Order relations and compile-time halfspace predicates. More...

import dedekind.order:inclusion;

Include dependency graph for order.cppm:

This graph shows which files directly or indirectly include this file:

Detailed Description

Order relations and compile-time halfspace predicates.

Copyright: 2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

order__Partitions

:poset — preorders, partial orders, directed sets; the homogeneous HasPartialOrderOperators shape and its heterogeneous sibling HasPartialOrderOperatorsWith<T, U>.
:total — total orders, linear orders, strict weak orders, chains; the homogeneous HasTotalOrderOperators (spaceship) shape and its heterogeneous sibling HasTotalOrderOperatorsWith<T, U>. Strictly stronger than :poset; mirrors :category:total's order/algebra split (per #410).
:lattice — meet / join / lattice / distributive lattice.
:completeness — successor, Archimedean, dense / discrete, Dedekind-complete.
:halfspace — NTTP halfspace DSL (bound<V>, Halfspace, Interval, Singleton, structured_and).

Wikipedia: Partially ordered set, Total order, Half-space (geometry)

Note: "Mathematics is not the study of abstract objects; it is the study of clarity of thought." — William P. Thurston, On proof and progress in mathematics, Bulletin of the AMS 30, 2 (1994), §1.

#308 undergraduate probability and statistics: Sub holds the convex subobjects of an ordered carrier (intervals, not arbitrary subsets: no {0,2} in Sub<int>), so it is closed under meets but not under unions or complements; σ-algebras and measures are open.