The way to read A+ expressions is from left to right, like English. For the most part we also read mathematical notation from left to right, although not strictly, because the notation is two-dimensional. To illustrate reading A+ expressions from left to right, consider the following examples.
b+c+d ã Read as: "b plus the result of c plus d."
x-ßy ã Read as: "x minus the reciprocal of y."
As you can see, reading from left to right in the suggested style implies that execution takes place right to left. In the first example, to say "b plus the result of c plus d" means that c+d must be formed first, and then added to b. And in the second example, to say "x minus the reciprocal of y" means that ßy must be formed before it is subtracted from x.
To be sure, reading from left to right is not necessarily associated with execution from right to left. For example, the expression bßc+d is read left to right in conventional mathematical notation as well as A+, but the order of evaluation is different in the two; in mathematics b divided by c is formed and added to d, and consequently the expression is read as "b divided by c, [pause] plus d," while in A+, b is divided by c+d. The order of execution is controlled by the relative precedence of the functions, or operations. In mathematics, division has higher precedence than addition, so that in bßc+d, division is performed before addition.
Another way to say that A+ expressions are executed from right to left is that functions have long right scope and short left scope. For example, consider:
a+b-cße«f
The arguments of the subtraction function are b on the left (short scope) and cße«f on the right (long scope). The left argument is found by starting at the subtraction symbol and moving to the left until the smallest possible complete subexpression is found. In this example it is simply the name b. If the first nonblank character to the left of the symbol had been a right parenthesis, then the left argument would have included everything to the left up to the matching left parenthesis. For example, the left argument of subtraction in a+(xßb)-cße«f is xßb.
The right argument is found by starting at the function symbol and moving to the right, all the way to the end of the expression; or until a semicolon is encountered at the same level of parenthesization, bracketing, or braces; or until a right parenthesis, brace, or bracket is encountered whose matching left partner is to the left of the symbol. In the above example, the right argument of subtraction is everything to its right. If the case of a+b-(cße)«f, the right argument is also everything to its right. However, for a+(b-cße)«f, the right argument is cße.