docs: add proof of equivalence examples

Author: xkilldash9x

examples/proof.go

@@ -0,0 +1,79 @@
+package main
+
+import (
+	"fmt"
+	"log"
+	"os"
+
+	semanticfw "github.com/BlackVectorOps/semantic_firewall"
+)
+
+// PROOF OF EQUIVALENCE
+// The following three functions are syntactically distinct but semantically identical.
+// The Semantic Firewall (sfw) proves this by generating identical fingerprints for all three.
+
+// Implementation 1: Idiomatic Go Range Loop
+const srcRange = `package main
+func sum(items []int) int {
+	total := 0
+	for _, x := range items {
+		total += x
+	}
+	return total
+}
+`
+
+// Implementation 2: C-Style Index Loop
+const srcIndex = `package main
+func sum(items []int) int {
+	total := 0
+	for i := 0; i < len(items); i++ {
+		total += items[i]
+	}
+	return total
+}
+`
+
+// Implementation 3: Raw Goto Loop (The "Assembly" Approach)
+const srcGoto = `package main
+func sum(items []int) int {
+	total := 0
+	i := 0
+loop:
+	if i >= len(items) {
+		goto done
+	}
+	total += items[i]
+	i++
+	goto loop
+done:
+	return total
+}
+`
+
+func main() {
+	// 1. Analyze
+	// Note: We use the advanced policy to ensure we capture the logic correctly
+	resRange, _ := semanticfw.FingerprintSource("range.go", srcRange, semanticfw.DefaultLiteralPolicy)
+	resIndex, _ := semanticfw.FingerprintSource("index.go", srcIndex, semanticfw.DefaultLiteralPolicy)
+	resGoto, _ := semanticfw.FingerprintSource("goto.go", srcGoto, semanticfw.DefaultLiteralPolicy)
+
+	// 2. Extract Fingerprints
+	// We access the first function found in each file (which is 'sum')
+	h1 := resRange[0].Fingerprint
+	h2 := resIndex[0].Fingerprint
+	h3 := resGoto[0].Fingerprint
+
+	// 3. Verify
+	fmt.Printf("\n[Semantic Firewall Proof]\n")
+	fmt.Printf("1. Range Loop Hash:  %s\n", h1)
+	fmt.Printf("2. Index Loop Hash:  %s\n", h2)
+	fmt.Printf("3. Goto Loop Hash:   %s\n", h3)
+
+	if h1 == h2 && h2 == h3 {
+		fmt.Printf("\n[SUCCESS] All three implementations are logically identical.\n")
+		os.Exit(0)
+	} else {
+		log.Fatalf("\n[FAIL] Logic divergence detected.\n")
+	}
+}

examples/v1/range.go

@@ -0,0 +1,8 @@
+package main
+func sum(items []int) int {
+	total := 0
+	for _, x := range items {
+		total += x
+	}
+	return total
+}

examples/v2/index.go

@@ -0,0 +1,8 @@
+package main
+func sum(items []int) int {
+	total := 0
+	for i := 0; i < len(items); i++ {
+		total += items[i]
+	}
+	return total
+}