Predeclared in Source §2 Lazy

Constants

(constant) Infinity :number

The name Infinity refers to the special number value Infinity. See ECMAScript Specification, Section 4.3.23

Type:

number

(constant) math_E :number

The Number value for e, Euler's number, which is approximately 2.718281828459045.

Type:

number

(constant) math_LN2 :number

The Number value for the natural logarithm of 2, which is approximately 0.6931471805599453.

Type:

number

(constant) math_LN10 :number

The Number value for the natural logarithm of 10, which is approximately 2.302585092994046.

Type:

number

(constant) math_LOG2E :number

The Number value for the base-2 logarithm of eℝ, the base of the natural logarithms; this value is approximately 1.4426950408889634.

NOTE: The value of math_LOG2E is approximately the reciprocal of the value of math_LN2.

Type:

number

(constant) math_LOG10E :number

The Number value for the base-10 logarithm of e, the base of the natural logarithms; this value is approximately 0.4342944819032518.

NOTE: The value of math_LOG10E is approximately the reciprocal of the value of math_LN10.

Type:

number

(constant) math_PI :number

The Number value for π, the ratio of the circumference of a circle to its diameter, which is approximately 3.1415926535897932.

Type:

number

(constant) math_SQRT1_2 :number

The Number value for the square root of 0.5, which is approximately 0.7071067811865476.

NOTE: The value of math_SQRT1_2 is approximately the reciprocal of the value of math_SQRT2.

Type:

number

(constant) math_SQRT2 :number

The Number value for the square root of 2, which is approximately 1.4142135623730951.

Type:

number

(constant) NaN :number

The name NaN refers to the special number value NaN ("not a number"). Note that NaN is a number, as specified by is_number. See ECMAScript Specification, Section 4.3.24

Type:

number

(constant) undefined :undefined

The name undefined refers to the special value undefined. See also textbook explanation in section 4.1.1.

Type:

undefined

Functions

__access_export__(exports, lookup_name) → {value}

Searches for the specified name in the data structure of exported names. The data structure is a pair where the head element is the default export and the tail element is a list of pairs where each pair is a mapping from the exported name to the value being exported. If the lookup name is "default", the default export is returned instead of a named export. If the name does not exist, undefined is returned.

Parameters:

Name	Type	Description
`exports`	pair	The data structure of exported values
`lookup_name`	string	Name to import

Returns:

The value corresponding to the imported name

Type: value

__access_named_export__(named_exports, lookup_name) → {value}

Searches for the specified name in the data structure of exported names. The data structure is a list of pairs where each pair is a mapping from the exported name to the value being exported. If the name does not exist, undefined is returned.

Parameters:

Name	Type	Description
`named_exports`	list	The data structure of exported names
`lookup_name`	string	Name to import

Returns:

The value corresponding to the imported name

Type: value

accumulate(f, initial, xs) → {value}

Applies binary function f to the elements of xs from right-to-left order, first applying f to the last element and the value initial, resulting in r₁, then to the second-last element and r₁, resulting in r₂, etc, and finally to the first element and r_n-1, where n is the length of the list. Thus, accumulate(f,zero,list(1,2,3)) results in f(1, f(2, f(3, zero))). Iterative process; time: Theta(n) (apart from f), space: Theta(n) (apart from f), where n is the length of xs.

Parameters:

Name	Type	Description
`f`	function	binary function
`initial`	value	initial value
`xs`	list	given list

Returns:

result of accumulating xs using f starting with initial

Type: value

append(xs, ys) → {list}

Returns a list that results from appending the list ys to the list xs. Iterative process; time: Theta(n), space: Theta(n), where n is the length of xs. In the result, null at the end of the first argument list is replaced by the second argument, regardless what the second argument consists of.

Parameters:

Name	Type	Description
`xs`	list	given first list
`ys`	list	given second list

Returns:

result of appending xs and ys

Type: list

arity(f) → {number}

Returns the number of parameters the given function f expects, excluding the rest parameter.

Parameters:

Name	Type	Description
`f`	function	given function

Returns:

number of parameters f expects

Type: number

build_list(f, n) → {list}

Makes a list with n elements by applying the unary function f to the numbers 0 to n - 1, assumed to be a nonnegative integer. Iterative process; time: Theta(n) (apart from f), space: Theta(n) (apart from f).

Parameters:

Name	Type	Description
`f`	function	unary function
`n`	number	given nonnegative integer

Returns:

resulting list

Type: list

char_at(s, i) → {string}

Takes a string s as first argument and a nonnegative integer i as second argument. If i is less than the length of s, this function returns a one-character string that contains the character of s at position i, counting from 0. If i is larger than or equal to the length of s, this function returns undefined.

