_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.