diff --git a/compiler/backend/src/org/jetbrains/kotlin/codegen/inline/InlineCache.kt b/compiler/backend/src/org/jetbrains/kotlin/codegen/inline/InlineCache.kt
index 1ebc0d7cd45..efced94ca28 100644
--- a/compiler/backend/src/org/jetbrains/kotlin/codegen/inline/InlineCache.kt
+++ b/compiler/backend/src/org/jetbrains/kotlin/codegen/inline/InlineCache.kt
@@ -27,7 +27,7 @@ class InlineCache {
     val methodNodeById: SLRUMap<MethodId, SMAPAndMethodNode> = SLRUMap(60, 50)
 }
 
-inline fun <K, V> SLRUMap<K, V>.getOrPut(key: K, defaultValue: () -> V): V {
+inline fun <K, V : Any> SLRUMap<K, V>.getOrPut(key: K, defaultValue: () -> V): V {
     val value = get(key)
     return if (value == null) {
         val answer = defaultValue()
diff --git a/compiler/frontend/src/org/jetbrains/kotlin/cfg/pseudocode/TypePredicate.kt b/compiler/frontend/src/org/jetbrains/kotlin/cfg/pseudocode/TypePredicate.kt
index 50e4bfc6336..189d5f5de2b 100644
--- a/compiler/frontend/src/org/jetbrains/kotlin/cfg/pseudocode/TypePredicate.kt
+++ b/compiler/frontend/src/org/jetbrains/kotlin/cfg/pseudocode/TypePredicate.kt
@@ -80,5 +80,5 @@ fun KotlinType.getSubtypesPredicate(): TypePredicate = when {
 
 private fun KotlinType.render(): String = DescriptorRenderer.SHORT_NAMES_IN_TYPES.renderType(this)
 
-fun <T> TypePredicate.expectedTypeFor(keys: Iterable<T>): Map<T, TypePredicate> =
+fun <T : Any> TypePredicate.expectedTypeFor(keys: Iterable<T>): Map<T, TypePredicate> =
     keys.fold(SmartFMap.emptyMap<T, TypePredicate>()) { map, key -> map.plus(key, this) }
diff --git a/compiler/frontend/src/org/jetbrains/kotlin/extensions/ApplicationExtensionDescriptor.kt b/compiler/frontend/src/org/jetbrains/kotlin/extensions/ApplicationExtensionDescriptor.kt
index 4583b3ff717..e9f4940c425 100644
--- a/compiler/frontend/src/org/jetbrains/kotlin/extensions/ApplicationExtensionDescriptor.kt
+++ b/compiler/frontend/src/org/jetbrains/kotlin/extensions/ApplicationExtensionDescriptor.kt
@@ -9,7 +9,7 @@ import com.intellij.openapi.extensions.ExtensionPoint
 import com.intellij.openapi.extensions.ExtensionPointName
 import com.intellij.openapi.extensions.Extensions
 
-open class ApplicationExtensionDescriptor<T>(name: String, private val extensionClass: Class<T>) {
+open class ApplicationExtensionDescriptor<T : Any>(name: String, private val extensionClass: Class<T>) {
     val extensionPointName: ExtensionPointName<T> = ExtensionPointName.create(name)
 
     fun registerExtensionPoint() {
diff --git a/compiler/frontend/src/org/jetbrains/kotlin/extensions/ProjectExtensionDescriptor.kt b/compiler/frontend/src/org/jetbrains/kotlin/extensions/ProjectExtensionDescriptor.kt
index 4a183874216..55b8eabca1f 100644
--- a/compiler/frontend/src/org/jetbrains/kotlin/extensions/ProjectExtensionDescriptor.kt
+++ b/compiler/frontend/src/org/jetbrains/kotlin/extensions/ProjectExtensionDescriptor.kt
@@ -21,7 +21,7 @@ import com.intellij.openapi.extensions.ExtensionPointName
 import com.intellij.openapi.extensions.Extensions
 import com.intellij.openapi.project.Project
 
-open class ProjectExtensionDescriptor<T>(name: String, private val extensionClass: Class<T>) {
+open class ProjectExtensionDescriptor<T : Any>(name: String, private val extensionClass: Class<T>) {
     val extensionPointName: ExtensionPointName<T> = ExtensionPointName.create(name)
 
     fun registerExtensionPoint(project: Project) {
diff --git a/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterImpl.kt b/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterImpl.kt
index 81d4679790f..40604f798fb 100644
--- a/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterImpl.kt
+++ b/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterImpl.kt
@@ -47,7 +47,7 @@ object CallDiagnosticToDiagnostic {
         }
     }
 
-    private inline fun <reified E : PsiElement, A, C : KotlinCallDiagnostic> put(
+    private inline fun <reified E : PsiElement, A : Any, C : KotlinCallDiagnostic> put(
         factory1: DiagnosticFactory1<E, A>,
         klass: Class<C>,
         crossinline getA: C.() -> A
@@ -57,7 +57,7 @@ object CallDiagnosticToDiagnostic {
         }
     }
 
-    private inline fun <reified E : PsiElement, A, B, C : KotlinCallDiagnostic> put(
+    private inline fun <reified E : PsiElement, A : Any, B : Any, C : KotlinCallDiagnostic> put(
         factory2: DiagnosticFactory2<E, A, B>, klass: Class<C>, crossinline getA: C.() -> A, crossinline getB: C.() -> B
     ) {
         checkPut<E, C>(klass) {
diff --git a/plugins/scripting/scripting-compiler/src/org/jetbrains/kotlin/scripting/compiler/plugin/pluginRegisrar.kt b/plugins/scripting/scripting-compiler/src/org/jetbrains/kotlin/scripting/compiler/plugin/pluginRegisrar.kt
index 39bc85c4e4f..6a59e759c14 100644
--- a/plugins/scripting/scripting-compiler/src/org/jetbrains/kotlin/scripting/compiler/plugin/pluginRegisrar.kt
+++ b/plugins/scripting/scripting-compiler/src/org/jetbrains/kotlin/scripting/compiler/plugin/pluginRegisrar.kt
@@ -31,7 +31,7 @@ import org.jetbrains.kotlin.scripting.extensions.ScriptingResolveExtension
 import org.jetbrains.kotlin.scripting.resolve.ScriptReportSink
 import java.net.URLClassLoader
 
-private fun <T> ProjectExtensionDescriptor<T>.registerExtensionIfRequired(project: MockProject, extension: T) {
+private fun <T : Any> ProjectExtensionDescriptor<T>.registerExtensionIfRequired(project: MockProject, extension: T) {
     try {
         registerExtension(project, extension)
     } catch (ex: IllegalArgumentException) {