Scheme is primarily a functional programming language. It shares many characteristics with other members of the Lisp programming language family. Scheme's very simple syntax is based on s-expressions, parenthesized lists in which a prefix operator is followed by its arguments. Scheme programs thus consist of sequences of nested lists. Lists are also the main data structure in Scheme, leading to a close equivalence between source code and data formats (homoiconicity). Scheme programs can easily create and evaluate pieces of Scheme code dynamically.

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Scheme's input and output is based on the port datatype. (R5RS sec 6.6)[4] R5RS defines two default ports, accessible with the procedures current-input-port and current-output-port, which correspond to the Unix notions of standard input and standard output. Most implementations also provide current-error-port. Redirection of input and standard output is supported in the standard, by standard procedures such as with-input-from-file and with-output-to-file. Most implementations provide string ports with similar redirection capabilities, enabling many normal input-output operations to be performed on string buffers instead of files, using procedures described in SRFI 6.[30] The R6RS standard specifies much more sophisticated and capable port procedures and many new types of port.

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A formal lambda system has axioms and a complete calculation rule. It is helpful for the analysis using mathematical logic and tools. In this system, calculation can be seen as a directional deduction. The syntax of lambda calculus follows the recursive expressions from x, y, z, ...,parentheses, spaces, the period and the symbol λ.[21] The function of lambda calculation includes: First, serve as a starting point of powerful mathematical logic. Second, it can reduce the requirement of programmers to consider the implementation details, because it can use for imitate machine evaluation. Finally, the lambda calculation created a substantial meta-theory.[22]
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1550s, "figure of speech," from Medieval Latin schema "shape, figure, form, appearance; figure of speech; posture in dancing," from Greek skhema (genitive skhematos) "figure, appearance, the nature of a thing," related to skhein "to get," and ekhein "to have," from PIE root *segh- "to hold, to hold in one's power, to have" (cf. Sanskrit sahate "he masters, overcomes," sahah "power, victory;" Avestan hazah "power, victory;" Greek ekhein "to have, hold;" Gothic sigis, Old High German sigu, Old Norse sigr, Old English sige "victory").

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Entrepreneurs with a business concept would want to accumulate all the necessary resources including capital to venture into a market. Funding is part of the process, as some businesses would require large start-up sums that individuals would not have.[5] These start-up funds are essential to kick-start a business idea, without it, entrepreneurs would not have the ability to carry out their concepts in the business world.

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Scheme is widely used by a number[37] of schools; in particular, a number of introductory Computer Science courses use Scheme in conjunction with the textbook Structure and Interpretation of Computer Programs (SICP).[38] For the past 12 years, PLT has run the ProgramByDesign (formerly TeachScheme!) project, which has exposed close to 600 high school teachers and thousands of high school students to rudimentary Scheme programming. MIT's old introductory programming class 6.001 was taught in Scheme,[39] Although 6.001 has been replaced by more modern courses, SICP continues to be taught at MIT.[40] The textbook How to Design Programs by Matthias Felleisen, currently at Northeastern University, is used by some institutes of higher education for their introductory computer science courses. Both Northeastern University and Worcester Polytechnic Institute use Scheme exclusively for their introductory courses Fundamentals of Computer Science (CS2500) and Introduction to Program Design (CS1101), respectively.[41][42] Rose-Hulman uses Scheme in its more advanced Programming Language Concepts course.[43] Indiana University's introductory class, C211, is taught entirely in Scheme. The introductory class at UC Berkeley, CS 61A, was until 2015 taught entirely in Scheme, save minor diversions into Logo to demonstrate dynamic scope; all course materials, including lecture webcasts, are available online free of charge.[44] A self-paced version of the course, CS 61AS, continues to use Scheme.[45] The introductory computer science courses at Yale and Grinnell College are also taught in Scheme.[46] Programming Design Paradigms,[47] a mandatory course for the Computer science Graduate Students at Northeastern University, also extensively uses Scheme. The introductory Computer Science course at the University of Minnesota - Twin Cities, CSCI 1901, also uses Scheme as its primary language, followed by a course that introduces students to the Java programming language.[48] In the software industry, Tata Consultancy Services, Asia's largest software consultancy firm, uses Scheme in their month-long training program for fresh college graduates.[citation needed]

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R5RS resolves this confusion by specifying three procedures that return environments and providing a procedure eval that takes an s-expression and an environment and evaluates the expression in the environment provided. (R5RS sec. 6.5)[4] R6RS extends this by providing a procedure called environment by which the programmer can specify exactly which objects to import into the evaluation environment. 

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Up to the R5RS standard, the standard comment in Scheme was a semicolon, which makes the rest of the line invisible to Scheme. Numerous implementations have supported alternative conventions permitting comments to extend for more than a single line, and the R6RS standard permits two of them: an entire s-expression may be turned into a comment (or "commented out") by preceding it with #; (introduced in SRFI 62[29]) and a multiline comment or "block comment" may be produced by surrounding text with #| and |#.

