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.

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

NameIRISubclass OfDisjoint WithComment
ProductiveStreamhttps://uor.foundation/stream/ProductiveStreamhttp://www.w3.org/2002/07/owl#ThingAn unbounded sequence of reduction epochs where each epoch terminates and produces a well-typed output. The coinductive dual of a finite computation.
Epochhttps://uor.foundation/stream/Epochhttp://www.w3.org/2002/07/owl#ThingA single bounded iteration within a productive stream. Each epoch is a complete reduction execution from Initialization through Convergence.
EpochBoundaryhttps://uor.foundation/stream/EpochBoundaryhttp://www.w3.org/2002/07/owl#ThingThe transition point between consecutive epochs. Carries the continuation context and the epoch output.
StreamPrefixhttps://uor.foundation/stream/StreamPrefixhttp://www.w3.org/2002/07/owl#ThingA finite prefix of a productive stream: the first k epochs and their outputs. Every finite prefix is computable in finite time.
StreamMorphismhttps://uor.foundation/stream/StreamMorphismhttps://uor.foundation/morphism/TransformA transform between productive streams: maps each epoch of the source to an epoch of the target while preserving the productive property.
Unfoldhttps://uor.foundation/stream/Unfoldhttp://www.w3.org/2002/07/owl#ThingThe 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

NameKindFunctionalDomainRangeComment
epochReductionObjecttruehttps://uor.foundation/stream/Epochhttps://uor.foundation/reduction/EulerReductionThe reduction execution for this epoch.
epochOutputObjecttruehttps://uor.foundation/stream/Epochhttps://uor.foundation/schema/DatumThe output datum produced by this epoch.
epochContextObjecttruehttps://uor.foundation/stream/Epochhttps://uor.foundation/state/ContextThe context at the start of this epoch.
boundaryFromObjecttruehttps://uor.foundation/stream/EpochBoundaryhttps://uor.foundation/stream/EpochThe epoch that just completed.
boundaryToObjecttruehttps://uor.foundation/stream/EpochBoundaryhttps://uor.foundation/stream/EpochThe epoch about to begin.
continuationContextObjecttruehttps://uor.foundation/stream/EpochBoundaryhttps://uor.foundation/state/ContextThe context carried across the boundary.
prefixEpochsObjectfalsehttps://uor.foundation/stream/StreamPrefixhttps://uor.foundation/stream/EpochThe epochs in this prefix (ordered by stream:epochIndex).
unfoldSeedObjecttruehttps://uor.foundation/stream/Unfoldhttps://uor.foundation/state/ContextThe initial context for the stream.
unfoldStepObjecttruehttps://uor.foundation/stream/Unfoldhttps://uor.foundation/morphism/ComputationDatumThe certified step function producing each epoch.
unfoldResultObjecttruehttps://uor.foundation/stream/Unfoldhttps://uor.foundation/stream/ProductiveStreamThe stream produced by this unfold.
epochIndexDatatypetruehttps://uor.foundation/stream/Epochhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerZero-based index of this epoch in the stream.
prefixLengthDatatypetruehttps://uor.foundation/stream/StreamPrefixhttp://www.w3.org/2001/XMLSchema#positiveIntegerNumber of epochs in this prefix.
isProductiveDatatypetruehttps://uor.foundation/stream/ProductiveStreamhttp://www.w3.org/2001/XMLSchema#booleanAlways true by construction: every epoch terminates. Invariant, not computed.
stepTermObjecttruehttps://uor.foundation/stream/ProductiveStreamhttps://uor.foundation/schema/TermA term denoting a function from the current seed value to a pair (head, next_seed).
productivityWitnessDatatypetruehttps://uor.foundation/stream/ProductiveStreamhttp://www.w3.org/2001/XMLSchema#stringIRI of a proof of stream productivity (coinductive well-foundedness).