+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Constants
+
+
+
+
+
(constant) Infinity :number
+
+
+
+
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(constant) math_E :number
+
+
+
+
+
+ The Number value for e, Euler's number,
+which is approximately 2.718281828459045.
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(constant) math_LN2 :number
+
+
+
+
+
+ The Number value for the natural logarithm of 2,
+which is approximately 0.6931471805599453.
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(constant) math_LN10 :number
+
+
+
+
+
+ The Number value for the natural logarithm of 10,
+which is approximately 2.302585092994046.
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(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:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(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:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(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:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(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:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(constant) math_SQRT2 :number
+
+
+
+
+
+ The Number value for the square root of 2, which is approximately 1.4142135623730951.
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(constant) NaN :number
+
+
+
+
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
(constant) undefined :undefined
+
+
+
+
+
+
+
+
+
Type:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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 rn-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: O(n), space: O(n),
+where n is the length of xs
+assuming f takes constant time.
+
+
+
+
+
+
+
+
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
amb() → {value}
+
+
+
+
+
+
+
+ Given n values, creates a choice point whose value is chosen,
+at run-time, from the set e1, e2, ..., en.
+If n is 0, it forces the language processor to backtrack to
+the most recent amb expression without returning a value.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ e1,e2,...en |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given values |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ a value from the given values chosen sequentially
+
+
+
+
+
+ -
+ Type
+
+ -
+
+value
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ambR() → {value}
+
+
+
+
+
+
+
+ Given n values, creates a choice point whose value is chosen,
+at run-time, randomly from the set e1, e2, ..., en.
+If n is 0, it forces the language processor to backtrack to
+the most recent amb expression without returning a value.
+Functions similarly to the amb operator but makes choices randomly
+instead of sequentially.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ e1,e2,...en |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given values |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ a value from the given values chosen randomly
+
+
+
+
+
+ -
+ Type
+
+ -
+
+value
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
an_element_of(xs) → {value}
+
+
+
+
+
+
+
+ Nondeterministically returns an element from a given list.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+list
+
+
+
+ |
+
+
+
+
+
+ given list |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ - an element from xs
+
+
+
+
+
+ -
+ Type
+
+ -
+
+value
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
an_integer_between(n, m) → {number}
+
+
+
+
+
+
+
+ Nondeterministically returns an integer between n and
+m (inclusively).
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ n |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ lower bound |
+
+
+
+
+
+
+ m |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ upper bound |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ - a number between n and m (inclusive)
+
+
+
+
+
+ -
+ Type
+
+ -
+
+number
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
append(xs, ys) → {list}
+
+
+
+
+
+
+
+ Returns a list that results from
+appending the list ys to the list xs.
+Iterative process; time: O(n), space:
+O(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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
array_length(x) → {number}
+
+
+
+
+
+
+
+ returns
+the current length of array x, which is 1 plus the
+highest index that has been used so far in an array assignment on
+x. Here literal array expressions are counted too: The
+array [10, 20, 30] has a length of 3.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ x |
+
+
+
+
+
+array
+
+
+
+ |
+
+
+
+
+
+ given array |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ current length of array
+
+
+
+
+
+ -
+ Type
+
+ -
+
+number
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bi_implication(P, Q) → {boolean}
+
+
+
+
+
+
+
+ Returns true if and only if P and Q
+satisfy the boolean equation P <--> Q.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ P |
+
+
+
+
+
+boolean
+
+
+
+ |
+
+
+
+
+
+ antecedent and consequent of the conditional |
+
+
+
+
+
+
+ Q |
+
+
+
+
+
+boolean
+
+
+
+ |
+
+
+
+
+
+ antecedent and consequent of the conditional |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ - a boolean according to the truth table of
+Material Biconditional
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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: O(n), space: O(n).
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ f |
+
+
+
+
+
+function
+
+
+
+ |
+
+
+
+
+
+ unary function |
+
+
+
+
+
+
+ n |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ given nonnegative integer |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ resulting list
+
+
+
+
+
+ -
+ Type
+
+ -
+
+list
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
build_stream(f, n) → {stream}
+
+
+
+
+
+
+
+ Makes a stream with n
+elements by applying the unary function f
+to the numbers 0 to n - 1, assumed to be a nonnegative integer.
