Spivak, preface to “Calculus on Manifolds” )

In type theory a *definition* is the construction of a term of a certain type.

As such definitions are no different from proofs of theorems (due propositions-as-types). For instance the constructive proof that there *exists* a natural number consists of exhibiting one, and hence the definition of, say $2 \in \mathbb{N}$ is the same as a specific proof that $\exists x \in \mathbb{N}$.

Last revised on February 17, 2015 at 10:12:44. See the history of this page for a list of all contributions to it.