Parameters:

Name	Type	Description
`s`	string	given string
`i`	number	index

Returns:

one-character or undefined

Type: string

display(v, s) → {value}

Optional second argument. If present, displays the given string s, followed by a space character, followed by the value v in the console. If second argument not present, just displays the value v in the console. The notation used for the display of values is consistent with JSON, but also displays undefined, NaN, Infinity, and function objects.

Parameters:

Name	Type	Description
`v`	value	to be displayed
`s`	string	to be displayed, preceding `v`, optional argument

Returns:

v, the first argument value

Type: value

display_list(xs, s) → {value}

Optional second argument. Similar to display, but formats well-formed lists nicely if detected; time, space: Theta(n), where n is the total number of data structures such as pairs in x.

Parameters:

Name	Type	Description
`xs`	value	list structure to be displayed
`s`	string	to be displayed, preceding `xs`

Returns:

xs, the first argument value

Type: value

draw_data() → {value}

visualizes the arguments in a separate drawing area in the Source Academy using box-and-pointer diagrams; time, space: Theta(n), where n is the total number of data structures such as pairs in the arguments.

Parameters:

Name	Type	Description
`value1,value2,...,value_n`	value	given values

Returns:

given x

Type: value

enum_list(start, end) → {list}

Returns a list that enumerates numbers starting from start using a step size of 1, until the number exceeds (>) end. Iterative process; time: Theta(n), space: Theta(n), where n is end - start.

Parameters:

Name	Type	Description
`start`	number	starting number
`end`	number	ending number

Returns:

list from start to end

Type: list

equal(x, y) → {boolean}

Returns true if both have the same structure with respect to pair, and identical values at corresponding leave positions (places that are not themselves pairs), and false otherwise. For the "identical", the values need to have the same type, otherwise the result is false. If corresponding leaves are boolean values, these values need to be the same. If both are undefined or both are null, the result is true. Otherwise they are compared with === (using the definition of === in the respective Source language in use). Time, space: Theta(n), where n is the total number of data structures such as pairs in x and y.

Parameters:

Name	Type	Description
`x`	value	given value
`y`	value	given value

Returns:

whether x is structurally equal to y

Type: boolean

error(v, s)

Optional second argument. If present, displays the given string s, followed by a space character, followed by the value v in the console with error flag. If second argument not present, just displays the value v in the console with error flag. The evaluation of any call of error aborts the running program immediately. The notation used for the display of values is consistent with JSON, but also displays undefined, NaN, Infinity, and function objects.

Parameters:

Name	Type	Description
`v`	value	to be displayed
`s`	string	to be displayed, preceding `v`

filter(pred, xs) → {list}

Returns a list that contains only those elements for which the one-argument function pred returns true. Iterative process; time: Theta(n) (apart from pred), space: Theta(n) (apart from pred), where n is the length of xs.

Parameters:

Name	Type	Description
`pred`	function	unary function returning boolean value
`xs`	list	given list

Returns:

list with those elements of xs for which pred holds.

Type: list

for_each(f, xs) → {boolean}

Applies unary function f to every element of the list xs. Iterative process; time: Theta(n) (apart from f), space: Theta(1) (apart from f), where n is the length of xs. f is applied element-by-element: for_each(fun, list(1, 2)) results in the calls fun(1) and fun(2).

Parameters:

Name	Type	Description
`f`	function	unary
`xs`	list	given list

Returns:

true

Type: boolean

get_time() → {number}

Returns number of milliseconds elapsed since January 1, 1970 00:00:00 UTC. See also textbook example.

Returns:

current time in milliseconds

Type: number

head(p) → {value}

**primitive**; returns head (first component) of given pair p; time: Theta(1)Theta(1).

Parameters:

Name	Type	Description
`p`	pair	given pair

Returns:

head of p

Type: value

is_boolean(v) → {boolean}

checks whether a given value is a boolean

Parameters:

Name	Type	Description
`v`	value	to be checked

Returns:

indicating whether the value is a boolean

Type: boolean

is_function(v) → {boolean}

checks whether a given value is a function

Parameters:

Name	Type	Description
`v`	value	to be checked

Returns:

indicating whether the value is a function

Type: boolean

is_list(xs) → {xs}

**primitive**; returns true if xs is a list as defined in the textbook, and false otherwise. Iterative process; time: Theta(n), space: Theta(1), where n is the length of the chain of tail operations that can be applied to xs. is_list recurses down the list and checks that it ends with the empty list null

Parameters:

Name	Type	Description
`xs`	value	given candidate

Returns:

whether is a list

Type: xs

is_null(x) → {boolean}

**primitive**; returns true if x is the empty list null, and false otherwise; time: Theta(1)Theta(1).

Parameters:

Name	Type	Description
`x`	value	given value

Returns:

whether x is null

Type: boolean

is_number(v) → {boolean}

checks whether a given value is a number. See also textbook example.

