ITEC 380 2023spring ibarland

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working with a union type
hw03

Due: Feb.02 (Thu) at start of class (hardcopy and D2L)
Your submitted file should be named “hw03.rkt”.

We wish to write code about whether or not the Radford Highlanders won their basketball game, this last weekend. We want to capture: whether they won/lost, or tied, or there wasn't any game this weekend, or (if the game is still in-progress) what the name of the team currently being played is. (Oddly, we will not track the opposing team's name when the game isn't in progress¹. Perhaps we don't care about such details once a game is over?)

1. (20pts) Complete steps 1-3 of the design recipe for representing this information. Remember that step 1 should be a function named “game-result?”.

   Hint: To represent whether they won or lost, a boolean would be appropriate. What types seem appropriate for each of the other variants?

2. (20pts) Write a function payout which takes in the amount of a bet² placed that the Highlanders’ would win their game (non-negative) and a game-result and returns how much money is to be repaid:
   • If the Highlanders win, twice the money is repaid, minus a 10% house cut. (That is, 1.8x the original bet.)
   • If the Highlanders lose, $0 is repaid.
   • If the Highlanders are still playing, nothing ($0) is repaid (yet).
   • If the Highlanders tie, the amount of the bet is repaid, minus a 10% house cut.
   • If the Highlanders didn't play, then the amount of the bet is fully refunded.

   hint: This function's signature is (->                          game-result?                         .

3. (20pts) Write a function game-result->string which returns a user-friendly message similar to one of the following, as appropriate:
   • "The Radford Highlanders won!" (or, “…lost :-(”)
   • "The Radford Highlanders tied their last game."
   • "The Radford Highlanders are still playing The Wytheville Wallabies."

     Hint: Of course, it is not “as appropriate” to return a string mentioning The Wytheville Wallabies when we're actually playing The Dublin Dingoes, or The Pulaski Pangolins! Recall from our data-definition in #1, a game-result should capable of representing, among other things, the name of a team (which therefore means that the game must be in-progress). (Moreover, this means your function does not need to be given any additional information, since the game-result already represents the info you need.)

     Team names: We'll consider the word “The” to be part of the team-name. This covers the situation where RU's soccer team might play, say, Manchester United.

   • "The Radford Highlanders did not play this week."
   (You will, of course, follow the applicable steps 4,5,7,8 of the design recipe.)

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4. (40pts) Various rovers on Mars (Curiosity) and the moon (Yutu 2) take scientific measurements, including oxygen-levels in the atmosphere (indicating the capability to support life), and actual signs of life (by-products like methane, or perhaps finding actual bacteria or other life!) Occasionally, the equipment might malfunction and give no result.

   A rover-measurement is one of:

   • an inexact? number (interpretation: Oxygen density, in g/l; e.g. earth has about 0.3g/l at STP³ )
   • a lifesign (see below)
   • #false (interpretation: sensor error / no reading)

   In turn, a lifesign is one of:

   • symbol? (interpretation: a by-product of metabolism, e.g. 'methane or 'ammonia.)
   • string? (interpretation: a species name, e.g. "Escherichia coli" or "Mellivora capensis"⁴)

   Some lifesigns are stronger indicators than others; we'll say the "strength" of a lifesign (on a scale of 0 to 1) is: 1.0 for a species, and for by-products it's 0.1 per character in the chemical-name (with a maximum possible value of 1, of course). (Longer, fancier chemical-names are more likely the result of an organic process?) E.g. 'urea has a strength of 0.4; 'ammonia a strength of 0.7; 'monosodium-glutamate (20 characters) would max out at 1.0.

   hint: In addition to string-length and max, symbol->string will be helpful.

   Write the function newsworthy, which takes a rover-measurement, and returns how newsworthy it is (on a scale of 0 to 1): A sensor-failure rates 0.10. For a life-sign, the newsworthiness is twice its strength (maxing out at 1, of course). Oxygen levels only start to become newsworthy after 5% of earth's level, increasing linearly⁵ until they are totally newsworthy at 25% (or more) of earth's level.

   hint: Figuring out exactly what your code needs to do becomes easier after writing your unit-tests.

   remember: Follow all steps of the design recipe as appropriate, of course. If handling a union-type, and one variant happens to itself be another union-type, a helper-function is more appropriate than having one function which does all the details of two different union types.

   “One function, one task”: If a concept like "lifesign strength" is its own definition (described in its own paragraph above), then good design suggests it’s probably worth its own function, rather than being anonymously folded into a larger function that does even more.

Standard instructions for all homeworks (unless instructed otherwise):

• Your name, the assignment-number, and the URL of this assignment must be in a comment at the start of the file.
• Test cases may be worth half the points or perhaps even more. Don't comment-out tests cases that don't pass (unless they cause an error, preventing the rest of the program from running).
• Any code which results in syntax errors will generally not earn more than 50% of the points-possible. For grading, I will ignore any commented-out code.
• Format well (in particular, each open-paren should be preceded by a space⁶).

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