imperative-to-coq-model-extractor

Imperative to Coq Model Extractor

Overview

Extract abstract mathematical models from imperative code that can be used for formal reasoning and verification in Coq. This skill transforms imperative programs into functional Coq definitions with explicit state modeling, enabling formal proofs about program behavior.

Extraction Workflow

Step 1: Analyze Imperative Code

Understand the program structure and semantics:

1. Identify components:

   • Functions and their signatures
   • Data structures and types
   • State and mutable variables
   • Control flow (loops, conditionals)
   • Side effects and I/O

2. Understand semantics:

   • What does the program compute?
   • What state does it maintain?
   • What are the invariants?
   • What are preconditions and postconditions?

3. Note modeling challenges:

   • Mutable state
   • Imperative loops
   • Pointers and memory
   • Side effects

Step 2: Design Coq Model Structure

Plan the Coq representation:

1. Choose appropriate types:

   • Z for arbitrary precision integers
   • nat for natural numbers
   • bool for booleans
   • list for sequences
   • Record for structured state
   • Inductive types for enumerations

2. Model state explicitly:

   • Pure functions: Direct translation
   • Mutable state: State transformation functions
   • Side effects: Explicit state passing

3. Plan control flow translation:

   • Conditionals → Pattern matching or if-then-else
   • Loops → Recursive functions (Fixpoint)
   • Early returns → Conditional expressions

Step 3: Extract Core Model

Translate imperative constructs to Coq:

Pattern: Pure function

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

(* Coq Model *)
Definition add (a b : Z) : Z := a + b.

Pattern: Function with state

// Imperative
int counter = 0;
void increment() {
    counter++;
}

(* Coq Model *)
Definition counter_state : Type := Z.
Definition increment (c : counter_state) : counter_state := c + 1.