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authorJakob Kaivo <jkk@ung.org>2022-03-04 12:32:20 -0500
committerJakob Kaivo <jkk@ung.org>2022-03-04 12:32:20 -0500
commit55f277e77428d7423ae906a8e1f1324d35b07a7d (patch)
tree5c1c04703dff89c46b349025d2d3ec88ea9b3819 /miralib/manual/15
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+_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.
+