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The basic expressions in Lua are the following:

    exp ::= prefixexp
    exp ::= nil | false | true
    exp ::= Numeral
    exp ::= LiteralString
    exp ::= functiondef
    exp ::= tableconstructor
    exp ::= ‘...’
    exp ::= exp binop exp
    exp ::= unop exp
    prefixexp ::= var | functioncall | ‘(’ exp ‘)’

Numerals and literal strings are explained in Lexical Conventions; variables are explained in Variables; function definitions are explained in Function Definitions; function calls are explained in Function Calls; table constructors are explained in Table Constructors. Vararg expressions, denoted by three dots ('...'), can only be used when directly inside a vararg function; they are explained in Function Definitions.

Binary operators comprise arithmetic operators (see Arithmetic Operators), bitwise operators (see Bitwise Operators), relational operators (see Relational Operators), logical operators (see Logical Operators), and the concatenation operator (see Concatenation). Unary operators comprise the unary minus (see Arithmetic Operators), the unary bitwise NOT (see Bitwise Operators), the unary logical not (see Logical Operators), and the unary length operator (see The Length Operator).

Both function calls and vararg expressions can result in multiple values. If a function call is used as a statement (see Function Calls as Statements), then its return list is adjusted to zero elements, thus discarding all returned values. If an expression is used as the last (or the only) element of a list of expressions, then no adjustment is made (unless the expression is enclosed in parentheses). In all other contexts, Lua adjusts the result list to one element, either discarding all values except the first one or adding a single nil if there are no values.

Here are some examples:

     f()                -- adjusted to 0 results
     g(f(), x)          -- f() is adjusted to 1 result
     g(x, f())          -- g gets x plus all results from f()
     a,b,c = f(), x     -- f() is adjusted to 1 result (c gets nil)
     a,b = ...          -- a gets the first vararg argument, b gets
                        -- the second (both a and b can get nil if there
                        -- is no corresponding vararg argument)
     a,b,c = x, f()     -- f() is adjusted to 2 results
     a,b,c = f()        -- f() is adjusted to 3 results
     return f()         -- returns all results from f()
     return ...         -- returns all received vararg arguments
     return x,y,f()     -- returns x, y, and all results from f()
     {f()}              -- creates a list with all results from f()
     {...}              -- creates a list with all vararg arguments
     {f(), nil}         -- f() is adjusted to 1 result

Any expression enclosed in parentheses always results in only one value. Thus, (f(x,y,z)) is always a single value, even if f returns several values. (The value of (f(x,y,z)) is the first value returned by f or nil if f does not return any values.)

Arithmetic Operators

Lua supports the following arithmetic operators:

  • +: addition
  • -: subtraction
  • *: multiplication
  • /: float division
  • //: floor division
  • %: modulo
  • ^: exponentiation
  • -: unary minus

With the exception of exponentiation and float division, the arithmetic operators work as follows: If both operands are integers, the operation is performed over integers and the result is an integer. Otherwise, if both operands are numbers, then they are converted to floats, the operation is performed following the machine's rules for floating-point arithmetic (usually the IEEE 754 standard), and the result is a float. (The string library coerces strings to numbers in arithmetic operations; see Coercions and Conversions for details.)

Exponentiation and float division (/) always convert their operands to floats and the result is always a float. Exponentiation uses the ISO C function pow, so that it works for non-integer exponents too.

Floor division (//) is a division that rounds the quotient towards minus infinity, resulting in the floor of the division of its operands.

Modulo is defined as the remainder of a division that rounds the quotient towards minus infinity (floor division).

In case of overflows in integer arithmetic, all operations wrap around.

Bitwise Operators

Lua supports the following bitwise operators:

  • &: bitwise AND
  • |: bitwise OR
  • ~: bitwise exclusive OR
  • >>: right shift
  • <<: left shift
  • ~: unary bitwise NOT

All bitwise operations convert its operands to integers (see Coercions and Conversions), operate on all bits of those integers, and result in an integer.

Both right and left shifts fill the vacant bits with zeros. Negative displacements shift to the other direction; displacements with absolute values equal to or higher than the number of bits in an integer result in zero (as all bits are shifted out).

