Compose is the basic mechanism for combining operations. It takes two operators and produces a new operator that applies the first and then the second.
Formal Signature
Compose : (Op, Op) → Op
Definition
Compose(f, g)(x) = g(f(x)). The input passes through f first, then the result passes through g. This is diagrammatic (left-to-right) composition: the order of arguments matches the order of application.
Composition is associative: Compose(Compose(f, g), h) = Compose(f, Compose(g, h)). It has an identity element (the operator that returns its input unchanged). These two properties make the collection of operators a category.
Every compound operation in the relational algebra is built from Compose. Closure operators, iteration, flow --- all are defined by composing simpler operations. Compose is the structural glue that turns individual operations into a coherent calculus.
Derivational context
Compose is a utility term that operates across all five movements. It provides the basic mechanism for building compound operations — every closure operator, every iteration, every flow is constructed by composing simpler operations. Compose appears as early as Movement I: Logical Origination, where the logical operations (Together, Either, Implies, Negate) are combined to form more complex recognitions, and it remains active through Movement V where meta-level operators are composed.
Relations to Other Terms
- Define --- names composed expressions for reuse