CS52 - Spring 2017 - Class 11

Example code in this lecture

   compose.sml
   binTree.sml

Lecture notes

  • admin
       - Midterm 2
          - next Thursday
          - we will provide summary page of CS52 machine instructions at the end of the manual
          - Can additionally bring one page (one side of an 8.5 x 11 piece of paper) of notes
          - Topics
             - CS52 machine
                - assembly code
                - memory layout
                - stacks
                - etc
             - number representation (different bases)
                - signed binary representation (we'll talk about it next Tuesday), so there will be light coverage


  • function composition
       - In math, if we have two functions:
          f(x) = x+2
          g(x) = x*x

       - what is the composition of those two function (written f o g)?
          f(g(x))

          - For example, what is (f o g)(2)?
             - g(2) = 4
             - f(4) = 6
       
       - In SML, we can also compose functions using the composition operator "o" (lowercase o)

       - For SML functions f and g, what are the type requirements for us to compose them, f o g?
          - f: 'a -> 'b
          - g: 'c -> 'a

          - and the composition returns a function, of type 'c -> 'b
             

  • look at compose.sml code
       - what do the following return?
          c1 8
          c2 8
          c3 8

          - 100
          - 66
          - 100
       - what is the type of f o g?
          - int -> int (a function!)
       
  • Recursive data structures
       - See slides

  • Write a function called sumTree sums the numbers in a tree:
       sumTree: int binTree -> int

       - How many patterns will we have?
          - at least 2, one for each of the constructors of the datatype

          fun sumTree Empty = ?
           | sumTree (Node (left,v,right)) = ?

       - Look at the sumTree function in binTree.sml code

       - Notice that recursive structures lend themselves very nicely to recursive functions

  • Write a function called maxTree that finds the larges value in a tree:
       maxTree: int binTree -> int

       ASSUMING:
          1) non-negative values in the tree
          2) maxTree Empty = -1

       - Again, this should follow a very similar structure as sumTree

          fun maxTree Empty = ?
           | maxTree (Node (left,v,right)) = ?

       - Intuitively the max of a tree is either:
          1) the value at that node
          2) the largest value in the left subtree
          3) the largest value in the right subtree

          - Just need to get these three things and then compare

       - Look at maxTreeSimple function in binTree.sml code

  • For those curious, maxTree in binTree.sml code uses exceptions and exception handling to remove our assumptions

  • parsing
       - What is parsing?

  • EBNF syntax

    EBNF for numbers:

    N ::= [S]D[F]
    S ::= + | -
    F ::= .D
    D ::= {0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9}


  • EBNF syntax
       - EBNF = Extended Backus-Naur Form
       - | denotes 'or', i.e. pick one of the options
       - [] denotes optionally include
       - {} denotes include 1 or more repetitions
          - Note that each repetition doesn't necessarily have to choose the same options

  • For example:

       - -10
          N
          SD (N -> SD)
          -10
       - 15.2
          N
          DF (N -> DF)
          15F (D -> 15)
          15.D (F -> .D)
          15.2 (D -> 2)

  • Which of the following are described by the language above?
       - +12
       - -10.542
       - 10.
       - +-7
    •