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.
Use cons to build lists.
When building a list, describe the first typical element, and then cons it onto the natural recursion.
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 will null? and when using sub1, test termination with zero?
When building a value with +, always use 0 for the value of the termination 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 multiplication.
When building a value with cons, always consider () for the value of the terminating line.
Simplify only after the function is correct.
Recur on the subparts that are of the same nature:
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On the sub-lists of a list.
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On the sub-expressions of an arithmetic expression.
Use help functions to abstract from representations.
Abstract common patterns with a new function.
Build functions to collect more than one value at a time.
The primitive car is defined only for non-empty lists.
The primitive cdr is defined only on non-empty lists. The cdr of any non-empty list is always another list.
The primitive null? is defined only for lists.
The primitive eq? takes two arguments. Each must be a non-numeric atom.