Coercions and Conversions

Lua provides some automatic conversions between some types and representations at run time. Bitwise operators always convert float operands to integers. Exponentiation and float division always convert integer operands to floats. All other arithmetic operations applied to mixed numbers (integers and floats) convert the integer operand to a float. The C API also converts both integers to floats and floats to integers, as needed. Moreover, string concatenation accepts numbers as arguments, besides strings.

In a conversion from integer to float, if the integer value has an exact representation as a float, that is the result. Otherwise, the conversion gets the nearest higher or the nearest lower representable value. This kind of conversion never fails.

The conversion from float to integer checks whether the float has an exact representation as an integer (that is, the float has an integral value and it is in the range of integer representation). If it does, that representation is the result. Otherwise, the conversion fails.

Several places in Lua coerce strings to numbers when necessary. In particular, the string library sets metamethods that try to coerce strings to numbers in all arithmetic operations. If the conversion fails, the library calls the metamethod of the other operand (if present) or it raises an error. Note that bitwise operators do not do this coercion.

Nonetheless, it is always a good practice not to rely on these implicit coercions, as they are not always applied; in particular, "1"==1 is false and "1"<1 raises an error (see Relational Operators). These coercions exist mainly for compatibility and may be removed in future versions of the language.

A string is converted to an integer or a float following its syntax and the rules of the Lua lexer. The string may have also leading and trailing whitespaces and a sign. All conversions from strings to numbers accept both a dot and the current locale mark as the radix character. (The Lua lexer, however, accepts only a dot.) If the string is not a valid numeral, the conversion fails. If necessary, the result of this first step is then converted to a specific number subtype following the previous rules for conversions between floats and integers.

The conversion from numbers to strings uses a non-specified human-readable format. To convert numbers to strings in any specific way, use the function string.format.

Relational Operators

Lua supports the following relational operators:

  • ==: equality
  • ~=: inequality
  • <: less than
  • >: greater than
  • <=: less or equal
  • >=: greater or equal

These operators always result in false or true.

Equality (==) first compares the type of its operands. If the types are different, then the result is false. Otherwise, the values of the operands are compared. Strings are equal if they have the same byte content. Numbers are equal if they denote the same mathematical value.

Tables, userdata, and threads are compared by reference: two objects are considered equal only if they are the same object. Every time you create a new object (a table, a userdata, or a thread), this new object is different from any previously existing object. A function is always equal to itself. Functions with any detectable difference (different behavior, different definition) are always different. Functions created at different times but with no detectable differences may be classified as equal or not (depending on internal caching details).

You can change the way that Lua compares tables and userdata by using the __eq metamethod (see Metatables and Metamethods).

Equality comparisons do not convert strings to numbers or vice versa. Thus, "0"==0 evaluates to false, and t[0] and t["0"] denote different entries in a table.

The operator ~= is exactly the negation of equality (==).

The order operators work as follows. If both arguments are numbers, then they are compared according to their mathematical values, regardless of their subtypes. Otherwise, if both arguments are strings, then their values are compared according to the current locale. Otherwise, Lua tries to call the __lt or the __le metamethod (see Metatables and Metamethods). A comparison a > b is translated to b < a and a >= b is translated to b <= a.

Following the IEEE 754 standard, the special value NaN is considered neither less than, nor equal to, nor greater than any value, including itself.

Logical Operators

The logical operators in Lua are and, or, and not. Like the control structures (see Control Structures), all logical operators consider both false and nil as false and anything else as true.

The negation operator not always returns false or true. The conjunction operator and returns its first argument if this value is false or nil; otherwise, and returns its second argument. The disjunction operator or returns its first argument if this value is different from nil and false; otherwise, or returns its second argument. Both and and or use short-circuit evaluation; that is, the second operand is evaluated only if necessary. Here are some examples:

     10 or 20            --> 10
     10 or error()       --> 10
     nil or "a"          --> "a"
     nil and 10          --> nil
     false and error()   --> false
     false and nil       --> false
     false or nil        --> nil
     10 and 20           --> 20


The string concatenation operator in Lua is denoted by two dots ('..'). If both operands are strings or numbers, then the numbers are converted to strings in a non-specified format (see Coercions and Conversions). Otherwise, the __concat metamethod is called (see Metatables and Metamethods).

