Elamur Groupantsmath-deduct-gold
The groupant beside math/src/deduct.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | executed bounded checks | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
memo_key_asymmetry | memo_key_asymmetry | partial source derived model | memo_key_asymmetry |
postfix_index_guard | postfix_index_guard | partial source derived model | postfix_index_guard |
Model text
descriptant
math-deduct-gold
Postfix traversal memoizes ordered subtree keys, recursively obtains child ids, rejects child ids>255, normalizes +/* operand index order, emits a node and memoizes its new id. It returns None for0 or>8 operations; otherwise appends Stop.
Epoch 2026-10-31: replaced duplicate catalog sentences with concrete exclusions, compatible-antecedent examples and two distinct scoped behavioral views. Source and prior execution evidence are unchanged; this revision ran no tests.
approximant
Scoped forward relation
Postfix traversal memoizes ordered subtree keys, recursively obtains child ids, rejects child ids>255, normalizes +/* operand index order, emits a node and memoizes its new id. It returns None for0 or>8 operations; otherwise appends Stop.
This source-derived relation is partial; no executable percentage surrogate or replacement is supplied.
invariant
Scoped domain and invariants
Accepted gold has1..8 arithmetic nodes plus final Stop. Caller must separately establish source leaf range and search candidate reachability.
Cost
Recursive key generation can revisit descendants at multiple ancestors; memo lookup and retained strings add work beyond one constant-time visit per tree node.
models
behavior_complement
A returned sequence cannot have more than8 Comb steps or an encoded child index>255. It can contain equal child ids and leaf ids>=n, so general validity/reachability cannot be inferred from success.
reverse_reconstruction
Two occurrences of the identical (leaf0+leaf1) subtree collapse to one pool node. Swapping the children changes the memo key even though tkey canonicalizes the commutative tree; some equivalent arithmetic trees therefore have different memoization histories.
memo_key_asymmetry
gold_steps' internal key preserves left/right order; tkey sorts Add/Mul child strings. Equality of tkey is weaker than equality of gold memo key.
postfix_index_guard
A newly assigned node id may itself exceed255; rejection happens if a later parent attempts to use it. The checks constrain consumed operands, not all allocated pool ids.
tests
Scoped evidence
Commutative tkey, reused identical subtree, leaf-only and operand256 rejection.
Named actual source fixtures: deduct::wave28::{dag_gold_reuses_subtrees_and_canonicalizes}.
Parent tests.md records commands and paired profiles. No additional coverage inferred from parent fixtures outside this byte range; source-scoped numeric/parse properties remain partial.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/deduct.rs.groupant/gold.groupant/