added examples to README

README.md

@@ -5,3 +5,29 @@ into a repl where you can type an expression in lambda calculus. Upon parsing
 this, you will be put into a new repl, where pressing enter will beta reduce
 the current term by one step. You can exit this by typing 'q' and pressing
 enter. I would recommend using `rlwrap`, as the repls are rather basic.
+
+Here's an example interaction showing each step of the beta reduction.
+```
+> (lambda x y z. x z (y z)) (lambda x y. x) (lambda x y. x)
+(λx y z. x z (y z)) (λx y. x) (λx y. x)
+?
+(λy z. (λx y. x) z (y z)) (λx y. x)
+?
+λz. (λx y. x) z ((λx y. x) z)
+?
+λz. (λy. z) (λy. z)
+?
+λz. z
+? q
+```
+
+It will even handle name collisions and automatically alpha-rename.
+```
+> (lambda x y. x y) (lambda x. y)
+(λx y. x y) (λx. y)
+?
+λz. (λx. y) z
+?
+λz. y
+? q
+```