A triple (x, y, z) of positive integers is Pythagorean if it...

A triple $(x, y, z)$ of positive integers is Pythagorean if it satisfies the equation $x^2+y^2=z^2$. Using a list comprehension with three generators, define a function pyths :: Int $\rightarrow$ [(Int, Int, Int)] that returns the list of all such triples whose components are at most a given limit. For example: $$ \begin{aligned} & >\text { pyths } 10 \\ & {[(3,4,5),(4,3,5),(6,8,10),(8,6,10)]} \end{aligned} $$

A triple $(x, y, z)$ of positive integers is Pythagorean if it satisfies the equation $x^2+y^2=z^2$. Using a list comprehension with three generators, define a function pyths :: Int $\rightarrow$ [(Int, Int, Int)] that returns the list of all such triples whose components are at most a given limit. For example:
$$
\begin{aligned}
& >\text { pyths } 10 \\
& {[(3,4,5),(4,3,5),(6,8,10),(8,6,10)]}
\end{aligned}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Haskell Function Definition and Type Annotations

Haskell functions are defined with clear syntax and strong typing, which includes specifying the types of inputs and outputs. In this context, the function pyths is designed to take an integer limit and return a list of triples, emphasizing the importance of type annotations and functional definitions in Haskell programming.

Generators in List Comprehension

Generators are components within list comprehensions that extract elements from a list or range. They facilitate the iteration over potential values of variables in a structured way, enabling the formation of combinations that can later be filtered by specified conditions, such as checking the Pythagorean equation.

Pythagorean Triple

A Pythagorean triple consists of three positive integers that satisfy the equation x² + y² = z². This concept is significant in number theory and geometry because it represents the side lengths of right triangles that adhere to the Pythagorean theorem.

List Comprehension in Haskell

List comprehensions in Haskell provide a concise and expressive syntax to generate lists by specifying a pattern and conditions. They allow the developer to build lists by iterating over one or more sources, making them ideal for constructing collections that meet specific criteria.

Transcript

Please give Ace some feedback