UOR Parallel Composition

IRI: https://uor.foundation/parallel/
Prefix: parallel:
Space: kernel
Comment: Independent computations over provably disjoint site budgets. Formalizes when execution order is irrelevant.

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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/effect/
https://uor.foundation/monoidal/
https://uor.foundation/partition/
https://uor.foundation/cert/
https://uor.foundation/trace/

Classes

Name	Subclass Of	Disjoint With	Comment
`ParallelProduct`	`Thing`		A ∥ B: two computations with provably disjoint site targets. Execution order does not affect the result.
`DisjointnessCertificate`	`Certificate`		A kernel-produced certificate attesting that the site targets of two computations are disjoint.
`SynchronizationPoint`	`Thing`		A point where two parallel computations must agree on shared state before proceeding. Only applicable when parallelism is partial.
`ParallelTrace`	`ComputationTrace`		A computation trace recording interleaved steps from two parallel computations. Valid iff every interleaving produces the same final context.
`SitePartitioning`	`Thing`		A partition of the total site budget into disjoint subsets, one per parallel component. The sum of subset cardinalities equals the total site budget.

Properties

Name	Kind	Functional	Domain	Range	Comment
`leftComputation`	Object	true	`ParallelProduct`	`MonoidalProduct`	The left parallel component (itself a sequential computation).
`rightComputation`	Object	true	`ParallelProduct`	`MonoidalProduct`	The right parallel component.
`disjointnessCert`	Object	true	`ParallelProduct`	`DisjointnessCertificate`	The certificate proving site disjointness.
`certLeftTarget`	Object	true	`DisjointnessCertificate`	`EffectTarget`	The site target of the left computation.
`certRightTarget`	Object	true	`DisjointnessCertificate`	`EffectTarget`	The site target of the right computation.
`syncSites`	Object	false	`SynchronizationPoint`	`SiteIndex`	The shared sites requiring synchronization.
`partitionComponents`	Object	false	`SitePartitioning`	`EffectTarget`	The disjoint subsets composing the full site budget.
`componentCount`	Datatype	true	`SitePartitioning`	`positiveInteger`	Number of parallel components.
`isFullyDisjoint`	Datatype	true	`ParallelProduct`	`boolean`	True iff site targets have zero overlap (no SynchronizationPoints required).
`disjointnessCommutation`	Datatype	true	`ParallelProduct`	`boolean`	Declares whether this parallel product commutes with disjoint effects per FX_4.