This page is a quick reference describing briefly the syntax and functionality of the more useful things in Scheme.  The descriptions here are not meant to be the official documentation for the Scheme language.  For more information, or notes on how something in Scheme evaluates, consult the Revised⁵ Report on the Algorithmic Language Scheme. If you find any mistakes or things that need to be changed/added in this handout, send a message to Brandon.

Notation

Notation used in this handout:

• Things in fixed font are things that are typed in.
• Things in italics are parameters.
• "expr ..." means zero or more expressions.
• "expr₁ expr₂ ..." means one or more expressions.
• "[...]" means an optional syntax.

Identifiers

You can use letters, numbers and "=", "-", ">", "<", "/", "*", "?", "!" and "+" in identifiers (names). "?" is typically used as a suffix for a predicate, "!" for state modification functions, "->" in the middle of type conversions (as in number->string), and ":" for symbols from different packages (as in primes:fast-prime?).

Values

• Strings - Anything enclosed with quotation marks (e.g. "String")
• Characters - #\char-name (e.g. #\a, #\A, or #\space)
• Numbers - We have integers, floats, rationals, complex (3+4i) and +inf.0 or -inf.0.  Scheme does not impose any limitation in the range of numbers.
• Symbols - Unevaluated identifiers (Can get a symbol with the quote function)

Predicates

Scheme provides a predicate for each type it supports. Predicates are followed by ? and return either #t or #f

No input can satisfy more than one of these predicates: boolean?, pair?, symbol?, number?, char?, string?, vector?, procedure?.

Booleans

• #t means true
• #f means false

In addition, any object other than #f means true as well. It is good programming style however to use #t when you explicitly mean true.

Lists

• A pair is anything that can be taken apart with the head and tail functions (see below).
• The constant "()" or empty is the empty list constant.
• A list is either a pair or the empty list (). See the Induction Examples for the inductive definition of a properly defined list.

Special Forms

Special forms are expressions that do not follow standard evaluation rules:

• (quote object) or 'object
  Both of these expressions return object (unevaluated). For instance, '(1 2 3) returns the list (1 2 3).
• (lambda (var ...) body ...)
  this expression returns a procedure that takes some values as arguments, and when called, evaluates the body expression/s.
  For example, (lambda (x) (* x x)) has the value of a one-argument method. To use the lambda expression, put it in the first position of a combination ((lambda (x) (* x x)) 5) will evaluate to 25.
• (if test consequent [alternate])
  Evaluates test, and if it evaluates to true, then it evaluates consequent, otherwise, it evaluates alternate. Keep in mind that anything that is not #f is true, so (if 0 1 2) evaluates to 1.
• (when test body₁ body₂...)
  Evaluates test, and, if true, evaluates body, otherwise it is unspecified.
• (unless test body₁ body₂...)
  Evaluates test, and, if false, evaluates body, otherwise it is unspecified. In other words, it's the opposite of when.
• (cond (test₁ body₁₁ body₁₂...)
        (test₂ body₂₁ body₂₂...)
         ...
        [(else body_else1 body_else2...)] )
  Evaluates test₁, test₂, ... until one evaluates to true, then evaluate its corresponding body_n. If all of the clauses are false, the value of the cond is unspecified. You may also use the "else" optional keyword to specify that the value of the cond is body_else if all the tests are false.
• (case compare
        ((value₁₁ value₁₂...) expr₁)
      ((value₂₁ value₂₂...) expr₂)
      ...
     [(else expr_n)] )
  Evaluates compare and compares it to each value_ij and if there's a match, expr_i is evaluated and returned. If no values match, the value of the case is unspecified. You may also use the "else" optional keyword to specify that the value of the case is expr_else if no values match. 
• (and expr ...)
  Checks the exprs from left to right until one evaluates to false, in which case it returns #f. If they all return true, and returns the value of the last expr.
• (or expr ...)
  Checks the exprs from left to right until one evaluates to true, in which case it returns that value. If they all return false, or returns #f.
• (not expr)
  If expr evaluates to #f, not returns #t. Otherwise, not returns #f. Note that not is not actually a special form, but specified here next to its relatives.
• (define var expr)
  Bind the variable name var to the value of expr. define can be used inside bodies of functions, let forms and so on - in any of these cases, it is allowed only at the beginning of a block, and it is equivalent to a letrec binding. It is considered extremely bad style to define something more than once.
• (let ((var₁ expr₁)
        (var₂ expr₂)
         ...)
     body)
  Evaluates expr₁ through expr_n and binds these values to val₁ through val_n respectively, then evaluates body in an environment with all the vars set.
• (let* ((var₁ expr₁)
         (var₂ expr₂)
          ...)
     body)
  Evaluates expr_n in an environment that has var₁ to var_n-1 set and binds this value to var_n, then evaluates body in an environment with all the vars set.
• (letrec ((name₁ expr₁)
           (name₂ expr₂)
            ...)
     body)
  Evaluates each expr_n in some unspecified order in such a way that each body can refer to another name in the letrec, and binds the resulting value to each respective name_n. It then evaluates the body in the new environment created. exprs can refer to other exprs if the reference is inside a lambda expression. One restriction on letrec is that it must be possible to evaluate each expr without assigning or referring to the value of any name. In the most common uses of letrec, all the exprs are lambda expressions and the restriction is satisfied automatically.
• (set! var expr)
  Changes the value of var to that of expr. The return value of set! is unspecified. CS212 students may not use this form until covered in class.
• (begin expr₁ expr₂ ... expr_n)
  Evaluates the exprs from left to right and returns the the value of expr_n. Useful for putting a sequence of expressions where only one is expected. begin is useful only for side-effect functions, otherwise it doesn't make much sense.
• (delay expr)
  Creates a promise containing expr unevaluated.
• (force expr)
  Evaluates expr, which should return a promise. The unevaluated contents of the promise are then evaluated and returned. force is the only way to evaluate the contents of a promise.
• (write expr) or (display expr)
  Evaluates expr and displays the result to the screen. The return value of print or display is unspecified.

