📐mlab-ops

The groupant beside mlab/src/ops.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

Components

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.

Parts

• mlab-ops-broadcast
• mlab-ops-finite-range

Model text

descriptant

Broadcast, matrix arithmetic and finite ranges

map2 uses equal-shape zip, then scalar fast paths, else singleton-dimension broadcast with k=(cols==1?0:j)rows+(rows==1?0:i). matmul delegates scalars to EMul, checks inner dimensions, uses small loops or faer at mnk>=32768; complex large products combine four real products. range_spec computes n=floor((b-a)/s+3epsmax(abs(span),1))+1 with endpoint snapping and evaluates from nearer end. Concatenation discards empty pieces for shape matching, but includes classes in result class choice.

Modeling epoch 2026-10-31

Prospective source reading precedes test additions. Retained observations: parser distinguishes matrix and elementwise operators; interp owns short-circuit &&/|| rather than this binary entrypoint. value storage and index output shape determine broadcast. linalg owns solves/inverse; core colon delegates range while reshape preserves storage rather than transpose.

This is partial source-derived modeling, not proof, full semantic coverage, or a performance result. Public malformed representations, unbounded allocations and exhaustive numerical edge cases remain outside the checked fixtures.

approximant

Broadcast, matrix arithmetic and finite ranges forward relation

map2 uses equal-shape zip, then scalar fast paths, else singleton-dimension broadcast with k=(cols==1?0:j)rows+(rows==1?0:i). matmul delegates scalars to EMul, checks inner dimensions, uses small loops or faer at mnk>=32768; complex large products combine four real products. range_spec computes n=floor((b-a)/s+3epsmax(abs(span),1))+1 with endpoint snapping and evaluates from nearer end. Concatenation discards empty pieces for shape matching, but includes classes in result class choice.

Domain: Well-formed bounded Mat; finite modest range spans fitting usize count and memory; f64 overflow/NaN otherwise follows individual branch, no uniform numerical bound. Linalg callbacks can warn through Interp; no GPU required.

No executable Rust surrogate is supplied: categorical decisions require exact observations; numerical kernels have no measured approximation metric here. Future supported caps are 1%, 2%, 5%, 10% only.

invariant

Invariant and cost

Arithmetic outputs double, comparisons/logical outputs logical; complex constructors narrow all-zero imaginary parts. truthy is nonempty and all complex elements nonzero. RangeSpec::at only modeled for k<n; dimension products/count conversion are unchecked. Scalar zero powers use cpow integer branch before zero-base fallback.

Cost: Broadcast O(output cells), small matmul O(mnk), matrix power O(log |p|) products plus inverse for negative p; large products delegate faer. Materialized range O(n), lazy at O(1). Concat allocates/clones linear total cells. No measured speed claim.

Failure ordering: binary handles strings before matrix extraction; left mat extraction before right; scalar division before shape/linalg. mpower scalar/scalar before square integer path. map2 equal shape/scalars before bshape rows then cols; range checks invalid direction/NaN/zero before count arithmetic.

composition

Parent composition

parser distinguishes matrix and elementwise operators; interp owns short-circuit &&/|| rather than this binary entrypoint. value storage and index output shape determine broadcast. linalg owns solves/inverse; core colon delegates range while reshape preserves storage rather than transpose.

Scoped fragments are projections over exact byte intervals in this source; they share one parent syntax projection. Uncovered declarations and embedded checks remain parent modeled. binary handles strings before matrix extraction; left mat extraction before right; scalar division before shape/linalg. mpower scalar/scalar before square integer path. map2 equal shape/scalars before bshape rows then cols; range checks invalid direction/NaN/zero before count arithmetic.

The relation is source-derived and finite checks cannot establish complete correctness or a composition-wide numerical error bound.

models

behavior_complement

Bounded broadcast excludes incompatible nonsingleton dimensions and incorrect column-major ordering. Wrong-direction/zero-step/NaN ranges exclude elements. Small real matmul skips zero RHS coefficients, therefore does not guarantee dense IEEE NaN*0 propagation. Comparisons < <= > >= ignore imaginary parts; no mathematical complex order is claimed.

reverse_reconstruction

Broadcast result preimage includes all operand shapes allowed by singleton expansion and values satisfying per-cell operator relation; addition admits many decompositions. Matmul preimages are factorization relations, nonunique with nullspaces. Range vectors constrain start/step/endpoint up to floating rounding and snapping; empty ranges have many causes.

representation_transport

Arithmetic outputs double, comparisons/logical outputs logical; complex constructors narrow all-zero imaginary parts. truthy is nonempty and all complex elements nonzero. RangeSpec::at only modeled for k<n; dimension products/count conversion are unchecked. Scalar zero powers use cpow integer branch before zero-base fallback.

failure_precedence

binary handles strings before matrix extraction; left mat extraction before right; scalar division before shape/linalg. mpower scalar/scalar before square integer path. map2 equal shape/scalars before bshape rows then cols; range checks invalid direction/NaN/zero before count arithmetic.

resource_domain

Well-formed bounded Mat; finite modest range spans fitting usize count and memory; f64 overflow/NaN otherwise follows individual branch, no uniform numerical bound. Linalg callbacks can warn through Interp; no GPU required.

interaction_relation

parser distinguishes matrix and elementwise operators; interp owns short-circuit &&/|| rather than this binary entrypoint. value storage and index output shape determine broadcast. linalg owns solves/inverse; core colon delegates range while reshape preserves storage rather than transpose.

tests

Source-specific bounded evidence

ops::wave30::arithmetic: column-major broadcast, empty truth, small complex product, finite ranges, concat shape error, zero-skipping NaN behavior.

Seven named tests each passed twice debug and twice release on 2026-10-31, with actual named log lines sorted and identical across all four runs (28 selected successful executions). Each source has a compiled changed-assertion negative control; six runtime sources additionally have compiled production-body mutants that fail those unchanged tests. AST has representation evidence only. Every mutant is byte-restored and its positive test rerun. See evidence.json for this source's exact hash, mutation and exit statuses. External receipts retain full logs, command metadata, control records and prospective notes.

Unexecuted here: No large faer, solve/power, strings, nonfinite range resource execution. No corpus, GPU, live filesystem, timer or callback run. No broad Clippy claim; dependency/style checks were not repeated. Only appended test blocks were rustfmt-formatted; original production bytes are unchanged.

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