Higher-Order Functions¶

Project Goals¶

This assignment invites you to run and observe two Python programs stored in files called demonstrate-map-function.py and demonstrate-reduce-function.py. Both of these programs demonstrate the use of higher-order functions that can accept as input a callable function and then use that function to perform a computation. Specifically, the demonstrate-map-function.py illustrates the use of a map(f, sequence) function that applies the function f to a list of data values called sequence. The demonstrate-reduce-function.py shows the use of a reduce(f, sequence, initial) function that starts at an initial value and then applies a function f to all of the values in sequence and returns a result. As you run these two programs and study their output you will explore an alternative approach to programming, called functional programming.

Project Access¶

If you are a student enrolled in a Computer Science class at Allegheny College, you can access this assignment by clicking the link provided to you in Discord. Once you click this link it will create a GitHub repository that you can clone to your computer by following the general-purpose instructions in the description of the technical skills. Specifically, you will need to use the git clone command to download the project from GitHub to your computer. Now you are ready to add source code and documentation to the project!

Code Survey¶

If you change into the source directory of your GitHub repository, you will see a Python program called demonstrate-map-function.py. Your goal for this project is to implement both a map higher-order function and a square function that can serve as the input to the map function. When you run the command python demonstrate-map-function.py after adding the required source code to the program, it should produce the following output:

Squaring all of the numbers in the values tuple
   (4, 9, 25, 49, 121)
Squaring all of the numbers output by range(10)
   (0, 1, 4, 9, 16, 25, 36, 49, 64, 81)

It is worth noting that the demonstrate-map-function.py should contain the following source code that calls the map function to produce the aforementioned output. Line 1 of this code creates a tuple called values that contains five numbers and line 2 calls the map function by providing it square and the values. After you have correctly implemented the map and square functions the two print statements on lines 3 and 4 will produce the first two lines of output. As shown in the output, the next source code segment in demonstrate-map-function.py performs the same operation while using range(10) instead of the specific numbers in the values tuple.

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values = (2, 3, 5, 7, 11)
squared = map(square, values)
print("Squaring all of the numbers in the values tuple")
print("   " + str(squared))

You should also notice that the source directory of your GitHub repository contains a Python program called demonstrate-map-function.py. Your goal for this project is to implement a reduce higher-order function and both a plus and a multiply function that perform arithmetic on two input numbers and can serve as the input to the map function. When you run the command python after adding the required source code to the program, it should produce the following output:

Adding all of the numbers together with a reduce function
   15
Multiplying all of the numbers together with a reduce function
   120

It is worth noting that the demonstrate-reduce-function.py should contain the following source code that calls the reduce function to produce the aforementioned output. Line 1 of this code creates a list called numbers that contains five numbers and line 2 calls the reduce function by providing it plus and the numbers list. After you have correctly implemented the reduce and plus functions the two print statements on lines 3 and 4 will produce the first two lines of output. As shown in the output, the next source code segment in demonstrate-reduce-function.py performs a similar computation while calling reduce(multiply, numbers, 1) instead of reduce(plus, numbers, 0). Why it is sensible to specify that the initial parameter for reduce should be 1 instead of 0 when using the multiply function instead of plus?

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numbers = [1, 2, 3, 4, 5]
added_numbers = reduce(plus, numbers, 0)
print("Adding all of the numbers together with a reduce function")
print("   " + str(added_numbers))

As you continue this source code survey, make sure to note that the function signatures in demonstrate-map-function.py look like those in the following list. This list demonstrates that these functions do not have type annotations. After providing the source code for the square and map functions in this file, please determine and add the type annotations for the formal parameters called value, f, and sequence. Similarly, there are three functions called plus, multiply, and reduce in the demonstrate-reduce-function.py file that do not have type annotations. You can study the source code of these functions and the way that they are called in the demonstrate-reduce-function.py script to learn more about what type annotations you should add to the formal parameters called number_one, number_two, f, sequence, and initial. When you add these type annotations, you should leverage them to enhance your understanding of the inputs, outputs, and behavior of a map-reduce computation.

• Functions in the demonstrate-map-function.py file:
  • def square(value)
  • def map(f, sequence)
• Functions in the demonstrate-reduce-function.py file:
  • def plus(number_one, number_two)
  • def multiply(number_one, number_two)
  • def reduce(f, sequence, initial)

Running Checks¶

Since this project does not use Poetry to manage project dependencies and virtual environments, it does not support the use of commands like poetry run task test. However, you can leverage the relevant instructions in the technical skills to enter into a Docker container and run the command gradle grade to check your work. If gradle grade shows that all checks pass, you will know that you made progress towards correctly implementing and writing about this project's two programs.

Project Reflection¶

Once you have finished all of the previous technical tasks, you can use a text editor to answer all of the questions in the writing/reflection.md file. Since this is a source code survey, you should provide output from running each of the provided Python programs on your own laptop and then explain how the program's source code produced that output. A specific goal for this project is for you to understand each line of source code needed to implement a simplified version of the map and reduce functions. You should also think carefully about the steps that you would need to take to implement a distributed and/or parallel computation that uses map and reduce to improve the efficiency of a program.

Project Assessment¶

Since this project is source code survey, it is aligned with the remembering and understanding levels of Bloom's taxonomy. You can learn more about how a proactive programming expert will assess your work by examining the assessment strategy. From the start to the end of this project you may make an unlimited number of reattempts at submitting source code and technical writing that meet the project's specification.

Seeking Assistance¶

Emerging proactive programmers who have questions about this project are invited to ask them in either the GitHub discussions forum or the Proactive Programmers Discord server. Before you ask your question, please read the advice concerning how to best participate in the Proactive Programmers community. If you find a mistake in this project, please describe it and propose a solution by creating an issue in the GitHub Issue Tracker.