The Little Schemer - Ten Commandments

The Ten Commandments

1. When recurring on a list of atoms, $lat$ , ask two questions about it: (null? lat) and else . When recurring on a number, $n$, ask two questions about it: (zero? n) and else . When recurring on a list of S-expressions, $l$, ask three questions about it: (null? l) , (atom? (car l)) , and else .

2. Use cons to build lists.

3. When building a list, describe the first typical element, and then cons it onto the natural recursion.

4. Always change at least one argument while recurring. When recurring on a list of atoms, $lat$ , use (cdr lat) . When recurring on a number, $n$ , use (sub1 n) . And when recurring on a list of S-expressions, $l$, use (car l) and (cdr l) if neither (null? l) nor (atom? (car l)) are true. It must be changed to be closer to termination. The changing argument must be tested in the termination condition:

   • when using cdr, test termination with null?.
   • when using sub1, test termination with zero?.

5. When building a value with +, always use 0 for the value of terminating line, for add 0 does not change the value of an addition. When building a value with *, always use 1 for the value of terminating line, for multiplying by 1 does not change the value of multiplication. When building a value with cons, always consider () for the value of the value of the terminating line.

6. Simplify only after the function is correct.

7. Recur on the subparts that are of the same nature:

   • On the sublists of a list.
   • On the subexpressions of an arithmetic expression.

8. Use help function to abstract from representations.

9. Abstract common patterns with a new function.

10. Build functions to collect more than one value at a time.