+Lazy? Yes: The result stream forces the application of f
+ for the next element
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ f |
+
+
+
+
+
+function
+
+
+
+ |
+
+
+
+
+
+ unary function |
+
+
+
+
+
+
+ n |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ given nonnegative integer |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ resulting stream
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
cut()
+
+
+
+
+
+
+
+ Prevents the language processor from backtracking any further
+beyond the current statement.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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.
+
+
+
+
+
+
+
+
+
+
+
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 x in a separate drawing
+area in the Source Academy using a box-and-pointer diagram; time, space:
+O(n), where n is the total number of data structures such as
+pairs in all the separate structures provided in x.
+
+
+
+
+
+
+
+
+
+
+
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: O(n), space: O(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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
enum_stream(start, end) → {stream}
+
+
+
+
+
+
+
+ Returns a stream that enumerates
+numbers starting from start using a step size of 1, until
+the number exceeds (>) end.
+Lazy? Yes: The result stream forces the construction of
+ each next element
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ start |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ starting number |
+
+
+
+
+
+
+ end |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ ending number |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ stream from start to end
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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:
+O(n), where n is the number of pairs in
+x.
+
+
+
+
+
+
+
+
+
+
+
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 |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
eval_stream(s, n) → {list}
+
+
+
+
+
+
+
+ Constructs the list of the first n elements
+of a given stream s
+Lazy? Sort-of: eval_stream only forces the computation of
+the first n elements, and leaves the rest of
+the stream untouched.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ s |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+ n |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ nonnegative number of elements to place in result list |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ result list
+
+
+
+
+
+ -
+ Type
+
+ -
+
+list
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
filter(pred, xs) → {list}
+
+
+
+
+
+
+
+ Returns a list that contains
+only those elements for which the one-argument function
+pred
+returns true.
+Iterative process;
+time: O(n), space: O(n),
+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: O(n), space: O(1),
+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}
+
+
+
+
+
+
+
+ returns head (first component) of given pair p
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ p |
+
+
+
+
+
+pair
+
+
+
+ |
+
+
+
+
+
+ given pair |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ head of p
+
+
+
+
+
+ -
+ Type
+
+ -
+
+value
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
implication(P, Q) → {boolean}
+
+
+
+
+
+
+
+ Returns true if and only if P and Q
+satisfy the boolean equation P --> Q.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ P |
+
+
+
+
+
+boolean
+
+
+
+ |
+
+
+
+
+
+ antecedent of the conditional |
+
+
+
+
+
+
+ Q |
+
+
+
+
+
+boolean
+
+
+
+ |
+
+
+
+
+
+ consequent of the conditional |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ - a boolean according to the truth table of
+Material Conditional
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
integers_from(start) → {stream}
+
+
+
+
+
+
+
+ Returns infinite stream if integers starting
+at given number n using a step size of 1.
+Lazy? Yes: The result stream forces the construction of
+ each next element
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ start |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ starting number |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ infinite stream from n
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
is_array(x) → {boolean}
+
+
+
+
+
+
+
+ returns true if x
+is an array, and false if it is not.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ x |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ whether x is an array
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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}
+
+
+
+
+
+
+
+ Returns true if
+xs is a list as defined in the textbook, and
+false otherwise. Iterative process;
+time: O(n), space: O(1), where n
+is the length of the
+chain of tail operations that can be applied to xs.
+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}
+
+
+
+
+
+
+
+ returns true if x is the
+empty list null, and false otherwise.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ x |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ whether x is null
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
is_number(v) → {boolean}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ v |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ to be checked |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ indicating whether the value is a number
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
is_pair(x) → {boolean}
+
+
+
+
+
+
+
+ returns true if x is a
+pair and false otherwise.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ x |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ whether x is a pair
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
is_stream(xs) → {boolean}
+
+
+
+
+
+
+
+ Returns true if
+xs is a stream as defined in the textbook, and
+false otherwise. Iterative process;
+time: O(n), space: O(1), where n
+is the length of the
+chain of stream_tail operations that can be applied to xs.
+recurses down the stream and checks that it ends with the empty stream null.
+Laziness: No: is_stream needs to force the given stream.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given candidate |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ whether xs is a stream
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
is_string(v) → {boolean}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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: O(n), space:
+O(1), where n is the length of xs.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+list
+
+
+
+ |
+
+
+
+
+
+ given list |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ length of xs
+
+
+
+
+
+ -
+ Type
+
+ -
+
+number
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
list() → {list}
+
+
+
+
+
+
+
+ Given n values, returns a list of length n.
+The elements of the list are the given values in the given order.
