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ITEC 380
2008fall
ibarland

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lect02b
scheme semantics; structs

Challenge: Write factorial, in Scheme.

Soln:
  ; ! : (-> natural-number natural-number)
  (define (! n)
    (if (= n 0)
        1
        (* n (! (- n 1)))))
Btw, I tend to use the primitives "zero?" and "sub1",
and will also use this as an excuse to introduce "cond" (Cf "if-else-if"):
  (define (! n)
    (cond [(zero? n) 1]
          [else (* n (! (sub1 n)))]))






Let's go back to the Law of Scheme:
An expression is...
Kind of expression Examples How to evaluate
Value 17, true, 'arugula You have the value already.
Placeholder pi, + Get its defined value.
Function application (+ (* 9 4) pi), (fahr->celc -40) Evaluate the subexpressions (exp0 exp1 ... expn) to get the values (val0 val1 ... valn).
  • If val0 is primitive, e.g., +, do the appropriate built-in computation, resulting in the desired value.
  • If val0 is user-defined, rewrite the function's body, replacing1 the definition parameters with the values. Evaluate the rewritten body.
Special form define, define-struct cond; and, or various, but not shocking

Note anything interesting? The definition of an expression is recursive, and the rules of how to evaluate an expression are likewise recursive. It's not a coincidence! — recursive data is naturally handled by recursive code.

Speaking of writing code: If you wanted, you could write your own Scheme interpreter: You'd make your own data definitions to represent (your versions of) numbers, placeholders, function-call, and define; then you could write a function which takes in such a data-struct (and a list of define'd placeholders), and returns a value. This is the core of drscheme -- yourself! After seeing mutually-recursive data structures, this is a reasonable week-6 beginner scheme homework (book exercises 14.4.1–4 and 17.7.1–4). Elegance speaks for itself!

Note: A thorough intro-to-programming might teach just three other special forms in Scheme (local, set-struct-field!, set!). (The formal definition of the corresponding part of C++ or Java requires about dense 30 pages, instead of 1. Those specifications have also been found to contain inconsistencies and errors, which have taken a long time to get revised.) 





Aggregate data


; Data definition:
; A boa is:
;   (make-boa string number)

(define-struct boa (name length))
;   name: string?
;   length: positive?

; Creates a struct 'boa', along with:
;  constructor: make-boa
;  accessors:   boa-name, boa-length
;  predicate:   boa?
;  mutators:    set-boa-name!, set-boa-length!  [DISALLOWED for this course.]


(define (can-fit? a-boa carrier-len)
  (<= (boa-length a-boa) carrier-len))

1 We need to be careful here: When replacing every t in (define (celc->fahr t) (+ (* 9/5 t) 32)) it's easy. But what about the technically-correct expression (define (celc->fahr t) (+ (* 9/5 t) ((lambda (t) t) 32)))? Really, there are two placeholders, each named t, in this expression. So “replacing” needs to be defined carefully, to correctly handle scope and shadowing.      ↩

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