372: Some exercises related to types

Create a file named types1.hs and put these lines in it:
```
add x y = x + y

addInt::Int -> Int -> Int
addInt x y = x + y

i = 10
j = 10

k = addInt i i

f1 = add 10
f2 = addInt 10
-- (end of lines for file) --
```
Then...
1. Load the file using :load and then do :browse to see the types of the bindings.
2. A series of expressions, :types, and let bindings follow some of which produce errors. Go through them, first trying to predict the result, and then seeing what actually happens. If an error, see if you can understand its cause.
```
i

j

k

add i i

add j j

addInt i i

addInt j j

let i2 = 5

:type i2

let i3 = 5::Int

:type i3

addInt i2 i2

addInt i3 i3
```
3. Add min3 and eq3 from slide 81 to types1.hs and then use :r to reload it. See what :browse now shows.
4. Try the following, first predicting the result.
```
eq3 i i i
eq3 j j j
eq3 i j i
min3 i 1 2
min3 i 100 23432423423423423432423242423423 -- Actual value not important. Try several big integers!  What's going on?!
```
If you use :type to see the type of each of the following functions, you'll see that some type variables are a's, b's, etc. and some are t, t1, t2, etc. See if you can discern a pattern in which of the two sequences the type variable is chosen from.
```
let f1 x = x
let f2 x = 10
let f3 x y z = y
let f4 x y z = x ^ y + 0
```