+
+
+
+
+
+
+
+
+
+
+
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: O(n), space: O(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_stream(xs) → {stream}
+
+
+
+
+
+
+
+ Given list xs, returns a stream of same length with
+the same elements as xs in the same order.
+Laziness: Yes: list_to_stream
+goes down the list only when forced.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+list
+
+
+
+ |
+
+
+
+
+
+ given list |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ stream containing all elements of xs
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
list_to_string(xs) → {string}
+
+
+
+
+
+
+
+ Returns a string that represents
+list xs using the text-based box-and-pointer notation
+[...].
+
+
+
+
+
+
+
+
+
+
+
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: O(n),
+space: O(n), 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: O(n),
+space: O(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}
+
+
+
+
+
+
+
+ makes a pair whose head (first component) is x
+and whose tail (second component) is y.
+
+
+
+
+
+
+
+
+
+
+
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: O(n), space: O(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: O(n), space: O(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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
require(pred) → {string}
+
+
+
+
+
+
+
+ Forces the language processor to backtrack to the most recent
+amb expression, if and only if pred evaluates
+to false.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ pred |
+
+
+
+
+
+boolean
+
+
+
+ |
+
+
+
+
+
+ given predicate |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ - a message indicating that the given predicate
+is true
+
+
+
+
+
+ -
+ Type
+
+ -
+
+string
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
reverse(xs) → {list}
+
+
+
+
+
+
+
+ Returns list xs in reverse
+order. Iterative process; time: O(n),
+space: O(n), where n is the length of xs.
+The process is iterative, but consumes space O(n)
+because of the result list.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+list
+
+
+
+ |
+
+
+
+
+
+ given list |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ xs in reverse
+
+
+
+
+
+ -
+ Type
+
+ -
+
+list
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
set_head(p, x) → {undefined}
+
+
+
+
+
+
+
+ changes the pair p such that its head is x.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ p |
+
+
+
+
+
+pair
+
+
+
+ |
+
+
+
+
+
+ given pair |
+
+
+
+
+
+
+ x |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ undefined
+
+
+
+
+
+ -
+ Type
+
+ -
+
+undefined
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
set_tail(p, x) → {undefined}
+
+
+
+
+
+
+
+ changes the pair p such that its tail is x.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ p |
+
+
+
+
+
+pair
+
+
+
+ |
+
+
+
+
+
+ given pair |
+
+
+
+
+
+
+ x |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ undefined
+
+
+
+
+
+ -
+ Type
+
+ -
+
+undefined
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream() → {stream}
+
+
+
+
+
+
+
+ Given n values, returns a stream of length n.
+The elements of the stream are the given values in the given order.
+Lazy? No: A
+complete list is generated,
+and then a stream using list_to_stream is generated from it.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ value1,value2,...,value_n |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given values |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ stream containing all values
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_append(xs, ys) → {stream}
+
+
+
+
+
+
+
+ Returns a stream that results from
+appending the stream ys to the stream xs.
+In the result, null at the end of the first argument stream
+is replaced by the second argument, regardless what the second
+argument consists of.
+Lazy? Yes: the result stream forces the actual append operation
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given first stream |
+
+
+
+
+
+
+ ys |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given second stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ result of appending xs and ys
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_filter(pred, xs) → {stream}
+
+
+
+
+
+
+
+ Returns a stream that contains
+only those elements of given stream xs
+for which the one-argument function
+pred
+returns true.
+Lazy? Yes: The result stream forces the construction of
+ each next element. Of course, the construction
+ of the next element needs to go down the stream
+ until an element is found for which pred holds.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ pred |
+
+
+
+
+
+function
+
+
+
+ |
+
+
+
+
+
+ unary function returning boolean value |
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ stream with those elements of xs for which pred holds.
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_for_each(f, xs) → {boolean}
+
+
+
+
+
+
+
+ Applies unary function f to every
+element of the stream xs.
+Iterative process; time: O(n), space: O(1),
+Where n is the length of xs.
+f is applied element-by-element:
+stream_for_each(f, stream(1, 2)) results in the calls
+f(1) and f(2).
+Lazy? No: stream_for_each
+forces the exploration of the entire stream
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ f |
+
+
+
+
+
+function
+
+
+
+ |
+
+
+
+
+
+ unary |
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ true
+
+
+
+
+
+ -
+ Type
+
+ -
+
+boolean
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_length(xs) → {number}
+
+
+
+
+
+
+
+ Returns the length of the stream
+xs.
