Sections

An infix operator can be partially applied, by supplying it with only one of its operands, the result being a function of one argument. Such expressions are always parenthesised, to avoid ambiguity, and are called sections. Two different kinds of sections (called presections and postsections) are possible since either the first or the second operand can be supplied.

An example of a presection is

        (1/)

which denotes the reciprocal function. An example of a postsection is

        (/3)

which gives a concise notation for the divide by three function. Note that both of these examples are functions of type (num->num). With one exception (see below) sections can be formed using any infix operator. Further examples are (0:) which is a function for prefixing lists of numbers with zero, and (^2) which is the square function.

Sections may be regarded as the analogue of currying for infix operators. They are a minor syntactic convenience, and do not really add any power to the language, since any function denoted in this way could have been introduced by explicit definition. For the first two examples given above we could have written, say

    reciprocal y = 1/y
    divide_by_three x = x/3

and then used the function names, although this would have been somewhat more verbose.

To summarise the conventions for infixes, taking infix division as an example, note that the following expressions are all equivalent.

    a / b
    (/) a b
    (a /) b
    (/ b) a

The usual rules about operator precedence (see manual section on operators) apply to sections. For example we can write (ab+) but not (a+b), because *' is more binding than+`. The latter example should have been written ((a+b)*). As always when writing complicated expressions, if there is any possibility of ambiguity it is better to put in extra parentheses.

Special case It is not possible to form a postsection in infix minus, because of a conflict of meaning with unary minus. For example:

    (-b)

is a parenthesised occurrence of negative b, not a section. As a way round this there is a function subtract in the standard environment with the definition:- subtract x y = y - x. This is a normal curried function, so we can write (subtract b) to get the function that subtracts b from things.

Presections in infix minus, such as (a-), cause no ambiguity. There are no problems with infix plus because Miranda does not have a unary plus operator.

Acknowledgement:

The idea of sections is due to Richard Bird (of Oxford University Programming Research Group) and David Wile (of USC Information Sciences Institute).