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| (define (tokenize s)
(regexp-match* #px"\\(|[0-9]+|\\+|-|\\*|/|\\(|\\))" s))
(define (parse tokens)
(define (parse-expr tokens)
(define-values (expr rest-tokens) (parse-term tokens))
(cond
[(null? rest-tokens) expr]
[(equal? (first rest-tokens) "+")
(define-values (rhs rest-tokens2) (parse-expr (rest rest-tokens)))
(values `(+ ,expr ,rhs) rest-tokens2)]
[(equal? (first rest-tokens) "-")
(define-values (rhs rest-tokens2) (parse-expr (rest rest-tokens)))
(values `(- ,expr ,rhs) rest-tokens2)]
[else (values expr rest-tokens)]))
(define (parse-term tokens)
(define-values (expr rest-tokens) (parse-factor tokens))
(cond
[(null? rest-tokens) expr]
[(equal? (first rest-tokens) "*")
(define-values (rhs rest-tokens2) (parse-term (rest rest-tokens)))
(values `(* ,expr ,rhs) rest-tokens2)]
[(equal? (first rest-tokens) "/")
(define-values (rhs rest-tokens2) (parse-term (rest rest-tokens)))
(values `(/ ,expr ,rhs) rest-tokens2)]
[else (values expr rest-tokens)]))
(define (parse-factor tokens)
(cond
[(number? (string->number (first tokens)))
(values (string->number (first tokens)) (rest tokens))]
[(equal? (first tokens) "(")
(define-values (expr rest-tokens) (parse-expr (rest tokens)))
(when (not (equal? (first rest-tokens) ")"))
(error "Expected closing parenthesis"))
(values expr (rest rest-tokens))]
[else
(error "Unexpected token" (first tokens))]))
(first (parse-expr tokens)))
(define (evaluate ast)
(cond
[(number? ast) ast]
[(list? ast)
(match ast
['(+ lhs rhs) (+ (evaluate lhs) (evaluate rhs))]
['(- lhs rhs) (- (evaluate lhs) (evaluate rhs))]
['(* lhs rhs) (* (evaluate lhs) (evaluate rhs))]
['(/ lhs rhs) (/ (evaluate lhs) (evaluate rhs))]
[else (error "Unknown operation" ast)])]
[else (error "Invalid expression" ast)]))
(define (calculate-expression expr)
(evaluate (parse (tokenize expr))))
(calculate-expression "(1 + 7) * 13 - 1")
|
tokenize 函数将字符串分解成词法单元，parse 函数构建语法树，evaluate 函数对语法树求值。