#+title: CS 3MI3 Tutorial
#+subtitle: Possible midterm questions ;; things to know
#+date: October 29
* How does a type differ from a set?
* What type formers are supported in the languages covered in this class?
* Why does every language support product types?
* Give an example of a language that does not have one-input one-output functions types.
* Intersection related to subtyping, how?
*Golden Rule*
x ↑ y = y  ≡  x ≤ y
x ∨ y = y  ≡  x ⇒ y
x ∪ y = y  ≡  x ⊆ y

How is the intersection Golden Rule useful for simlifying redundant code?
Akin to ~b && true~ replaced by ~b~.

** What is the diamond problem?

* In C/C++/C#, how is the infinite list [1,2,3,…] implemented?

  + [1, 1, 1, …] ≈  λ i → 1
    - Representation :: Entire RHS.
    - Element at particular index :: Always 1.
  + [1, 2, 3, …] ≈  λ i → i
  + [1, 1, 2, 3, 5, 8, …] ≈ λ i → Fibonacci i

  *Actually* open a language and implement infinite lists, “streams”.

  + “Function patching” is how you ‘update’ lists in functional representation.
  + There are *many* possible representations of lists.
* Explain “Arrays are continuous blocks of memory, while lists are not”
** What is an ArrayList --e.g., Java.
* Difference between strongly typed and weakly typed; examples in languages?
* Explain: Untyped programming is unityped programming.
* Implement a parametrically prolymorphic function
** How does this differ from inheritance, ad-hoc polymorphism? Overloading?
   - Casing along types ≈ overloading
   - Parameteric  ≈ only one definition
   - Inhertiance ≈ Define the function on a per-child basis

* Know what an inductive type is, give common examples.

   - English letters
   - Colours: Red, Green, Blue
     + In generally, any enumeration is an inductive type.
     + E.g., 𝔹ooleans!
   - ℕatural numbers
   - Linked Lists!

* Given an inductive type, what is its induction principle?
    induction principle
  ≈ recursion principles
  ≈ super powerful switch/case statements
    - i.e., pattern matching and more

  E.g., ℕ-induction principle gives us for-loops!

  See the Agda cheat sheet for examples.
* Explain how to /prove/ a theorem by writing a /program/