certora

Declare contract functions in a methods block, capture state before a call, execute the function with an env argument, then assert the postcondition. Use mathint for spec arithmetic and @withrevert with lastReverted to test revert conditions.

Certora proves properties exhaustively for all inputs using SMT solving, while Foundry fuzzing samples random inputs and Slither does fast static pattern checks. Use Slither first for quick scans, fuzz tests for edge cases, and Certora for critical invariants needing mathematical certainty.

A vacuous pass means contradictory or over-constrained require statements exclude all valid executions, so the assert is never reached. Enable rule_sanity basic or advanced, then relax require statements one at a time and add a satisfy true reachability check.

Yes, the Prover runs on Certora's cloud infrastructure and requires a CERTORAKEY environment variable. Academic and open-source projects get free access, while commercial usage is priced per verification minute.

Increase smt_timeout in the config, split complex rules into smaller ones, bound large values with require, and enable optimistic_loop with a loop_iter of 3-5. Running a single rule with --rule also reduces memory pressure.

Ghosts are spec-side variables tracking derived state the contract does not expose, like the sum of all balances. Hooks update ghosts when storage changes — an Sstore hook on the balances mapping keeps sumOfBalances synchronized for the total supply invariant.