diff --git a/compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.kt b/compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.kt
new file mode 100644
index 00000000000..7a1446811da
--- /dev/null
+++ b/compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.kt
@@ -0,0 +1,44 @@
+interface CommonBackendContext
+
+interface PhaserState<Data> {
+    var depth: Int
+}
+
+interface PhaseConfig {
+    val needProfiling: Boolean
+}
+
+inline fun <R, D> PhaserState<D>.downlevel(nlevels: Int, block: () -> R): R {
+    depth += nlevels
+    val result = block()
+    depth -= nlevels
+    return result
+}
+
+interface CompilerPhase<in Context : CommonBackendContext, Input, Output> {
+    fun invoke(phaseConfig: PhaseConfig, phaserState: PhaserState<Input>, context: Context, input: Input): Output
+}
+
+class NamedCompilerPhase<in Context : CommonBackendContext, Data>(
+    private val lower: CompilerPhase<Context, Data, Data>
+) : CompilerPhase<Context, Data, Data> {
+    override fun invoke(phaseConfig: PhaseConfig, phaserState: PhaserState<Data>, context: Context, input: Data): Data {
+        // Expected: output: Data, Actual: output: Data?
+        val output = if (phaseConfig.needProfiling) {
+            runAndProfile(phaseConfig, phaserState, context, input)
+        } else {
+            phaserState.downlevel(1) {
+                lower.invoke(phaseConfig, phaserState, context, input)
+            }
+        }
+        runAfter(phaseConfig, phaserState, context, output)
+    }
+
+    private fun runAfter(phaseConfig: PhaseConfig, phaserState: PhaserState<Data>, context: Context, output: Data) {
+
+    }
+
+    private fun runAndProfile(phaseConfig: PhaseConfig, phaserState: PhaserState<Data>, context: Context, source: Data): Data {
+
+    }
+}
\ No newline at end of file
diff --git a/compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.txt b/compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.txt
new file mode 100644
index 00000000000..e574055d543
--- /dev/null
+++ b/compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.txt
@@ -0,0 +1,55 @@
+FILE: compilerPhase.kt
+    public abstract interface CommonBackendContext : R|kotlin/Any| {
+    }
+    public abstract interface PhaserState<Data> : R|kotlin/Any| {
+        public abstract var depth: R|kotlin/Int|
+            public get(): R|kotlin/Int|
+            public set(value: R|kotlin/Int|): R|kotlin/Unit|
+
+    }
+    public abstract interface PhaseConfig : R|kotlin/Any| {
+        public abstract val needProfiling: R|kotlin/Boolean|
+            public get(): R|kotlin/Boolean|
+
+    }
+    public final inline fun <R, D> R|PhaserState<D>|.downlevel(nlevels: R|kotlin/Int|, block: R|() -> R|): R|R| {
+        this@R|/downlevel|.R|/PhaserState.depth| = this@R|/downlevel|.R|/PhaserState.depth|.R|kotlin/Int.plus|(R|<local>/nlevels|)
+        lval result: R|R| = R|<local>/block|.R|SubstitutionOverride<kotlin/Function0.invoke: R|R|>|()
+        this@R|/downlevel|.R|/PhaserState.depth| = this@R|/downlevel|.R|/PhaserState.depth|.R|kotlin/Int.minus|(R|<local>/nlevels|)
+        ^downlevel R|<local>/result|
+    }
+    public abstract interface CompilerPhase<in Context : R|CommonBackendContext|, Input, Output> : R|kotlin/Any| {
+        public abstract fun invoke(phaseConfig: R|PhaseConfig|, phaserState: R|PhaserState<Input>|, context: R|Context|, input: R|Input|): R|Output|
+
+    }
+    public final class NamedCompilerPhase<in Context : R|CommonBackendContext|, Data> : R|CompilerPhase<Context, Data, Data>| {
+        public constructor<in Context : R|CommonBackendContext|, Data>(lower: R|CompilerPhase<Context, Data, Data>|): R|NamedCompilerPhase<Context, Data>| {
+            super<R|kotlin/Any|>()
+        }
+
+        private final val lower: R|CompilerPhase<Context, Data, Data>| = R|<local>/lower|
+            private get(): R|CompilerPhase<Context, Data, Data>|
+
+        public final override fun invoke(phaseConfig: R|PhaseConfig|, phaserState: R|PhaserState<Data>|, context: R|Context|, input: R|Data|): R|Data| {
+            lval output: R|Data| = when () {
+                R|<local>/phaseConfig|.R|/PhaseConfig.needProfiling| ->  {
+                    this@R|/NamedCompilerPhase|.R|/NamedCompilerPhase.runAndProfile|(R|<local>/phaseConfig|, R|<local>/phaserState|, R|<local>/context|, R|<local>/input|)
+                }
+                else ->  {
+                    R|<local>/phaserState|.R|/downlevel|<R|Data|, R|Data|>(Int(1), <L> = downlevel@fun <anonymous>(): R|Data| <kind=UNKNOWN>  {
+                        ^ this@R|/NamedCompilerPhase|.R|/NamedCompilerPhase.lower|.R|SubstitutionOverride</CompilerPhase.invoke: R|Data|>|(R|<local>/phaseConfig|, R|<local>/phaserState|, R|<local>/context|, R|<local>/input|)
+                    }
+                    )
+                }
+            }
+
+            this@R|/NamedCompilerPhase|.R|/NamedCompilerPhase.runAfter|(R|<local>/phaseConfig|, R|<local>/phaserState|, R|<local>/context|, R|<local>/output|)
+        }
+
+        private final fun runAfter(phaseConfig: R|PhaseConfig|, phaserState: R|PhaserState<Data>|, context: R|Context|, output: R|Data|): R|kotlin/Unit| {
+        }
+
+        private final fun runAndProfile(phaseConfig: R|PhaseConfig|, phaserState: R|PhaserState<Data>|, context: R|Context|, source: R|Data|): R|Data| {
+        }
+
+    }
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java
index 39cc95f6058..9e8a81ab802 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java
@@ -2024,6 +2024,11 @@ public class FirDiagnosticsTestGenerated extends AbstractFirDiagnosticsTest {
             KotlinTestUtils.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("compiler/fir/analysis-tests/testData/resolve/problems"), Pattern.compile("^([^.]+)\\.kt$"), null, true);
         }
 
