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The Ten Commandments

The First Commandment

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 question about it: (null? l), (atom? (car l)), and else.

The Second Commandment

Use cons to build lists.

The Third Commandment

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

The Fourth Commandment

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?

The Fifth Commandment

When building a value with +, always use 0 for the value of the terminating line, for adding 0 does not change the value of an addition.

When building a value with x, always use 1 for the value of the terminating line, for multiplying by 1 does not change the value of a multiplication.

When building a value with cons, always consider () for the value of the terminating line.

The Sixth Commandment

Simplify only after the function is correct.

The Seventh Commandment

Recur on the subparts that are of the same nature:

  • On the sub-lists of a list.
  • On the sub-expressions of an arithmetic expression.

The Eighth Commandment

Use help functions to abstract from representations.

The Ninth Commandment

Abstract common patterns with a new function.

The Tenth Commandment

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

The Five Rules

The Law of Car

The primitive car is defined only for non-empty lists.

The Law of Cdr

The primitive cdr is defined only for non-empty lists. The cdr of any non-empty list is always another list.

The Law of Cons

The primitive cons takes two arguments. The second argument to cons must be a list. The result is a list.

The Law of Null?

The primitive null? is defined only for lists.

The Law of Eq?

The primitive eq? takes two arguments. Each must be a non-numeric atom.

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