c-cpp-to-lean4-translator

C/C++ to Lean4 Translator

Overview

Transform C or C++ programs into equivalent Lean4 code that preserves the original semantics while leveraging Lean4's functional programming paradigm, strong type system, and proof capabilities.

Translation Workflow

Step 1: Analyze Input Code

Understand the C/C++ program structure and semantics:

1. Identify program components:

   • Functions and their signatures
   • Data structures (structs, classes, arrays)
   • Control flow patterns (loops, conditionals)
   • Memory management (allocation, pointers)
   • I/O operations
   • Dependencies and includes

2. Understand semantics:

   • What does the program compute?
   • What are the inputs and outputs?
   • Are there side effects?
   • What are the invariants and preconditions?

3. Note translation challenges:

   • Pointer arithmetic
   • Mutable state
   • Imperative loops
   • Manual memory management
   • Undefined behavior

Step 2: Design Lean4 Structure

Plan the Lean4 equivalent before writing code:

1. Choose appropriate types:

   • Int for signed integers
   • Nat for unsigned integers and array indices
   • Float for floating-point numbers
   • Array for dynamic arrays
   • List for linked lists
   • Custom structure types for structs/classes

2. Determine purity:

   • Pure functions: return values directly
   • Side effects: use IO monad
   • Mutable state: use IO.Ref or ST monad

3. Plan control flow translation:

   • Loops → Recursive functions
   • Mutable variables → Function parameters
   • Early returns → Conditional expressions

4. Handle memory:

   • Stack allocation → Direct values
   • Heap allocation → Automatic memory management
   • Pointers → Direct values or references

Step 3: Translate Code

Follow these translation principles:

Functions

Pattern: Pure function

// C/C++
int add(int a, int b) {
    return a + b;
}

-- Lean4
def add (a b : Int) : Int :=
  a + b