Lab #3 Solution




This lab will help you practice:


de ning structs


writing programs which consume structs as arguments


writing programs that consume structs and output structs working with nested structs


writing interactive graphical programs with complex, structured state


Relevant sections of text: HtDP/2e Chapters 5 and 6.




no \magic numbers”! De ne constants and use the constant names instead.


follow the design pattern: in particular, for each function de nition, give a signature, purpose statement, unit tests, and nally the de nition itself.


use precise data de nitions: this lab is focused on structs, which require very thorough documentation, reviewed below.




  1. Review of Structure Definitions


The following example shows all the components of a complete structure de nition. Do this every time you de ne a struct.


(define-struct entry [name phone email])




An Entry is a (make-entry String String String)




String name : a person’s name


String phone : the person’s phone number


String email : person’s email address




make-entry: String String String -> Entry Selectors:


entry-name : Entry -> String


entry-phone : Entry -> String


entry-email : Entry -> String


Type predicate:


entry? : Any -> Boolean




;; Examples:


(define SIEGEL (make-entry “Siegel” “302-123-4566” “”))


(define JOE (make-entry “Smith” “800-123-5683” “”))




Template for function consuming an Entry:


(define (entry-fun an-entry)


… (entry-name an-entry) …







… (entry-phone an-entry) …


… (entry-email an-entry) …)




  1. Using structures for batch programming



Problem 1. De ne a type Date for representing dates. This should be a structure with three components, in this order: day, month, and year. All three components are Natural Numbers: a day is in the range 1..31; a month is in 1..12; a year is any natural number. Make sure to give all components of the complete de nition, including the documentation (see example above). You must do this every time you de ne a struct, even if we don’t remind you.


Problem 2. Design a function date->string which converts a Date to a String of the form \month/day/year”.


Problem 3. The State of Delaware’s information system maintains a record for each taxpayer. De ne a structured type Person for this purpose. It contains the following elds: rst name, last name, birthday, city of residence, state of residence. For the birthday, use the Date type you de ned in Problem 1.


Problem 4. Design a function update-name to change a person’s name in the information system. This function should consume a Person and two Strings ( rst name and last name) and return a Person which is identical to the given one except that the rst and last name elds have been replaced with the new names.


Problem 5.        Now we want three functions which are all similar. All three functions consume a


Person and return a Boolean:


  • can-drink? determines if the person can legally consume alcohol in Delaware, i.e., is the person at least 21 years of age?


  • can-vote? determines if the person can vote in state and federal elections, i.e., is the person at least 18 years of age?


  • soc-sec-eligible? determines if the person is eligible to receive social security bene ts, which means s/he is at least 65 years old.


Since these functions are obviously very similar, you should de ne one or more helper functions rst, and use those helpers in the de nitions of the three main functions. This will prevent needless duplication of code, make the code easier to read, maintain, test, and understand, and make your solution shorter. You have to gure out what the appropriate helpers should be: what should they be named? what are their signatures? The helpers must be designed just like any other function. A hint is provided in the starter le.


  1. Using structures for interactive programming: SpaceX


The company SpaceX, led by Elon Musk, is designing a re-useable Falcon rocket. After delivering its payload, the rocket should be able to land on a oating platform at sea. This turns out to be very di cult:


In the remaining problems, you will develop a game to aid in the design of the rocket. This game will show the rocket descending from the top of the scene. The rocket will naturally accelerate downwards due to the force of gravity. By ring its thrusters, it can more than counter gravity and




accelerate upwards. However, it has only a limited supply of fuel with which it can do this. There is also a horizontal component to the velocity, which is naturally constant (since there is no gravity in the horizontal direction). The horizontal velocity can be adjusted by small thrusters which do not consume signi cant fuel.


Images are provided in the starter le. You may use them, or nd or make your own. As usual, creative graphics and particularly elegant solutions receive extra credit.



Problem 6. De ne constants. Your solution will need at least the following constants (and probably more).


images for the rocket, the re beneath the rocket when it burns, the landing platform, some picture of an explosion


dimensions of the overall scene which should have width 1000 and height 800


constants for the positioning of the landing platform on the bottom of the scene: it should be in bottom middle


constants de ning the exact left and right borders of the safe landing zone, which should obviously be inside the platform; any landing outside of this zone results in failure (explo-




the acceleration due to gravity, which for this problem should be something like :01 pixels/tick2. Note positive is down.


the acceleration when the rocket is ring, which should be something like :05 pixels/tick2. Note that negative is up.


the maximum safe speed for landing; any landing at a greater speed results in failure; approximately 1.5 pixels/tick


the amount the horizontal (x-) velocity changes when a left or right arrow key is pressed, e.g., 0.5 pixels/tick


START-FUEL, the amount of fuel at the beginning, e.g., 100 units


FUEL-PER-TICK: the amount of fuel consumed in one clock tick, when the rocket is burning, e.g., 1.0 units


Most of these are given to you in the starter    le, but there are two places you must   ll in.


