UOR Productive Streams

IRI: https://uor.foundation/stream/
Prefix: stream:
Space: kernel
Comment: Coinductive sequences of reduction epochs. Each epoch terminates independently; the stream is the unbounded composition of terminating epochs.

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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/reduction/
https://uor.foundation/state/
https://uor.foundation/monoidal/
https://uor.foundation/cert/
https://uor.foundation/morphism/
https://uor.foundation/schema/

Classes

Name	Subclass Of	Disjoint With	Comment
`ProductiveStream`	`Thing`		An unbounded sequence of reduction epochs where each epoch terminates and produces a well-typed output. The coinductive dual of a finite computation.
`Epoch`	`Thing`		A single bounded iteration within a productive stream. Each epoch is a complete reduction execution from Initialization through Convergence.
`EpochBoundary`	`Thing`		The transition point between consecutive epochs. Carries the continuation context and the epoch output.
`StreamPrefix`	`Thing`		A finite prefix of a productive stream: the first k epochs and their outputs. Every finite prefix is computable in finite time.
`StreamMorphism`	`Transform`		A transform between productive streams: maps each epoch of the source to an epoch of the target while preserving the productive property.
`Unfold`	`Thing`		The coinductive constructor: given an initial context and a step function (a morphism:ComputationDatum), produces a ProductiveStream. The step function must be certified to always reach reduction convergence.

Properties

Name	Kind	Functional	Domain	Range	Comment
`epochReduction`	Object	true	`Epoch`	`EulerReduction`	The reduction execution for this epoch.
`epochOutput`	Object	true	`Epoch`	`Datum`	The output datum produced by this epoch.
`epochContext`	Object	true	`Epoch`	`Context`	The context at the start of this epoch.
`boundaryFrom`	Object	true	`EpochBoundary`	`Epoch`	The epoch that just completed.
`boundaryTo`	Object	true	`EpochBoundary`	`Epoch`	The epoch about to begin.
`continuationContext`	Object	true	`EpochBoundary`	`Context`	The context carried across the boundary.
`prefixEpochs`	Object	false	`StreamPrefix`	`Epoch`	The epochs in this prefix (ordered by stream:epochIndex).
`unfoldSeed`	Object	true	`Unfold`	`Context`	The initial context for the stream.
`unfoldStep`	Object	true	`Unfold`	`ComputationDatum`	The certified step function producing each epoch.
`unfoldResult`	Object	true	`Unfold`	`ProductiveStream`	The stream produced by this unfold.
`epochIndex`	Datatype	true	`Epoch`	`nonNegativeInteger`	Zero-based index of this epoch in the stream.
`prefixLength`	Datatype	true	`StreamPrefix`	`positiveInteger`	Number of epochs in this prefix.
`isProductive`	Datatype	true	`ProductiveStream`	`boolean`	Always true by construction: every epoch terminates. Invariant, not computed.