module _ where
open import bool
open import eq


{- 

0. set up agda. 

  Visit the installation section of the agda website:

    https://agda.readthedocs.io/en/latest/getting-started/installation.html

  Also, get a copy of the text book: 

    https://dl.acm.org/citation.cfm?id=2841316

  The book points to the IAL agda library but it points to an old
  version. You want the latest, which you can get here:

    https://github.com/cedille/ial

  You will need to also add this pull request:

   https://github.com/cedille/ial/pull/8

  If that causes you trouble, there is a virtual machine that has
  everything set up that I've put in box:

   https://northwestern.box.com/s/knldpeew9cafko28qv4y5b2q1enfdyzb

  but it got deleted somehow. This link should start working at
  some point on October 20th

   http://www.cs.northwestern.edu/~robby/courses/396-2021-fall/Ubuntu_20_IAL.ova

  You should be able to import that into virtual box. The main user's
  name is `ial` and so's the password.

  To solve the rest of these exercises, I recommend you create a file
  in the same directory as the IAL library you've checked out (icky, I
  know). I will grade your homework by putting it there to try it out.

-}


{- 1. Do exercises 1.1 and 1.2 (page 14) in the text. -}

{- 2. Do exercise 2.3 (page 41) in the text -} 

{- 3. prove the following identities: -}

curry : ∀ (b1 b2 b3 : 𝔹) -> b1 imp (b2 imp b3) ≡ (b1 && b2) imp b3
curry b1 b2 b3 = {!!}

demorgan : ∀ b1 b2 -> ~ (b1 && b2) ≡ ~ b1 || ~ b2
demorgan b1 b2 = {!!}

imp-not-or : ∀ b1 b2 -> ~ b1 || b2 ≡ b1 imp b2
imp-not-or b1 b2 = {!!}