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These meditations were entirely employed on Mr Allworthy's fortune; for, first, he exercised much thought in calculating, as well as he could, the exact value of the whole: which calculations he often saw occasion to alter in his own favour: and, secondly and chiefly, he pleased himself with intended alterations in the house and gardens, and in projecting many other schemes, as well for the improvement of the estate as of the grandeur of the place: for this purpose he applied himself to the studies of architecture and gardening, and read over many books on both these subjects; for these sciences, indeed, employed his whole time, and formed his only amusement.

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The introduction of lexical scope resolved the problem by making an equivalence between some forms of lambda notation and their practical expression in a working programming language. Sussman and Steele showed that the new language could be used to elegantly derive all the imperative and declarative semantics of other programming languages including ALGOL and Fortran, and the dynamic scope of other Lisps, by using lambda expressions not as simple procedure instantiations but as "control structures and environment modifiers".[23] They introduced continuation-passing style along with their first description of Scheme in the first of the Lambda Papers, and in subsequent papers, they proceeded to demonstrate the raw power of this practical use of lambda calculus.

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1660s, from French fond "a bottom, floor, ground" (12c.), also "a merchant's basic stock or capital," from Latin fundus "bottom, foundation, piece of land," from PIE root *bhudh- "bottom, base" (cf. Sanskrit budhnah, Greek pythmen "foundation, bottom," Old English botm "lowest part;" see bottom (n.)). Funds "money at one's disposal" is from 1728. Fund-raiser (also fundraiser) first attested 1957.

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verb arrange, be cunning, cabal, calculate, chart, collude, complot, compose, concoct, connive, contrive, design, devise, diagram, engineer, fabricate, fashion, frame, hatch, have designs, improvise, intrigue, invent, lay a plan, machinate, make arrangements, maneuver, manipulate, map, map out, outline, plan, plot, predesign, predetermine, prepare, project, ratio, think ahead, think out, weave a plot, work out, work up

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In contrast to Common Lisp, all data and procedures in Scheme share a common namespace, whereas in Common Lisp functions and data have separate namespaces making it possible for a function and a variable to have the same name, and requiring special notation for referring to a function as a value. This is sometimes known as the "Lisp-1 vs. Lisp-2" distinction, referring to the unified namespace of Scheme and the separate namespaces of Common Lisp.[24]

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Entrepreneurs with a business concept would want to accumulate all the necessary resources including capital to venture into a market. Funding is part of the process, as some businesses would require large start-up sums that individuals would not have.[5] These start-up funds are essential to kick-start a business idea, without it, entrepreneurs would not have the ability to carry out their concepts in the business world.

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^ Joel Moses (June 1970), The Function of FUNCTION in LISP, or Why the FUNARG Problem Should Be Called the Environment Problem, hdl:1721.1/5854, AI Memo 199, A useful metaphor for the difference between FUNCTION and QUOTE in LISP is to think of QUOTE as a porous or an open covering of the function since free variables escape to the current environment. FUNCTION acts as a closed or nonporous covering (hence the term "closure" used by Landin). Thus we talk of "open" Lambda expressions (functions in LISP are usually Lambda expressions) and "closed" Lambda expressions. [...] My interest in the environment problem began while Landin, who had a deep understanding of the problem, visited MIT during 1966-67. I then realized the correspondence between the FUNARG lists which are the results of the evaluation of "closed" Lambda expressions in LISP and ISWIM's Lambda Closures.


Scheme was created during the 1970s at the MIT AI Lab and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support first-class continuations. It had a significant influence on the effort that led to the development of Common Lisp.[2]

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Scheme started in the 1970s as an attempt to understand Carl Hewitt's Actor model, for which purpose Steele and Sussman wrote a "tiny Lisp interpreter" using Maclisp and then "added mechanisms for creating actors and sending messages".[8] Scheme was originally called "Schemer", in the tradition of other Lisp-derived languages such as 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.

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Entrepreneurs with a business concept would want to accumulate all the necessary resources including capital to venture into a market. Funding is part of the process, as some businesses would require large start-up sums that individuals would not have.[5] These start-up funds are essential to kick-start a business idea, without it, entrepreneurs would not have the ability to carry out their concepts in the business world.

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The introduction of lexical scope resolved the problem by making an equivalence between some forms of lambda notation and their practical expression in a working programming language. Sussman and Steele showed that the new language could be used to elegantly derive all the imperative and declarative semantics of other programming languages including ALGOL and Fortran, and the dynamic scope of other Lisps, by using lambda expressions not as simple procedure instantiations but as "control structures and environment modifiers".[23] They introduced continuation-passing style along with their first description of Scheme in the first of the Lambda Papers, and in subsequent papers, they proceeded to demonstrate the raw power of this practical use of lambda calculus.

