Generate satisfiable model for isSatisfiable#1127

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copybara-service merged 1 commit into from
Jul 20, 2026
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Generate satisfiable model for isSatisfiable #1127

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9 changes: 7 additions & 2 deletions verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java
View file
Open in desktop
Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
public abstract VerificationStatus status();

/**
* Returns a message detailing why the verification failed or was inconclusive (e.g., the
* counterexample input or truncation reason). Empty if status is VERIFIED.
* Returns a message detailing the outcome of the verification check, such as a counterexample
* input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
* and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
*/
public abstract String message();

static CelVerificationResult verified() {
return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
}

static CelVerificationResult verified(String message) {
return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
}

static CelVerificationResult failed(String message) {
return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
}
Expand Down
4 changes: 3 additions & 1 deletion verifier/src/main/java/dev/cel/verifier/CelVerifier.java
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Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

/**
* Returns verified if there is at least one input combination where the AST evaluates to true.
* Returns verified if there is at least one input combination where the AST evaluates to true. If
* the expression is satisfiable and depends on input variables, the result message will contain a
* satisfying model (witness) with concrete variable assignments.
*
* @param ast The input expression to verify. Must be a type-checked AST.
*/
Expand Down
39 changes: 32 additions & 7 deletions verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java
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Open in desktop
Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
return CelVerificationResult.failed(
"Equivalence violation detected."
+ getCounterexampleString(
ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
ctx,
translator.getTypeSystem(),
result.model,
/* isApproximate= */ false,
/* isCounterexample= */ true));
case APPROXIMATE_MATCH:
return CelVerificationResult.inconclusive(
"Inconclusive: a divergence may exist, but it depends on approximations, missing"
+ " theories, or loop bounds."
+ getCounterexampleString(
ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
ctx,
translator.getTypeSystem(),
result.model,
/* isApproximate= */ true,
/* isCounterexample= */ true));
case TRUNCATED:
return CelVerificationResult.inconclusive(
"Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
ctx,
translator.getTypeSystem(),
result.model,
/* isApproximate= */ false))
: CelVerificationResult.verified();
/* isApproximate= */ false,
/* isCounterexample= */ true))
: CelVerificationResult.verified(
"Condition is satisfiable."
+ getCounterexampleString(
ctx,
translator.getTypeSystem(),
result.model,
/* isApproximate= */ false,
/* isCounterexample= */ false));

case APPROXIMATE_MATCH:
String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
return CelVerificationResult.inconclusive(
prefix
+ getCounterexampleString(
ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
ctx,
translator.getTypeSystem(),
result.model,
/* isApproximate= */ true,
/* isCounterexample= */ searchForCounterexample));

case TRUNCATED:
return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
}

private static String getCounterexampleString(
Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
Context ctx,
CelZ3TypeSystem typeSystem,
Model model,
boolean isApproximate,
boolean isCounterexample) {
return CelZ3CounterexampleGenerator.generate(
ctx, typeSystem, model, isApproximate, isCounterexample);
}

CelVerifierZ3Impl(
Expand Down
20 changes: 17 additions & 3 deletions verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java
View file
Open in desktop
Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
private CelZ3CounterexampleGenerator() {}

static String generate(
Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
Context ctx,
CelZ3TypeSystem typeSystem,
Model model,
boolean isApproximate,
boolean isCounterexample) {
FuncDecl[] constDecls = model.getConstDecls();

List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
}

if (bindings.isEmpty()) {
return " (The expression fails unconditionally, regardless of input state)";
return isCounterexample
? " (The expression fails unconditionally, regardless of input state)"
: " (The expression is satisfiable unconditionally, regardless of input state)";
}

String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
String prefix;
if (isCounterexample) {
prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
} else {
prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
}
return prefix + String.join("", bindings);
}

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
if (++iterations > 100_000) {
throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
}
if (!arrayExpr.isApp()) {
break;
}
FuncDecl<?> decl = arrayExpr.getFuncDecl();
String declName = decl.getName().toString();

Expand Down
37 changes: 37 additions & 0 deletions verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java
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Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
}

@Test
public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

CelVerificationResult result = VERIFIER.isSatisfiable(ast);

assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
assertThat(result.message()).contains("Condition is satisfiable.");
assertThat(result.message()).contains("Satisfying input:");
assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
}