The Length Operator

The length operator is denoted by the unary prefix operator #.

The length of a string is its number of bytes. (That is the usual meaning of string length when each character is one byte.)

The length operator applied on a table returns a border in that table. A border in a table t is any non-negative integer that satisfies the following condition:

     (border == 0 or t[border] ~= nil) and
     (t[border + 1] == nil or border == math.maxinteger)

In words, a border is any positive integer index present in the table that is followed by an absent index, plus two limit cases: zero, when index 1 is absent; and the maximum value for an integer, when that index is present. Note that keys that are not positive integers do not interfere with borders.

A table with exactly one border is called a sequence. For instance, the table {10, 20, 30, 40, 50} is a sequence, as it has only one border (5). The table {10, 20, 30, nil, 50} has two borders (3 and 5), and therefore it is not a sequence. (The nil at index 4 is called a hole.) The table {nil, 20, 30, nil, nil, 60, nil} has three borders (0, 3, and 6), so it is not a sequence, too. The table {} is a sequence with border 0.

When t is a sequence, #t returns its only border, which corresponds to the intuitive notion of the length of the sequence. When t is not a sequence, #t can return any of its borders. (The exact one depends on details of the internal representation of the table, which in turn can depend on how the table was populated and the memory addresses of its non-numeric keys.)

The computation of the length of a table has a guaranteed worst time of O(log n), where n is the largest integer key in the table.

A program can modify the behavior of the length operator for any value but strings through the __len metamethod (see Metatables and Metamethods).


Operator precedence in Lua follows the table below, from lower to higher priority:

     <     >     <=    >=    ~=    ==
     <<    >>
     +     -
     *     /     //    %
     unary operators (not   #     -     ~)

As usual, you can use parentheses to change the precedences of an expression. The concatenation ('..') and exponentiation ('^') operators are right associative. All other binary operators are left associative.

Table Constructors

Table constructors are expressions that create tables. Every time a constructor is evaluated, a new table is created. A constructor can be used to create an empty table or to create a table and initialize some of its fields. The general syntax for constructors is

    tableconstructor ::= ‘{’ [fieldlist] ‘}’
    fieldlist ::= field {fieldsep field} [fieldsep]
    field ::= ‘[’ exp ‘]’ ‘=’ exp | Name ‘=’ exp | exp
    fieldsep ::= ‘,’ | ‘;’

Each field of the form [exp1] = exp2 adds to the new table an entry with key exp1 and value exp2. A field of the form name = exp is equivalent to ["name"] = exp. Fields of the form exp are equivalent to [i] = exp, where i are consecutive integers starting with 1; fields in the other formats do not affect this counting. For example,

     a = { [f(1)] = g; "x", "y"; x = 1, f(x), [30] = 23; 45 }

is equivalent to

       local t = {}
       t[f(1)] = g
       t[1] = "x"         -- 1st exp
       t[2] = "y"         -- 2nd exp
       t.x = 1            -- t["x"] = 1
       t[3] = f(x)        -- 3rd exp
       t[30] = 23
       t[4] = 45          -- 4th exp
       a = t

The order of the assignments in a constructor is undefined. (This order would be relevant only when there are repeated keys.)

If the last field in the list has the form exp and the expression is a function call or a vararg expression, then all values returned by this expression enter the list consecutively (see Function Calls).

The field list can have an optional trailing separator, as a convenience for machine-generated code.

Function Calls

A function call in Lua has the following syntax:

    functioncall ::= prefixexp args

In a function call, first prefixexp and args are evaluated. If the value of prefixexp has type function, then this function is called with the given arguments. Otherwise, if present, the prefixexp __call metamethod is called: its first argument is the value of prefixexp, followed by the original call arguments (see Metatables and Metamethods).

