F-Algebras

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Prev: Comonads Next: Algebras for Monads

Exercises

1. Implement the evaluation function for a ring of polynomials of one variable. You can represent a polynomial as a list of coefficients in front of powers of $x$. For instance, $4x^2-1$ would be represented as (starting with the zero’th power) [-1, 0, 4].
2. Generalize the previous construction to polynomials of many independent variables, like $x^{2}y-3y^{3}z$.
3. Implement the algebra for the ring of $2\times 2$ matrices.
4. Define a coalgebra whose anamorphism produces a list of squares of natural numbers.
5. Use unfoldr to generate a list of the first $n$ primes.