Joyfully Universal Language for (Inline) Assembly

JULIA is an intermediate language that can compile to various different backends (EVM 1.0, EVM 1.5 and eWASM are planned). Because of that, it is designed to be a usable common denominator of all three platforms. It can already be used for “inline assembly” inside Solidity and future versions of the Solidity compiler will even use JULIA as intermediate language. It should also be easy to build high-level optimizer stages for JULIA.

The core components of JULIA are functions, blocks, variables, literals, for-loops, if-statements, switch-statements, expressions and assignments to variables.

JULIA is typed, both variables and literals must specify the type with postfix notation. The supported types are bool, u8, s8, u32, s32, u64, s64, u128, s128, u256 and s256.

JULIA in itself does not even provide operators. If the EVM is targeted, opcodes will be available as built-in functions, but they can be reimplemented if the backend changes. For a list of mandatory built-in functions, see the section below.

The following example program assumes that the EVM opcodes mul, div and mod are available either natively or as functions and computes exponentiation.

{
    function power(base:u256, exponent:u256) -> result:u256
    {
        switch exponent
        case 0:u256 { result := 1:u256 }
        case 1:u256 { result := base }
        default:
        {
            result := power(mul(base, base), div(exponent, 2:u256))
            switch mod(exponent, 2:u256)
                case 1:u256 { result := mul(base, result) }
        }
    }
}

It is also possible to implement the same function using a for-loop instead of with recursion. Here, we need the EVM opcodes lt (less-than) and add to be available.

{
    function power(base:u256, exponent:u256) -> result:u256
    {
        result := 1:u256
        for { let i := 0:u256 } lt(i, exponent) { i := add(i, 1:u256) }
        {
            result := mul(result, base)
        }
    }
}

Specification of JULIA

JULIA code is described in this chapter. JULIA code is usually placed into a JULIA object, which is described in the following chapter.

Grammar:

Block = '{' Statement* '}'
Statement =
    Block |
    FunctionDefinition |
    VariableDeclaration |
    Assignment |
    Expression |
    Switch |
    ForLoop |
    BreakContinue
FunctionDefinition =
    'function' Identifier '(' TypedIdentifierList? ')'
    ( '->' TypedIdentifierList )? Block
VariableDeclaration =
    'let' TypedIdentifierList ( ':=' Expression )?
Assignment =
    IdentifierList ':=' Expression
Expression =
    FunctionCall | Identifier | Literal
If =
    'if' Expression Block
Switch =
    'switch' Expression Case* ( 'default' Block )?
Case =
    'case' Literal Block
ForLoop =
    'for' Block Expression Block Block
BreakContinue =
    'break' | 'continue'
FunctionCall =
    Identifier '(' ( Expression ( ',' Expression )* )? ')'
Identifier = [a-zA-Z_$] [a-zA-Z_0-9]*
IdentifierList = Identifier ( ',' Identifier)*
TypeName = Identifier | BuiltinTypeName
BuiltinTypeName = 'bool' | [us] ( '8' | '32' | '64' | '128' | '256' )
TypedIdentifierList = Identifier ':' TypeName ( ',' Identifier ':' TypeName )*
Literal =
    (NumberLiteral | StringLiteral | HexLiteral | TrueLiteral | FalseLiteral) ':' TypeName
NumberLiteral = HexNumber | DecimalNumber
HexLiteral = 'hex' ('"' ([0-9a-fA-F]{2})* '"' | '\'' ([0-9a-fA-F]{2})* '\'')
StringLiteral = '"' ([^"\r\n\\] | '\\' .)* '"'
TrueLiteral = 'true'
FalseLiteral = 'false'
HexNumber = '0x' [0-9a-fA-F]+
DecimalNumber = [0-9]+

Restrictions on the Grammar

Switches must have at least one case (including the default case). If all possible values of the expression is covered, the default case should not be allowed (i.e. a switch with a bool expression and having both a true and false case should not allow a default case).

