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diff --git a/miralib/manual/9 b/miralib/manual/9 new file mode 100644 index 0000000..3d7599a --- /dev/null +++ b/miralib/manual/9 @@ -0,0 +1,62 @@ +_S_e_c_t_i_o_n_s + +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 (a*b+) 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. + +_S_p_e_c_i_a_l_ _c_a_s_e + 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. + +_A_c_k_n_o_w_l_e_d_g_e_m_e_n_t: + The idea of sections is due to Richard Bird (of Oxford University +Programming Research Group) and David Wile (of USC Information Sciences +Institute). + |