+Iterative process; time: O(n), space:
+O(1), where n is the length of xs.
+Lazy? No: The function needs to explore the whole stream
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ length of xs
+
+
+
+
+
+ -
+ Type
+
+ -
+
+number
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_map(f, xs) → {stream}
+
+
+
+
+
+
+
+ Returns a stream that results from stream
+xs by element-wise application
+of unary function f.
+f is applied element-by-element:
+stream_map(f, stream(1,2)) results in
+the same as stream(f(1),f(2)).
+Lazy? Yes: The argument stream is only explored as forced by
+ the result stream.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ f |
+
+
+
+
+
+function
+
+
+
+ |
+
+
+
+
+
+ unary |
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ result of mapping
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_member(v, xs) → {stream}
+
+
+
+
+
+
+
+ Returns first postfix substream
+whose head is identical to
+v (using ===); returns null if the
+element does not occur in the stream.
+Iterative process; time: O(n),
+space: O(1), where n is the length of xs.
+Lazy? Sort-of: stream_member
+forces the stream only until the element
+is found.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ v |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ postfix substream that starts with v
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_ref(xs, n) → {value}
+
+
+
+
+
+
+
+ Returns the element
+of stream xs at position n,
+where the first element has index 0.
+Iterative process;
+time: O(n), space: O(1),
+where n is the length of xs.
+Lazy? Sort-of: stream_ref only forces the computation of
+ the first n elements, and leaves the rest of
+ the stream untouched.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+ n |
+
+
+
+
+
+number
+
+
+
+ |
+
+
+
+
+
+ given position |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ item in xs at position n
+
+
+
+
+
+ -
+ Type
+
+ -
+
+value
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_remove(v, xs) → {stream}
+
+
+
+
+
+
+
+ Returns a stream that results from
+xs by removing the first item from xs that
+is identical (===) to v.
+Returns the original
+stream if there is no occurrence.
+Lazy? Yes: the result stream forces the construction of each next element
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ v |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ xs with first occurrence of v removed
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_remove_all(v, xs) → {stream}
+
+
+
+
+
+
+
+ Returns a stream that results from
+xs by removing all items from xs that
+are identical (===) to v.
+Returns the original
+stream if there is no occurrence.
+Recursive process.
+Lazy? Yes: the result stream forces the construction of each next
+element
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ v |
+
+
+
+
+
+value
+
+
+
+ |
+
+
+
+
+
+ given value |
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ xs with all occurrences of v removed
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_reverse(xs) → {stream}
+
+
+
+
+
+
+
+ Returns stream xs in reverse
+order. Iterative process; time: O(n),
+space: O(n), where n is the length of xs.
+The process is iterative, but consumes space O(n)
+because of the result stream.
+Lazy? No: stream_reverse
+forces the exploration of the entire stream
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ xs in reverse
+
+
+
+
+
+ -
+ Type
+
+ -
+
+stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_tail(xs) → {Stream}
+
+
+
+
+
+
+
+ assumes that the tail (second component) of the
+pair {x} is a nullary function, and returns the result of
+applying that function. Throws an exception if the argument
+is not a pair, or if the tail is not a function.
+Laziness: Yes: {stream_tail} only forces the direct tail
+stream, but not the rest of the stream, i.e. not the tail
+of the tail, etc.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+Stream
+
+
+
+ |
+
+
+
+
+
+ given stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ result stream (if stream discipline is used)
+
+
+
+
+
+ -
+ Type
+
+ -
+
+Stream
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
stream_to_list(xs) → {list}
+
+
+
+
+
+
+
+ Given stream xs, returns a list of same length with
+the same elements as xs in the same order.
+Laziness: No: stream_to_list needs to force the whole
+stream.
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ xs |
+
+
+
+
+
+stream
+
+
+
+ |
+
+
+
+
+
+ stream |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ containing all elements of xs
+
+
+
+
+
+ -
+ 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}
+
+
+
+
+
+
+
+ returns tail (second component of given pair p
+
+
+
+
+
+
+
+
+
+
+
Parameters:
+
+
+
+
+
+
+ | Name |
+
+
+ Type |
+
+
+
+
+
+ Description |
+
+
+
+
+
+
+
+
+ p |
+
+
+
+
+
+pair
+
+
+
+ |
+
+
+
+
+
+ given pair |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Returns:
+
+
+
+ tail of p
+
+
+
+
+
+ -
+ Type
+
+ -
+
+value
+
+
+
+
+
+
+
+
+
+
+
+