Add comprehensive slice notation tests

[ocots]

• Test slices in constraints: x[1:3](0), x[1:end](0), x[1:n](0)
• Test slices in dynamics: ∂(x[1:3])(t), ∂(x[1:end])(t), ∂(x[1:n])(t)
• Test slices in Mayer cost: x[1:3](tf), x[1:end](tf), x[1:n](tf)
• Mark broken tests for unsupported features (end keyword, variable n)
• Literal integer ranges work for parsing, some broken for discretisation

[ocots]

@jbcaillau

Comprehensive Slice Notation Tests

This PR adds extensive tests for slice notation (x[...]) in different contexts of optimal control problem definitions.

Test Coverage

The test suite covers 3 main contexts where slices can appear:

1. Constraints (initial conditions): x[...](0) == x0
2. Dynamics: ∂(x[...])(t) == ...
3. Mayer cost (terminal cost): x[...](tf)

For each context, we test 3 slice variants:

• Literal integer range: x[1:3] ✅ Most reliable
• end keyword: x[1:end] ❌ Parsing fails
• Variable: x[1:n] where n=3 ⚠️ Context-dependent

Current Status

✅ What Works (End-to-End)

Context	Slice Type	Status
Constraints	x[1:3](0)	✅ Parsing + Discretisation + Solve

⚠️ What Partially Works (Parsing OK, Discretisation Fails)

Context	Slice Type	Parsing	Discretisation
Dynamics	∂(x[1:3])(t)	✅	❌
Dynamics	∂(x[1:n])(t)	✅	❌
Mayer cost	x[1:3](tf)	✅	❌
Mayer cost	x[1:end](tf)	✅	❌
Mayer cost	x[1:n](tf)	✅	❌

❌ What's Broken (Parsing Fails)

Context	Slice Type	Error
Constraints	x[1:end](0)	MethodError: no method matching (::Colon)(::Int64, ::Symbol)
Constraints	x[1:n](0)	MethodError: no method matching (::Colon)(::Int64, ::Symbol)
Dynamics	∂(x[1:end])(t)	MethodError: no method matching (::Colon)(::Int64, ::Symbol)

Key Findings

1. Literal integer ranges (x[1:3]) work everywhere for parsing
2. end keyword fails during parsing in constraints and dynamics contexts
3. Variable slices (x[1:n]) work for parsing in dynamics and Mayer cost, but fail in constraints
4. Discretisation currently only works for constraints with literal ranges

Test Structure

Each context has:

• Model builders: Helper functions to create test problems
• Unit tests: Verify parsing and model construction
• Integration tests: Test discretisation and solver execution

All broken tests are marked with @test_broken to document known limitations without failing the test suite.

Next Steps

1. High Priority: Fix end keyword support in slice parsing (affects all contexts)
2. High Priority: Fix variable slice support (x[1:n]) in constraints
3. Medium Priority: Fix discretisation for sliced dynamics (∂(x[1:3])(t))
4. Medium Priority: Fix discretisation for sliced Mayer costs (x[...](tf))

[github-actions]

Breakage test results
Date: 2026-06-11 16:39:31

Name	Latest	Stable
OptimalControl	compat: v0.8.15	compat: v0.8.15

[jbcaillau]

@ocots agreed

• never thought about end, why not
• using 1:n is OK, should be evaluable at runtime
• the main issue seems to be the discrepancy between constraints and the rest
• top priority: correct that and add extensive tests as proposed

[jbcaillau]

@ocots NB. Also need to allow ẋ₁(t) (dotted notation for scalar components) for consistance. for slices, could be sth like ẋ[1:3](t), though the notation ∂(x[1:3])(t) seems more robust and versatile 👀

see also: #22 (comment)

PS. after a few years of usage, regarding the syntax, i find the instrumental parts are

• keeping scalars (instead of length one vectors), that is u(t) instead of u[1](t)
• using indices, that is u₂(t) instead of u[2](t)

[ocots]

@jbcaillau

Update (supersedes the earlier comment): the test file has been completely rebuilt as a systematic notation matrix. Current result: 111 passed, 42 broken, 0 errors (153 tests total). All broken cases use @test_broken so CI stays green.

---

Comprehensive Slice / Index Notation Test Matrix

The file test/test_slices.jl covers 11 sections × 3 assertion levels (build with the :fun backend → discretise_exa → solve with MadNLP). The :exa backend is activated at the top of the module so both backends are exercised simultaneously.

