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Catamorphisms

The example below illustrates the use of explicit recursion within an sxml-match form. This example implements a simple calculator for the basic arithmetic operations, which are represented by the XML elements plus, minus, times, and div.

(define simple-eval
  (lambda (x)
    (sxml-match x
      [,i (guard (integer? i)) i]
      [(plus ,x ,y) (+ (simple-eval x) (simple-eval y))]
      [(times ,x ,y) (* (simple-eval x) (simple-eval y))]
      [(minus ,x ,y) (- (simple-eval x) (simple-eval y))]
      [(div ,x ,y) (/ (simple-eval x) (simple-eval y))]
      [,otherwise (error "simple-eval: invalid expression" x)])))

Using the catamorphism feature of sxml-match, a more concise version of simple-eval can be written. The pattern ,[x] recursively invokes the pattern matcher on the value bound in this position.

(define simple-eval
  (lambda (x)
    (sxml-match x
      [,i (guard (integer? i)) i]
      [(plus ,[x] ,[y]) (+ x y)]
      [(times ,[x] ,[y]) (* x y)]
      [(minus ,[x] ,[y]) (- x y)]
      [(div ,[x] ,[y]) (/ x y)]
      [,otherwise (error "simple-eval: invalid expression" x)])))

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