TeXipedia

coloncolonminus

Represents a double colon followed by a minus sign, commonly used in type theory and programming language semantics.

Overview

Serves as a specialized notation primarily found in formal specifications, type systems, and mathematical logic.

  • Frequently appears in type declarations and judgments
  • Used to denote type ascription or typing relations
  • Common in programming language theory and formal methods
  • Often seen in academic papers and textbooks discussing type systems
  • Helps express relationships between terms and their types in a precise, formal manner

Examples

Type theory notation showing a function type with domain and codomain.

f:A∷−Bf : A \coloncolonminus B 
f : A \coloncolonminus B

Type declaration in formal logic or programming semantics.

x∷−Nx \coloncolonminus \mathbb{N} 
x \coloncolonminus \mathbb{N}

Specification of variable types in mathematical logic.

∀x∷−X,∃y∷−Y\forall x \coloncolonminus X, \exists y \coloncolonminus Y 
\forall x \coloncolonminus X, \exists y \coloncolonminus Y