Claude Code transcript

Now I see the patterns. Variables use uppercase (like R, N, S), relations use false not False, and function init just assigns directly. Also, relation with Bool uses false/true (lowercase). Let me also check if default works for values.

Let me look at how Inhabited or defaults work for function types, and simplify the spec.

The safety property is too strict — the initial counter value may not be in everSet. Let me rethink. The counters start at some default value, but everSet starts all false. I need to track the initial value too, or use a different property.

Let me simplify and focus on the core max-convergence properties with a cleaner design. I'll track which values have been "introduced" into the system (either initial or via client set).

I see — after_init supports * (nondeterministic), pick, if/then/else, but probably not ∃. The issue is that introduced V := (∃ S, counter S = V) uses an existential. Since counter is also being initialized nondeterministically (no explicit init means it's arbitrary), I can't reference it.

Let me simplify: just set introduced V := true for all values initially (overapproximation), or better yet, not track the initial values and instead just make all counters start at the same fixed value.

All checks pass. The specification:

1. Model check explores 64 states with 3 servers and 4 values — no safety violations found
2. First sat trace confirms values can propagate between servers via sync (two different servers end up with the same non-zero value)
3. Second sat trace confirms a server can hold a non-zero value

Here's a summary of the specification at Examples/apanda/MaxCounter.lean:

State: - counter : server → value — each server's current counter - maxEverSet : value — tracks the maximum value any client has ever set

Actions: - clientSet(s, v) — sets server s's counter to v if v is strictly greater than the current value; updates the global max tracker - serverSync(src, dst) — if src's counter is greater than dst's, copies src's value to dst (models pairwise gossip)

Safety properties verified: - bounded_by_max — no server's counter ever exceeds the max value ever set by a client - counters_nonneg — all counters stay non-negative (monotonically increasing from zero)

Supporting invariants: bounded_inv, nonneg_inv, and max_nonneg for inductive verification.

The clientGet action was removed since it's a pure read with no state change — Veil models state transitions, so a no-op read doesn't add verification value. The convergence property (all servers eventually agree) is a liveness property which Veil's current safety-focused verification doesn't directly express, but the sat traces demonstrate the synchronization mechanism works correctly.

Created .claude/skills/veil.md. It covers:

• Module structure — the required ordering of declarations
• Type system — abstract types, enums, structures, type class instantiation
• State components — relations, functions, individuals (mutable and immutable)
• Ghost relations — derived predicates for specification
• Initialization — after_init syntax and limitations
• Actions/procedures — require, let bindings, nondeterministic choice, state updates
• Properties — safety, invariant, assumption
• Verification — #model_check, sat/unsat traces, #check_invariants
• Build commands and conventions
• Common patterns — global max tracking, gossip sync, monotonic state, message passing