[Lean Squad] feat(fv): Task 2 + Task 9 — CommandLineOptionsValidator informal spec & CI simplification

[Evangelink]

Task 2: add informal spec for CommandLineOptionsValidator.ValidateOptionsArgumentArity

• Detailed preconditions, postconditions, algorithm, invariants
• 7 proposed Lean theorems (valid_iff_all_in_range, independent errors, etc.)
• 4 open questions including the KeyNotFoundException design issue (OQ-1)
• Approximations documented for Lean modelling (MaxInt as ⊤, provider elision)
• Advance target Bug Fix #258333 : Tests running multiple times in case we have multiple test projects #4 to phase 2 in TARGETS.md

Task 9: remove Mathlib from lakefile.toml (no .lean files use it yet)

• Eliminates heavy network fetch of Mathlib in CI
• Remove the lake update step from lean-proofs.yml (no external deps)
• Will be re-added when first .lean file imports Mathlib

Co-authored-by: Copilot 223556219+Copilot@users.noreply.github.com

Fixes #7964

[Copilot]

Pull request overview

This PR advances the Lean Squad formal-verification effort by adding an informal specification for CommandLineOptionsValidator.ValidateOptionsArgumentArity, updating FV target tracking to reflect Phase 2 progress, and simplifying Lean CI/dependencies by removing the unused Mathlib requirement.

Changes:

• Added a new informal spec markdown document for ValidateOptionsArgumentArity, including proposed theorems and design questions.
• Updated formal-verification/TARGETS.md to reflect Phase 2 (“Informal spec extracted”) for the arity validator and parse-result equality targets.
• Removed Mathlib from the Lean lakefile.toml and dropped the lake update CI step to avoid unnecessary dependency resolution.

Show a summary per file

File	Description
formal-verification/TARGETS.md	Updates FV target phases/status to reflect informal spec extraction progress.
formal-verification/specs/commandlineoptionsvalidator_arity_informal.md	Adds the informal spec for ValidateOptionsArgumentArity (pre/postconditions, algorithm, invariants, theorems, open questions).
formal-verification/lean/lakefile.toml	Removes unused Mathlib dependency and documents when to re-add it.
.github/workflows/lean-proofs.yml	Simplifies Lean CI by removing the dependency-resolution step (lake update).

Copilot's findings

• Files reviewed: 4/4 changed files
• Comments generated: 2

[Evangelink]

Summary

Workflow: Expert Code Reviewer 🧠
Date: 2026-05-11
Repository: microsoft/testfx

Review Scope

4 files changed: .github/workflows/lean-proofs.yml (CI simplification), formal-verification/TARGETS.md (status updates), formal-verification/lean/lakefile.toml (Mathlib removal), formal-verification/specs/commandlineoptionsvalidator_arity_informal.md (new informal spec).

Verification Against Source

I cross-referenced the informal spec against the actual CommandLineOptionsValidator.ValidateOptionsArgumentArity implementation (CommandLineOptionsValidator.cs):

• Algorithm: The spec's pseudocode correctly represents arity > option.Arity.Max && option.Arity.Max == 0 as T > 0 AND Max == 0 — logically equivalent ✓
• Argument accumulation: Correctly describes the GroupBy+sum-over-Arguments.Length pattern ✓
• Error branches and message keys: Accurate ✓
• OQ-1 (KeyNotFoundException): The identified risk is real — the direct indexer providerAndOptionByOptionName[optionName] is used without TryGetValue, relying on ValidateNoUnknownOptions running first. Correctly flagged as an open question ✓
• OQ-3 (missing required options not flagged here): Accurate — GroupBy only groups options that appeared; absent options are handled downstream ✓

TARGETS.md consistency

Target #5 (CommandLineParseResult.Equals) advancing to phase 2 is consistent with the existing commandlineparseresult_equals_informal.md file already on main — no inconsistency.

CI change

Removing lake update is safe: (a) with no [[require]] blocks in lakefile.toml, the step would be a no-op, and (b) while there are zero .lean files, lean_count == 0 skips both lake update and lake build anyway.

Key Findings

No correctness, threading, performance, API compatibility, cross-TFM, resource management, security, or defensive coding issues found.

Positive Observations

• The informal spec document is thorough and accurate, covering preconditions, postconditions, invariants, edge cases, approximations for Lean modelling, and proposed theorems
• The CI simplification is well-justified and reversible
• Open questions are honestly documented, including the real KeyNotFoundException design risk in the underlying code

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🧠 Reviewed by Expert Code Reviewer 🧠

[Evangelink]

Summary

Workflow: PR Nitpick Reviewer 🔍
Date: 2026-05-11
Repository: microsoft/testfx

Key Findings

Three minor documentation nitpicks found across the two changed docs:

1. TARGETS.md — inconsistent "Next:" status tag (item 6): Missing "(blocked by Lean toolchain)" qualifier that every other item consistently carries. Either an accidental omission or needs a clarifying note if intentional.

2. Spec file — misleading pseudocode notation (Arguments["--filter A"].Length): The dict-index syntax implies a map keyed by raw command text; the actual model is a list of CommandLineParseOption occurrences, each with an .Arguments property. This matters most for a Lean modeller who needs the correct data-structure shape.

3. Spec file — "Not possible" edge-case description: The scenario is possible for users; the correct statement is that the function doesn't reach it due to GroupBy's contract.

Positive Highlights

• Removing lake update from CI in tandem with dropping the mathlib dependency is a clean, well-motivated change — the comment in lakefile.toml explains the rationale clearly.
• The informal spec is comprehensive and well-structured: preconditions, postconditions, algorithm, invariants, edge cases, examples, open questions, and proposed Lean theorems are all present. The "Why Max == 0 is a special case" sub-section is especially useful for a formal verifier.
• The PR title makes the scope clear; the TARGETS.md update correctly advances both items to phase 2.

Recommendations

• Clarify the "Next: Task 3." entry for item 6 in TARGETS.md.
• Replace the Arguments["..."].Length notation with occurrence-indexed notation.
• Replace "Not possible" with "Not reached by this function" in the Edge Cases table.

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