Problem Set 10


home work!

Programming Language ISL+

Purpose This problem set concerns trees and the design of functions on s-expression data.

Problem 1

Here is a data definition for s-expressions:

;;; An Atom is one of:

;;; - Number

;;; - Symbol

;;; - String


;;; An SExp is one of:

;;; - Atom

;;; - [List-of SExp]

Here are the rules for the written, textual representation of an s-expression (that is, as a string):
  • A number is represented as a base-ten numeral: "107", "-92".

  • A symbol is represented with the characters of the symbol: "foo", "bar". (You may assume that symbols don’t have odd characters, such as space, parentheses, quote characters, etc.)

  • A string is represented with the characters of the string, delimited by a pair of double-quote characters: "\"foo\"", "\"bar\"". (Note that backslash-doublequote is how you put a doublequote character in a string. You may assume that strings don’t have odd characters, such as double-quote characters themselves.)

  • A list of s-expressions is represented by (1) a left parenthesis; (2) the items of the list, separated by one or more spaces; (3) a close parenthesis. For example, "(a (37 \"foo\") c)" is the string encoding of a three-element list, whose first element is the symbol "a", whose second element is a two-element list (a number and a string), and whose third element is the symbol "c".

Design a function (and any necessary helper functions) that will consume an s-expression and produce a string with the textual representation of that s-expression. For example:

(check-expect (sexp->string '(a (37 "foo") c)) "(a (37 \"foo\") c)")

  • Your function can add a bit of extra whitespace before/after list elements if it makes it simpler; that’s fine. For example, this is a fine three-element list of symbols: "(a b c )".

  • You will probably want to look up the useful functions number->string and symbol->string.

  • If you raise the language level to "Advanced Student", you can use the display function to make DrRacket print out data in the interaction window.


Let’s build some lego buildings out of lego bricks. Here are data definitions for lego bricks and lego buildings:
(define-struct lego (label color width))
; A Lego is a structure:
;    (make-lego Number Symbol Number)
; interpretation: (make-lego l c w) is the lego brick
; with label l, color c, and width w (in pixels).
(define-struct bigger (lego left right))
; A LegoBldg (lego building) is one of:
; - Lego
; - (make-bigger Lego LegoBldg LegoBldg)
; interpretation: (make-bigger l lft rgt) makes a bigger
; lego building by putting a lego brick l on top of two lego
; buildings lft (left) and rgt (right).

Problem 2 Design a function, count-bricks, that takes a lego building and produces the total number of lego bricks in that building.

Problem 3 Each lego brick is 10 pixels tall. Design a function, how-high, that takes a lego building and produces the total height of the lego building (in pixels).

Problem 4 Design a function, contains-colored-brick?, that takes a lego building and a color, and determines whether the building contains a lego brick of the given color.

Problem 5 Design a function, find-colored-brick?, that takes a lego building and a color and finds any lego with the given color in the building, or returns false if there are no such legos.

Here is the data definition for the type of data this function returns:
; A MaybeLego is one of:
; - false
; - Lego

Your function should not use contains-colored-brick?, it should not traverse/examine parts of the building more than once, and it should stop searching once any brick of the given color is found.

Problem 6 Design a function, lb->image, that takes a lego building and produces an image of the building.

Hints: You may want to look up above and beside/align in Help Desk. Also, you may want to design a helper function, lego->image, that takes a lego and produces an image of the lego. All legos are rectangular and 10 pixels tall.

Here are some examples:
(make-bigger (make-lego 4 'purple 80)
             (make-bigger (make-lego 2 'blue 60)
                          (make-lego 1 'yellow 40)
                          (make-lego 3 'red 40))
             (make-bigger (make-lego 6 'orange 60)
                          (make-lego 5 'green 40)
                          (make-lego 7 'red 40)))

(make-bigger (make-lego 4 'purple 80)
             (make-bigger (make-lego 2 'blue 60)
                          (make-lego 1 'yellow 40)
                          (make-lego 3 'red 40))
             (make-lego 6 'orange 60))