Operators and their binding powers
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.
: ++ -- right associative
> >= = ~= <= < continued relations allowed, eg 0div mod left associative
^ right associative
! 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.
* / div mod
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
div and mod can only be applied to integers and
give integer results, eg 7 div 2 is 3, 7 mod 2 is 1.
div and mod obey the following laws, for a b any integers
with b ~= 0
(i) b * (a div b) + a mod b = a
(ii) if b>0 then 0 <= a mod b < b
if b<0 then b < a mod 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)
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.
Note on list subtraction
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