Every expression evaluates to zero or more values. Identifiers and Literals evaluate to exactly one value and function calls evaluate to a number of values equal to the number of return values of the function called.

In variable declarations and assignments, the right-hand-side expression (if present) has to evaluate to a number of values equal to the number of variables on the left-hand-side. This is the only situation where an expression evaluating to more than one value is allowed.

Expressions that are also statements (i.e. at the block level) have to evaluate to zero values.

In all other situations, expressions have to evaluate to exactly one value.

The continue and break statements can only be used inside loop bodies and have to be in the same function as the loop (or both have to be at the top level). The condition part of the for-loop has to evaluate to exactly one value.

Literals cannot be larger than the their type. The largest type defined is 256-bit wide.

Scoping Rules

Scopes in JULIA are tied to Blocks (exceptions are functions and the for loop as explained below) and all declarations (FunctionDefinition, VariableDeclaration) introduce new identifiers into these scopes.

Identifiers are visible in the block they are defined in (including all sub-nodes and sub-blocks). As an exception, identifiers defined in the “init” part of the for-loop (the first block) are visible in all other parts of the for-loop (but not outside of the loop). Identifiers declared in the other parts of the for loop respect the regular syntatical scoping rules. The parameters and return parameters of functions are visible in the function body and their names cannot overlap.

Variables can only be referenced after their declaration. In particular, variables cannot be referenced in the right hand side of their own variable declaration. Functions can be referenced already before their declaration (if they are visible).

Shadowing is disallowed, i.e. you cannot declare an identifier at a point where another identifier with the same name is also visible, even if it is not accessible.

Inside functions, it is not possible to access a variable that was declared outside of that function.

Formal Specification

We formally specify JULIA by providing an evaluation function E overloaded on the various nodes of the AST. Any functions can have side effects, so E takes two state objects and the AST node and returns two new state objects and a variable number of other values. The two state objects are the global state object (which in the context of the EVM is the memory, storage and state of the blockchain) and the local state object (the state of local variables, i.e. a segment of the stack in the EVM). If the AST node is a statement, E returns the two state objects and a “mode”, which is used for the break and continue statements. If the AST node is an expression, E returns the two state objects and as many values as the expression evaluates to.

The exact nature of the global state is unspecified for this high level description. The local state L is a mapping of identifiers i to values v, denoted as L[i] = v.

For an identifier v, let $v be the name of the identifier.

We will use a destructuring notation for the AST nodes.

E(G, L, <{St1, ..., Stn}>: Block) =
    let G1, L1, mode = E(G, L, St1, ..., Stn)
    let L2 be a restriction of L1 to the identifiers of L
    G1, L2, mode
E(G, L, St1, ..., Stn: Statement) =
    if n is zero:
        G, L, regular
    else:
        let G1, L1, mode = E(G, L, St1)
        if mode is regular then
            E(G1, L1, St2, ..., Stn)
        otherwise
            G1, L1, mode
E(G, L, FunctionDefinition) =
    G, L, regular
E(G, L, <let var1, ..., varn := rhs>: VariableDeclaration) =
    E(G, L, <var1, ..., varn := rhs>: Assignment)
E(G, L, <let var1, ..., varn>: VariableDeclaration) =
    let L1 be a copy of L where L1[$vari] = 0 for i = 1, ..., n
    G, L1, regular
E(G, L, <var1, ..., varn := rhs>: Assignment) =
    let G1, L1, v1, ..., vn = E(G, L, rhs)
    let L2 be a copy of L1 where L2[$vari] = vi for i = 1, ..., n
    G, L2, regular
E(G, L, <for { i1, ..., in } condition post body>: ForLoop) =
    if n >= 1:
        let G1, L1, mode = E(G, L, i1, ..., in)
        // mode has to be regular due to the syntactic restrictions
        let G2, L2, mode = E(G1, L1, for {} condition post body)
        // mode has to be regular due to the syntactic restrictions
        let L3 be the restriction of L2 to only variables of L
        G2, L3, regular
    else:
        let G1, L1, v = E(G, L, condition)
        if v is false:
            G1, L1, regular
        else:
            let G2, L2, mode = E(G1, L, body)
            if mode is break:
                G2, L2, regular
            else:
                G3, L3, mode = E(G2, L2, post)
                E(G3, L3, for {} condition post body)
E(G, L, break: BreakContinue) =
    G, L, break
E(G, L, continue: BreakContinue) =
    G, L, continue
E(G, L, <if condition body>: If) =
    let G0, L0, v = E(G, L, condition)
    if v is true:
        E(G0, L0, body)
    else:
        G0, L0, regular
E(G, L, <switch condition case l1:t1 st1 ... case ln:tn stn>: Switch) =
    E(G, L, switch condition case l1:t1 st1 ... case ln:tn stn default {})
E(G, L, <switch condition case l1:t1 st1 ... case ln:tn stn default st'>: Switch) =
    let G0, L0, v = E(G, L, condition)
    // i = 1 .. n
    // Evaluate literals, context doesn't matter
    let _, _, v1 = E(G0, L0, l1)
    ...
    let _, _, vn = E(G0, L0, ln)
    if there exists smallest i such that vi = v:
        E(G0, L0, sti)
    else:
        E(G0, L0, st')

