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109 changes: 109 additions & 0 deletions GLOSSARY.adoc
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// SPDX-License-Identifier: CC-BY-SA-4.0
= Tropical Resource Typing β€” Glossary
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Cross-reference glossary for link:README.adoc[README.adoc], link:EXPLAINME.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).

== Algebraic structures

[[tropical-semiring]]
Tropical semiring (max-plus)::
The semiring `(ℝ βˆͺ {-∞}, βŠ• = max, βŠ— = +)`. Addition is maximum; multiplication is standard addition.
*Classification:* **standard** (tropical geometry / idempotent mathematics).
*See also:* <<min-max-semiring>>

[[min-max-semiring]]
Min-max semiring (bottleneck)::
The semiring `(ℝ βˆͺ {+∞}, βŠ• = min, βŠ— = max)`. Addition is minimum; multiplication is maximum.
*Classification:* **standard**.
*See also:* <<tropical-semiring>>, <<hub-ceiling>>

[[dioid]]
Dioid::
An idempotent semiring (where `a βŠ• a = a`) with a natural preorder induced by `a ≀ b ↔ a βŠ• b = b`.
*Classification:* **standard**.
*Usage in this repo:* `ResourceAlgebra` bundles a `ResourceSemiring` with the dioid order and monotonicity laws.

[[involution]]
Involution (g ↦ maxGrade βˆ’ g)::
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).

== Typing and resources

[[resource-grade]]
Resource grade::
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 β‰  resource algebra β‰  residue measure. See <<foundation-contract>>.

[[resource-algebra]]
Resource algebra::
The algebraic structure `(carrier, βŠ•, βŠ—, ≀)` satisfying `ResourceSemiring` and `ResourceAlgebra` laws. The interface that downstream languages instantiate.
*Classification:* **rephrased**. Dioids / idempotent semirings are standard; the specific packaging as `ResourceAlgebra` with parametric transport is project-specific.

[[speculative-session-type]]
Speculative session type::
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]]
Adapter path::
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).

== Theorems and boundaries

[[hub-ceiling]]
hub_ceiling::
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-transport]]
parametric_resource_transport::
The parametric transport theorem: satisfying `ConsumerLawBundle` is sufficient to transport resource laws from the abstract `ResourceAlgebra` to a concrete consumer.
*Classification:* **project-specific** (mechanisation).

[[qtt-refinement]]
tropical_grade_le_sequentialTotal::
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]]
Resource.Stress::
The proof that tropical carriers (`MaxPlus`, `MinPlus`) are infinite, distinguishing them from finite `{0, 1, Ο‰}` reifications.
*Classification:* **project-specific** (separation proof).

== Bridge concepts

[[echo-bridge]]
EchoBridge::
The formalisation that a resource algebra may measure Echo residues (direction E β†’ R), but Echo is *not* a resource instance. No echo-types dependency.
*Classification:* **project-specific** (separation proof matching echo-types).

[[foundation-contract]]
Foundation contract::
The stable API surface (`Resource.*` namespace + `FOUNDATION_CONTRACT.md`) for downstream languages. Establishes vocabulary: resource grade β‰  resource algebra β‰  tropical instance β‰  residue measure; "tropical is not Echo".
*Classification:* **project-specific**.

== Pronunciation guide

[cols="1,2", options="header"]
|===
| Written | Spoken

| `βŠ•`
| "tropical plus" or "max"

| `βŠ—`
| "tropical times" or "plus"

| `hub_ceiling`
| "hub ceiling"

| `{0,1,Ο‰}`
| "zero-one-omega"
|===
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