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In economics funds are injected into the market as capital by lenders and taken as loans by borrowers. There are two ways in which the capital can end up at the borrower. The lender can lend the capital to a financial intermediary against interest. These financial intermediaries then reinvest the money against a higher rate. The use of financial intermediaries to finance operations is called indirect finance. A lender can also go the financial markets to directly lend to a borrower. This method is called direct finance.[3]

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Up to the R5RS standard, the standard comment in Scheme was a semicolon, which makes the rest of the line invisible to Scheme. Numerous implementations have supported alternative conventions permitting comments to extend for more than a single line, and the R6RS standard permits two of them: an entire s-expression may be turned into a comment (or "commented out") by preceding it with #; (introduced in SRFI 62[29]) and a multiline comment or "block comment" may be produced by surrounding text with #| and |#.

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plan, design, plot, scheme, project mean a method devised for making or doing something or achieving an end. plan always implies mental formulation and sometimes graphic representation. plans for a house design often suggests a particular pattern and some degree of achieved order or harmony. a design for a new dress plot implies a laying out in clearly distinguished sections with attention to their relations and proportions. the plot of the play scheme stresses calculation of the end in view and may apply to a plan motivated by craftiness and self-interest. a scheme to defraud the government project often stresses imaginative scope and vision. a project to develop the waterfront

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The key insights on how to introduce lexical scoping into a Lisp dialect were popularized in Sussman and Steele's 1975 Lambda Paper, "Scheme: An Interpreter for Extended Lambda Calculus",[19] where they adopted the concept of the lexical closure (on page 21), which had been described in an AI Memo in 1970 by Joel Moses, who attributed the idea to Peter J. Landin.[20]

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Scheme has an iteration construct, do, but it is more idiomatic in Scheme to use tail recursion to express iteration. Standard-conforming Scheme implementations are required to optimize tail calls so as to support an unbounded number of active tail calls (R5RS sec. 3.5)[4]—a property the Scheme report describes as proper tail recursion—making it safe for Scheme programmers to write iterative algorithms using recursive structures, which are sometimes more intuitive. Tail recursive procedures and the named let form provide support for iteration using tail recursion.

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The introduction of lexical scope resolved the problem by making an equivalence between some forms of lambda notation and their practical expression in a working programming language. Sussman and Steele showed that the new language could be used to elegantly derive all the imperative and declarative semantics of other programming languages including ALGOL and Fortran, and the dynamic scope of other Lisps, by using lambda expressions not as simple procedure instantiations but as "control structures and environment modifiers".[23] They introduced continuation-passing style along with their first description of Scheme in the first of the Lambda Papers, and in subsequent papers, they proceeded to demonstrate the raw power of this practical use of lambda calculus.

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1550s, "figure of speech," from Medieval Latin schema "shape, figure, form, appearance; figure of speech; posture in dancing," from Greek skhema (genitive skhematos) "figure, appearance, the nature of a thing," related to skhein "to get," and ekhein "to have," from PIE root *segh- "to hold, to hold in one's power, to have" (cf. Sanskrit sahate "he masters, overcomes," sahah "power, victory;" Avestan hazah "power, victory;" Greek ekhein "to have, hold;" Gothic sigis, Old High German sigu, Old Norse sigr, Old English sige "victory").
^ Joel Moses (June 1970), The Function of FUNCTION in LISP, or Why the FUNARG Problem Should Be Called the Environment Problem, hdl:1721.1/5854, AI Memo 199, A useful metaphor for the difference between FUNCTION and QUOTE in LISP is to think of QUOTE as a porous or an open covering of the function since free variables escape to the current environment. FUNCTION acts as a closed or nonporous covering (hence the term "closure" used by Landin). Thus we talk of "open" Lambda expressions (functions in LISP are usually Lambda expressions) and "closed" Lambda expressions. [...] My interest in the environment problem began while Landin, who had a deep understanding of the problem, visited MIT during 1966-67. I then realized the correspondence between the FUNARG lists which are the results of the evaluation of "closed" Lambda expressions in LISP and ISWIM's Lambda Closures.

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Chez scheme is a notable example for individual type of implementation of Scheme, it was created by R. Kent Dybvig in 1985. Chez Scheme includes completely different implementation of Scheme, which could replace some of the functions of Racket. Chez scheme has a relatively different core part in distribution. As a result, the application of Chez scheme can make every Racket runs magically fast.[36]

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In the R5RS standard and also in later reports, the syntax of Scheme can easily be extended via the macro system. The R5RS standard introduced a powerful hygienic macro system that allows the programmer to add new syntactic constructs to the language using a simple pattern matching sublanguage (R5RS sec 4.3).[4] Prior to this, the hygienic macro system had been relegated to an appendix of the R4RS standard, as a "high level" system alongside a "low level" macro system, both of which were treated as extensions to Scheme rather than an essential part of the language.[26]

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R5RS resolves this confusion by specifying three procedures that return environments and providing a procedure eval that takes an s-expression and an environment and evaluates the expression in the environment provided. (R5RS sec. 6.5)[4] R6RS extends this by providing a procedure called environment by which the programmer can specify exactly which objects to import into the evaluation environment.

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