E(G, L, <name>: Identifier) =
    G, L, L[$name]
E(G, L, <fname(arg1, ..., argn)>: FunctionCall) =
    G1, L1, vn = E(G, L, argn)
    ...
    G(n-1), L(n-1), v2 = E(G(n-2), L(n-2), arg2)
    Gn, Ln, v1 = E(G(n-1), L(n-1), arg1)
    Let <function fname (param1, ..., paramn) -> ret1, ..., retm block>
    be the function of name $fname visible at the point of the call.
    Let L' be a new local state such that
    L'[$parami] = vi and L'[$reti] = 0 for all i.
    Let G'', L'', mode = E(Gn, L', block)
    G'', Ln, L''[$ret1], ..., L''[$retm]
E(G, L, l: HexLiteral) = G, L, hexString(l),
    where hexString decodes l from hex and left-aligns it into 32 bytes
E(G, L, l: StringLiteral) = G, L, utf8EncodeLeftAligned(l),
    where utf8EncodeLeftAligned performs a utf8 encoding of l
    and aligns it left into 32 bytes
E(G, L, n: HexNumber) = G, L, hex(n)
    where hex is the hexadecimal decoding function
E(G, L, n: DecimalNumber) = G, L, dec(n),
    where dec is the decimal decoding function

Type Conversion Functions

JULIA has no support for implicit type conversion and therefore functions exists to provide explicit conversion. When converting a larger type to a shorter type a runtime exception can occur in case of an overflow.

The following type conversion functions must be available: - u32tobool(x:u32) -> y:bool - booltou32(x:bool) -> y:u32 - u32tou64(x:u32) -> y:u64 - u64tou32(x:u64) -> y:u32 - etc. (TBD)

Low-level Functions

The following functions must be available:

