nice readme, rename M to MIU system

readme.md

@@ -1,18 +1,53 @@
-Statement logic !!!
+# statement logic !!!
 
-# Compile it
+things you can do with this:
+
+### general things
+
+- parse string -> statement
+- parse L (the formal language) string -> statement
+- serialize a statement to plaintext, LaTeX, L (the formal language)
+
+### semantic things (statements have meaning I guess)
+
+- evaluate statements
+- from a statement generate a LaTeX truth table
+- match/replace patterns in statements (e.g. logical laws)
+- verify logical-law equivalence of statements (TODO)
+- find logical-law equivalence of statements with breadth-first search
+
+### syntactic things (statements are strings of symbols)
+
+- implement formal languages (symbols, axioms schemas, and inference rules):
+  <https://en.wikipedia.org/wiki/Post_canonical_system>
+- verify derivations in formal languages
+
+### formal languages implemented
+
+- the MIU system (from "Gödel, Escher, Bach")
+- L
+
+## Requirements
+
+a haskell compiler e.g. GHC
+
+## Compile it
 
 ```sh
 make
 ```
 
-# Usage
+or look in `Makefile`
+
+## Usage
+
+only this has been implemented in the main function:
 
 ```sh
 echo '((p->q)<->(!q->!p))' | ./logic
 ```
 
-## Output
+### Output
 
 ```
 Iff (Implies (Atom "p") (Atom "q")) (Implies (Not (Atom "q")) (Not (Atom "p")))