Contents

precedence

Usage:

This topic has information on the precedence and grouping properities of
arithmetic, matrix, logical, comparison and bit operations.

Keywords: syntax, operations

Operators in MacAnova such as '+', '/', '<', '&&' and '<-' have rules of
association and precedence which determine the order in which they are
evaluated when used together.  As much as possible these mimic the rules
of ordinary algebra where they apply and for most purposes that is all
you need to know.  This topic summarizes the rules and includes a
precedence table for all operators.

                  Association properties of operators
A binary operator OP such as '+', '^' or '<=' either associates from
left to right, that is, x OP y OP z means (x OP y) OP z, or from right
to left, that is x OP y OP z means x OP (y OP z), or does not associate
at all, that is x OP y OP z is meaningless.

Binary arithmetic operators '+', '-', '*', '/', and '%%' associate from
left to right.  For example, x - y - z means (x - y) - z and x/y/z means
(x/y)/z.  See topic 'arithmetic'.

Exponentiation ('^' or '**') associates from right to left, that is
x^y^z is x^(y^z), not (x^y)^z.  See topic 'arithmetic'.

Binary logical operators '&&' and '||' associate from left to right.
For example, u && v && w means ((u && v) && w).  See topic 'logic'.

Matrix multiplication operators '%*%', '%c%' and '%C%' associate from
left to right.  For example, x %*% y %c% z %C% w is interpreted as
((x %*% y) %c% z) %C% w.  See topic 'matrices'.

The assignment operator '<-' and arithmetic assignment operators '<-+',
'<--', '<-*', '<-/', '<-^' and <-%%' (see topic 'arithmetic') also
associate from right to left.  That is, x <- y <- z is interpreted as x
<- (y <- z) and x <-+ y <-+ z is interpreted as x <-+ (y <-+ z).  See
topics 'assignment' and 'arithmetic'.

Comparison operators do not associate, that is, for example, x < y < z
has no meaning.  See topic 'logic'.

                        Precedence of operators
"Precedence" has to do with the interpretations of expressions involving
more than one operator, for example 'x <- 3 + 4/5^2' which involves
operators '<-', '+', '/' and '^'.  Every operator has a numerical
precedence level.

The rule is simple: Operators with higher precedence are evaluated
before operators with lower precedence.

Here is a table of precedence levels for MacAnova operators:
                    Precedence   Meaning
    x %| y               1       Bitwise Or (OR)
    x %^ y               2       Bitwise Exclusive Or (XOR)
    x %& y               3       Bitwise And (AND)
    %!x                  4       Bitwise Complement (COMPL)
    x || y               5       Logical Or
    x && y               6       Logical And
    !x                   7       Logical Not
    x == y               8       Equal or same
    x != y               8       Not equal or different
    x < y                8       Less than
    x <= y               8       Less than or equal
    x > y                8       Greater than
    x >= y               8       Greater than or equal
    x + y                9       Addition (sum of x and y)
    x - y                9       Subtraction (difference of x and y)
    x * y               10       Multiplication (product of x and y)
    x / y               10       Division (x divided by y)
    x %% y              10       Modular division (x - y*floor(x/y))
    x %*% y             11       x MatMult y
    x %c% y             11       transpose(x) MatMult y
    x %C% y             11       x MatMult transpose(y)
    -x                  12       Unary minus ((-1)*x)
    +x                  12       Unary plus ((+1)*x)
    x ^ y or x ** y     13       Exponentiation (x to the y-th power)
    x <- y            14 or 0    Assign value of y to x
    x <-+ y           14 or 0    x <- x + y
    x <-- y           14 or 0    x <- x - y
    x <-* y           14 or 0    x <- x * y
    x <-/ y           14 or 0    x <- x / y
    x <-^ y           14 or 0    x <- x ^ y
    x <-** y          14 or 0    x <- x ** y
    x <-%% y          14 or 0    x <- x %% y

In the above MatMult is ordinary matrix multiplication.

You may use parentheses to group terms and change the order of
evaluation.  Subexpressions within '(...)' or '{...}' are evaluated
before the bracketed terms are combined.

The dual levels 0 and 14 for the assignment operators reflect the fact
that they have lower precedence than any operator to their right and
higher precedence than any operator to their left.  For example, x <- y
+ z sets x to y + z while x + y <- z assigns z to y and then computes
the sum of x and the new value of y.  Similarly x <-+ y + z is
equivalent to x <-+ (y+z) and x + y <-+ z is equivalent to x + (y <-+
z).

                                Examples
Expression  Interpretation   Value     Explanation
 30/5/2        (30/5)/2          3     / associates to left
 3^2^4         3^(2^4)       43046721  ^ associates to right
 4*3-2       (4*3) - 2    12 - 2 = 10  * has higher precedence than -
 3*2^4        3*(2^4)       3*16 = 48  ^ has higher precedence than *
 3<2+4        3 < (2+4)    3 < 6 =  T  + has higher precedence than <
 (3*2)^4                    6^4 = 1296 Parentheses change evaluation
                                       order
 -2^4          -(2^4)          -16     ^ has higher precedence than
                                       prefix -
 (-2)^4                         16     Parentheses change evaluation
                                       order
 T||F&&F      T||(F&&F)      T||F = T  && has higher precedence than ||
 !T||T         (!T)||T       F||T = T  ! has higher precedence than ||
 !(T||T)                     !T = F    Parentheses change evaluation
                                       order

See topic 'bit_ops' for examples of how precedence and parentheses
affect the order of evaluation of operations '%&', '%|', '%^' and '%!'.