Parameters:

Name	Type	Description
`v`	value	to be checked

Returns:

indicating whether the value is a number

Type: boolean

is_pair(x) → {boolean}

**primitive**; returns true if x is a pair and false otherwise; time: Theta(1)Theta(1).

Parameters:

Name	Type	Description
`x`	value	given value

Returns:

whether x is a pair

Type: boolean

is_string(v) → {boolean}

checks whether a given value is a string. See also textbook example.

Parameters:

Name	Type	Description
`v`	value	to be checked

Returns:

indicating whether the value is a string

Type: boolean

is_undefined(v) → {boolean}

checks whether a given value is the special value undefined

Parameters:

Name	Type	Description
`v`	value	to be checked

Returns:

indicating whether the value is undefined

Type: boolean

length(xs) → {number}

Returns the length of the list xs. Iterative process; time: Theta(n), space: Theta(1), where n is the length of xs.

Parameters:

Name	Type	Description
`xs`	list	given list

Returns:

length of xs

Type: number

list() → {list}

**primitive**; given n values, returns a list of length n. The elements of the list are the given values in the given order; time: Theta(n)Theta(n).

Parameters:

Name	Type	Description
`value1,value2,...,value_n`	value	given values

Returns:

list containing all values

Type: list

list_ref(xs, n) → {value}

Returns the element of list xs at position n, where the first element has index 0. Iterative process; time: Theta(n), space: Theta(1), where n is the length of xs.

Parameters:

Name	Type	Description
`xs`	list	given list
`n`	number	given position

Returns:

item in xs at position n

Type: value

list_to_string(xs) → {string}

Returns a string that represents list xs using the text-based box-and-pointer notation [...]. Iterative process; time: Theta(n) where n is the size of the list, space: Theta(m) where m is the length of the string. The process is iterative, but consumes space O(m) because of the result string.

Parameters:

Name	Type	Description
`xs`	list	given list

Returns:

xs converted to string

Type: string

map(f, xs) → {list}

Returns a list that results from list xs by element-wise application of unary function f. Iterative process; time: Theta(n) (apart from f), space: Theta(n) (apart from f), where n is the length of xs. f is applied element-by-element: map(f, list(1, 2)) results in list(f(1), f(2)).

Parameters:

Name	Type	Description
`f`	function	unary
`xs`	list	given list

Returns:

result of mapping

Type: list

math_abs(`x`) → {number}

computes the absolute value of x; the result has the same magnitude as x but has positive sign.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

absolute value of x

Type: number

math_acos(`x`) → {number}

computes the arc cosine of x. The result is expressed in radians and ranges from +0 to +π.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

arc cosine of x

Type: number

math_acosh(`x`) → {number}

computes the inverse hyperbolic cosine of x.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

inverse hyperbolic cosine of x.

Type: number

math_asin(`x`) → {number}

computes the arc sine of x. The result is expressed in radians and ranges from -π / 2 to +π / 2.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

arc sine of x.

Type: number

math_asinh(`x`) → {number}

computes the inverse hyperbolic sine of x. The result is expressed in radians and ranges from -π / 2 to +π / 2.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

inverse hyperbolic sine of x

Type: number

math_atan(`x`) → {number}

computes the arc tangent of x. The result is expressed in radians and ranges from -π / 2 to +π / 2.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

arc tangent of x

Type: number

math_atan2(`y`, `x`) → {number}

computes the arc tangent of the quotient y / x of the arguments y and x, where the signs of y and x are used to determine the quadrant of the result. Note that it is intentional and traditional for the two-argument arc tangent function that the argument named y be first and the argument named x be second. The result is expressed in radians and ranges from -π to +π.

Parameters:

Name	Type	Description
`y`	number	given first number
`x`	number	given second number

Returns:

arc tangent of y / x.

Type: number

math_atanh(`x`) → {number}

computes the inverse hyperbolic tangent of x.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

inverse hyperbolic tangent of x.

Type: number

math_cbrt(`x`) → {number}

computes the cube root of x.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

cube root of x.

Type: number

math_ceil(`x`) → {number}

computes the smallest (closest to -∞) Number value that is not less than x and is an integer. If x is already an integer, the result is x. The value of math_ceil(x) is the same as the value of -math_floor(-x).

