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A Scheme expression is a construct that returns a value, such as avariable reference, literal, procedure call, or conditional.
In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + is an elementary example of a geometric series that converges absolutely. There are many different expressions that can be shown to be equivalent to the problem, such as the form: 2 −1 + 2 −2 + 2 −3 +. Refer to Expression 1 and Expression 2. Expression 1: 6. 7 - 3^2. 9 + 4^3 Expression 2: 5 + 4. 2 + 6 - 2. 2 -1 (a) What is the value of Expression 1? (b) Insert parentheses in Expression 2 so that it has a value of 19. Then show why your expression has a value of 19. Although many values can be written literally as an expression, a value is not an expression. For example, the expression 1 evaluates to the value 1; the expression 1+1 evaluates to the value 2. This distinction is subtle, but important. Expressions are recipes for evaluation; values are the results of evaluation. ((1.) expression 1 expression 2.), where each is an external representation of some object. All the s must be distinct. The last may be an 'else clause,' which has the form (else expression 1 expression 2.). Semantics: A case expression is evaluated as follows.
Expression types are categorized as primitive or derived.Primitive expression types include variables and procedure calls.Derived expression types are not semantically primitive, but can insteadbe explained in terms of the primitive constructs as insection derived expression types. They are redundant in the strict sense ofthe word, but they capture common patterns of usage, and are thereforeprovided as convenient abbreviations.
Primitive expression types
Variable references
essential syntax:
An expression consisting of a variable Clearview 2 0 6.
(section Variables and regions) is a variable reference. The value ofthe variable reference is the value stored in the location to which thevariable is bound. It is an error to reference anunboundvariable.
Literal expressions
essential syntax:quote
essential syntax:'
essential syntax:
(quote ) evaluates to . may be any external representation of a Scheme object (seesection External representations). This notation is used toinclude literal constants in Scheme code.
(quote ) may be abbreviated as'. The two notations are equivalent in allrespects.
Numerical constants, string constants, character constants, and booleanconstants evaluate 'to themselves'; they need not be quoted.
As noted in section Storage model, it is an error to alter a constant(i.e. the value of a literal expression) using a mutation procedure likeset-car! or string-set!.
Procedure calls
Meta movie 2 4 0 torrent. essential syntax: .
A procedure call is written by simply enclosing in parenthesesexpressions for the procedure to be called and the arguments to bepassed to it. The operator and operand expressions are evaluated (in anunspecified order) and the resulting procedure is passed the resultingarguments.
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A number of procedures are available as the values of variables in theinitial environment; for example, the addition and multiplicationprocedures in the above examples are the values of the variables+ and *.New procedures are created by evaluating lambda expressions (see sectionsection Lambda expressions).
Procedure calls are also called combinations.
Note: In contrast to other dialects of Lisp, the order ofevaluation is unspecified, and the operator expression and the operandexpressions are always evaluated with the same evaluation rules.
Note: Although the order of evaluation is otherwise unspecified, the effect ofany concurrent evaluation of the operator and operand expressions isconstrained to be consistent with some sequential order of evaluation.The order of evaluation may be chosen differently for each procedure call.
Note: In many dialects of Lisp, the empty combination,(), is a legitimate expression. In Scheme, combinations musthave atleast one subexpression, so () is not a syntactically validexpression.
Lambda expressions
essential syntax:lambda
Syntax: should be a formal arguments list as described below,and should be a sequence of one or more expressions.
Semantics: A lambda expression evaluates to a procedure. The environment ineffect when the lambda expression was evaluated is remembered as part of theprocedure. When the procedure is later called with some actualarguments, the environment in which the lambda expression was evaluated willbe extended by binding the variables in the formal argument list tofresh locations, the corresponding actual argument values will be storedin those locations, and the expressions in the body of the lambda expressionwill be evaluated sequentially in the extended environment. The resultof the last expression in the body will be returned as the result ofthe procedure call.
should have one of the following forms:
( .):The procedure takes a fixed number of arguments; when the procedure iscalled, the arguments will be stored in the bindings of thecorresponding variables.- :The procedure takes any number of arguments; when the procedure iscalled, the sequence of actual arguments is converted into a newlyallocated list, and the list is stored in the binding of the.
