Composition

Components combine structures, independent state, explicit policies, and host commands. Each fact has one owner, so changing a policy cannot silently rewrite a structure or duplicate state authority.

Listbox

Structure

sequence

State

cursor + selection

Policy

eligibility + selection follows focus

Slider

Structure

range

State

tick

Policy

increment + page step

Calendar

Structure

grid

State

cursor + selection

Policy

date arithmetic + eligibility

Tree view

Structure

tree

State

expansion + cursor + selection

Policy

visible projection

Combobox

Structure

sequence | grid | tree

State

text + popup + cursor + selection

Policy

filter + acceptance

Tree grid

Structure

tree + grid

State

expansion + cursor + selection + edit mode

Policy

row/cell mapping

Composition operators

Operator	Meaning
Product	Combine independent state or structure authorities.
Sum	Select one mutually exclusive mode.
Refinement	Restrict valid models with additional laws.
Projection	Derive a canonical observable view.
Parameterization	Inject an explicit policy or capability.
Transaction	Compute child transitions and commit them atomically.
Revision	Reject stale input through an ordered snapshot wrapper.

Example: listbox

sequence
× cursor
× selection
× eligibility policy
× selection-follows-focus policy
× focus command

The sequence owns item order. The cursor owns the current item. Selection owns chosen identities. Policy decides whether cursor movement also changes selection. The host executes the resulting focus command.

Example: combobox

text
× popup state
× (sequence | grid | tree)
× cursor
× selection
× filter and acceptance policy
× focus and acceptance commands

IME composition remains text state until it is explicitly committed or cancelled. Candidate acceptance cannot reinterpret active composing text as committed query text.

Example: tree grid

tree hierarchy
× grid coordinates
× expansion
× cursor
× selection
× edit mode

The composite owns the mapping between row identity and cell coordinate. Tree and grid retain their individual laws instead of becoming one ambiguous hybrid structure.