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

"ceiling" of the number

Type: number

math_clz32(n) → {number}

When math_clz32 is called with one argument x, the following steps are taken: Let n be ToUint32(x). Let p be the number of leading zero bits in the 32-bit binary representation of n. Return p.

NOTE:
If n is 0, p will be 32. If the most significant bit of the 32-bit binary encoding of n is 1, p will be 0.

Parameters:

Name	Type	Description
`n`	number	given number

Returns:

p - leading zero bits

Type: number

math_cos(`x`) → {number}

Computes the cosine of x. The argument is expressed in radians.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

- cosine of x

Type: number

math_cosh(`x`) → {number}

computes the hyperbolic cosine of x.

NOTE: The value of cosh(x) is the same as (exp(x) + exp(-x)) / 2.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

hyperbolic cosine of x

Type: number

math_exp(`x`) → {number}

computes the exponential function of x (e raised to the power of x, where e is the base of the natural logarithms).

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

e to the power of x

Type: number

math_expm1(`x`) → {number}

computes subtracting 1 from the exponential function of x (e raised to the power of x, where e is the base of the natural logarithms). The result is computed in a way that is accurate even when the value of x is close to 0.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

-1 plus e to the power of x

Type: number

math_floor(`x`) → {number}

computes the greatest (closest to +∞) Number value that is not greater than x and is an integer.
If x is already an integer, the result is x.

NOTE: The value of math_floor(x) is the same as the value of -math_ceil(-x).

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

floor of x

Type: number

math_fround(`x`) → {number}

When math_fround is called with argument x, the following steps are taken:

If x is NaN, return NaN.
If x is one of +0, -0, +∞, -∞, return x.
Let x32 be the result of converting x to a value in IEEE 754-2008 binary32 format using roundTiesToEven mode.
Let x64 be the result of converting x32 to a value in IEEE 754-2008 binary64 format.
Return the ECMAScript Number value corresponding to x64.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

fround of x

Type: number

math_hypot() → {number}

computes the square root of the sum of squares of its arguments.
If no arguments are passed, the result is +0.

Parameters:

Name	Type	Description
`value1,value2,...`	number	given numbers

Returns:

square root of sum of squares of arguments

Type: number

math_imul(`x`, `x`) → {number}

When math_imul is called with arguments x and y, the following steps are taken:

Let a be ToUint32(x).
Let b be ToUint32(y).
Let product be (a × b) modulo 2³².
If product ≥ 2³¹, return product - 2³²; otherwise return product.

Parameters:

Name	Type	Description
`x`	number	given first number
`x`	number	given second number

Returns:

- x imul y

Type: number

math_log(`x`) → {number}

Computes the natural logarithm of x.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

- natural logarithm of x

Type: number

math_log1p(`x`) → {number}

computes the natural logarithm of 1 + x. The result is computed in a way that is accurate even when the value of x is close to zero.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

math_log(1 + x)

Type: number

math_log2(`x`) → {number}

computes the base 2 logarithm of x.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

base 2 logarithm of x

Type: number

math_log10(`x`) → {number}

computes the base 10 logarithm of x.

Parameters:

Name	Type	Description
`x`	number	given number

Returns:

base 10 logarithm of x

Type: number

math_max() → {number}

Given zero or more numbers, returns the largest of them.
If no arguments are given, the result is -∞.
If any value is NaN, the result is NaN. The comparison of values to determine the largest value is done using the Abstract Relational Comparison algorithm except that +0 is considered to be larger than -0.

Parameters:

Name	Type	Description
`value1,value2,...`	number	given numbers

Returns:

largest of them

Type: number

math_min() → {number}

Given zero or more arguments, returns the smallest of them.
If no arguments are given, the result is +∞.
If any value is NaN, the result is NaN. The comparison of values to determine the smallest value is done using the Abstract Relational Comparison algorithm except that +0 is considered to be larger than -0.

Parameters:

Name	Type	Description
`value1,value2,...`	number	given numbers

Returns:

smallest of them

Type: number

math_pow(base, exponent) → {number}

Computes the result of raising base to the power of exponent.

Parameters:

Name	Type	Description
`base`	number	the given base
`exponent`	number	the given exponent

Returns:

base to the power of exponent

Type: number

math_random() → {number}

Returns a number value with positive sign, greater than or equal to 0 but less than 1, chosen randomly or pseudo randomly with approximately uniform distribution over that range, using an implementation-dependent algorithm or strategy. This function takes no arguments. Each math_random function created for distinct realms must produce a distinct sequence of values from successive calls.