@Test
public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

CelVerificationResult result = VERIFIER.isSatisfiable(ast);

assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
assertThat(result.message())
.isEqualTo(
"Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
+ " of input state)");
}

@Test
public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

CelVerificationResult result = VERIFIER.isSatisfiable(ast);

assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
assertThat(result.message()).contains("Potential satisfying input:");
assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
}

private enum IsSatisfiableInconclusiveTestCase {
MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading
, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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Generate satisfiable model for isSatisfiable#1127

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 Merged

copybara-service
merged 1 commit into

from

Jul 20, 2026
 Merged


Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
Expand Down

20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

Expand Down

37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Generate satisfiable model for isSatisfiable#1127

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 Merged

copybara-service
merged 1 commit into

from

Jul 20, 2026
 Merged


Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
Expand Down

20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

Expand Down

37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
Expand Down

20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

Expand Down

37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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Generate satisfiable model for isSatisfiable#1127

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 Merged

copybara-service
merged 1 commit into

from

Jul 20, 2026
 Merged


Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
Expand Down

20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

Expand Down

37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
Generate satisfiable model for isSatisfiable#1127

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Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

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Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
Expand Down

20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

Expand Down

37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Generate satisfiable model for isSatisfiable#1127

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 Merged

copybara-service
merged 1 commit into

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Jul 20, 2026
 Merged


Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
Expand Down

20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

Expand Down

37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
Expand Down
Loading

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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Generate satisfiable model for isSatisfiable#1127

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 Merged

copybara-service
merged 1 commit into

from

Jul 20, 2026
 Merged


Generate satisfiable model for isSatisfiable
#1127
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9 changes: 7 additions & 2 deletions
verifier/src/main/java/dev/cel/verifier/CelVerificationResult.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -34,15 +34,20 @@ public enum VerificationStatus {
 public abstract VerificationStatus status();

 /**
 * Returns a message detailing why the verification failed or was inconclusive (e.g., the
 * counterexample input or truncation reason). Empty if status is VERIFIED.
 * Returns a message detailing the outcome of the verification check, such as a counterexample
 * input, satisfying model assignments, or truncation reason. May be empty if status is VERIFIED
 * and no model inputs apply (e.g., when verifying isAlwaysTrue without counterexamples).
 */
 public abstract String message();

 static CelVerificationResult verified() {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, "");
 }

 static CelVerificationResult verified(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VERIFIED, message);
 }

 static CelVerificationResult failed(String message) {
 return new AutoValue_CelVerificationResult(VerificationStatus.VIOLATED, message);
 }
Expand Down

4 changes: 3 additions & 1 deletion
verifier/src/main/java/dev/cel/verifier/CelVerifier.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -22,7 +22,9 @@
public interface CelVerifier {

 /**
 * Returns verified if there is at least one input combination where the AST evaluates to true.
 * Returns verified if there is at least one input combination where the AST evaluates to true. If
 * the expression is satisfiable and depends on input variables, the result message will contain a
 * satisfying model (witness) with concrete variable assignments.
 *
 * @param ast The input expression to verify. Must be a type-checked AST.
 */
Expand Down

39 changes: 32 additions & 7 deletions
verifier/src/main/java/dev/cel/verifier/CelVerifierZ3Impl.java

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -192,13 +192,21 @@ public CelVerificationResult verifyEquivalence(
 return CelVerificationResult.failed(
 "Equivalence violation detected."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ false));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ true));
 case APPROXIMATE_MATCH:
 return CelVerificationResult.inconclusive(
 "Inconclusive: a divergence may exist, but it depends on approximations, missing"
 + " theories, or loop bounds."
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ true));
 case TRUNCATED:
 return CelVerificationResult.inconclusive(
 "Inconclusive: expressions are equivalent within the current loop unroll limit, but"
Expand DownExpand Up@@ -250,8 +258,16 @@ private CelVerificationResult checkSatisfiability(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false))
 : CelVerificationResult.verified();
 /* isApproximate= */ false,
 /* isCounterexample= */ true))
 : CelVerificationResult.verified(
 "Condition is satisfiable."
 + getCounterexampleString(
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ false,
 /* isCounterexample= */ false));