Arithmetics
addu256(x:u256, y:u256) -> z:u256 | x + y
subu256(x:u256, y:u256) -> z:u256 | x - y
mulu256(x:u256, y:u256) -> z:u256 | x * y
divu256(x:u256, y:u256) -> z:u256 | x / y
divs256(x:s256, y:s256) -> z:s256 | x / y, for signed numbers in two’s complement
modu256(x:u256, y:u256) -> z:u256 | x % y
mods256(x:s256, y:s256) -> z:s256 | x % y, for signed numbers in two’s complement
signextendu256(i:u256, x:u256) -> z:u256 | sign extend from (i*8+7)th bit counting from least significant
expu256(x:u256, y:u256) -> z:u256 | x to the power of y
addmodu256(x:u256, y:u256, m:u256) -> z:u256| (x + y) % m with arbitrary precision arithmetics
mulmodu256(x:u256, y:u256, m:u256) -> z:u256| (x * y) % m with arbitrary precision arithmetics
ltu256(x:u256, y:u256) -> z:bool | 1 if x < y, 0 otherwise
gtu256(x:u256, y:u256) -> z:bool | 1 if x > y, 0 otherwise
sltu256(x:s256, y:s256) -> z:bool | 1 if x < y, 0 otherwise, for signed numbers in two’s complement
sgtu256(x:s256, y:s256) -> z:bool | 1 if x > y, 0 otherwise, for signed numbers in two’s complement
equ256(x:u256, y:u256) -> z:bool | 1 if x == y, 0 otherwise
notu256(x:u256) -> z:u256 | ~x, every bit of x is negated
andu256(x:u256, y:u256) -> z:u256 | bitwise and of x and y
oru256(x:u256, y:u256) -> z:u256 | bitwise or of x and y
xoru256(x:u256, y:u256) -> z:u256 | bitwise xor of x and y
shlu256(x:u256, y:u256) -> z:u256 | logical left shift of x by y
shru256(x:u256, y:u256) -> z:u256 | logical right shift of x by y
saru256(x:u256, y:u256) -> z:u256 | arithmetic right shift of x by y
byte(n:u256, x:u256) -> v:u256 | nth byte of x, where the most significant byte is the 0th byte Cannot this be just replaced by and256(shr256(n, x), 0xff) and let it be optimised out by the EVM backend?
Memory and storage
mload(p:u256) -> v:u256 | mem[p..(p+32))
mstore(p:u256, v:u256) | mem[p..(p+32)) := v
mstore8(p:u256, v:u256) | mem[p] := v & 0xff - only modifies a single byte
sload(p:u256) -> v:u256 | storage[p]
sstore(p:u256, v:u256) | storage[p] := v
msize() -> size:u256 | size of memory, i.e. largest accessed memory index, albeit due
due to the memory extension function, which extends by words,
this will always be a multiple of 32 bytes
Execution control
create(v:u256, p:u256, s:u256) | create new contract with code mem[p..(p+s)) and send v wei
and return the new address
call(g:u256, a:u256, v:u256, in:u256, | call contract at address a with input mem[in..(in+insize)) insize:u256, out:u256, | providing g gas and v wei and output area outsize:u256) | mem[out..(out+outsize)) returning 0 on error (eg. out of gas) -> r:u256 | and 1 on success
callcode(g:u256, a:u256, v:u256, in:u256, | identical to call but only use the code from a insize:u256, out:u256, | and stay in the context of the outsize:u256) -> r:u256 | current contract otherwise
delegatecall(g:u256, a:u256, in:u256, | identical to callcode, insize:u256, out:u256, | but also keep caller outsize:u256) -> r:u256 | and callvalue
stop() | stop execution, identical to return(0,0) Perhaps it would make sense retiring this as it equals to return(0,0). It can be an optimisation by the EVM backend.
abort() | abort (equals to invalid instruction on EVM)
return(p:u256, s:u256) | end execution, return data mem[p..(p+s))
revert(p:u256, s:u256) | end execution, revert state changes, return data mem[p..(p+s))
selfdestruct(a:u256) | end execution, destroy current contract and send funds to a
log0(p:u256, s:u256) | log without topics and data mem[p..(p+s))
log1(p:u256, s:u256, t1:u256) | log with topic t1 and data mem[p..(p+s))
log2(p:u256, s:u256, t1:u256, t2:u256) | log with topics t1, t2 and data mem[p..(p+s))
log3(p:u256, s:u256, t1:u256, t2:u256, | log with topics t, t2, t3 and data mem[p..(p+s)) t3:u256) |
log4(p:u256, s:u256, t1:u256, t2:u256, | log with topics t1, t2, t3, t4 and data mem[p..(p+s)) t3:u256, t4:u256) |
State queries
blockcoinbase() -> address:u256 | current mining beneficiary
blockdifficulty() -> difficulty:u256 | difficulty of the current block
blockgaslimit() -> limit:u256 | block gas limit of the current block
blockhash(b:u256) -> hash:u256 | hash of block nr b - only for last 256 blocks excluding current
blocknumber() -> block:u256 | current block number
blocktimestamp() -> timestamp:u256 | timestamp of the current block in seconds since the epoch
txorigin() -> address:u256 | transaction sender
txgasprice() -> price:u256 | gas price of the transaction
gasleft() -> gas:u256 | gas still available to execution
balance(a:u256) -> v:u256 | wei balance at address a
this() -> address:u256 | address of the current contract / execution context
caller() -> address:u256 | call sender (excluding delegatecall)
callvalue() -> v:u256 | wei sent together with the current call
calldataload(p:u256) -> v:u256 | call data starting from position p (32 bytes)
calldatasize() -> v:u256 | size of call data in bytes
calldatacopy(t:u256, f:u256, s:u256) | copy s bytes from calldata at position f to mem at position t
codesize() -> size:u256 | size of the code of the current contract / execution context
codecopy(t:u256, f:u256, s:u256) | copy s bytes from code at position f to mem at position t
extcodesize(a:u256) -> size:u256 | size of the code at address a
extcodecopy(a:u256, t:u256, f:u256, s:u256) | like codecopy(t, f, s) but take code at address a
Others
discardu256(unused:u256) | discard value
splitu256tou64(x:u256) -> (x1:u64, x2:u64, | split u256 to four u64’s
x3:u64, x4:u64) |
combineu64tou256(x1:u64, x2:u64, x3:u64, | combine four u64’s into a single u256
x4:u64) -> (x:u256) |
sha3(p:u256, s:u256) -> v:u256 | keccak(mem[p...(p+s)))

