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Diffstat (limited to 'miralib/manual/8')
| -rw-r--r-- | miralib/manual/8 | 75 |
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diff --git a/miralib/manual/8 b/miralib/manual/8 new file mode 100644 index 0000000..8909b5c --- /dev/null +++ b/miralib/manual/8 @@ -0,0 +1,75 @@ +_O_p_e_r_a_t_o_r_s_ _a_n_d_ _t_h_e_i_r_ _b_i_n_d_i_n_g_ _p_o_w_e_r_s + +Here is a list of all prefix and infix operators, in order of increasing +binding power. Operators given on the same line are of the same binding +power. Prefix operators are identified as such in the comments - all +others are infix. + + operator comments + + : ++ -- right associative + \/ associative + & associative + ~ prefix + > >= = ~= <= < continued relations allowed, eg 0<x<=10 + + - left associative + - prefix + * / _d_i_v _m_o_d left associative + ^ right associative + . associative + # prefix + ! left associative + $identifier $IDENTIFIER right associative + +Brief explanation of each operator: +: prefix an element to a list, type *->[*]->[*] +++ -- list concatenation, list subtraction, both of type [*]->[*]->[*] + A formal definition of list subtraction is given below. +\/ & logical `or', `and', both of type bool->bool->bool +~ logical negation, type bool->bool +> >= = ~= <= < + comparison operators, all of type *->*->bool + Note that there is an ordering defined on every (non-function) + type. In the case of numbers, characters and strings the order + is as you would expect, on other types it as an arbitrary but + reproducible ordering. Equality on structured data is a test + for isomorphism. (i.e. in LISP terms it is "EQUAL" not "EQ"). + It is an error to test functions for equality or order. ++ - plus, minus, type num->num->num +- unary minus, type num->num + Note that in Miranda unary minus binds less tightly than + the multiplication and division operators. This is the + usual algebraic convention, but is different from PASCAL. +* / _d_i_v _m_o_d + times, divide, integer divide, integer remainder, + all of type num->num->num + `/' can be applied to integers or fractional numbers, and + always gives a fractional result, so eg 6/2 is 3.0 + _d_i_v and _m_o_d can only be applied to integers and + give integer results, eg 7 div 2 is 3, 7 mod 2 is 1. + _d_i_v and _m_o_d obey the following laws, for a b any integers + with b ~= 0 + (i) b * (a _d_i_v b) + a _m_o_d b = a + (ii) if b>0 then 0 <= a _m_o_d b < b + if b<0 then b < a _m_o_d b <= 0 +^ `to the power of', type num->num->num +. function composition, type (**->***)->(*->**)->*->*** +# length of list, type [*]->num +! list subscripting, type [*]->num->* + note that the first element of a non-empty list x is x!0 and the + last element is x!(#x-1) +$identifier $IDENTIFIER + do-it-yourself infix, `a $f b' is equivalent in all contexts to + `f a b'. Also works for constructors of two or more arguments. + +_N_o_t_e_ _o_n_ _l_i_s_t_ _s_u_b_t_r_a_c_t_i_o_n + Here is a formal definition of the `--' operator in Miranda. It is +defined using an auxiliary function `remove' which removes the first +occurrence (if any) of a given item from a list. + + x -- [] = x + x -- (b:y) = (remove b x) -- y + remove b [] = [] + remove b (a:x) = x, if a=b + = a:remove b x, otherwise + |