Scheme

Paradigm:	multi-paradigm: functional, procedural
Appeared in:	1970s
Designed by:	Guy L. Steele and Gerald Jay Sussman
Typing discipline:	strong, dynamic
Major implementations:	PLT Scheme, , , Chicken, , Guile, bigloo, , STk
Dialects:	many
Influenced by:	Lisp, ALGOL
Influenced:	Common Lisp

Scheme is a multi-paradigm programming language and a dialect of Lisp which supports functional and procedural programming. It was developed by Guy L. Steele and Gerald Jay Sussman in the 1970s. Scheme was introduced to the academic world via a series of papers now referred to as Sussman and Steele's Lambda Papers. There are two standards that define the Scheme language: the official IEEE standard, and a de facto standard called the Revisedⁿ Report on the Algorithmic Language Scheme, nearly always abbreviated RnRS, where n is the number of the revision.

Scheme's philosophy is minimalist. Scheme provides as few primitive notions as possible, and, where practical, lets everything else be provided by programming libraries. Scheme, like all Lisp dialects, has very little syntax compared to many other programming languages. There are no operator precedence rules because fully nested and parenthesized notation is used for all function calls, and so there are no ambiguities as are found in infix notation, which mimics conventional algebraic notation.

Scheme uses lists as the primary data structure, but also has support for vectors. Scheme was the first dialect of Lisp to choose static (a.k.a. lexical) over dynamic variable scope.^{[citation needed]} It was also one of the first programming languages to support first-class continuations.^{[citation needed]}

Contents 1 History 1.1 Origin 1.2 Future 2 Advantages 3 Disadvantages 4 Language elements 4.1 Comments 4.2 Variables 4.3 Functions 4.4 Lists 4.5 Data types 4.6 Equality 4.7 Control structures 4.7.1 Conditional evaluation 4.7.2 Loops 4.8 Input/output 5 Examples 5.1 Hello world 5.2 OOP by alist (association list) 6 See also 7 References 8 External links

History

Origin

Scheme started as an attempt to understand Carl Hewitt's Actor model.^[1] Scheme was originally called "Schemer", in the tradition of other Lisp-derived languages like Planner or Conniver. The current name resulted from the authors' use of the ITS operating system, which limited filenames to two components of at most six characters each. Currently, "Schemer" is commonly used to refer to a Scheme programmer.

Future

A new language standardization process began at the 2003 Scheme workshop, with the goal of producing an R6RS standard in 2006. It breaks with the earlier RnRS approach of unanimity. R6RS will feature a standard module system; allowing a split between the core language and libraries.

Advantages

Scheme's macro facilities allow it to be adapted to many different problem domains. They can be used to add support for new paradigms, like object-oriented programming, logic programming, etc.^{[citation needed]} Scheme provides a hygienic macro system which, while not quite as powerful as Common Lisp's macro system, is much safer and often easier to work with.^{[citation needed]} The advantage of a hygienic macro system (as found in Scheme and other languages such as Dylan) is that any name clashes in the macro and surrounding code will be automatically avoided.^{[citation needed]} The hygienic macro system is usually built on some low-level facility which provides the full power of non-hygienic macros, including arbitrary syntax-time computations.

Scheme encourages functional programming. Purely functional programs have no state and no side effects, and are therefore automatically thread-safe and considerably easier to verify, optimize, and parallelize than imperative programs.

In Scheme, functions are first-class objects. This allows for higher-order functions which can further abstract program logic. Functions can also be created anonymously with lambda.^[2]

Scheme has a minimalistic standard. While this can be seen as a disadvantage, it can also be valuable. For example, writing a conforming Scheme compiler is easier (since there are fewer features to implement) than for a Common Lisp compiler.^{[citation needed]} The complete Scheme standard is smaller than the index to Guy Steele's Common Lisp: The Language (that is, about 50 pages).

Disadvantages

The Scheme standard is very minimalist, specifying only the core language. This means that there are many different implementations, each with its own extension to the language and libraries. The Scheme Requests for Implementation (SRFI) process has done much to remedy this.

The Scheme community is still somewhat fragmented, and some libraries only work in specific implementations.

Some Common Lisp users see functions and variables declared in the same namespace as a disadvantage, since that makes it impossible to use the same name for a function and a separate variable in the same scope. Many Scheme programmers (and a few Common Lisp users, who prefer CL for other reasons) see this as an advantage, since it makes use of higher-order functions easier. ^[3]

Language elements

Comments

Each comment is preceded by a semicolon (;) and extends for the rest of the line. Some implementations allow comments to span multiple lines by wrapping them with a #|...|# (possibly nested). Other implementations provide a way of commenting out an entire s-expression by prepending it with #;.^[4]

Variables

Variables are dynamically typed. Variables are bound by a define, a let expression, and a few other Scheme forms. Variables bound at the top level with a define are in global scope.

