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The Little Schemer
============================
:by: Daniel Friedman and Matthias Felleisen
:Edition: Fourth (4rth)
See also `Scheme `_.
I read this book before starting on a scheme/physics project. I had programmed
in scheme previously as an algebra/analysis tool, but never really sat down
and got comfortable with the language. Working through all the examples
has made me *much* more comfortable with this style of programming. Despite
the humble tone and ambitions of the book I think I learned deeply.
The first 7 chapters were very straight forward, the end of chapter 8 took
some more thought and I'm not sure how happy I am with the description of
collectors and continuations.
For a better description of the Y-combinator, see these `course notes
`_.
This book is followed by `The Seasoned Schemer `_
and The Reasoned Schemer.
Preface Definitions
------------------------
This primitive function is required for most of the functions in the book::
(define atom?
(lambda (x)
(and (not (pair? x)) (not (null? x)))))
Laws
-----------------------
Law of Car
The primitive *car* is defined only for non-empty lists.
Law of Cdr
The primitive *cdr* is defined only for non-empty lists. The *cdr* of any
non-empty list is always another list.
Law of Cons
The primitive *cons* takes two arguments. The second argument to *cons*
must be a list. The result is a list.
Law of Null?
The primitive *null?* is defined only for lists.
Law of Eq?
The primitive *eq?* takes two arguments. Each must be a non-numeric atom.
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 questions
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. 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?* and
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 subpart that are of the same nature:
* on the sublists of a list.
* on the subexpressions 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.