Notation forms tested

Form	Example	Description
scalar bracket	x[2](t)	integer index
scalar subscript	x₂(t)	Unicode subscript alias
scalar ASCII	x2(t)	ASCII alias
range from 1	x[1:3]	full literal range
offset range	x[2:3]	range not starting at 1
step range	x[1:2:3]	range with step
end range	x[1:end]	symbolic end
variable range	x[1:n]	outer-scope variable
dotted full	ẋ(t)	alias for ∂(x)(t)
dotted scalar	ẋ₁(t), ẋ1(t)	per-coordinate dotted
dotted slice	ẋ[1:3](t)	sliced dotted derivative

---

Summary table (✅ = @test passing · 🔧 = @test_broken · — = not tested)

Context	Scalar	[1:3]	[2:3] offset	[1:2:3] step	[1:end]	[1:n] var
IC x[…](0) == c
build	✅	✅	✅	✅	🔧	🔧
discretise	✅	✅	✅	✅	🔧	🔧
solve	✅	✅	✅	✅	🔧	🔧
FC x[…](tf) == c
build	✅	✅	✅	✅	🔧	🔧
discretise	✅	✅	✅	✅	🔧	🔧
solve	✅	✅	✅	✅	🔧	🔧
Path x[…](t) ≤ c
build	✅	✅	✅	✅	🔧	🔧
discretise	✅	✅	🔧	🔧	🔧	🔧
solve	✅	✅	🔧	🔧	🔧	🔧
Box -c ≤ x[…](t) ≤ c
build	—	🔧	—	—	—	—
Dynamics ∂(x[…])(t) == e
build	✅	✅	✅	—	🔧	✅
discretise	✅	🔧	🔧	—	🔧	🔧
solve	✅	🔧	—	—	—	🔧
Dotted ẋ(t) / ẋᵢ(t) / ẋ[1:3](t)
build (ẋ full)	✅	—	—	—	—	—
build (ẋᵢ / ẋi)	🔧	—	—	—	—	—
build (ẋ[1:3])	—	🔧	—	—	—	—
discretise / solve (ẋ)	✅	—	—	—	—	—
Lagrange ∫(f(x[…](t))) → min
build	✅	✅	✅	—	✅	✅
discretise	✅	🔧	🔧	—	🔧	🔧
solve	✅	🔧	—	—	—	—
Mayer x[…](tf) in cost
build	✅	✅	✅	—	✅	✅
discretise	✅	🔧	🔧	—	🔧	🔧
solve	✅	🔧	🔧	—	🔧	🔧
Control u[…](t)
build (path cstr)	✅	✅	✅	—	🔧	🔧
discretise	✅	✅	🔧	—	—	—
solve	✅	✅	🔧	—	—	—
Variable v[…] in cost
build (v[1]+v[2], sum(v[1:2].^2))	✅	✅	—	—	—	—
discretise ((v[1]+v[2])+∫(…))	✅	🔧	—	—	—	—

---

Key findings

• Offset/step ranges in boundary constraints (x[2:3](0), x[1:2:3](0), same for tf) work at all three levels — this was a pleasant surprise.
• Literal range x[1:3] in path constraints works end-to-end (build + discretise + solve); offset x[2:3] and step x[1:2:3] build but fail at the exa discretisation step.
• Range dynamics ∂(x[1:3])(t) builds with :fun but fails at :exa discretisation because p_dynamics_coord_exa! only accepts Integer coordinates (src/onepass.jl:985-989).
• ẋᵢ and ẋ[1:3] are not yet aliased in p_state! (TODO at src/onepass.jl:519) — both fail at build.
• x[1:end] and x[1:n] fail at build in constraint contexts (eager range evaluation hits (::Colon)(::Int64, ::Symbol)); they work in Lagrange/Mayer cost contexts where they appear inside sum(…).
• Bolza cost with variable brackets: (v[1] + v[2]) + ∫(u(t)²) → min works with explicit parentheses; the unparenthesised form v[1] + v[2] + ∫(…) is a parser ambiguity and fails.
• Notation equivalence: x[2](t), x₂(t), x2(t) produce identical dynamics (confirmed by evaluating at a sample point).
• Idiomatic forms u(t) (scalar control) and u₁(t), u₂(t) (index notation for vector control) work end-to-end as expected.