docs: update README

Author: nos1dot618

README.md

@@ -1,3 +1,7 @@
+> Functional Programming Language based on [Lambda Calculus](https://en.wikipedia.org/wiki/Lambda_calculus) highly
+> inspired by this video [Programming with Math | The Lambda Calculus - Eyesomorphic](https://youtu.be/ViPNHMSUcog) made
+> from scratch, entirely in `C++`.
+
 ## Getting Started
 
 ### Prerequisites
@@ -22,6 +26,72 @@ bash ./scripts/setup.sh
 
 ---
 
+## Samples
+
+Booleans and If-Then construct built entirely using Lambda Expressions.
+
+```haskell
+true: Bool = \x: Any. \y: Any. x
+false: Bool = \x: Any. \y: Any. y
+
+if_then: Any = \condition: Any.
+    \then_clause: Any. \else_clause: Any.
+        (condition then_clause else_clause)
+
+(print (if_then true "True" "False"))
+(print (if_then false "True" "False"))
+```
+
+```console
+$ ./cmake-build-debug/lbd.exe -f ./examples/if_then.lbd
+True
+False
+```
+
+Shapes Demo
+
+```haskell
+-- Define Pi as constant
+pi: Float = 3.14
+
+-- Define function to calculate square
+square: Float -> Float = \x: Float. (mul x x)
+
+-- Define function to calculate area of circle
+area_of_circle: Float -> Float = \r: Float.
+    (mul pi (square r))
+
+-- Define function to calculate volume of cylinder
+volume_of_cylinder: Float -> Float -> Float = \r: Float.
+	\h: Float. (mul (area_of_circle r) h)
+
+-- Calculate the volume of a cylinder
+(print "Volume of cylinder is: ")
+(print (volume_of_cylinder 5.0 10.0))
+```
+
+```console
+$ ./cmake-build-debug/lbd -f ./examples/shapes.lbd
+Volume of cylinder is:
+785.000000
+```
+
+Fibonacci
+
+```haskell
+fibonacci: Any = \num: Float.
+    (if_zero (cmp 0 num) 0
+        (if_zero (cmp 1 num) 1
+            (add (fibonacci (sub num 1.0)) (fibonacci (sub num 2.0)))))
+
+(print (fibonacci 10))
+```
+
+```console
+$ ./cmake-build-debug/lbd -f ./examples/math_demos.lbd
+55.000000
+```
+
 ## Usage
 
 After building, you can run the interpreter with:
@@ -49,5 +119,5 @@ lbd [options]
 
 ## TODO
 
-- TODO: Provide better examples (e.g., Advent of Code snippets).
+- TODO: Add better examples (e.g., Advent of Code snippets).
 - TODO: Maybe use rere.py for testing

examples/if_then.lbd

@@ -5,6 +5,5 @@ if_then: Any = \condition: Any.
     \then_clause: Any. \else_clause: Any.
         (condition then_clause else_clause)
 
-
 (print (if_then true "True" "False"))
-(print (if_then false "True" "False"))
+(print (if_then false "True" "False"))