Cross-reference glossary for README.adoc, EXPLAINME.adoc, and the tropical-resource-typing wiki. Terms are classified as standard (existing concept used without modification), rephrased (standard concept with project-specific vocabulary), or project-specific (originating in this project).
- Tropical semiring (max-plus)
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The semiring
(ℝ ∪ {-∞}, ⊕ = max, ⊗ = +). Addition is maximum; multiplication is standard addition. Classification: standard (tropical geometry / idempotent mathematics). See also: [min-max-semiring]
- Min-max semiring (bottleneck)
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The semiring
(ℝ ∪ {+∞}, ⊕ = min, ⊗ = max). Addition is minimum; multiplication is maximum. Classification: standard. See also: [tropical-semiring], [hub-ceiling]
- Dioid
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An idempotent semiring (where
a ⊕ a = a) with a natural preorder induced bya ≤ b ↔ a ⊕ b = b. Classification: standard. Usage in this repo:ResourceAlgebrabundles aResourceSemiringwith the dioid order and monotonicity laws.
- Involution (g ↦ maxGrade − g)
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The order-reversing map connecting the max-plus and min-max semirings. Exchanges min and max (De Morgan duality). Proved as a lattice anti-isomorphism; explicitly not a semiring homomorphism. Classification: standard (lattice theory).
- Resource grade
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The tropical value attached to a type, representing a worst-case resource bound (latency, stack, heap, round-count). Classification: project-specific (vocabulary). Distinction: Resource grade ≠ resource algebra ≠ residue measure. See [foundation-contract].
- Resource algebra
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The algebraic structure
(carrier, ⊕, ⊗, ≤)satisfyingResourceSemiringandResourceAlgebralaws. The interface that downstream languages instantiate. Classification: rephrased. Dioids / idempotent semirings are standard; the specific packaging asResourceAlgebrawith parametric transport is project-specific.
- Speculative session type
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A session type graded by a tropical resource grade, representing the worst-case cost of the interaction. Classification: project-specific (application of tropical algebra to session types).
- Adapter path
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A path between protocol participants graded by the min-max semiring, representing the bottleneck cost of adaptation. Classification: project-specific (application of min-max algebra to adapter paths).
- hub_ceiling
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The no-go corollary closing Protocol Squisher’s universal-interoperability claim. Proves there is an upper bound (ceiling) on the interoperability achievable through a single universal adapter hub. Classification: project-specific (novel theorem).
- parametric_resource_transport
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The parametric transport theorem: satisfying
ConsumerLawBundleis sufficient to transport resource laws from the abstractResourceAlgebrato a concrete consumer. Classification: project-specific (mechanisation).
- tropical_grade_le_sequentialTotal
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The QTT refinement:
max ≤ sum. The tropical (max-plus) grade is always at most the sequential total, making it a sound worst-case approximation. Classification: project-specific (mechanisation within this application).
- Resource.Stress
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The proof that tropical carriers (
MaxPlus,MinPlus) are infinite, distinguishing them from finite{0, 1, ω}reifications. Classification: project-specific (separation proof).
- EchoBridge
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The formalisation that a resource algebra may measure Echo residues (direction E → R), but Echo is not a resource instance. No echo-types dependency. Classification: project-specific (separation proof matching echo-types).
- Foundation contract
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The stable API surface (
Resource.namespace +FOUNDATION_CONTRACT.md) for downstream languages. Establishes vocabulary: resource grade ≠ resource algebra ≠ tropical instance ≠ residue measure; "tropical is not Echo". *Classification: project-specific.