Like Solidity, CVL is a statically typed language. There is overlap between the types supported by Solidity and the types supported by CVL, but CVL has some additional types and is also missing support for some Solidity types.

The additional CVL types are:


The syntax for types in CVL is given by the following EBNF grammar:

basic_type ::= "int*" | "uint*" | "address" | "bool"
             | "string" | "bytes*"
             | basic_type "[" [ number ] "]"
             | id "." id

evm_type ::= basic_type
           | "(" evm_type { "," evm_type } ")"
           | evm_type "[" [ number ] "]"

cvl_type ::= basic_type
           | "mathint" | "calldataarg" | "storage" | "env" | "method"
           | id

See Basic Syntax for the id and number productions.

Solidity Types

You can declare variables in CVL of any of the following solidity types:

The following are not directly supported in CVL, although you can interact with contracts that use them (see Conversions between CVL and Solidity types):

  • Function types

  • Multi-dimensional arrays

  • Mappings

Integer types

CVL integer types are mostly identical to Solidity integer types. See Basic operations for details.

Array access

Array accesses in CVL behave slightly differently from Solidity accesses. In Solidity, an out-of-bounds array access will result in an exception, causing the transaction to revert.

By contrast, out-of-bounds array accesses in CVL are treated as undefined values: if i > a.length then the Prover considers every possible value for a[i] when constructing counterexamples.

CVL arrays also have the following limitations:

  • Only single dimensional arrays are supported

  • The push and pop methods are not supported. You can use harnessing to work around these limitations.

User-defined types

Specifications can use structs, enums, or user-defined value types that are defined in Solidity contracts.

Struct types have the following limitations:

  • Assignment to struct fields is unsupported. You can achieve the same effect using a require statement. For example, instead of s.f = x; you can write require s.f == x;. However, be aware that require statements can introduce vacuity if there are multiple conflicting constraints.

All user-defined type names (structs, enums, and user-defined values) must be explicitly qualified by the contract name that contains them.

  • For types defined within a contract, the named contract must be the contract containing the type definition. Note that if a contract inherits a type from a supertype, the contract that actually contains the type must be named, not the inheriting contract.

  • For types defined at the file level, the named contract can be any contract in the scene from which the type is visible.


If you do not qualify the type name with a contract name, the type name will be misinterpreted as a sort.

For example, consider the files parent.sol and child.sol, defined as follows:

type ParentFileType is uint64;

contract Parent {
    enum ParentContractType { member1, member2 }
import 'parent.sol';

type ChildFileType is bool;

contract Child is Parent {
    type alias ChildContractType is uint128;

Given these definitions, types can be named as follows:

// valid types
Parent.ParentFileType     valid1;
Child .ParentFileType     valid2;
Parent.ParentContractType valid3;

// invalid types
Child .ParentContractType invalid1; // user-defined types are not inherited
Parent.ChildFileType      invalid2; // ChildFileType is not visible in Parent

Additional CVL types

The mathint type

Arithmetic overflow and underflow are difficult to reason about and often lead to bugs. To avoid this complexity, CVL provides the mathint type that can represent an integer of any size; operations on mathints can never overflow or underflow.

See Basic operations for details on mathematical operations and casting between mathint and Solidity integer types.

The env type

Rules often reason about the effects of multiple transactions. In different transactions, the global Solidity variables (such as msg.sender or block.timestamp) may have different values.

To support reasoning about multiple transactions, CVL groups some of the solidity global variables into an “environment”: an object of the special type env. Environments must be passed as the first argument of a call from CVL into a contract function (unless the contract function is declared envfree).

For example, to call a Solidity function deposit(uint amount), a spec must explicitly pass in an additional environment argument:

rule check_deposit() {
    env e;
    uint amount;
    deposit(e, amount); // increases e.msg.sender's balance by `amount`

The value of the Solidity global variables can be extracted from the env object using a field-like syntax. The following fields are available on an environment e:

  • e.msg.sender - address of the sender of the message

  • e.msg.value - number of Wei sent with the message

  • e.block.number - current block number

  • e.block.timestamp - current block’s time stamp

  • e.block.basefee - current block’s base fee

  • e.block.coinbase - current block’s coinbase

  • e.block.difficulty - current block’s difficulty

  • e.block.gaslimit - current block’s gas limit

  • e.tx.origin - original message sender

The remaining solidity global variables are not accessible from CVL.

