Type System

Definition

The UOR type system provides a structured way to classify objects in the ring. The base class is TypeDefinition.

Type Hierarchy

Class	Description
TypeDefinition	Base type
PrimitiveType	Atomic type (e.g., u8, u16)
ProductType	Cartesian product of types
SumType	Discriminated union of types
ConstrainedType	Type with additional constraints

Properties

Property	Domain	Range	Description
bitWidth	PrimitiveType	xsd:nonNegativeInteger	Bit width
component	ProductType	TypeDefinition	Component types
baseType	SumType/ConstrainedType	TypeDefinition	Base type
contentAddress	TypeDefinition	u:Element	Content address

Example: Primitive Types

<https://uor.foundation/instance/type-u8>
    a               type:PrimitiveType ;
    type:bitWidth   "8"^^xsd:nonNegativeInteger .

<https://uor.foundation/instance/type-u64>
    a               type:PrimitiveType ;
    type:bitWidth   "64"^^xsd:nonNegativeInteger .

Integration with State

Types are used in Binding to record the type of bound values:

<https://uor.foundation/instance/binding-x>
    a               state:Binding ;
    state:boundType <https://uor.foundation/instance/type-u8> .

Integration with Partition

Types serve as the source for partition computations via sourceType.

Constrained Types

A ConstrainedType wraps a base type with additional constraints that restrict the set of valid values. Constraints are combined using CompositeConstraint:

<https://uor.foundation/instance/constrained-odd-shallow>
    a                   type:ConstrainedType ;
    type:baseType       <https://uor.foundation/instance/type-u8> ;
    type:constraint     "residue(2,1) AND depth(1,2)" .

This constrained type accepts only values in Z/256Z that are odd (residue 1 mod 2) and have valuation depth between 1 and 2. Each constraint pins specific sites of the Z/2Z fibration:

ResidueConstraint (mod 2, residue 1) pins site 0.
DepthConstraint (depth 1–2) pins sites 0 and 1.

Types and Free Rank

Each constraint pins sites, and the type's total free rank tracks how many sites remain free. A fully resolved type has zero free sites — every site is pinned by at least one constraint. See Free Rank for the accounting and Constraint Algebra for how constraints compose.