( . . ):If a space-delimited period precedes the last variable, thenthe value stored in the binding of the last variable will be anewly allocatedlist of the actual arguments left over after all the other actualarguments have been matched up against the other formal arguments.
It is an error for a to appear more than once in.
Each procedure created as the result of evaluating a lambda expressionis tagged with a storage location, in order to make eqv? andeq? work on procedures (see section Equivalence predicates).
Conditionals
essential syntax:if
syntax:if
Syntax: , , and may be arbitraryexpressions.
Semantics: An if expression is evaluated as follows: first, is evaluated. If it yields a true value(see section Booleans), then is evaluatedand its value is returned. Otherwise is evaluated andits value is returned. If yields a false value and no is specified, then the result of the expression isunspecified.
Assignments
essential syntax:set!
is evaluated, and the resulting value is stored inthe location to which is bound. mustbe bound either in some regionenclosing the set! expressionor at top level. The result of the set! expression isunspecified.
Derived expression types
For reference purposes, section derived expression types gives rewrite rulesthat will convert constructs described in this section into theprimitive constructs described in the previous section.
Conditionals
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essential syntax:cond .
Syntax: Each should be of the formwhere is any expression. The last may bean 'else clause,' which has the form
Semantics: A cond expression is evaluated by evaluating the expressions of successive s in order until one of themevaluates to a true value(see section Booleans). When a evaluates to atrue value, then the remaining s in its areevaluated in order, and the result of the last in the is returned as the result of the entire condexpression. If the selected contains only the and no s, then the value of the is returnedas the result. If all s evaluate to false values, and thereis no else clause, then the result of the conditional expression isunspecified; if there is an else clause, then its s areevaluated, and the value of the last one is returned.
Some implementations support an alternative syntax,( => ), where is anexpression. If evaluates to a true value, then is evaluated. Its value must be a procedure of oneargument; this procedure is then invoked on the value of the.
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essential syntax:case .
Syntax: may be any expression. Each should havethe formwhere each is an external representation of some object.All the s must be distinct.The last may be an 'else clause,' which has the form
Semantics: A case expression is evaluated as follows. isevaluated and its result is compared against each . If theresult of evaluating is equivalent (in the sense ofeqv?; see section Equivalence predicates) to a , then theexpressions in the corresponding are evaluated from leftto right and the result of the last expression in the isreturned as the result of the case expression. If the result ofevaluating is different from every , then ifthere is an else clause its expressions are evaluated and theresult of the last is the result of the case expression;otherwisethe result of the case expression is unspecified.
essential syntax:and .
The expressions are evaluated from left to right, and thevalue of the first expression that evaluates to a false value (seesection Booleans) is returned. Any remaining expressionsare not evaluated. If all the expressions evaluate to true values, thevalue of the last expression is returned. If there are no expressionsthen #t is returned.
essential syntax:or .
The expressions are evaluated from left to right, and the value of thefirst expression that evaluates to a true value (seesection Booleans) is returned. Any remaining expressionsare not evaluated. If all expressions evaluate to false values, thevalue of the last expression is returned. If there are noexpressions then #f is returned.
Binding constructs
The three binding constructs let, let*, and letrecgive Scheme a block structure, like Algol 60. The syntax of the threeconstructs is identical, but they differ in the regionsthey establishfor their variable bindings. In a let expression, the initialvalues are computed before any of the variables become bound; in alet* expression, the bindings and evaluations are performedsequentially; while in a letrec expression, all the bindings areineffect while their initial values are being computed, thus allowingmutually recursive definitions.
essential syntax:let
Syntax: should have the formwhere each is an expression, and should be asequence of one or more expressions. It isan error for a to appear more than once in the list of variablesbeing bound.
Semantics: The s are evaluated in the current environment (in someunspecified order), the s are bound to fresh locationsholding the results, the is evaluated in the extendedenvironment, and the value of the last expression of isreturned. Each binding of a has as itsregion.
See also named let, section Iteration.
syntax:let*
Syntax: should have the formand should be a sequence ofone or more expressions.