Backends

Backends or targets are the translators from JULIA to a specific bytecode. Each of the backends can expose functions prefixed with the name of the backend. We reserve evm_ and ewasm_ prefixes for the two proposed backends.

Backend: EVM

The EVM target will have all the underlying EVM opcodes exposed with the evm_ prefix.

Backend: “EVM 1.5”

TBD

Backend: eWASM

TBD

Specification of JULIA Object

Grammar:

TopLevelObject = 'object' '{' Code? ( Object | Data )* '}'
Object = 'object' StringLiteral '{' Code? ( Object | Data )* '}'
Code = 'code' Block
Data = 'data' StringLiteral HexLiteral
HexLiteral = 'hex' ('"' ([0-9a-fA-F]{2})* '"' | '\'' ([0-9a-fA-F]{2})* '\'')
StringLiteral = '"' ([^"\r\n\\] | '\\' .)* '"'

Above, Block refers to Block in the JULIA code grammar explained in the previous chapter.

An example JULIA Object is shown below:

..code:

// Code consists of a single object. A single "code" node is the code of the object.
// Every (other) named object or data section is serialized and
// made accessible to the special built-in functions datacopy / dataoffset / datasize
object {
    code {
        let size = datasize("runtime")
        let offset = allocate(size)
        // This will turn into a memory->memory copy for eWASM and
        // a codecopy for EVM
        datacopy(dataoffset("runtime"), offset, size)
        // this is a constructor and the runtime code is returned
        return(offset, size)
    }

    data "Table2" hex"4123"

    object "runtime" {
        code {
            // runtime code

            let size = datasize("Contract2")
            let offset = allocate(size)
            // This will turn into a memory->memory copy for eWASM and
            // a codecopy for EVM
            datacopy(dataoffset("Contract2"), offset, size)
            // constructor parameter is a single number 0x1234
            mstore(add(offset, size), 0x1234)
            create(offset, add(size, 32))
        }

        // Embedded object. Use case is that the outside is a factory contract,
        // and Contract2 is the code to be created by the factory
        object "Contract2" {
            code {
                // code here ...
            }

            object "runtime" {
                code {
                    // code here ...
                }
             }

             data "Table1" hex"4123"
        }
    }
}