Scheme (programming language): Difference between revisions

The Scheme programming language is a functional programming language and a dialect of Lisp. It was developed by Guy L. Steele and Gerald Jay Sussman in the 1970s and introduced to the academic world via a series of papers now referred to as Sussman and Steele's Lambda Papers.

Scheme's philosophy is unashamedly minimalist. Its goal is not to pile feature upon feature, but to remove weaknesses and restrictions that make new features appear necessary. Therefore, Scheme provides as few primitive notions as possible, and lets everything else be implemented on top of them. For example, the main mechanism for governing control flow is tail recursion.

Scheme was the first variety of Lisp to use lexical variable scoping (as opposed to dynamic variable scoping) exclusively. It was also one of the first programming languages to support explicit continuations. Scheme supports garbage collection of unreferenced data.

It uses lists as the primary data structure, but also has good support for arrays. Owing to the minimalist specification, there is no standard syntax for creating structures with named fields, or for doing object oriented programming, but many individual implementations have such features.

Scheme was originally called "Schemer", in the tradition of the languages Planner and Conniver. The current name resulted from the authors' use of the ITS operating system, which limited filenames to 6 characters.

Advantages of Scheme

Scheme, as all Lisp dialects, has very little syntax compared to many other programming languages. It has no operator precedence rules because there are essentially no operators—prefix notation is used for all function calls.

Scheme's macro facilities allow it to be adapted to any problem domain. They can be used to add support for object-oriented programming. 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. 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. The disadvantage is that the macro may not introduce any new symbols.

Scheme encourages functional programming. Purely functional programs need no global variables and don't have side-effects, and are therefore automatically thread-safe and automatically verifiable.

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.

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 less features to implement) than a Common Lisp one; embedding lisp in low-memory hardware may also be more feasible with Scheme than Common Lisp. Schemers find it amusing to note that the Scheme standard is smaller than the index to Guy Steele's Common Lisp: The Language (that is, about 50 pages).

Disadvantages of Scheme

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

Some see the fact that functions and variables lie in the same namespace as a disadvantage, because some functions have names that are common for variables. For example, list is the name of a function, so one often sees lst or lyst as variable names instead of the obvious "list".

Standards

There are two standards that define the Scheme language: the official IEEE standard, and a de facto standard called the Revised^n-th Report on the Algorithmic Language Scheme, nearly always abbreviated RnRS, where n is the number of the revision. The latest RnRS version is R5RS, also available online.

Language elements

Comments

Comments are preceded by a semicolon (;) and continue for the rest of the line.

Variables

Variables are dynamically typed. Variables are bound by a define, a let statement, 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

Functions are first-class objects in Scheme. They can be assigned to variables. For example a function with two arguments arg1 and arg2 can be defined as

 (define fun
   (lambda (arg1 arg2)
      ...))

which can be abbreviated as follows:

 (define (fun arg1 arg2)
   ...)

Functions can be called with the following syntax:

 (fun value1 value2)

Note that the function being called is in the first position of the list while the rest of the list contain the arguments. The apply function will take the first argument and apply the rest of the arguments to the first argument, so the previous function call can also be written as

 (apply fun (list value1 value2))

In Scheme, functions are divided into two basic categories: the procedures and the 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 +
  (lambda (x y)
    (- x y)))

actually redefines the + primitive to subtract, rather than add. This code turns the + primitive into a + procedure.

Lists

Scheme uses the linked list data structure in the same form as it exists in Lisp.

Data types

Other common data types in Scheme besides functions and lists are: integer, rational, real, complex numbers, symbols, strings, ports. Most Scheme implementations also offer association lists, hash tables, vectors, arrays and structures.

Most Scheme implementations offer a full numerical tower as well as exact and inexact arithmetic.

True and false are represented by the symbols #t and #f. Actually only #f is really false when a Boolean type is required, everything else will be interpreted by Scheme as #t including the empty list. This is in contrast with LISP where the empty list is also interpreted as representing false.

Symbols can be defined in at least the following ways:

 'symbol
 (string->symbol "symbol")

Equality

Scheme has three different types of equality:

eq?

Returns #t if the two objects are the exact same object, going as far as to check where they're stored in physical storage.

eqv?

Generally the same as eq? but treats some objects (eg. characters and numbers) specially so that numbers that are = are eqv? even if they're not eq?

equal?

Compares the content of data structures such as lists, vectors and strings to determine if they are the same.

Type dependent equivalence operations also exist in Scheme:

string=?

To compare two strings

char=?