Semantics:Let* is similar to let, but the bindings are performedsequentially from left to right, and the regionof a binding indicatedby ( ) is that part of the let*expression to the right of the binding. Thus the second binding is donein an environment in which the first binding is visible, and so on.
essential syntax:letrec Imusic 2 2 0 1.
Syntax: should have the formand should be a sequence ofone or more expressions. It is an error for a to appear morethan once in the list of variables being bound.
Semantics: The s are bound to fresh locationsholding undefined values, the s are evaluated in the resultingenvironment (in some unspecified order), each is assignedto the result of the corresponding , the isevaluated in the resulting environment, and the value of the lastexpression in is returned. Rider 2019 2 4. Each binding of a has the entire letrec expression as its region , making itpossible to define mutually recursive procedures.
One restriction on letrec is very important: it must be possibleto evaluate each without assigning or referring to the value of any. If this restriction is violated, then it is an error. Therestriction is necessary because Scheme passes arguments by value rather than byname. In the most common uses of letrec, all the s arelambda expressions and the restriction is satisfied automatically. Airbnb app for mac.
Sequencing
essential syntax:begin .
The s are evaluated sequentially from left to right,and the value of the last is returned. Thisexpression type is used to sequence side effects such as input andoutput.
Note:[SICP] uses the keyword sequence instead of begin.
Iteration
syntax:do
Syntax: should have the form should be of the formand should be a sequence of one or more expressions.
Do is an iteration construct. It specifies a set of variables tobe bound, how they are to be initialized at the start, and how they areto be updated on each iteration. When a termination condition is met,the loop exits with a specified result value.
Do expressions are evaluated as follows:The expressions are evaluated (in some unspecified order),the s are bound to fresh locations, the results of the expressions are stored in the bindings of thes, and then the iteration phase begins.
Each iteration begins by evaluating ; if the result isfalse (see section Booleans), then the expressions are evaluated in order for effect, the expressions are evaluated in some unspecified order, thes are bound to fresh locations, the results of thes are stored in the bindings of thes, and the next iteration begins.
If evaluates to a true value, then thes are evaluated from left to right and the value ofthe last is returned as the value of the doexpression. If no s are present, then the value ofthe do expression is unspecified.
The regionof the binding of a consists of the entire doexpression except for the s. It is an error for a to appear more than once in the list of dovariables.
A may be omitted, in which case the effect is thesame as if ( ) hadbeen written instead of ( ).
syntax:let
Some implementations of Scheme permit a variant on the syntax oflet called 'named let' which provides a more generallooping construct than do, and may also be used to expressrecursions.
Named let has the same syntax and semantics as ordinarylet except that is bound within to aprocedure whose formal arguments are the bound variables and whose bodyis . Thus the execution of may be repeated byinvoking the procedure named by .
Delayed evaluation
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syntax:delay
The delay construct is used together with theprocedure force toimplement lazy evaluation or call by need.(delay ) returns an object called apromise which at some point in the future may be asked (bythe force procedure)to evaluate and deliver the resulting value.
See the description of force (section Control features) for amore complete description of delay.
Quasiquotation
essential syntax:quasiquote
essential syntax:`
'Backquote' or 'quasiquote'expressions are usefulfor constructing a list or vector structure when most but not all of thedesired structure is known in advance. If nocommasappear within the , the result of evaluating` is equivalent to the result of evaluating'. If a commaappears within the, however, the expression following the comma isevaluated ('unquoted') and its result is inserted into the structureinstead of the comma and the expression. If a comma appears followedimmediately by an at-sign (@),then the followingexpression must evaluate to a list; the opening and closing parenthesesof the list are then 'stripped away' and the elements of the list areinserted in place of the comma at-sign expression sequence.
Quasiquote forms may be nested. Substitutions are made only forunquoted components appearing at the same nesting levelas the outermost backquote. The nesting level increases by one insideeach successive quasiquotation, and decreases by one inside eachunquotation.
The notations ` and(quasiquote ) are identical in all respects., is identical to (unquote), and , is identical to(unquote-splicing ). The external syntaxgenerated by write for two-element lists whosecar is one of these symbols may vary between implementations.
Unpredictable behavior can result if any of the symbolsquasiquote, unquote, or unquote-splicingappear inpositions within a otherwise than as described above.
