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Transformation Vocabulary

Transformation theory provides a structured vocabulary for describing change.

It defines transformation kinds, transformation families, named operations, atomic effect semantics, composition relations, and orthogonality relations.

Scope

This theory names and organizes kinds of change and formalizes constraints on the intrinsic effects of individual transformation operations.

One application of an operator is modeled as an atomic step between abstract transformation configurations.

For each operator:

  • footprint gives a conservative upper bound on the dimensions the atomic step may change;
  • requirements gives the required-change clauses that every step must satisfy; and
  • characteristic, when defined, identifies the single required dimension of an operator whose complete requirement is one singleton clause.

Composition and orthogonality remain explicitly declared, partial relations among operators. The effect semantics supplies additional derived predicates and necessary conditions; it does not replace those declarations.

Persistence judgments and operational policy are out of this scope.

Transformation Kinds

Transformation kinds are the broadest categories of change.

17 Operations (named transformations)

Operations are the concrete named transformations.

Each operator belongs to exactly one family and therefore one kind.

The generated operator registry also exposes the current footprint and requirements for every operator.

Transformation Families

Transformation families group operations by shared behavior within the broad transformation kinds.

Each operation belongs to exactly one transformation family, and each transformation family belongs to exactly one transformation kind.

Effect Semantics

Effect semantics formalize effect dimensions, operator footprints, required-change conditions, and abstract atomic operator steps.

Composition Relations

Composition relations describe selected ordered pairs of operations.

Composition relations describe sequencing between operations.

Orthogonality Relations

Orthogonality relations describe selected unordered pairs of operations.

Composition and orthogonality are independent ways of describing relationships among operations.

Summary

Transformation theory provides a structured vocabulary for

  • what kind of change occurred;
  • how concrete operations are grouped;
  • what dimensions an atomic operation may or must change; and
  • how selected operations relate to one another.