The method and calldataarg types

Changed in version 5.0: Formerly, parametric method calls would only call methods of currentContract; now they call methods of all contracts. This version also introduced the f.contract field.

An important feature of CVL is the ability to reason about the effects of an arbitrary method called with arbitrary arguments. To support this, CVL provides the method type to represent an arbitrary method, and the calldataarg type to represent an arbitrary set of arguments.

For example, the following rule checks that no method can decrease the user’s balance:

rule balance_increasing() {
    address user;
    uint balance_before = balance(user);

    method f;
    env e;
    calldataarg args;


    uint balance_after = balance(user);
    assert balance_after >= balance_before, "balance must be increasing";

Since f, e, and args are not given values, the Prover will consider every possible assignment. This means that when evaluating the call to f(e,args), the Prover will check the rule on every method of every contract on the scene, with every possible set of method arguments.

See Parametric rules for more information about how rules that declare method variables are verified.

Variables of type method can only be declared as an argument to the rule or directly in the body of a rule. They may not be nested inside of if statements or declared in CVL functions. They may be passed as arguments to CVL functions.

Properties of methods can be extracted from method variables using a field-like syntax. The following fields are available on a method m:

  • m.selector  - the ABI signature of the method

  • m.isPure  - true when m is declared with the pure attribute

  • m.isView  - true when m is declared with the view attribute

  • m.isFallback - true when m is the fallback function

  • m.numberOfArguments - the number of arguments to method m

  • m.contract - the receiver contract for the method

There is no way to examine the contents of a calldataarg variable, because the type of its contents vary depending on which method the Prover is checking. The only thing you can do with it is pass it as an argument to a contract method call. It is possible to work around this limitation; see Partially Parametric Rules for further details.

The storage type

The Certora Prover can compare different hypothetical transactions starting from the same state and compare their results. For example, checking a property like “if you stake more, you earn more” requires comparing the earnings after two possible transactions starting in the same initial state: one where you stake less, and one where you stake more.

Properties that compare the results of different hypothetical executions are sometimes called hyperproperties.

CVL supports this kind of specification using the special storage type. A variable of type storage represents a snapshot of the EVM storage and the state of ghosts at a given point in time.

The EVM storage can be reset to a saved storage value s by appending at s to the end of a function call. For example, the following rule checks that “if you stake more, you earn more”:

rule bigger_stake_more_earnings() {
    storage initial = lastStorage;
    env e;

    uint less; uint more;
    require less < more;

    // stake less
    stake(e, less) at initial;
    earnings_less = earnings(e);

    // stake more
    stake(e, more) at initial;
    earnings_more = earnings(e);

    assert earnings_less < earnings_more, "if you stake more, you earn more";

The lastStorage variable contains the state of the EVM after the most recent contract function call.

Variables of storage type can also be compared for equality, allowing simple rules that check the equivalence of different functions. See Comparing storage for details.

Uninterpreted sorts

Conversions between CVL and Solidity types

When a specification calls a contract function, the Prover must convert the arguments from their CVL types to the corresponding Solidity types, and must convert the return values from Solidity back to CVL. The Prover must also apply these conversions when inlining hooks and function summaries.

There are restrictions on what types can be converted from CVL to Solidity and vice-versa. In general, if a contract uses a type that is not convertible, you can still interact with it, but you cannot access the corresponding values. For example, if a contract function returns a type that isn’t convertible to CVL, you can call the function from CVL but you cannot access its return type. Similarly, if the function accepts an argument of a type that is not representable in CVL, you can still call the function from CVL, but only by providing it a generic `calldataarg` argument.

The following restrictions apply when converting between CVL types and Solidity types:

  • The type must be a valid CVL type (except for contract or interface types, which are represented by address).

  • Reference types (arrays and structs) can only be passed to Solidity functions that expect calldata or memory arguments; there is no way to pass storage arrays.

  • Arrays returned from Solidity can only be converted to CVL if their elements have value types that are representable in CVL.

There are additional restrictions on the types for arguments and return values for internal function summaries; see Function summaries.