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 MIT's old introductory programming class 6.001 was taught in Scheme,[39] Although 6.001 has been replaced by more modern courses, SICP continues to be taught at MIT.[40] The textbook How to Design Programs by Matthias Felleisen, currently at Northeastern University,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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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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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.
The R6RS standard has caused controversy because it is seen to have departed from the minimalist philosophy.[13][14] In August 2009, the Scheme Steering Committee, which oversees the standardization process, announced its intention to recommend splitting Scheme into two languages: a large modern programming language for programmers; and a small version, a subset of the large version retaining the minimalism praised by educators and casual implementors.[7] Two working groups were created to work on these two new versions of Scheme. The Scheme Reports Process site has links to the working groups' charters, public discussions and issue tracking system.

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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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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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Whoever considers the populousness and strength of several of these States singly at the present juncture, and looks forward to what they will become, even at the distance of half a century, will at once dismiss as idle and visionary any scheme which aims at regulating their movements by laws to operate upon them in their collective capacities, and to be executed by a coercion applicable to them in the same capacities. 

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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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The R5RS standard specifies procedures exact->inexact and inexact->exact which can be used to change the exactness of a number. inexact->exact produces "the exact number that is numerically closest to the argument". exact->inexact produces "the inexact number that is numerically closest to the argument". The R6RS standard omits these procedures from the main report, but specifies them as R5RS compatibility procedures in the standard library (rnrs r5rs (6)).

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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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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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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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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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The R5RS standard specifies procedures exact->inexact and inexact->exact which can be used to change the exactness of a number. inexact->exact produces "the exact number that is numerically closest to the argument". exact->inexact produces "the inexact number that is numerically closest to the argument". The R6RS standard omits these procedures from the main report, but specifies them as R5RS compatibility procedures in the standard library (rnrs r5rs (6)).

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Continuations in Scheme are first-class objects. Scheme provides the procedure call-with-current-continuation (also known as call/cc) to capture the current continuation by packing it up as an escape procedure bound to a formal argument in a procedure provided by the programmer. (R5RS sec. 6.4)[4] First-class continuations enable the programmer to create non-local control constructs such as iterators, coroutines, and backtracking.

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The R5RS standard specifies procedures exact->inexact and inexact->exact which can be used to change the exactness of a number. inexact->exact produces "the exact number that is numerically closest to the argument". exact->inexact produces "the inexact number that is numerically closest to the argument". The R6RS standard omits these procedures from the main report, but specifies them as R5RS compatibility procedures in the standard library (rnrs r5rs (6)).

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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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Government could allocate funds itself or through government agencies to projects that benefit the public through selection process to students or researchers and even organisations. At least two external peer-reviewers and internal research award committee review each application. The research awards committee would meet some time to discuss shortlisted applications. A further shortlist and ranking is made. Projects are funded and applicants are informed.[7]

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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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The R5RS standard specifies procedures exact->inexact and inexact->exact which can be used to change the exactness of a number. inexact->exact produces "the exact number that is numerically closest to the argument". exact->inexact produces "the inexact number that is numerically closest to the argument". The R6RS standard omits these procedures from the main report, but specifies them as R5RS compatibility procedures in the standard library (rnrs r5rs (6)).

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Alonzo Church's mathematical notation, the lambda calculus, has inspired Lisp's use of "lambda" as a keyword for introducing a procedure, as well as influencing the development of functional programming techniques involving the use of higher-order functions in Lisp. But early Lisps were not suitable expressions of the lambda calculus because of their treatment of free variables.[8]

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For generations, Nazarenes have supported the World Evangelism Fund. Working together, we accomplish so much as the Body of Christ. Become a part of missions work and partner with the Church of the Nazarene to make Christlike disciples in the nations. In the Funding the Mission plan, the World Evangelism Fund is the vehicle through which we deliver the message of hope – and your church drives that mission.

