1.1.5 Calculations in Scheme

Scheme can be used to do calculations. It uses prefix syntax. Adding 1 and 2 is written as (+ 1 2) rather than the traditional 1+2.

guile> (+ 1 2)
3

Calculations may be nested; the result of a function may be used for another calculation.

guile> (+ 1 (* 3 4))
13

These calculations are examples of evaluations; an expression like (* 3 4) is replaced by its value 12.

Scheme calculations are sensitive to the differences between integers and non-integers. Integer calculations are exact, while non-integers are calculated to the appropriate limits of precision:

guile> (/ 7 3)
7/3
guile> (/ 7.0 3.0)
2.33333333333333

When the Scheme interpreter encounters an expression that is a list, the first element of the list is treated as a procedure to be evaluated with the arguments of the remainder of the list. Therefore, all operators in Scheme are prefix operators.

If the first element of a Scheme expression that is a list passed to the interpreter is not an operator or procedure, an error will occur:

guile> (1 2 3)

Backtrace:
In current input:
  52: 0* [1 2 3]

<unnamed port>:52:1: In expression (1 2 3):
<unnamed port>:52:1: Wrong type to apply: 1
ABORT: (misc-error)
guile>

Here you can see that the interpreter was trying to treat 1 as an operator or procedure, and it couldn’t. Hence the error is "Wrong type to apply: 1".

Therefore, to create a list we need to use the list operator, or to quote the list so that the interpreter will not try to evaluate it.

guile> (list 1 2 3)
(1 2 3)
guile> '(1 2 3)
(1 2 3)
guile>

This is an error that can appear as you are working with Scheme in LilyPond.