--- format: rst categories: book toc: no ... ============================ 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.