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Exercise 1.

Question 1. Define a small hierarchy with Semigroups and Monoids.

Question 2. Show that bool is a SemiGroup and then a Monoid.

Question 3. Add Magmas to the hierarchy.

  • You will need to ammend the code before the start of question 1.
  • However, Everything after HB.structure Definition SemiGroup must be left untouched.

Question 3 bis. Also add Unital Magmas


Exercise 2.

Question 1. Define Lie Algebras

Uncomment this when you're done

Question 2.

Show that square matrices form a lie algebra.

Exercise 3. Monads!

  • Define monads and show that some classic monads are monads
  • Also redefine monads with ret, bind and join, and define factories with just ret and bind or ret and join.