module Calculator where

import Question

calculator = do

  h2 $ text "Using the computer as a calculator"

  p <#>One use of a computer is as a calculator, i.e. to
       interactively make computations. In this course, we will use a
       program named Hugs for this purpose. The program is started from
       the terminal window by typing <tt>hugs</tt>: </#>

  fixed "> hugs"

  p <#>While reading this text, you should really perform what is
       being described. If you haven't started Hugs already, do it now! As a response
       you get the Hugs welcome message: </#>

  fixed $ unlines
    [ "__   __ __  __  ____   ___      _________________________________________"
    , "||   || ||  || ||  || ||__      Hugs 98: Based on the Haskell 98 standard"
    , "||___|| ||__|| ||__||  __||     Copyright (c) 1994-2003"
    , "||---||         ___||           World Wide Web: http://haskell.org/hugs"
    , "||   ||                         Report bugs to: hugs-bugs@haskell.org"
    , "||   || Version: November 2003  _________________________________________"
    , ""
    , "Haskell 98 mode: Restart with command line option -98 to enable extensions"
    , ""
    , "Type :? for help"
    , "Prelude> "
    ]

  p <#>For the time being, we aren't concerned about what is being said here.
           Instead we focus on the last line where the cursor (i.e. where the typing
           appears on the screen) is. On this line we find the text <tt>Prelude></tt>,
           which indicates that Hugs is ready to be given a command. We will come back
           to the meaning of the word Prelude at a later stage. The simplest command is
           to just type an expression, after which Hugs will calculate and print out the
           value of that expression.
       </#>

  prompts' [ ("4+5*6", "34")
           , ("", "")
           ]

  p <#>Now, as indicated by the cursor, the system is prepared for
           another command. We can repeat this interaction an infinite number of
           times, as demonstrated in the dialogue below:</#>

  prompts' [ ("4*(8-5)+3", "15")
           , ("3.5/(3+4)*4.5", "2.25")
           , ("sin 1.57", "0.999999682931835")
           ]

  <#>The first of these three expressions consists of a multiplication,
           an addition and a subtraction. In which order are they carried out
           and what values are being multiplied, added and subtracted?</#> ?> do

    p <#>The expression to be computed is <tt>4*(8-5)+3</tt>.</#>

    p <#>First <tt>8-5</tt> is computed, which results in <tt>3</tt>, then
         <tt>4*3=12</tt> and finally <tt>12+3=15</tt>.</#>

  <#>What result can we expect when we omit all parentheses in the
       first expression, i.e. <tt>4*8-5+3</tt>?</#> ?> do

      p <#>The expression to be computed is <tt>4*8-5+3</tt>. Unlike
           the previous expression, the right hand side operand of <tt>*</tt>
           is simply the number <tt>8</tt>. First, <tt>4*8=32</tt> is computed,
           then <tt>5</tt> is subtracted, resulting in <tt>27</tt>
                   and finally <tt>3</tt> is added, giving the final result <tt>30</tt>.
                   Try it out yourselves in Hugs:

           </#>

      prompts' [ ("4*8-5+3","30") ]

      p <#>It is important to understand in what order subcomputations
           are carried out and why.</#>

  <#>When computing the second expression, what operations are carried out
       and in what order?</#> ?> do

     p <#>The expression to be computed is <tt>3.5/(3+4)*4.5</tt>.</#>

     p <#>First <tt>3+4</tt> is computed, which results in <tt>7</tt>, then
          <tt>3.5/7=0.5</tt> and finally <tt>0.5*4.5=2.25</tt>.</#>

  p <#>The last expression suggests that Hugs is familiar with the trigonometric
           functions, as well as the exponential function (<tt>exp</tt>), the square
           root function (<tt>sqrt</tt>), and many more.</#>

  p <#>We aren't always given a value as result when Hugs is given an
           expression to calculate. There can be something wrong with
           the expression, making it impossible to calculate a
           value:</#>

  prompts' [ ( "3+5*"
             , "ERROR: Syntax error in expression \
               \(unexpected end of input)"
             )
           , ( "div 4 0", "Program error: divide by zero")
           ]

  p <#>In the first case, the expression is syntactically wrong since the
           multiplication has no right hand side operand. In the
           second case, we're trying to divide by zero, which results
           in an error during the computation. To recognize different
           kinds of errors and to understand their causes take a lot
           of time in the beginning. We will return to this later
           on.</#>