To compare characters

=

To compare numbers

Control structures

Conditional evaluation

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

The first expression for which the test evaluates to true (anything other than #f counts as true) will be evaluated. If all test 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.

Scheme also has

 (if test then-expr else-expr)

but it is used much less because cond is both more general and has overall better readability.

Loops

Loops in Scheme usually take the form of tail recursion. A classical example is the factorial function, which can be defined non-tail-recursively:

 (define (factorial n)
   (cond ((= n 0) 1)
         (else (* n (factorial (- n 1))))))

 (factorial 5)
 ;; => 120

or 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)
   (cond ((null? lst) lst)
         (else (cons (f (car lst))
                     (map f (cdr lst))))))

 (map (lambda (x) (* x x)) '(1 2 3 4))
 ;;  => (1 4 9 16)

We can define both of these tail-recursively as follows. The named let statement and the do statement are syntactic sugar which simplify tail-recursive definitions. To use factorial and map again to illustrate both forms:

 (define (factorial n)
   (let loop ((fact 1)
              (n n))
     (cond ((= n 0) fact)
           (else (loop (* n fact) (- n 1))))))

 (factorial 5)
 ;; => 120

 (define (map f lst)
   (do ((lst lst (cdr lst))
        (res '() (cons (f (car lst)) res)))
       ((null? lst) (reverse res))))

 (map (lambda (x) (* x x)) '(1 2 3 4))
 ;; => (1 4 9 16)

Please note that in both cases the tail-recursive version is preferable due to its decreased use of space.

Input/output

Scheme has the concept of ports to read from or to write to. Scheme defines three default ports, accessible with the functions: current-input-port, current-output-port and current-error-port.

Hello World

(define hello-world

  (lambda ()
        (begin

(write ‘Hello-World)

           (newline)

(hello-world))))

Examples

Scheme code can be found in the following Wikipedia articles:

• Arithmetic-geometric mean
• Currying
• Fibonacci number program
• Hello world program
• Tail recursion
• Toki Pona language
• Queue

Implementations

• MIT/GNU Scheme is a free (GPL-licensed) implementation for the x86 architecture only. It runs on GNU/Linux, FreeBSD, IBM OS/2, and Microsoft Windows (95, 98, ME, NT, 2000, and XP)
• Chez Scheme is a proprietary freeware Scheme interpreter and commercial Scheme compiler for Microsoft Windows and several UNIX systems.
• Chicken is a Scheme-to-C compiler.
• Guile is the GNU project's official extension language. This Scheme interpreter is packaged as a library to provide scripting to applications. It can be found here.
• The PLT Scheme suite is a suite of Scheme programs for Windows, Mac, and Unix platforms including an interpreter (MzScheme), a graphical toolkit (MrEd), a pedagogically-oriented graphical editor (DrScheme), and various other components including Component object model and ODBC libraries.
• Gauche is an R5RS Scheme implementation developed to be a handy script interpreter. It can be found here.
• Bigloo is a Scheme-to-C and Scheme-to-Java compiler. It has much more to offer than just a compiler: Bigloo features a mediocore type system, which greatly improves readability and debugging of code. Bigloo is a good Scheme implementation if you are looking to write numerical applications.
• Kawa is a Scheme environment, written in Java, that compiles Scheme source code into Java bytecode. Any Java library can be easily used in Kawa.
• Sisc (Second Interpreter of Scheme Code) is a Scheme environment written in Java, it doesn't compile Scheme. It also has a Java FFI.
• STklos is a Scheme implementation which provides an object system similar to CLOS and a simple interface to the GTK toolkit
• The GIMP includes a Scheme interpreter for scripted image manipulation.
• Many more implementations are listed in the schemers.org FAQ.

Additional resources

• A large collection of Scheme resources.
• Scheme Requests for Implementation (SRFI).
• Structure and Interpretation of Computer Programs by Abelson, Sussman and Sussman, considered a classic computer science text.
• How to Design Programs by Felleisen et al. Intended to teach programming using Scheme.
• The Scheme Programming Language by R. Kent Dybvig. A useful language reference.
• A bibliography of Scheme-related research, with links to online versions of many academic papers, including all of the original Lambda Papers.
• Comprehensive Scheme Archive (Network) Here, a CSAN site has been started at the beginning of 2004.
• Perl5 binding for MzScheme includes mixing Perl5 and Scheme code in the same program.
• SPOD - POD for Scheme www.elemental-programming.org provides the Scheme Plain Old Documentation text processor.