UOR Derivations

IRI
https://uor.foundation/derivation/
Prefix
derivation:
Space
bridge
Comment
Computation witnesses recording term rewriting sequences from original terms to their canonical forms.

This is a bridge-space namespace in the Resolve stage of the PRISM pipeline. It provides the resolution infrastructure — queries, partitions, observables, proofs, derivations, and traces that transform inputs into certified results.

Learn more: Pipeline Overview · Proofs, Derivations & Traces

Class hierarchy
Class hierarchy for UOR Derivations namespace Derivation DerivationStep RewriteStep RefinementStep RewriteRule TermMetrics SynthesisStep SynthesisCheck

Imports

Classes

NameSubclass OfDisjoint WithComment
DerivationThingA complete term rewriting witness: the full sequence of rewrite steps transforming an original term into its canonical form.
DerivationStepThingAn abstract step in a derivation. Concrete subclasses are RewriteStep (term-level rewriting) and RefinementStep (type-level refinement).
RewriteStepDerivationStepA single rewrite step in a derivation: the application of one rewrite rule to transform a term.
RefinementStepDerivationStepA type-level refinement step: the application of a constraint to narrow a type, pinning additional site coordinates. Complements RewriteStep (term-level) in the derivation hierarchy.
RewriteRuleThingA named rewrite rule that can be applied in a derivation step. Each RewriteRule individual represents a specific algebraic law or normalization strategy used during term rewriting.
TermMetricsThingMetrics describing the size and complexity of a term.
SynthesisStepThingA single step in the construction of a SynthesizedType: one constraint added to the synthesis candidate and the resulting change in the constraint nerve's topological signature. Ordered by derivation:stepIndex. Analogous to derivation:RewriteStep in the forward pipeline.
SynthesisCheckpointThingA persistent snapshot of a ConstraintSearchState at a specific SynthesisStep, allowing a TypeSynthesisResolver to resume exploration after interruption. Essential at Q1+ scale where exhaustive synthesis is computationally significant.

Properties

NameKindFunctionalDomainRangeComment
originalTermObjecttrueDerivationTermThe term at the start of the derivation, before any rewriting.
canonicalTermObjecttrueDerivationTermThe canonical form produced at the end of the derivation.
resultObjecttrueDerivationDatumThe datum value obtained by evaluating the canonical term.
stepObjectfalseDerivationRewriteStepA rewrite step in this derivation.
termMetricsObjecttrueDerivationTermMetricsMetrics for the canonical term produced by this derivation.
fromObjecttrueRewriteStepTermThe term before this rewrite step.
toObjecttrueRewriteStepTermThe term after this rewrite step.
hasRewriteRuleObjecttrueRewriteStepRewriteRuleThe typed rewrite rule applied in this step. Provides a structured reference to a named RewriteRule individual, complementing the string-valued derivation:rule property.
groundedInObjecttrueRewriteRuleIdentityThe algebraic identity that grounds this rewrite rule. Links a RewriteRule to the op:Identity individual that justifies its application.
stepCountDatatypetrueTermMetricsnonNegativeIntegerThe total number of rewrite steps in this derivation.
termSizeDatatypetrueTermMetricsnonNegativeIntegerThe number of nodes in the canonical term's syntax tree.
previousTypeObjecttrueRefinementStepTypeDefinitionThe type before this refinement step was applied.
appliedConstraintObjecttrueRefinementStepConstraintThe constraint that was applied in this refinement step.
refinedTypeObjecttrueRefinementStepTypeDefinitionThe type after this refinement step was applied.
sitesClosedDatatypetrueRefinementStepnonNegativeIntegerThe number of site coordinates pinned by this refinement step.
stepIndexDatatypetrueSynthesisStepnonNegativeIntegerZero-based sequential index of this step within the synthesis derivation.
addedConstraintObjecttrueSynthesisStepConstraintThe constraint added in this synthesis step.
signatureBeforeObjecttrueSynthesisStepSynthesisSignatureThe constraint nerve signature before this synthesis step.
signatureAfterObjecttrueSynthesisStepSynthesisSignatureThe constraint nerve signature after this synthesis step.
checkpointStepObjecttrueSynthesisCheckpointSynthesisStepThe SynthesisStep at which this checkpoint was taken.
checkpointStateObjecttrueSynthesisCheckpointConstraintSearchStateThe ConstraintSearchState snapshot captured by this checkpoint.
towerCheckpointObjectfalseTowerCompletenessResolverSynthesisCheckpointLinks a TowerCompletenessResolver to a SynthesisCheckpoint issued at each completed step. Cross-namespace bridge property: domain is resolver:TowerCompletenessResolver.

Named Individuals

NameTypeComment
CriticalIdentityRuleRewriteRuleThe rewrite rule applying the critical identity: neg(bnot(x)) → succ(x). Grounded in op:criticalIdentity.
  • groundedIn: criticalIdentity
InvolutionRuleRewriteRuleThe rewrite rule applying involution cancellation: f(f(x)) → x for any involution f.
AssociativityRuleRewriteRuleThe rewrite rule applying associativity to re-bracket nested binary operations.
CommutativityRuleRewriteRuleThe rewrite rule applying commutativity to reorder operands of commutative operations.
IdentityElementRuleRewriteRuleThe rewrite rule eliminating identity elements: add(x, 0) → x, mul(x, 1) → x, xor(x, 0) → x.
NormalizationRuleRewriteRuleThe rewrite rule normalizing compound expressions to canonical ordering (e.g., sorting operands by address).