When to use Symbolic Execution

In the cryptocurrency world, it is exceedingly easy to lose a lot of assets due to bugs. While fuzz testing can help find potential issues with digital contracts, it is a tool that can only execute the program concretely, one execution at a time. In contrast, Symbolic Execution can execute all potential values in a decision path "in one go", creating a symbolic expression out of a path, and checking whether it can trigger a fault. Hence, Symbolic Execution tends to be more efficient at finding bugs than fuzzing when the bugs are rare, or explicitly (i.e. maliciously) hidden. Symbolic Execution can also prove that no postcondition can be violated, increasing the overall confidence in the contract. Note, however, that Symbolic Execution does not automatically generate postconditions for well-known bug classes like static code analysis tools do. Instead, these postconditions, and their sometimes associated preconditions, need to be explicitly written.

Fuzzing versus Symbolic Execution

Fuzzing tests usually have a set of (sometimes implicit) pre- and postconditions, but the actual action (e.g. function call) is performed by an external entity, the fuzzer. For C/C++ fuzzing, the implicit postcondition is often e.g. that the system does not throw a segmentation fault. For EVM bytecode, postconditions need to be explicit. Let's see an example:

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.19;
import "forge-std/Test.sol";

contract MyContract is Test {
  uint balance;
  function test_overflow(uint amt) public {
    unchecked {
     balance += amt;
    }
    assert(balance >= amt);
  }
}

This function is easy to break by picking an amt that overflows balance, so that the postcondition balance > amt will not hold. A fuzzer finds this kind of bug very easily. However, fuzzers have trouble finding bugs that are either specifically hidden (e.g. by a malicious developer), or that have a complicated code path towards them. Let's see a simple one:

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.19;
import "foge-std/Test.sol";

contract MyContract is Test {
  uint balance;
  function prove_multiply(uint amt, uint amt2) public {
    require(amt != 1);
    require(amt2 != 1);
    require(amt < amt2);
    uint tmp;
    tmp = amt * amt2;
    if (tmp == 119274257) balance = 1337;
    else balance += tmp;
    assert(balance >= tmp);
  }
}

Calling this contract with amt = 9479 and amt2 = 12583 will set the balance to 1337 which is less than amt*amt2, breaking the postcondition. However, a fuzzer, e.g. Echidna will likely not find those numbers, because uint has a potential range of 2**256 and so it'd be looking for a needle in a haystack, when looking randomly. Here's how to run Echidna on the multiplication test:

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.19;
contract MyContract {
 // the rest is the same
}

Then run:

echidna --test-mode assertion src/multiply-test.sol

Echidna will terminate after 50k runs, with all tests passing. Notice that the difference here, compared to the previous example, is that the overflow example has many different inputs that can break the postcondition, whereas here only one can.

Hevm finds the bug in both of these functions. This is because hevm (and symbolic execution frameworks in general) try to find the bug via proof-directed search rather than using random inputs. In hevm, we try to prove that there are no inputs to the test case such that given the preconditions, the postconditions can be broken. While trying to construct this mathematical proof, hevm finds a countereexample, an input that breaks the postconditions:

$ hevm test
Checking 1 function(s) in contract src/multiply-test.sol:MyContract
[RUNNING] prove_multiply(uint256,uint256)
   [FAIL] prove_multiply(uint256,uint256)
   Counterexample:
     result:   Revert: 0x4e487b710000000000000000000000000000000000000000000000000000000000000001
     calldata: prove_multiply(9479,12583)

Checking 1 function(s) in contract src/overflow-test.sol:MyContract
[RUNNING] prove_overflow(uint256)
   [FAIL] prove_overflow(uint256)
   Counterexample:
     result:   Revert: 0x4e487b710000000000000000000000000000000000000000000000000000000000000001
     calldata: prove_overflow(00000000000000000000000000000000000000000000000100000000000000000182dad8c17bd5e89e8043a08ada90a6d5efdee4425f85cb863109783e158ba4fba908a0e6fae6c6b51002)

Similarities and Differences to Other Tools

Fuzzers are exceedingly fast and efficient when there are many potential faults with a function/contract, or if the faults are of a type that's easy to search for (e.g. off-by-one). However, they rarely, if ever, find cases where the bug is hidden deep in the branch logic, or needs very specific input parameters. Hence, it is best to use fuzzers at first to find easy-to-find bugs, as fuzzers are very efficient at that. Then, once the tests pass the fuzzer, it is recommended to use a symbolic execution engine such as hevm.

hevm is similar to Halmos and Kontrol in its approach. However, it is quite different from static code analysis tools such as Oyente, Slither, and Mythril. While these 3 tools typically use some form of symbolic execution to try to validate their results, their main method of operation is not via symbolic execution, and they can, and do, report false positives.

Notice that static code analysis tools can find bugs that the author(s) didn't write a test case for, as they typically have a (large) set of preconfigured test-cases that they can report on, if they can find a way to violate them. Hence, it may be valuable to run static analysis tools alongside symbolic execution tools such as hevm.

Finally, SMTChecker may also be interesting to run alongside hevm. SMTChecker is very different from both approaches detailed above. While SMTChecker is capable of reliably finding both reentrancy and loop-related bugs, the tools above can only do so on a best effort basis. Hevm often reports a warning of incompleteness for such problems, while static code analysis tools either report potential positives or may even not discover them at all.