 (define var1 value)

Variables bound in a let are in scope for the body of the let.

 (let ((var1 value))
   ...
   ; scope of var1
   ...)

Functions

1  (define fun
     (lambda (arg1 arg2)
       ...))
2  (define (fun arg1 arg2)
     ...)
3  (fun value1 value2)
4  (apply fun (list value1 value2))

Functions are first-class objects in Scheme. They can be arguments to other functions and be returned by them. They can be assigned to variables. For example a function with two arguments arg1 and arg2 is defined in line 1 and line 2 is an abbreviation of it. Line 3 shows how functions are applied. Note that the function being applied is in the first position of the list while the rest of the list contains the arguments. The apply function will take the first argument and apply it to a given list of arguments, so the previous function call can also be written as seen on line 4.

In Scheme, functions are divided into two basic categories: procedures and primitives. All primitives are procedures, but not all procedures are primitives. Primitives are pre-defined functions in the Scheme language. These include +, -, *, /, set!, car, cdr, and other basic procedures. Procedures are user-defined functions. In several variations of Scheme, a user can redefine a primitive. For example, the code

(define (+ x y)
  (- x y))

actually redefines the + primitive to perform subtraction, rather than addition.

Lists

Scheme uses the linked list data structure in the same form as it exists in Lisp. "list" builds a new linked list structure, for example:

(list 1 2 3) (list (list 1 2) 3)

"car" (pronounced: [kɑr] listen (help·info)) gives the value of the head node of the list, for example:

(car (list 1 2 3))

gives

1

and

(car (list (list 1 2) 3))

gives

(1 2)

"cdr" (pronounced "could-er" ['kədər listen (help·info)] or ['kudər]) gives the list after the head node, for example:

(cdr (list 1 2 3))

gives

(2 3)

and

(cdr (list (list 1 2) 3)

gives

(3)

"cons" constructs a new list with a given car value and cdr list, for example:

(cons 1 (list 2 3))

gives

(1 2 3)

and

(cons (list 1 2) (list 3))

gives

((1 2) 3)

Each node in the linked list is a cons cell, also called a pair. As the name pair implies, a cons cell consists of two values: the first one is the car, and the second is the cdr. For

(list 1 2 3)

there are three cons cells, or pairs. The first cons cell has the number 1 in the first slot, and a pointer to the second cons cell in the second. The second cons cell has the number 2 in the first slot, and a pointer to the third cons cell in the second slot. The third cons cell has the number 3 in the first slot and a null constant in the second slot. The null constant is usually represented by '() or (quote ()). The cons function constructs these cons cells, which is why

(cons 1 (list 2 3))

gives the list

(1 2 3)

If both of the arguments are not lists, then a pair is created, represented with a dot. For example

(cons 1 2)

gives

(1 . 2)

where the cons cell consists of 1 and 2 in its slots instead of a pointer to another cons cell in its second slot.

The names of the two primitive operations for decomposing lists, car and cdr, originally come from assembly language macros for the IBM 704; they stood for "contents of address register" and "contents of decrement register" respectively.^{[citation needed]}

Data types

Other common data types in Scheme besides functions and lists are: integer, rational, real, complex numbers, symbols, strings, and ports.^[2] Most Scheme implementations also offer association lists, hash tables, vectors, arrays and structures.^{[citation needed]} Since the IEEE Scheme standard and the R4RS Scheme standard, Scheme has asserted that all of the above types are disjoint, that is no value can belong to more than one of these types; however some ancient implementations of Scheme predate these standards such that #f and '() refer to the same value, as is the case in Common Lisp.^{[citation needed]}

Most Scheme implementations offer a full numerical tower as well as exact and inexact arithmetic.^[2]

True and false are represented by #t and #f. Actually only #f is really false when a Boolean type is required, everything else will be considered true, including the empty list.^[2] Symbols can be created in at least the following ways:

 'symbol
 (string->symbol "symbol")

Equality

Scheme has three different types of equality: "eq?" returns #t if its parameters represent the same data object in memory; "eqv?" is generally the same as eq? but treats some objects (eg. characters and numbers) specially so that numbers that are = are eqv? even if they are not eq?; equal? compares data structures such as lists, vectors and strings to determine if they have congruent structure and eqv? contents.^[2]

Type dependent equivalence operations also exist in Scheme: string=?; compares two strings; char=? compares characters; = compares numbers.^[2]

Control structures

Conditional evaluation

 (if test then-expr else-expr)

The test expression is evaluated, and if the evaluation result is true (anything other than #f) then the then-expr is evaluated, otherwise else-expr is evaluated.

