writing_exercises.md

Writing exercises

This page deals in more details with the Statement command and all the options you have to write better exercises/levels.

Local let definitions

If you want to make a local definition/notation which only holds for this exercise (e.g. a function f : ℤ → ℤ := fun x ↦ 2 * x) the recommended way is to use a let-statement:

Statement (a : ℤ) (h : 0 < a) :
    let f : ℤ → ℤ := fun x ↦ 2 * x
    0 < f a := by
  sorry

The game automatically intros such let-statements, such that you and the player will see the following initial proof state:

a: ℤ
h: 0 < a
f: ℤ → ℤ := fun x => 2 * x
⊢ 0 < f a

"Preamble" & non-Prop-valued exercises

You can use the following syntax with (preamble := tac) where tac is a tactic sequence.

Statement my_statement (preamble := dsimp) (a : ℤ) (h : 0 < a) :
    0 < f a := by
  sorry

This tactic sequence will be executed before the exercise is handed to the player.

For example, if your exercise is to construct a structure, you could use preamble to fill all data fields correctly, leaving all Prop-valued fields of the structure as separate goals for the player to proof.

Note: (preamble := tac) always has to be written between the optional name and the first hypothesis. Nevertheless, you can use all hypotheses in the tactic sequence, because it is only evaluated at the beginning of the proof.

Attributes

You can add attributes as you would for a theorem. Most notably, you can make your named exercise a simp lemma:

@[simp]
Statement my_simp_lemma ...