Replace AbstractArray lazy types with LinearBroadcasted and Mul

[mtfishman]

Summary

Replace the old AbstractArray lazy types and macro system with a cleaner, non-AbstractArray design that avoids method ambiguities with ArrayLayouts/BlockArrays.

What changed

• Replace ScaledArray, ConjArray, AddArray, MulArray (<: AbstractArray) with LinearBroadcasted subtypes (ScaledBroadcasted, ConjBroadcasted, AddBroadcasted) and standalone Mul — none subtype AbstractArray
• Replace Unicode operators (*ₗ, +ₗ, etc.) and macro system with linearbroadcasted(f, args...) constructor that dispatches on f to create the appropriate subtype
• Delete LinearBroadcastedStyle and all BC.broadcasted overloads — broadcast integration moves to instantiation-time conversion via tryflattenlinear(bc::Broadcasted), which downstream styles call from Base.copy
• All LinearBroadcasted materialization funnels through permutedimsopadd!(dest, op, src, perm, α, β) as the single overload point for downstream types
• Op composition with simplification rules (conj ∘ conj = identity, etc.) modeled on StridedViews
• Delete entire macro system and old lazy array types (~600 lines removed, net -564 lines)
• Breaking: bump to v0.8.0

Broadcast integration design

Three functions for downstream opt-in:

• islinearbroadcast(f, args...) — per-node trait
• linearbroadcasted(f, args...) — constructor with algebraic simplifications
• tryflattenlinear(bc::Broadcasted) — recursive conversion, returns nothing on failure

Downstream styles choose strict (error on nonlinear) or opportunistic (fall back to standard broadcasting).

Materialization chain

copy(lb) → copyto!(similar(lb), lb) → add!(dest, lb, true, false) → permutedimsopadd!(dest, identity, src, perm, α, β)
copy(m::Mul) → copyto!(similar(m), m) → mul!(dest, factors...)

permutedimsopadd! dispatches on LinearBroadcasted subtypes to unwrap scaling, conjugation, and addition before hitting the base case.

Remaining work

• Downstream companion PRs: NamedDimsArrays, GradedArrays (delete per-package lazy types, opt in via tryflattenlinear)
• OpBroadcasted{F} for general element-wise ops (e.g. Float64.(a))
• Multiplicative-side op primitives (contractopadd!)
• TensorOperations extension update for permutedimsopadd! with op
• Styles in LinearBroadcasted/Mul types (deferred)
• PermutedDimsArray unwrapping in permutedimsopadd! (TBD — may not be needed)

Test plan

• CI passes
• Downstream package compatibility (GradedArrays, NamedDimsArrays)

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[codecov]

Codecov Report

❌ Patch coverage is 72.61905% with 46 lines in your changes missing coverage. Please review.
✅ Project coverage is 80.32%. Comparing base (9a88120) to head (6d7ab0c).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/linearbroadcasted.jl	69.73%	46 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #156      +/-   ##
==========================================
+ Coverage   72.57%   80.32%   +7.74%     
==========================================
  Files          24       24              
  Lines        1258      935     -323     
==========================================
- Hits          913      751     -162     
+ Misses        345      184     -161     

Flag	Coverage Δ
docs	0.00% <0.00%> (ø)

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