10. Appendix B: The Standard ML Basis Library

The bool datatype is either false or true.

not true = false, not false = true.

Converts a true/false value to a string for printing or other purposes.

Converts from a string to a bool. An option is either NONE or SOME val. If the string cannot be converted to a bool (i.e. it does not contain true or false), then NONE is returned. Otherwise SOME true or SOME false is returned. Pattern-matching can be used to determine the return value.

The type of integers.

An option indicating the precision of integers. For instance, SOME 31 indicating 32-bit integers from to . If the value is NONE it indicates arbitrary precision.

Conversion functions from and to large integers.

Conversion functions from and to 32-bit integers. Depending on implementation these may be identity functions.

Unary negation. ~6 is a negative 6.

Typical integer operations. Note that div and mod are infix operators returning the integer division and remainder respectively. For instance, 6 div 4 = 1 and 6 mod 4 = 2. These operations are infix operators.

These two operations reflect that most hardware implementations of integer division behave differently than the mathematical definition used by div and mod for negative integers. Consider the following. This shows that mod and div factor –6 as –2 * 4 2 while quot and rem factor –6 as –1 * 4 –2. The mathematical definition of mod always results in a positive remainder. However, computer hardware often calculates using quot and rem semantics possibly resulting in faster calculations.

Maximum and minimum functions of two integers. Returns the max or min value of the pair of integers.

Returns the absolute value.

Returns either 1 or −1 depending on the sign of the integer.

True or false depending on the two integers.

Relational operators for the ordering of integers. These operators are infix operators.

Returns one of the order values of GREATER, LESS, or EQUAL depending on the integers.

Constant values for convenience for pi and e. e is the base of natural log values, ln e = 1.

The square root of a non-negative real yields a real. For negative numbers it yields nan which stands for Not A Number.

Various trigonometric functions.

Raises the first argument to the power specified by the second argument.

Natural and log base 10 functions.

Hyperbolic functions.

The base used in the floating point representation, either 2 or 10.

The number of digits in the mantissa in the base specified by radix.

Various constant values.

Normal binary operations. These operators are infix operators.

Multiply by a factor and add a term as in *+(6.0, 5.0, 3.0) which yields 33.0.

Unary negation.

Absolute value.

Binary max and min.

Returns −1 or 1 depending on the sign.

True if negative and false otherwise.

True if both have same sign.

The result is the first argument with the sign of the second argument.

Returns GREATER, LESS, or EQUAL depending on how the first argument compares to the second. The compareReal has slightly different semantics for unordered real numbers (i.e. nan) returning IEEEReal.UNORDERED in those cases.

Binary relational operators. These are infix operators.

Tests for real values.

Returns the IEEE class to which the real belongs.

Various real to string or stream conversion functions. See int or bool for details on these functions.

Mantissa, exponent and fractional part functions.

Determines if it is a proper real number (not nan or inf). If it is proper, it returns the argument, otherwise an exception is raised.

Various truncation and rounding functions.

Numeric conversion functions.

The character type.

Conversion from and to ASCII values.

Various constants.

Moves through ASCII values.

Infix relational operators.

See other compare functions for a description of the order type.

Various conversion functions to and from strings.

String search functions.

Character test functions.

Upper and lowercase conversion functions.

Maximum string size.

Current size of a string.

String subscript operator.

Convert char to string.

A couple of substring operations. Extract’s third argument is either SOME x where x is the ending lcoation+1 for the substring, or NONE to have extract extend to the the end of the string.

Binary string concatenation.

N-ary string concatenation.

A variation on the other two concatenation operations.

Conversion to/from a list of characters to a string. These are useful when writing recursive string functions.

This is a higher order function that applies a character to character function to each character of a string and returns the string of collected results.

Same as map above, but applies a character to string function to each character returning the string of collected strings.

These two functions return tokens from a string. The char to bool function defines the delimiters of tokens. In other words the first argument is a function that returns true when white space is encountered. The tokens function always returns a non-empty token, the fields function may return empty tokens.

These are substring dectecting functions.

Returns one of GREATER, LESS, or EQUAL depending on the two values being compared.

Compares two strings lexicographically according to the provided character ordering.

Four infix, normal lexicographical comparisons.

Replaces non-printing characters with SML escape character sequences.

Various string conversion functions and stream reading functions.

A list is formed from an element and a list. It is a recursive data structure with O(n) access to any element of the list. This should not be confused with an array that provides O(1) element access. The : : is called cons and stands for list construction or constructor. It forms a list from an element, e, and a list, lst as in e: :lst. The nil keyword is used to represent an empty list. Writing [] is equivalent to nil in Standard ML. Lists in Standard ML must be homogenous, containing all the same type of elements.

