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The Little Schemer

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The Little Schemer

Many little exercises with little test suites written in racket.


Type Parameter name Description
Atom a A string of characters (not containing parenthesis or starting with numerics)
List l A series of S expressions separated by spaces enclosed in parenthesis
Number n A series of numeric characters (excluding floating point numbers)
S Expression sexp Any of the above
Flat list lat A list containing no lists as children
Tuple tup A list containing only numbers
Arithmetic Expression nexp A 3 item list, the 1st and 3rd entries are also nexp, the 2nd is an atom representing an operation or a number
Set set A list of atoms containing no duplicates
Pair p A list of length 2
Relation rel A set of pairs
Function fun A relation where the first element of each pair forms a set
Test test? A lambda which compares two s expressions for equality
Expression e A S expression representing a computation

Compound types

Sometimes we write functions with parameters that take multiple types, there are some conventions for these types.

Paramter naming convention Implicit types
sorn Symbol, Number
pora Pair, Atom


Naming conventions

  • *-lambdas: Recurse over a list.
  • multi-lambdas: Recurse over a list performing an action multiple times.
  • &co-lambdas: Recurse over a list performing the collector lambda each time.

Total vs Partial

(Relevant from chapter 9 onwards)

Total functions are guaranteed to terminate however partial functions may not terminate. Total functions are referred to as natural and partial as unnatural.


We assume the existence of the following functions:

Function Parameters
define (a l)
lambda (args body)
cond (((bool) (sexp))+)
atom? (sexp)
eq? (a1 a2)
null? (l)
quote (sexp)
car (l)
cdr (l)
cons (sexp l)
not (bool)
and (sexp+)
or (sexp+)
add1 (n)
sub1 (n)
zero? (n)
number? (sexp)


We write a lot of functions using the primitive functions we've been given.

Equality lambdas

  • (eq? a1 a2) - Checks equality of non-numeric atoms. (builtin)
  • (eqan? a1 a2) - Checks equality of atoms and numbers.
  • (eqlist? l1 l2) - Checks equality of two lists.
  • (equal? s1 s2) - Checks equality of two S-expressions. (builtin)

List lambdas

  • (firsts l)
  • (length l)
  • (rember* a l)
  • (occur* a l)
  • (insertR* new old l)
  • (insertL* new old l)
  • (subst* new old l)
  • (member* a l)
  • (leftmost l)
  • (eqlist? l1 l2)
  • (third l)
  • (evens-only* l)

Flat list lambdas

  • (lat? l)
  • (member? a lat)
  • (rember a lat)
  • (insertR new old lat)
  • (insertL new old lat)
  • (subst new old lat)
  • (subst2 new o1 o2 lat)
  • (multirember new old lat)
  • (multiinsertR new old lat)
  • (multiinsertL new old lat)
  • (multisubst new old lat)
  • (pick n lat)
  • (rempick n lat)
  • (no-nums lat)
  • (all-nums lat)
  • (occur a lat)
  • (multiinsertLR new oldL oldR lat)
  • (looking a lat)
  • (keep-looking a sorn lat)

Number lambdas

  • (+ n m)
  • (- n m)
  • (× n m) (note this is a unicode multiplication sign and not the letter x)
  • (> n m)
  • (< n m)
  • (= n m)
  • (↑ n m)
  • (÷ n m)
  • (one? n)

Arithmetic expression lambdas

  • (numbered? aexp)
  • (value nexp)
  • (operator nexp)
  • (1st-sub-exp nexp)
  • (2nd-sub-exp nexp)
  • (atom-to-function x)

Tuple lambdas

  • (tup? l)
  • (addtup tup)
  • (tup+ tup1 tup2)

Set lambdas

  • (set? lat)
  • (makeset lat)
  • (subset? set1 set2)
  • (eqset? set1 set2)
  • (intersect? set1 set2)
  • (intersect set1 set2)
  • (union set1 set2)
  • (intersectall l-set)

Pair lambdas

  • (a-pair? x)
  • (first p)
  • (second p)
  • (build s1 s2)
  • (revpair p)
  • (shift p)
  • (length* pora)
  • (weight* pora)
  • (shuffle pora) (partial)

Relation lambdas

  • (fun? rel)
  • (revrel rel)
  • (fullfun? rel) (aka one-to-one?)

Higher order lambdas

Where a function returns a function, I have noted the parameters of the returned function after a -> followed by a _ to represent the anonymous function.

  • (rember-f test?) -> (_ a l)
  • (eq-c? a) -> (_ x)
  • (insertL-f test?) -> (_ new old l)
  • (insertR-f test?) -> (_ new old l)
  • (insert-g seq) -> (_ new old l)

Collector lambdas

  • (multirember&co a lat col)
    • (a-friend x y)
    • (new-friend x y)
    • (latest-friend x y)
    • (last-friend x y)
  • (multiinsertLR&co new oldL oldR lat col)
  • (evens-only*&co l col)


  • (sero? n)
  • (edd1 n)
  • (zub1 n)

Table lambdas

Tables are composed of entries which are pairs of lists (of the same length), the first list is names, the second is values thus representing the binding of names to values.

Lookup lambdas take a -f lambda that runs in the case the name is not found in the entry/table. The lambda is passed the name that was not found.

  • (new-entry names values)
  • (look-up-in-entry name entry entry-f)
  • (extend-table entry table)
  • (look-in-table name table)

Interpreter lambdas

e stands for expression.

value dependencies

  • (value e)
  • (expression-to-action e)
  • (atom-to-action e)
  • (list-to-action e)
  • (meaning e table)
  • (*const e table)
  • (*quote e table)
  • (*identifier e table)
  • (*lambda e table)
    • (table-of non-primitive-lambda)
    • (formals-of non-primitive-lambda)
    • (body-of non-primitive-lambda)
  • (*cond e table)
  • (*application e table)
    • (function-of e)
    • (arguments-of e)
  • (primitive? lambda-meaning)
  • (non-primitive? lambda-meaning)
  • (initial-table name)
  • (evcon lines table)
  • (evlis args table)
  • (apply-primitive name vals)
  • (apply-closure closure vals)
  • (apply fun vals)


  • Fork the repository.
  • Add function(s) with associated test suite(s).
  • Run tests with
$ ./
  • Add an entry to the README with the function, it's signature and purpose. Hyperlink the function name to the source of the function.
  • Commit with a description of the function added.
  • Rebase onto the main branch.


Exercises from The Little Schemer (4th Ed) by Daniel P. Friedman and Matthias Felleisen




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