The form

    functioncall ::= prefixexp ‘:’ Name args

can be used to emulate methods. A call v:name(args) is syntactic sugar for,args), except that v is evaluated only once.

Arguments have the following syntax:

    args ::= ‘(’ [explist] ‘)’
    args ::= tableconstructor
    args ::= LiteralString

All argument expressions are evaluated before the call. A call of the form f{fields} is syntactic sugar for f({fields}); that is, the argument list is a single new table. A call of the form f'string' (or f"string" or f[[string]]) is syntactic sugar for f('string'); that is, the argument list is a single literal string.

A call of the form return functioncall not in the scope of a to-be-closed variable is called a tail call. Lua implements proper tail calls (or proper tail recursion): in a tail call, the called function reuses the stack entry of the calling function. Therefore, there is no limit on the number of nested tail calls that a program can execute. However, a tail call erases any debug information about the calling function. Note that a tail call only happens with a particular syntax, where the return has one single function call as argument, and it is outside the scope of any to-be-closed variable. This syntax makes the calling function return exactly the returns of the called function, without any intervening action. So, none of the following examples are tail calls:

     return (f(x))        -- results adjusted to 1
     return 2 * f(x)      -- result multiplied by 2
     return x, f(x)       -- additional results
     f(x); return         -- results discarded
     return x or f(x)     -- results adjusted to 1

Function Definitions

The syntax for function definition is

    functiondef ::= function funcbody
    funcbody ::= ‘(’ [parlist] ‘)’ block end

The following syntactic sugar simplifies function definitions:

    stat ::= function funcname funcbody
    stat ::= local function Name funcbody
    funcname ::= Name {‘.’ Name} [‘:’ Name]

The statement

     function f () body end

translates to

     f = function () body end

The statement

     function t.a.b.c.f () body end

translates to

     t.a.b.c.f = function () body end

The statement

     local function f () body end

translates to

     local f; f = function () body end

not to

     local f = function () body end

(This only makes a difference when the body of the function contains references to f.)

A function definition is an executable expression, whose value has type function. When Lua precompiles a chunk, all its function bodies are precompiled too, but they are not created yet. Then, whenever Lua executes the function definition, the function is instantiated (or closed). This function instance, or closure, is the final value of the expression.

Parameters act as local variables that are initialized with the argument values:

    parlist ::= namelist [‘,’ ‘...’] | ‘...’

When a Lua function is called, it adjusts its list of arguments to the length of its list of parameters, unless the function is a vararg function, which is indicated by three dots ('...') at the end of its parameter list. A vararg function does not adjust its argument list; instead, it collects all extra arguments and supplies them to the function through a vararg expression, which is also written as three dots. The value of this expression is a list of all actual extra arguments, similar to a function with multiple results. If a vararg expression is used inside another expression or in the middle of a list of expressions, then its return list is adjusted to one element. If the expression is used as the last element of a list of expressions, then no adjustment is made (unless that last expression is enclosed in parentheses).

As an example, consider the following definitions:

     function f(a, b) end
     function g(a, b, ...) end
     function r() return 1,2,3 end

Then, we have the following mapping from arguments to parameters and to the vararg expression:

     CALL             PARAMETERS
     f(3)             a=3, b=nil
     f(3, 4)          a=3, b=4
     f(3, 4, 5)       a=3, b=4
     f(r(), 10)       a=1, b=10
     f(r())           a=1, b=2
     g(3)             a=3, b=nil, ... -->  (nothing)
     g(3, 4)          a=3, b=4,   ... -->  (nothing)
     g(3, 4, 5, 8)    a=3, b=4,   ... -->  5  8
     g(5, r())        a=5, b=1,   ... -->  2  3

Results are returned using the return statement (see Control Structures). If control reaches the end of a function without encountering a return statement, then the function returns with no results.

There is a system-dependent limit on the number of values that a function may return. This limit is guaranteed to be greater than 1000.

The colon syntax is used to emulate methods, adding an implicit extra parameter self to the function. Thus, the statement

     function t.a.b.c:f (params) body end

is syntactic sugar for

     t.a.b.c.f = function (self, params) body end