Outline
- ● Higher-order functions recap
- ● Exercise: using foldl, map and filter
- ● Exercise: rendering 2D grid with higher-order functions
Warm-up exercises: length and average
Exercise 3.1.
Implement function len-via-foldl that computes the length of the list using foldl. Exercise 3.2.
Implement function len-via-map that computes the length of the list using map.
Exercise 3.3.
Implement function average that computes the average for a list of numbers.
Removing duplicates
Exercise 3.4.
Implement function my-remove-duplicates that produces a new list without duplicate values. Use equal? predicate to compare values in the list.
Exercise 3.5.
Implement function my-remove-duplicates-with that produces a new list without duplicate values and uses a user-provided predicate to check for equality.
Exercise 3.6.
Formulate assumptions (restrictions) about the input predicate used in Exercise 3.5.
Rendering 2D grid
Exercise 3.7.
Implement function for-range that produces a list by applying a given function to each number in a given range.
Exercise 3.8.
Implement function for-range-2D that produces a list of lists by applying a given function to each pair of integer 2D coordinates in a given 2D area.
Exercise 3.9.
Implement function render-2D that produces a picture by appending 1×1 pictures generated from a given function at every integer 2D coordinates in a given range.
Extra exercises
Exercise 3.10.
Implement map using foldl. Exercise 3.11.
Implement reverse using foldl.
Exercise 3.12.
Using render-2D implement a function that renders a given vector field. Represent a vector field as a function from a point in space to a vector (represented by a pair of numeric values). Render the gradient vector field for F(x, y) = sin x cos y
