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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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Prior to R5RS, Scheme had no standard equivalent of the eval procedure which is ubiquitous in other Lisps, although the first Lambda Paper had described evaluate as "similar to the LISP function EVAL"[19] and the first Revised Report in 1978 replaced this with enclose, which took two arguments. The second, third and fourth revised reports omitted any equivalent of eval.

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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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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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Prior to R5RS, Scheme had no standard equivalent of the eval procedure which is ubiquitous in other Lisps, although the first Lambda Paper had described evaluate as "similar to the LISP function EVAL"[19] and the first Revised Report in 1978 replaced this with enclose, which took two arguments. The second, third and fourth revised reports omitted any equivalent of eval.

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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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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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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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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.
^ Jump up to: a b 1178-1990 (Reaff 2008) IEEE Standard for the Scheme Programming Language. IEEE part number STDPD14209, unanimously reaffirmed at a meeting of the IEEE-SA Standards Board Standards Review Committee (RevCom), March 26, 2008 (item 6.3 on minutes), reaffirmation minutes accessed October 2009. NOTE: this document is only available for purchase from IEEE and is not available online at the time of writing (2009).

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