Problem 7. De ne a structured type RocketState (the name of the struct should be rocket-state) which encompasses all aspects of the state of the game at any moment in time. It contains the following elds:


pos-x : position of rocket in x-direction in pixels; 0 is the left edge of the scene; increases as you go to the right


pos-y : position of rocket in y-direction in pixels; 0 is the top of the scene, increases as you go down


vel-x : velocity of rocket in x-direction, in pixels per tick


vel-y : velocity of rocket in y-direction, in pixels per tick


fire? : a Boolean value telling you whether the rocket is currently  ring (burning)


fuel : amount of fuel remaining



Problem 8. Design helper function update-vel-x to update the vel-x component of a Rocket-State. This function consumes a RocketState and a number and produces a RocketState identical to the given one except that the vel-x component has been updated.




Problem 9. Design a helper function update-fire similar to above, but for the fire? component.



The rendering function for this program is complicated, so we will break it down into three major steps:


  • render-rocket : draws the rocket, including possible re underneath


  • render-data : draws the data window with statistics in the upper right corner of the scene


  • render-final : draws the nal image, either \You Win!” or the picture of an explosion (you lose).


Each of these functions consumes a RocketState and an Image. The given Image should be an entire scene, i.e., the big empty rectangle, possibly with various things drawn on top of it. The function returns a new scene obtained by adding one more thing to the given scene.


We rst focus on render-rocket. This function will require an auxiliary function which adds the re underneath the rocket if the state indicates the rocket is ring.



Problem 10. Design a function render-rocket-fire which consumes a RocketState and an Image (a scene) and returns an Image. If the state speci es that the rocket is not ring, then the scene returned should be the same one given. If the state speci es that the rocket is ring, then the scene returned is obtained by placing the re image over the appropriate point (just underneath the point where the rocket should be):





Note that the purpose of this function is only to add the re to the scene | not to add the rocket proper.


The starter    le provides a good hint for this function.


Problem 11. Design a function render-rocket which consumes a RocketState and an Image and returns a new Image in which the rocket has been placed on the scene at the coordinates speci ed by the state, and, if the rocket is ring, the re image appears underneath the rocket. Your function de nition should use render-rocket-fire, which you de ned in the previous problem.


Problem 12. Design a function data-image which consumes a RocketState and produces an Image. The image contains text and numbers which give the values of the remaining fuel, the x-and y-positions, and the x- and y-velocities. It should look something like this:

The values of x, y, vx, and vy should be multiplied by 10 and then rounded (i.e., these values will be presented in units of a tenth of a pixel). This will provide higher resolution information to the user. In designing this function, de ne helper-functions as needed to avoid code duplication. See the starter le for a hint.


Problem 13. Design a function render-data which consumes a RocketState and an Image and returns an Image in which the data image (de ned above) is placed in the upper right hand corner of the scene.


Problem 14.  Design a function landed? which consumes a RocketState and returns a Boolean.


It tells you if the rocket has reached the ground.



Problem 15. Design a function good-landing? which consumes a RocketState in which the rocket has reached the ground, and tells you if that landing was successful. The landing is successful if the x-position is between the two acceptable boundaries and the y-velocity does not exceed the maximum safe speed.


Problem 16. Design a function render-final which consumes a RocketState and an Image and returns an Image as follows: if the rocket has not landed, the original scene is returned unchanged. If the rocket has landed: if the landing was safe, the words \You Win!” are placed on top of the scene in big letters in the middle of the scene; otherwise, a picture of an explosion is placed on top of the rocket.


Problem 17. Design a function render which consumes a RocketState and produces an Im-age. Using function composition, it applies the following functions, in order: render-rocket, render-data, and render-final. Note that in the composition, render-rocket will be the in-nermost function application, since it should be evaluated rst.


That completes the rendering. Now for the tick- and key-handlers. . .



Problem 18.          Design a function handle-tick, which consumes a RocketState and returns a


RocketState. The state is updated as follows:


the x-position is incremented by the x-velocity


the y-position is incremented by the y-velocity | but don’t let the rocket go below the ground


the y-velocity is incremented by the acceleration due to gravity if the rocket is not ring, or by the acceleration due to ring if the rocket is ring


if the fuel level has reached 0, the fire?  eld is set to #false


if the rocket is ring, the fuel level is decremented by FUEL-PER-TICK | but don’t let it go below 0.


Problem 19. Design a function handle-key which consumes a RocketState and a Key and returns a RocketState. The keys are used as follows:


the space bar toggles the burning (rocket ring) on and o ; of course, if t he rocket is out of fuel this key should do nothing


the right arrow increments the x-velocity of the rocket by some xed small amount the left arrow decrements the x-velocity by the same xed amountother keys have no e ect


The nal \main” function is provided for you. It calls big-bang. Note how the big-bang application wraps up the functions render, handle-tick, handle-key, and landed?. It also uses the type predicate rocket-state? to check that each state is actually a value of that structured type. (This will help you debug your program if you make a mistake.)


Play the game. Note that it should end with the rocket either safely landed on the platform and \You Win!” displayed, or with an explosion.

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