56 lines
1.5 KiB
Racket
56 lines
1.5 KiB
Racket
#lang plait
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#| BNF for the AE language:
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ae: NUMBER
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| { ae + ae }
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| { ae - ae }
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| { ae * ae }
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| { ae / ae }
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|#
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;; AE abstract syntax trees
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(define-type AE
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[Num (val : Number)]
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[Add (l : AE) (r : AE)]
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[Sub (l : AE) (r : AE)]
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[Mul (l : AE) (r : AE)]
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[Div (l : AE) (r : AE)])
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;; to convert s-expressions into AEs
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(define (parse-sx sx)
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(let ([rec (lambda (fn sx)
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(parse-sx (fn (s-exp->list sx))))])
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(cond
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[(s-exp-match? `NUMBER sx)
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(Num (s-exp->number sx))]
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[(s-exp-match? `(ANY + ANY) sx)
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(Add (rec first sx) (rec third sx))]
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[(s-exp-match? `(ANY - ANY) sx)
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(Sub (rec first sx) (rec third sx))]
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[(s-exp-match? `(ANY * ANY) sx)
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(Mul (rec first sx) (rec third sx))]
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[(s-exp-match? `(ANY / ANY) sx)
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(Div (rec first sx) (rec third sx))]
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[else (error 'parse-sx (to-string sx))])))
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;; consumes an AE and computes the corresponding number
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(define (eval expr)
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(type-case AE expr
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[(Num n) n]
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[(Add l r) (+ (eval l) (eval r))]
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[(Sub l r) (- (eval l) (eval r))]
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[(Mul l r) (* (eval l) (eval r))]
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[(Div l r) (/ (eval l) (eval r))]))
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;; evaluate an AE program contained in an s-expr
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(define (run sx)
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(eval (parse-sx sx)))
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(test (run `3) 3)
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(test (run `{3 + 4}) 7)
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(test (run `{{3 - 4} + 7}) 6)
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(test (run `{8 * 9}) 72)
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(test (run `{8 / 2}) 4)
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(test (run `{-8 / 0}) -inf.0)
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(test (run `{8 / {5 - 5}}) +inf.0)
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(test (run `{1 / {1 / 0}}) 0.0) |