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105 lines
3 KiB
Org Mode
105 lines
3 KiB
Org Mode
#+TITLE: 2.3 - Symbolic Data
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* Quotation
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** Exercise 2.53
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What would the interpreter print in response to evaluating each of
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the following expressions?
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#+BEGIN_SRC scheme
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(list 'a 'b 'c)
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(list (list 'george))
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(cdr '((x1 x2) (y1 y2)))
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(cadr '((x1 x2) (y1 y2)))
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(pair? (car '(a short list)))
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(memq 'red '((red shoes) (blue socks)))
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(memq 'red '(red shoes blue socks))
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#+END_SRC
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----------------------------------------------------------------------
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#+BEGIN_SRC scheme :tangle yes
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;; -------------------------------------------------------------------
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;; Exercise 2.53
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;; -------------------------------------------------------------------
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(list 'a 'b 'c)
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;; (a b c)
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(list (list 'george))
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;; ((george))
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(cdr '((x1 x2) (y1 y2)))
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;; ((y1 y2))
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(cadr '((x1 x2) (y1 y2)))
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;; (y1 y2)
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(pair? (car '(a short list)))
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;; #f
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(memq 'red '((red shoes) (blue socks)))
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;; #f
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(memq 'red '(red shoes blue socks))
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;; (red shoes blue socks)
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#+END_SRC
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** Exercise 2.54
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Two lists are said to be `equal?' if they contain
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equal elements arranged in the same order. For example,
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#+BEGIN_SRC scheme
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(equal? '(this is a list) '(this is a list))
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#+END_SRC
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is true, but
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#+BEGIN_SRC scheme
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(equal? '(this is a list) '(this (is a) list))
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#+END_SRC
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is false. To be more precise, we can define `equal?' recursively
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in terms of the basic `eq?' equality of symbols by saying that `a'
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and `b' are `equal?' if they are both symbols and the symbols are
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`eq?', or if they are both lists such that `(car a)' is `equal?'
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to `(car b)' and `(cdr a)' is `equal?' to `(cdr b)'. Using this
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idea, implement `equal?' as a procedure.(5)
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----------------------------------------------------------------------
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#+BEGIN_SRC scheme :tangle yes
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;; -------------------------------------------------------------------
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;; Exercise 2.54
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;; -------------------------------------------------------------------
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(define (my-equal? a b)
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(cond ((and (null? a)
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(null? b))
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#t)
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((and (symbol? a)
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(symbol? b))
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(eq? a b))
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((and (pair? a)
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(pair? b))
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(and (eq? (car a) (car b))
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(my-equal? (cdr a) (cdr b))))
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(else #f)))
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#+END_SRC
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** Exercise 2.55
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Eva Lu Ator types to the interpreter the expression
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#+BEGIN_SRC scheme
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(car ''abracadabra)
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#+END_SRC
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To her surprise, the interpreter prints back `quote'. Explain.
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----------------------------------------------------------------------
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~'abracadabra~ expands to ~(quote abracadabra)~ Therefore
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~''abracadabra~ expands to ~'(quote abracadabra)~, which expands to
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~(quote (quote abracadabra))~, the car of which is the atom
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~quote~.
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* Example: Symbolic Differentiation
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* Example: Representing Sets
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* Example: Huffman Encoding Trees
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