Elamur Groupantsmath-calc-evaluation-ranged-binding
The groupant beside math/src/calc.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 | Forward |
| ast | partial | ../../syntax.json |
| cost | partial | Cost |
| descriptant | present | Epoch |
| invariant | partial | Invariant |
| tests | bounded actual helper 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 |
tick_insert_order | tick_insert_order | partial source derived model | tick_insert_order |
early_witness | early_witness | partial source derived model | early_witness |
empty_identities | empty_identities | partial source derived model | empty_identities |
restoration_cut | restoration_cut | partial source derived model | restoration_cut |
Model text
Scope
Source-derived bounded relation for the manifest byte interval. All relations observe one invocation and its stated state effects. Valid caller structures and finite values where specified are premises. No universal proof, percentage-error surrogate or production replacement is claimed.
Forward
Validate arity and variable, evaluate lo then hi, check span, save the current binding. Each inclusive iteration ticks, binds k, evaluates body, updates the selected accumulator or early-exits. Normal loop exit restores saved binding before result extraction and capped note. Any ? before restoration retains reached prefix state.
Invariant
Early forall/exists/first break restores binding. A body failure after insert retains current k; tick failure before insert retains previous k. Empty sum/prod return0/1; empty first/extrema error after restoration.
Cost
Sum of reached body and accumulator work over at most max(0,hi-lo+1) iterations, plus endpoint evaluation; list/filter retain O(iterations) values. Arbitrary precision body costs and deadlines are not bounded by tick count.
behavior_complement
Normal successful first excludes leaving the witness bound to k. Body-error transitions exclude guaranteed rollback to the saved k. Empty ranges exclude body evaluation.
reverse_reconstruction
A sum of0 admits an empty range or cancellation across nonempty iterations. An error with k=1 admits every prior k binding overwritten at that iteration. Returned first witness fixes only the earliest true predicate index within the admitted range, not predicate syntax.
tick_insert_order
At each step tick runs before env.vars.insert. Resource failure on the next iteration and body failure in that iteration produce different visible bindings.
early_witness
first/exists stop at the smallest visited true index; forall records the smallest false counterexample. Later body effects are absent. Restored binding and capped trace record follow the break.
empty_identities
For lo>hi: sum0,prod1,count0,list/filter[],forall true,exists false; first/maxof/minof error. Endpoint evaluation effects still occur.
restoration_cut
Restoration is after the loop but before first/extrema empty-result error. Errors from body/boolean conversion/arithmetic bypass it. No transaction is promised for vars,steps,approx or earlier notes.
Tests
Actual helper fixture: calc::wave34::syntax_zero_and_binding_boundaries. See file-root wave34-evidence.md for named profile/control receipts. Complement relations above are exclusions, not merely test lists; inverse relations retain compatible antecedents. Unexecuted paths remain source-derived.
Epoch
2026-10-31 wave34: new descendant refining the existing parent; prior parent descriptions and evidence retained as historical snapshots. Production code is unchanged; inline synthetic tests add bounded observations.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/calc.rs.groupant/evaluation.groupant/ranged-binding.groupant/