 case APPROXIMATE_MATCH:
 String prefix =
Expand All@@ -263,7 +279,11 @@ private CelVerificationResult checkSatisfiability(
 return CelVerificationResult.inconclusive(
 prefix
 + getCounterexampleString(
 ctx, translator.getTypeSystem(), result.model, /* isApproximate= */ true));
 ctx,
 translator.getTypeSystem(),
 result.model,
 /* isApproximate= */ true,
 /* isCounterexample= */ searchForCounterexample));

 case TRUNCATED:
 return CelVerificationResult.inconclusive(
Expand DownExpand Up@@ -357,8 +377,13 @@ private Solver newSolver(Context ctx) {
 }

 private static String getCounterexampleString(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 return CelZ3CounterexampleGenerator.generate(ctx, typeSystem, model, isApproximate);
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 return CelZ3CounterexampleGenerator.generate(
 ctx, typeSystem, model, isApproximate, isCounterexample);
 }

 CelVerifierZ3Impl(
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20 changes: 17 additions & 3 deletions
verifier/src/main/java/dev/cel/verifier/CelZ3CounterexampleGenerator.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -36,7 +36,11 @@ final class CelZ3CounterexampleGenerator {
 private CelZ3CounterexampleGenerator() {}

 static String generate(
 Context ctx, CelZ3TypeSystem typeSystem, Model model, boolean isApproximate) {
 Context ctx,
 CelZ3TypeSystem typeSystem,
 Model model,
 boolean isApproximate,
 boolean isCounterexample) {
 FuncDecl[] constDecls = model.getConstDecls();

 List<String> bindings = new ArrayList<>();
Expand All@@ -55,10 +59,17 @@ static String generate(
 }

 if (bindings.isEmpty()) {
 return " (The expression fails unconditionally, regardless of input state)";
 return isCounterexample
 ? " (The expression fails unconditionally, regardless of input state)"
 : " (The expression is satisfiable unconditionally, regardless of input state)";
 }

 String prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 String prefix;
 if (isCounterexample) {
 prefix = isApproximate ? " Potential counterexample input:" : " Counterexample input:";
 } else {
 prefix = isApproximate ? " Potential satisfying input:" : " Satisfying input:";
 }
 return prefix + String.join("", bindings);
 }

Expand DownExpand Up@@ -228,6 +239,9 @@ private static void extractKeys(Expr<?> arrayExpr, List<Expr<?>> keys) {
 if (++iterations > 100_000) {
 throw new IllegalStateException("Exceeded maximum number of extractKeys iterations.");
 }
 if (!arrayExpr.isApp()) {
 break;
 }
 FuncDecl<?> decl = arrayExpr.getFuncDecl();
 String declName = decl.getName().toString();

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37 changes: 37 additions & 0 deletions
verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java

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Original file line numberDiff line numberDiff line change
Expand Up@@ -172,6 +172,43 @@ public void isSatisfiable_success(@TestParameter IsSatisfiableTestCase testCase)
 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 }

 @Test
 public void isSatisfiable_withVariable_returnsSatisfyingModel() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("x > 5").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message()).contains("Condition is satisfiable.");
 assertThat(result.message()).contains("Satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 @Test
 public void isSatisfiable_unconditional_returnsUnconditionalMessage() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("1 + 1 == 2").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
 assertThat(result.message())
 .isEqualTo(
 "Condition is satisfiable. (The expression is satisfiable unconditionally, regardless"
 + " of input state)");
 }

 @Test
 public void isSatisfiable_approximate_returnsPotentialSatisfyingInput() throws Exception {
 CelAbstractSyntaxTree ast = CEL.compile("int('123') == 123 ? x > 5 : false").getAst();

 CelVerificationResult result = VERIFIER.isSatisfiable(ast);

 assertThat(result.status()).isEqualTo(VerificationStatus.INCONCLUSIVE);
 assertThat(result.message()).contains("Inconclusive: a satisfying model may exist");
 assertThat(result.message()).contains("Potential satisfying input:");
 assertThat(result.message()).containsMatch("x = (?:[6-9]|[1-9]\\d+)");
 }

 private enum IsSatisfiableInconclusiveTestCase {
 MASKED_BY_BMC("int_list == [1, 2, 3, 4, 5, 6] ? int_list.exists(x, x == 42) : false"),
 MASKED_BY_BMC_ALL("int_list == [1, 2, 3, 4, 5, 6] ? int_list.all(x, x > 0) : false"),
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