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All due respect, but in the grand scheme of things, who the hell is Morgan Sanson!?!??!? — SI.com, "Transfer Rumours: Kean to Dortmund, Tottenham's Trippier Replacement, 3 Rafael Leao Bids & More," 18 July 2019 These are small numbers in the grand scheme of things. — Jeffrey Kluger, Time, "Elon Musk Told Us Why He Thinks We Can Land on the Moon in ‘Less Than 2 Years’," 18 July 2019 In the grand scheme of NCAA basketball, Gottfried had turned into a pretty small fish. — Joseph Goodman | Jgoodman@al.com, al.com, "Basketball corruption could upstage SEC Media Days," 14 July 2019 In the larger scheme of things, unionized media workers are starting to see the world and themselves in a new light. — Clio Chang, The New Republic, "How to Save Journalism," 11 July 2019 In the grand scheme of things, respected players should be at the forefront of every conversation. — Julian Mcwilliams, BostonGlobe.com, "Mookie Betts is example of baseball’s brand-new problem," 10 July 2019 And winning 13-nil, in the grand scheme of things, can be counterproductive to the growth of the sport. — San Diego Union-Tribune, "Column: For U.S. women’s soccer team, problem is less the 13 goals than the 13 celebrations," 12 June 2019 Here’s the thing: In the grand scheme of the 2020 campaign, these transgressions by Biden are pretty minor. — NBC News, "Democratic rivals pile on Biden," 6 June 2019 In the grander scheme of Johnson Artur’s archive however, the show barely scratches the surface. — Vogue, "Photographer Liz Johnson Artur Explores the Ties That Bind the African Diaspora," 17 May 2019

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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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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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Full integration with Global Treasury Services' records will be the icing on the cake for the Funding the Mission plan. Pastors, church boards, treasurers, district officers, and other record keepers can log into the Reporting Calculator, enter a few line items, match up previous contributions, check progress toward Ten Percent recognition, and safely and securely transfer funds for World Evangelism.

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Most Lisps specify an order of evaluation for procedure arguments. Scheme does not. Order of evaluation—including the order in which the expression in the operator position is evaluated—may be chosen by an implementation on a call-by-call basis, and the only constraint is that "the effect of any concurrent evaluation of the operator and operand expressions is constrained to be consistent with some sequential order of evaluation." (R5RS sec. 4.1.3)[4] 

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Like most modern programming languages and unlike earlier Lisps such as Maclisp, Scheme is lexically scoped: all possible variable bindings in a program unit can be analyzed by reading the text of the program unit without consideration of the contexts in which it may be called. This contrasts with dynamic scoping which was characteristic of early Lisp dialects, because of the processing costs associated with the primitive textual substitution methods used to implement lexical scoping algorithms in compilers and interpreters of the day. In those Lisps, it was perfectly possible for a reference to a free variable inside a procedure to refer to quite distinct bindings external to the procedure, depending on the context of the call.
Invocations of macros and procedures bear a close resemblance—both are s-expressions—but they are treated differently. When the compiler encounters an s-expression in the program, it first checks to see if the symbol is defined as a syntactic keyword within the current lexical scope. If so, it then attempts to expand the macro, treating the items in the tail of the s-expression as arguments without compiling code to evaluate them, and this process is repeated recursively until no macro invocations remain. If it is not a syntactic keyword, the compiler compiles code to evaluate the arguments in the tail of the s-expression and then to evaluate the variable represented by the symbol at the head of the s-expression and call it as a procedure with the evaluated tail expressions passed as actual arguments to it. 

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Invocations of macros and procedures bear a close resemblance—both are s-expressions—but they are treated differently. When the compiler encounters an s-expression in the program, it first checks to see if the symbol is defined as a syntactic keyword within the current lexical scope. If so, it then attempts to expand the macro, treating the items in the tail of the s-expression as arguments without compiling code to evaluate them, and this process is repeated recursively until no macro invocations remain. If it is not a syntactic keyword, the compiler compiles code to evaluate the arguments in the tail of the s-expression and then to evaluate the variable represented by the symbol at the head of the s-expression and call it as a procedure with the evaluated tail expressions passed as actual arguments to it.

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