UOR Bounded Recursion

IRI: https://uor.foundation/recursion/
Prefix: recursion:
Space: kernel
Comment: Self-referential computations with well-founded descent measures guaranteeing termination.

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This is a kernel-space namespace in the Define stage of the PRISM pipeline. It provides the immutable algebraic substrate — ring structure, schema vocabulary, and operation algebra.

Learn more: Pipeline Overview

Class hierarchy

Imports

https://uor.foundation/op/
https://uor.foundation/schema/
https://uor.foundation/predicate/
https://uor.foundation/morphism/
https://uor.foundation/effect/
https://uor.foundation/failure/
https://uor.foundation/trace/

Classes

Name	Subclass Of	Disjoint With	Comment
`BoundedRecursion`	`Thing`		A self-referential computation parameterized by a descent measure. Each recursive step strictly decreases the measure; the computation terminates when the base case predicate is satisfied.
`DescentMeasure`	`Thing`		A well-founded function from computation state to xsd:nonNegativeInteger. Strictly decreases on every recursive step.
`BaseCase`	`MatchArm`		The match arm selected when the descent measure reaches zero or the base predicate is satisfied. Produces a direct result without further recursion.
`RecursiveCase`	`MatchArm`		The match arm selected when the descent measure is positive. Applies a decomposition step, decreases the measure, and invokes the recursion.
`RecursiveStep`	`Thing`		A single step in a bounded recursion: the decomposition applied before the recursive invocation. Must strictly decrease the DescentMeasure.
`RecursionTrace`	`ComputationTrace`		A computation trace recording the sequence of recursive steps, measure values, and the base case result. The trace length is bounded by the initial measure value.
`StructuralRecursion`	`BoundedRecursion`		A bounded recursion where the descent measure is the structural size of the input type (site count, constraint count, or operad nesting depth).

Properties

Name	Kind	Functional	Domain	Range	Comment
`measure`	Object	true	`BoundedRecursion`	`DescentMeasure`	The descent measure guaranteeing termination.
`baseCase`	Object	true	`BoundedRecursion`	`BaseCase`	The base case match arm.
`recursiveCase`	Object	true	`BoundedRecursion`	`RecursiveCase`	The recursive case match arm.
`stepDecomposition`	Object	true	`RecursiveStep`	`Transform`	The transform applied to decompose the input before recursion.
`stepMeasurePre`	Object	true	`RecursiveStep`	`DescentMeasure`	The measure value before this step.
`stepMeasurePost`	Object	true	`RecursiveStep`	`DescentMeasure`	The measure value after this step.
`basePredicate`	Object	true	`BoundedRecursion`	`Predicate`	The predicate that identifies the base case.
`recursionBody`	Object	true	`BoundedRecursion`	`ComputationDatum`	The computation applied at each recursive step (may reference itself via its content address).
`initialMeasure`	Datatype	true	`BoundedRecursion`	`nonNegativeInteger`	The measure value at the start of recursion. Bounds the maximum recursion depth.
`measureValue`	Datatype	true	`DescentMeasure`	`nonNegativeInteger`	The current value of the descent measure.