nLab assignment operator

Idea

A symbol in mathematics and computer science to indicate that a particular variable is being initialized or assigned a value or that a particular symbol is being defined.

One sometimes distinguishes between assignment operators which allow reassignment, with what are known as single assignment operators, which do not allow reassignment.

The assignment operator in purely functional programming languages like Haskell amd Agda is an example of a single assignment operator. As purely functional programming languages can be represented in type theory, and every foundations of mathematics could also be represented in type theory, the assignment operators used in definitions in mathematics, such as $\coloneqq$, are single assignment operators; see definition for more details.

Related concepts

• functional programming

• equality

mathematical statements

• theory

• judgement, assertion

• hypothesis, consequence

• axiom

• assignment

• definition (inductive, coinductive)

• lemma

• proposition/type (propositions as types)

• theorem

• proof/program (proofs as programs)

• example, counterexample

• conjecture, folklore

• exercise

• analogy

• tautology

• paradox

References

• Wikipedia, Assignment (computer science)