Raised as necessary by various functions should an empty list be used as an argument. Not raised unless necessary.

Returns true if the given list is empty.

hd e: :lst returns e while tl e: :lst returns lst. hd is short for head of the list and tl is short for tail of the list.

Returns SOME of the head and tail of a list or NONE if the list is empty. Calling getItem (e: :lst) returns SOME (e, lst).

Returns the first i elements of a list given a list and i. Raises Subscript if the list is too short.

Returns the rest of a list after the first i elements. Raises Subscript if the list is too short.

Returns the length of a list.

Returns the reverse of a list.

This is list concatenation, not to be confused with :: which is list construction. This is an infix operator. So [1, 2, 3]@[4, 5, 6] is legal and so is 1 ::[2, 3, 4, 5, 6] which both yield the same result.

This takes a list of lists of all the same element and concatenates each of the lists together returning one big list of all the elements.

Reverses the first list and appends it to the second.

This function applies the first argument, a function with a side-effect, to each element of a list. The unit type is another name for the empty tuple (i.e. ()) which is the return type of many functions that have side-effects.

The map function applies a function to each element of a list, building a new list of all the results.

This is like map except that if NONE is returned by the function, it is omitted from the resulting list. Only values of SOME val are included in the final result.

Given a predicate function and a list, the find function returns either SOME val for the found value or NONE indicating the predicate did not return true for any element of the list.

This function returns a new list of all elements of the list that satisfy the provided predicate function.

This function returns a tuple where the first list consists of all elements that satisfy the predicate function and the second is comprised of the elements that did not satisfy the predicate.

This function applies a provided function to each element and an initial value, folding all the results into one finals result. This function is called foldr because it is right-associative. Here is an example of calling foldr. The use of op - in the example transforms the infix - operator to a prefix function. The example computed (1 – (2 – (3 – (4 – 0)))). If the list is empty then the initial value, the second argument, is returned.

This function is the left-associative analog of foldr meaning that the initial value is applied along with the first element of the list and that result applied along with the second element of the list and so on. For example, The example computed (4 – (3 – (2 – (1 – 0)))). If the list is empty, then the initial value, the second argument, is returned.

Builds a list of n elements. The n is the first argument to tabulate. The each element is generated by passing one of 0 to n-1 to the second argument, a function. Raises Size if there are less than n elements in the list.

This performs a lexicographical comparison of two lists according to the provided ordering function for each element of the lists. Returns one of LESS, GREATER, or EQUAL.

Arrays must be homogeneous in Standard ML, comprised of all the same type of elements.

Maximum size of an array.

Build an array with size n, the first argument, and all elements initialized to the value of a, the second argument.

Build an array from a list.

See List.tabulate.

The length of an array.

The O(1) element retrieval operation not provided by lists in Standard ML.

The array element assignment operation, a O(1) mutating operation.

Builds a vector from an array.

Copy utility functions.

Applies a function to an array. The first supplies the function with i provided as the first argument where i is the index of the element. The second applies the function to each element of the vector without knowledge of its location. The function applied would have some side-effect.

Applies a function to an array. The first supplies the function with i provided as the first argument where i is the index of the element. The second applies the function to each element of the vector without knowledge of its location. The function applied results in a value that replaces the value in the array at the same location.

The fold equivalents (see List.fold functions) for arrays. The foldli and foldri functions provide the index of the value in addition to the value at each element of the array.

All similar to List functions. See the List equivalents for explanations.

Standard ML supports stream operations for both input and output streams.

These are blocking input functions. The input returns an empty vector if the input stream is closed, otherwise returning one or more items in the stream. The input1 reads just one element from the stream and returns NONE if the input stream is closed. The inputN returns at most n items. The inputAll returns everything up to the end of stream.

These two functions look at the state of the stream. They are useful in making input decisions.

The closeIn function closes a stream and endOfStream closes the given stream.

Writes all elements of a vector and one element, respectively, to a stream.

Reads an input line and returns either SOME line or NONE.

Writes a substring.

Opens an input stream for reading. The argument is a filename.

Opens a string stream for reading.

Opens an output stream for writing. The argument is a filename.

Opens an output stream for writing. The argument is a filename. If the file exists, the data written will be appended to the end of the file.

These are the names of the default input, output, and error streams supplied with every program. They are precreated objects.

Prints to standard output the given string.

Uses a stream and converts it to an imperative stream where conversions can be done while reading input. See the Basis Library for a more complete description of how this works.