A form that is more convenient when conditionals are nested is cond:

 (cond (test1 expr1 ...)
       (test2 expr2 ...)
       ...
       (else exprn))

The first expression for which the test evaluates to true will be evaluated. If all tests result in #f, the else clause is evaluated.

A variant of the cond clause is

 (cond ...
       (test => expr)
       ...)

In this case, expr should evaluate to a function that takes one argument. If test evaluates to true, the function is called with the return value of test.

Loops

Loops in Scheme usually take the form of tail recursion. Scheme implementations are required to optimize tail calls so as to eliminate use of stack space where possible, so arbitrarily long loops can be executed using this technique.^[2]

A classic example is the factorial function, which can be defined non-tail-recursively:

 (define (factorial n)
   (if (= n 0)
     1
     (* n (factorial (- n 1)))))
 
 (factorial 5)
 ;; => 120

This is a direct translation of the mathematical recursive definition of the factorial: the factorial of zero (usually written 0!) is equal to 1, while the factorial of any greater natural number n is defined as n! = n * (n − 1)!.

However, plain recursion is by nature less efficient, since the Scheme system must maintain a stack to keep track of the returns of all the nested function calls. A tail-recursive definition is one that ensures that in the recursive case, the outermost call is one back to the top of the recurring function. In this case, we recur not on the factorial function itself, but on a helper routine with two parameters representing the state of the iteration:

 (define (factorial n)
   (let loop ((total 1)
              (i n))
     (if (= i 0)
       total
       (loop (* i total) (- i 1)))))
 
 (factorial 5)
 ;; => 120

A higher order function like map which applies a function to every element of a list, and can be defined non-tail-recursively:

 (define (map f lst)
   (if (null? lst)
     lst
     (cons (f (car lst))
           (map f (cdr lst)))))
  
 (map (lambda (x) (* x x)) '(1 2 3 4))
 ;;  => (1 4 9 16)

This can also be defined tail-recursively:

 (define (map f lst)
   (let loop ((lst lst)
              (res '()))
     (if (null? lst)
       (reverse res)
       (loop (cdr lst)
             (cons (f (car lst)) res)))))
 
 (map (lambda (x) (* x x)) '(1 2 3 4))
 ;; => (1 4 9 16)

In both cases the tail-recursive version is preferable due to its decreased use of space.

For basic looping, Scheme supports a simple do iterator construct:

 (do ((<variable1> <init1> <step1>) 
    ...)
  (<test> <expression> ...)
  <command> ...)

For example:

 (let ((x '(1 3 5 7 9)))
   (do ((x x (cdr x))
        (sum 0 (+ sum (car x))))
      ((null? x) sum)))

Input/output

Scheme has the concept of ports to read from or to write to.^[2] R5RS defines two default ports, accessible with the functions current-input-port and current-output-port, which correspond to the Unix notions of stdin and stdout. Most implementations also provide current-error-port.

Examples

Hello world

 (begin
   (display "Hello, World!") 
   (newline))

OOP by alist (association list)

 ;; OOP(object-oriented programming) by alist(association list) example
 (define (cat-construct age color size) ;; constructor
   (list (cons 'age age)
         (cons 'color color)
         (cons 'size size)))
 
 ;; cat meows (its age) times
 (define (cat-meow cat)
   (let loop ((iteration (cdr (assoc 'age cat))))
     (if (> iteration 0)
         (begin
           (display "Meow!\n")
           (loop (- iteration 1))))))
 
 (define billy (cat-construct 3 'white 'small))
 (display "billy's age: ")
 (display (cdr (assoc 'age billy))) (newline)
 (display "billy's color: ")
 (display (cdr (assoc 'color billy))) (newline)
 (cat-meow billy)

Scheme code can be found in the following articles:

• Arithmetic-geometric mean
• Church numeral
• Continuation passing style
• Call-with-current-continuation (aka "call/cc")
• Currying
• Fibonacci number program
• List of hello world programs
• Infinite loop
• Tail recursion
• Queue
• Quine

See also

• Structure and Interpretation of Computer Programs, a classic Computer Science textbook with lots of Scheme programming exercises.
• How to Design Programs by Felleisen et al. Intended to teach program design using Scheme.
• Lisp programming language
• Comparison of programming languages

References

External links

• R6RS.org
• schemers.org FAQ
• Schemers.org Large set of resources.
  • Home of current scheme standardization process.
• Scheme Requests for Implementation (SRFI).
• Community Scheme Wiki A wiki for all things Scheme.
• Open Directory: Scheme Many resources.
• The Scheme Programming Language ISBN 0-262-54148-3 (available online) by R. Kent Dybvig. Useful language reference.
• Bibliography of Scheme-related research, with links to online versions of many academic papers, including all of the original Lambda Papers.
• The Scheme Cookbook Wiki-based book of Scheme snippets.
• Scheme tutorial
• Interactive Scheme