Derivation Loop

The derivation loop

Every algorithm grammar is an instance of the derivation loop, which has ten stages, each on one reasoning axis, joined by transitions that sequence, gate or refute back. Each stage is listed with the contracts that run at it and the records it grounds, and the traversal is taught in the loop on the methodology page.

How it is checked

Checked by

the reasoning-native check, which requires every process grammar's kernel to map the loop's stages and every staged record to name a real stage and that stage's axis

Population

Every process grammar, its kernel and its staged records

Freshness

A verdict stands until the loop, a grammar or a staged record changes

Refusal

The gate fails on an unknown stage, a stage whose axis does not match, or a kernel that omits the verify stage

Observation

None, because the loop is a procedure the grammars instantiate, and nothing observes it while a run executes

Evidence

Watched to fire and to accept: a suite plants an unknown stage, a mismatched axis and a kernel that omits the verify stage, and passes a fully typed staged record

Authoritative side

The loop's stage list, which every kernel and staged record cites

Depends on

Not answered

Shape it refuses

Not answered

flowchart TB
    n_orient["orient · ontology"]
    n_intent["intent · teleology"]
    n_see["see · analysis"]
    n_derive["derive · reasoning"]
    n_project["project · reasoning"]
    n_act["act · formalization"]
    n_constrain["constrain · teleology"]
    n_verify["verify · verification"]
    n_commit["commit · representation"]
    n_terminate["terminate · termination"]
    n_orient --> n_intent
    n_intent -- tel-priority --> n_see
    n_see --> n_derive
    n_derive --> n_project
    n_project --> n_act
    n_act --> n_constrain
    n_constrain --> n_verify
    n_verify -.-> n_derive
    n_verify --> n_commit
    n_commit --> n_terminate
    n_terminate --> n_orient