Appendix A: Arithmetic expressions
This appendix gives a rather fuller and more formal description of arithmetic
expressions for readers who are interested in using SIMULA's very powerful
facilities for mathematical programming.
The order of evaluation of expressions was said to be from left to right in
chapter 2. This is obviously not the whole story and SIMULA actually follows
normal rules of operator precedence and bracketing.
Any sub-expression within an expression may be enclosed in parantheses. This
may be done recursively to any desired depth, allowing sub-expressions to be
When an expression is evaluated any parenthesised sub-expressions within it are
evaluated fully first. This rule is applied recursively, so that nested
sub-expressions are always evaluated before their enclosing expression. Where
an expression contains more than one parenthesised sub-expression, these are
evaluated left to right.
Thus the following Boolean expressions are true.
2 * 2 + 3 + 4 * 5 = 27
2 *(2 + 3)+ 4 * 5 = 30
(2 *(2 + 3)+ 4)* 5 = 70
Terms separated by operators form triples and arithmetic expressions are made up
of such triples. Each triple yields a value. Parentheses and operator precedence
determine the order of evaluation of triples and, by implication, the combinations
which yield triples. The order of operator precedence is as follows.
- exponentiation **
- multiplication and division *, /, //
- addition and subtraction +, -
Within these categories, triples are evaluated from left to right.
Thus the following are true.
4 + 2 // 2 = (2 // 2) + 4
7 * 8 + 3 * 11 ** 4 = ((11 ** 4) * 3) + (7 * 8)
Note how parantheses can make expressions easier to read, even if they do not
change the meaning.
Implicit conversion is performed, where necessary, each time a term-operator-term
triple is evaluated. This may mean several conversions of the intermediate values
in an expression, with possible rounding errors each time, during the evaluation
of a complete expression.
The following rules govern where conversion is performed:
- If the operator is integer divide, //, both terms must be integer or short
integer. Use of reals or long reals constitutes a runtime error.
- All short integer values are converted to integer. This can never cause a
- If the operator is real divide, /, both terms are converted to real or long
real, in accordance with (4) below.
- Where the terms are of different types and at least one is real or long real
conversion is performed. If one term is long real the other is converted to long
real otherwise the non-real term is converted to real.
Thye type of the final value will depend on the type of the terms after application
of these rules. Type conversion is always performed before the operation is
Implicit conversion and conditional expressions
Where the alternatives of a conditional arithmetic expression yield values of
different types, rules (2) and (4) above are applied to determine the type
of the overall expression.