Lab 7: Call the Plumber,
or, A Tree by Any Other Name
28 October 2022
Learning objectives
The purpose of this lab is to give you practice:
- modeling parts of the world using trees,
- working with structurally recursive data definitions, and
- writing functions using a template for structurally recursive data definitions.
This lab can be completed in pairs!
If you choose to work in a pair, you’ll make a single code file which you’ll upload to Gradescope with both your names.
Introduction
We would like to write a program that represents pipelines, as you might do if you were building a computer model of real-world infrastructure – or if you were making a game like SimCity!
A pipeline has
- faucets, which can be opened or closed,
faucet open | faucet closed |
---|---|
- straight pipes, which can be copper or lead,
one straight pipe leading to a faucet | two straight pipes leading to a faucet |
---|---|
- and branches, where a pipe splits in two.
pipeline with one branch | pipeline with several branches |
---|---|
Data definition
We can represent pipelines as described above with the appropriate data definition. Since our pipelines consist of multiple instances of faucets, straight pipes, and branches, our data definition includes these three varieties.
Task: Copy the following data definitions and examples into your lab07.arr
file.
data
Pipeline
: | faucet(is-open :: Boolean) | straight(kind :: Metal, pl :: Pipeline) | branch(pl1 :: Pipeline, pl2 :: Pipeline)end
data
Metal
: | lead | copperend
# # Example pipelines #
f-closed = faucet(false
) f-open = faucet(true
) straight-c = straight(copper, f-closed) straight-c-l = straight(copper, straight(lead, f-closed)) branching-pipeline = branch( branch( straight(copper, f-open), f-closed), branch( f-closed, f-closed))
Template
Since we defined a new type of data (Pipeline
), it’s a good idea to write a template we can use for functions that take that data as input.
Task: Copy this template into your lab07.arr
file:
#|
fun pipeline-fun(pl :: Pipeline) -> ...:
doc: "Template for a function that takes a pipeline"
cases (Pipeline) pl:
| faucet(is-open) =>
... is-open ...
| straight(kind, pl1) =>
... kind ...
... pipeline-fun(pl1) ...
| branch(pl1, pl2) =>
... pipeline-fun(pl1) ...
... pipeline-fun(pl2) ...
end
where:
pipeline-fun(...) is ...
end
|#
#
# Exercise 1
#
#
# Exercise 2
#
#
# Exercise 3
#
#
# Exercise 4
#
#
# Exercise 5
#
Exercise 1
Task: Implement the function is-water-running
, which takes a Pipeline
and determines whether any faucets are open.
To help you get started with the lab, we’ve done this one for you!
# # Exercise 1 #
fun
is-water-running
(pl :: Pipeline) -> Boolean:doc
:"Determine whether any faucets are open in pl"
cases
(Pipeline) pl: | faucet(is-open) => is-open | straight(kind, pl1) => is-water-running(pl1) | branch(pl1, pl2) => is-water-running(pl1)or
is-water-running(pl2)end
where
: is-water-running(f-open)is
true
is-water-running(f-closed)is
false
is-water-running(straight-c)is
false
is-water-running(straight-c-l)is
false
is-water-running(branching-pipeline)is
true
end
Copy and paste it into your lab07.arr
file. Make sure you understand how this function works – how did we write this based on the template above?
Task: Why do we have so many examples for this function? Since it’s a predicate (a function returning a Boolean), why isn’t it enough to have one true
example and one false
example? Put your answer in a comment.
Exercise 2
Task: Implement the function count-faucets
, which takes a Pipeline
and counts the number of faucets it contains.
To do this,
- Copy and paste the template.
- Fill in
- the desired function name (everywhere it occurs),
- the docstring, and then
- the examples.
- Using the examples, replace the placeholders (
...
) in the template with appropriate code.
Exercise 3
Task: Implement the function count-open
, which takes a Pipeline
and counts the number of open (that is, running) faucets.
Follow the same steps!
Exercise 4
Task: Implement the function modernize
, which takes a Pipeline
and converts all the (straight
) lead
pipes to copper
ones.
Hint: You don’t need an if
to do this!
Exercise 5
Task: Implement the function off
, which takes a Pipeline
and turns off all the faucets.
Submitting the lab
When you’ve completed the exercises, show your code to your instructor or one of the coaches.
Then upload your
lab07.arr
file to the Lab 7 assignment on Gradescope.
Acknowledgments
This lab includes material adapted from Marc Smith, Vassar College.