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diff --git a/miralib/manual/15 b/miralib/manual/15 new file mode 100644 index 0000000..e299ae3 --- /dev/null +++ b/miralib/manual/15 @@ -0,0 +1,92 @@ +_D_e_f_i_n_i_t_i_o_n_s + +The purpose of a definition is to give a value to one or more variables. +There are two kinds of definition, `scalar' and `conformal'. A scalar +definition gives a value to a single variable, and consists of one or +more consecutive equations of the form + fnform = rhs + +where a `fnform' consists of the name being defined followed by zero or +more formal parameters. Here are three examples of scalar definitions, +of `answer', `sqdiff' and `equal' respectively + answer = 42 + + sqdiff a b = a^2 - b^2 + + equal a a = True + equal a b = False + +When a scalar definition consists of more than one equation, the order +of the equations can be significant, as the last example shows. (Notice +that `equals' as defined here is a function of two arguments with the +same action as the built in `=' operator of boolean expressions.) + +A conformal definition gives values to several variables simultaneously +and is an equation of the form + pattern = rhs + +An example of this kind of definition is + (x,y,z) = ploggle + +For this to make sense, the value of `ploggle' must of course be a +3-tuple. More information about the _p_a_t_t_e_r_n _m_a_t_c_h_i_n_g aspect of +definitions is given in the manual section of that name. + +Both fnform and pattern equations share a common notion of `right hand +side' + +_R_i_g_h_t_ _h_a_n_d_ _s_i_d_e_s + +The simplest form of rhs is just an expression (as in all the equations +above). It is also possible to give several alternative expressions, +distinguished by guards. A guard consists of the word `if' followed by +a boolean expression. An example of a right hand side with several +alternatives is given by the following definition of the greatest common +divisor function, using Euclid's algorithm + gcd a b = gcd (a-b) b, _i_f a>b + = gcd a (b-a), _i_f a<b + = a, _i_f a=b + +Note that the guards are written on the right, following a comma. The +layout is significant (because the offside rule is used to resolve any +ambiguities in the parse). + +The last guard can be written `otherwise', to indicate that this is the +case which applies if all the other guards are false. For example the +correct rule for recognising a leap year can be written: + leap y = y _d_i_v 400 = 0, _i_f y _m_o_d 100 = 0 + = y _d_i_v 4 = 0, _o_t_h_e_r_w_i_s_e + +The _o_t_h_e_r_w_i_s_e may here be regarded as standing for _i_f y _m_o_d 100 ~= 0. +In the general case it abbreviates the conjunction of the negation of +all the previous guards, and may be used to avoid writing out a long +boolean expression. + +Although it is better style to write guards that are mutually exclusive, +this is not something the compiler can enforce - in the general case the +alternative selected is the first (in the order they are written) whose +guard evaluates to True. + +[In older versions of Miranda the presence of the keyword `if' after the +guard comma was optional.] + +_B_l_o_c_k_ _s_t_r_u_c_t_u_r_e + +A right hand side can be qualified by a _w_h_e_r_e clause. This is written +after the last alternative. The bindings introduced by the _w_h_e_r_e govern +the whole rhs, including the guards. Example + foo x = p + q, _i_f p<q + = p - q, _i_f p>=q + _w_h_e_r_e + p = x^2 + 1 + q = 3*x^3 - 5 + +Notice that the whole _w_h_e_r_e clause must be indented, to show that it is +part of the rhs. Following a _w_h_e_r_e can be any number of definitions, +and the syntax of such local definitions is exactly the same as that for +top level definitions (including therefore, recursively, the possibility +that they may contain nested _w_h_e_r_e's). + +It is not permitted to have locally defined types, however. New +typenames can be introduced only at top level. + |