Returns:

random number greater than or equal to 0 but less than 1

Type: number

math_round(`x`) → {number}

Returns the number value that is closest to x and is an integer.
If two integers are equally close to x, then the result is the Number value that is closer to +∞. If x is already an integer, the result is x. NOTE 1: math_round(3.5) returns 4, but math_round(-3.5) returns -3.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

closest integer to x

Type: number

math_sign(`x`) → {number}

Computes the sign of x, indicating whether x is positive, negative, or zero.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the sign (-1, 0 or +1)

Type: number

math_sin(`x`) → {number}

Computes the sine of x. The argument is expressed in radians.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the sine of x

Type: number

math_sinh(`x`) → {number}

Computes the hyperbolic sine of x.

NOTE: The value of sinh(x) is the same as (exp(x) - exp(-x)) / 2.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the hyperbolic sine of x

Type: number

math_sqrt(`x`) → {number}

Computes the square root of x.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the square root of x

Type: number

math_tan(`x`) → {number}

Computes the tangent of x. The argument is expressed in radians.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the tangent of x

Type: number

math_tanh(`x`) → {number}

Computes the hyperbolic tangent of x.

NOTE: The value of math_tanh(x) is the same as (exp(x) - exp(-x))/(exp(x) + exp(-x)).

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the hyperbolic tangent of x

Type: number

math_trunc(`x`) → {number}

Computes the integral part of the number x, removing any fractional digits.

Parameters:

Name	Type	Description
`x`	number	the given number

Returns:

the integral part of x

Type: number

member(v, xs) → {list}

Returns first postfix sublist whose head is identical to v (using ===); returns null if the element does not occur in the list. Iterative process; time: Theta(n), space: Theta(1), where n is the length of xs.

Parameters:

Name	Type	Description
`v`	value	given value
`xs`	list	given list

Returns:

postfix sublist that starts with v

Type: list

pair(x, y) → {pair}

**primitive**; makes a pair whose head (first component) is x and whose tail (second component) is y; time: Theta(1)Theta(1).

Parameters:

Name	Type	Description
`x`	value	given head
`y`	value	given tail

Returns:

pair with x as head and y as tail.

Type: pair

parse_int(s, i) → {number}

Interprets a given string s as an integer, using the positive integer i as radix, and returns the respective value.
Examples: parse_int("909", 10) returns the number 909, and parse_int("-1111", 2) returns the number -15.
See ECMAScript Specification, Section 18.2.5 for details.

Parameters:

Name	Type	Description
`s`	string	string to be converted
`i`	number	radix

Returns:

result of conversion

Type: number

prompt(s) → {string}

Pops up a window that displays the string s, provides an input line for the user to enter a text, a Cancel button and an OK button. The call of prompt suspends execution of the program until one of the two buttons is pressed. If the OK button is pressed, prompt returns the entered text as a string. If the Cancel button is pressed, prompt returns a non-string value.

Parameters:

Name	Type	Description
`s`	string	to be displayed in popup

Returns:

entered text

Type: string

remove(v, xs) → {list}

Returns a list that results from xs by removing the first item from xs that is identical (===) to v. Returns the original list if there is no occurrence. Iterative process; time: Theta(n), space: Theta(n), where n is the length of xs.

Parameters:

Name	Type	Description
`v`	value	given value
`xs`	list	given list

Returns:

xs with first occurrence of v removed

Type: list

remove_all(v, xs) → {list}

Returns a list that results from xs by removing all items from xs that are identical (===) to v. Returns the original list if there is no occurrence. Iterative process; time: Theta(n), space: Theta(n), where n is the length of xs.

Parameters:

Name	Type	Description
`v`	value	given value
`xs`	list	given list

Returns:

xs with all occurrences of v removed

Type: list

reverse(xs) → {list}

Returns list xs in reverse order. Iterative process; time: Theta(n), space: Theta(n), where n is the length of xs. The process is iterative, but consumes space Theta(n) because of the result list.

Parameters:

Name	Type	Description
`xs`	list	given list

Returns:

xs in reverse

Type: list

stringify(v) → {string}

returns a string that represents the value v, using a notation that is is consistent with JSON, but also displays undefined, NaN, Infinity, and function objects. See also textbook example.

Parameters:

Name	Type	Description
`v`	value	the argument value

Returns:

string representation of v

Type: string

tail(p) → {value}

**primitive**; returns tail (second component of given pair p; time: Theta(1)Theta(1).

Parameters:

Name	Type	Description
`p`	pair	given pair

Returns:

tail of p

Type: value