session 2

haskell/sessions/16_03/notes.md

@@ -0,0 +1,64 @@
+## Table
+| Topic | Description | Confidence |
+|-------|-------------|------------|
+| Signatures | Checking whether the expression types are correct | 😐 |
+| Programming | Writing code to solve an algorithmic problem | 😐 |
+| Higher order functions | Demonstrate understanding of higher order functions, usually by chaining them | 😊 |
+| List comprehensions | Demonstrate understanding of list comprehensions | 😊 |
+| Recursion/infinite lists | Infinitely generating lists, usually by recursion and/or list comprehensions | 😐 |
+| ADTs | Algebraic Data Types, usually defining a data type and writing functions that operate on it | 😕 |
+| Proof on lists | Proving properties of functions that operate on lists | 😕 |
+| Proof on trees/ADTs | Proving properties of functions that operate on trees or ADTs | 😕 |
+
+```hs
+expr = (:) . (:)
+
+(:) :: a -> [a] -> [a]
+(.) :: (c -> d) -> (b -> c) -> b -> d
+
+=>
+
+a -> ([a] -> [a])  = b -> c
+
+b = a
+c = [a] -> [a]
+
+--- 
+
+a' -> [a'] -> [a']  = c -> d
+a -> [a] -> [a]  = b -> c
+
+b = a
+c = [a] -> [a]
+
+a' = [a] -> [a]
+[[a] -> [a]] -> [[a] -> [a]] = d
+
+
+expr :: b -> d
+ =>
+expr :: a -> [[a] -> [a]] -> [[a] -> [a]]
+```
+
+
+
+```hs
+f = \x y -> x (x (x y))
+```
+
+Rigorous solution of the above.
+
+
+## Look into
+> How does one do the equations?
+
+> CLI is functional lol
+
+> Lazy and singly-linked lists
+
+> Y combinator - ?
+
+
+## Resources
+- [course](https://www.cis.upenn.edu/~cis1940/spring15/lectures.html)
+- [standard list](https://hackage.haskell.org/package/base-4.21.0.0/docs/Data-List.html)