feat: add impl (#1)

Signed-off-by: Sn0rt <[email protected]>

Author: Sn0rt

Cargo.lock

@@ -4,3 +4,4 @@ version = "0.1.0"
 edition = "2021"
 
 [dependencies]
+uuid = { version = "1.3", features = ["v4"] }

Cargo.toml

@@ -0,0 +1,74 @@
+# Lambda Calculus Interpreter
+
+This project implements a Lambda Calculus interpreter in Rust. It supports various operations and Church encodings for numbers and boolean values.
+
+## Supported Instructions
+
+The interpreter supports the following instructions and operations:
+
+1. **Basic Lambda Calculus**
+   - Variable: `x`, `y`, `z`, etc.
+   - Abstraction: `λx. <expression>`
+   - Application: `(<expression> <expression>)`
+
+2. **Church Numerals**
+   - Encoding: Automatically handled by the interpreter
+   - Decoding: Automatically handled by the interpreter
+   - Addition: `add`
+   - Subtraction: `subtract`
+   - Multiplication: `multiply`
+   - Predecessor: `pred`
+   - Successor: `succ`
+   - Is Zero: `is_zero`
+
+3. **Church Booleans**
+   - True: `true` (encoded as `λx. λy. x`)
+   - False: `false` (encoded as `λx. λy. y`)
+   - And: `and`
+   - Or: `or`
+   - Not: `not`
+
+4. **Control Flow**
+   - If-Then-Else: `ifelse`
+
+5. **Pairs**
+   - Create Pair: `pair`
+   - First Element: `fst`
+   - Second Element: `snd`
+
+6. **Recursion**
+   - Y Combinator: `Y`
+
+## Usage Examples
+
+Here are some examples of how to use the interpreter:
+
+1. Church Numeral Addition:
+   ```
+   (add (church_encode 2) (church_encode 3))
+   ```
+
+2. Boolean Operations:
+   ```
+   (and true false)
+   (or true false)
+   (not true)
+   ```
+
+3. Conditional Statement:
+   ```
+   (ifelse (is_zero 0) 42 58)
+   ```
+
+4. Factorial using Y Combinator:
+   ```
+   (Y (λf. λn. (ifelse (is_zero n) 1 (multiply n (f (pred n))))))
+   ```
+
+## Running Tests
+
+To run the tests and see examples of the interpreter in action, use the following command:
+
+```rust
+$ cargo test
+```