Equality Testing

• (eq? x y): True if x and y reference the same object.
• (equal? x y): True if x and y are "congruent"; which roughly means if they print the same.
• (= x y): Used only for checking equality of numbers.

List Structure Operators

• (null? x): Returns #t if x is the the empty list () and #f for all other objects.
• (cons x y): Returns a pair whose head is x and whose tail is y.
• (head l): Returns the first element of the list l.
• (tail l): Returns the tail of the list l.
• (set-car! obj pair): set!s the head of pair. Don't use until presented in class.
• (set-cdr! obj pair): set!s the tail of pair. Don't use until presented in class.
• (list x₁ ...): Puts x₁, ... into a list.
• (list-ref l k): Returns the kth element of the list l.
• (length l): Returns the length of the list l.
• (append list₁ ...): Appends the lists together.
• (append! list₁ ...): Destructively appends the i^th list to the (i+1)^th list. Returns the first list. Don't use until presented in class.
• (reverse l): Turns the list l around.
• (member obj l): Searches the list l for something equal? to obj, returning the sub-list whose head is obj if found, else #f.
• (assoc obj l): For this function to work, l must be a list of pairs.  assoc searches the list looking for a pair whose head is equal? to obj, returning the pair whose head is obj if found, else #f.
• (memq obj l): Same as member, except it uses the eq? function.
• (assq obj l): Same as assoc, except it uses the eq? function.

Arithmetic and Numeric Operators

• (= x y), (< x y), (> x y), (<= x y), (>= x y): Various forms of numerical comparison.
• (max x₁ ...), (min x₁ ...): Return the maximum, minimum of all x's.
• (gcd x₁ ...), (lcm x₁ ...): Return the greatest common divisor, least common multiple of all x's.  The result is always non-negative.
• (+ x₁...): Addition.
• (* x₁...): Multiplication.
• (- x₁ x₂): Subtraction.
• (/ x₁ x₂): Division - result type depends on the input argument types.
• (expt x₁ x₂): Power operator. Raises x₁ to the x₂ power.
• (- x): Negation -x.
• (/ x): Reciprocal 1/x.
• (quotient n₁ n₂): Quotient after integer division. (Return value has sign of product of arguments).
• (remainder n₁ n₂): Remainder after integer division. (Return value has sign of dividend).
• (modulo n₁ n₂): Clock arithmetic, n₁ mod n₂. (Return value has sign of divisor).
• (zero? x), (positive? x), (negative? x): Checks whether x=0, x>0 or x<0.
• (even? x), (odd? x): Checks whether x is even or odd
• (1+ x), (1- x): Shorthand for (+ x 1) and (- x 1)
• (abs x): Absolute value of x.
• (floor x): Integer closest to x whose absolute value <= |x|. Result type depends upon x.
• (ceiling x): Integer closest to x whose absolute value >= |x|. Result type depends upon x.
• (round x): Integer closest to x, rounding to even when x is halfway between two integers.
• (sqrt x): Square root.
• (sin x), (cos x), (tan x): Trigonometric functions.
• (asin x), (acos x), (atan x): Inverse trigonometric functions.
• (exp x): The mathematical constant e raised to the power x
• (log x): The natural logaritm of x. (log 0) returns -inf.0.

Vector Operators

• (make-vector n [i]): Creates a new vector of n elements (if i is given the initial values of the elements are all i, otherwise all the elements are undefined), indexed from 0 to n-1.
• (vector x₁ ...): Evalutes x₁, ... and puts them into a vector.
• (vector-length vec): Returns the length of the vector vec, which is the number of elements it can store, (using constant time).
• (vector-ref vec i): Get i'th element of vec (in constant time). i must be a valid index.
• (vector-set! vec i val): Store val at element i of vec (in constant time).

Higher Order Functions

• (apply proc arg-list): Call proc with arg-list as arguments.
• (map func list₁ ...): Applies func element-wise to the elements of list₁, ... (that is, the first of each, the second of each, etc.) and collects the results in a list. The order it does it is not specified and probably not the one you want, but the order they appear in the result list is the right one.  If more than one list is given, each list must be of the same length.  There should be the same number of lists as there are parameters for func.
• (filter pred l): Returns the list of elements from l which satisfy pred.

Last update: 01/19/00 11:35 PM by BRB
Written by Brandon Bray and Eli Barzilay