+        @TestMetadata("compilerPhase.kt")
+        public void testCompilerPhase() throws Exception {
+            runTest("compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.kt");
+        }
+
         @TestMetadata("complexLambdaWithTypeVariableAsExpectedType.kt")
         public void testComplexLambdaWithTypeVariableAsExpectedType() throws Exception {
             runTest("compiler/fir/analysis-tests/testData/resolve/problems/complexLambdaWithTypeVariableAsExpectedType.kt");
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java
index ccb0b49c2ac..fb36942a569 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java
@@ -2024,6 +2024,11 @@ public class FirDiagnosticsWithLightTreeTestGenerated extends AbstractFirDiagnos
             KotlinTestUtils.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("compiler/fir/analysis-tests/testData/resolve/problems"), Pattern.compile("^([^.]+)\\.kt$"), null, true);
         }
 
+        @TestMetadata("compilerPhase.kt")
+        public void testCompilerPhase() throws Exception {
+            runTest("compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.kt");
+        }
+
         @TestMetadata("complexLambdaWithTypeVariableAsExpectedType.kt")
         public void testComplexLambdaWithTypeVariableAsExpectedType() throws Exception {
             runTest("compiler/fir/analysis-tests/testData/resolve/problems/complexLambdaWithTypeVariableAsExpectedType.kt");
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java
index 71463b1001f..3cb1851cae2 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java
@@ -2024,6 +2024,11 @@ public class LazyBodyIsNotTouchedTilContractsPhaseTestGenerated extends Abstract
             KotlinTestUtils.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("compiler/fir/analysis-tests/testData/resolve/problems"), Pattern.compile("^([^.]+)\\.kt$"), null, true);
         }
 
+        @TestMetadata("compilerPhase.kt")
+        public void testCompilerPhase() throws Exception {
+            runTest("compiler/fir/analysis-tests/testData/resolve/problems/compilerPhase.kt");
+        }
+
         @TestMetadata("complexLambdaWithTypeVariableAsExpectedType.kt")
         public void testComplexLambdaWithTypeVariableAsExpectedType() throws Exception {
             runTest("compiler/fir/analysis-tests/testData/resolve/problems/complexLambdaWithTypeVariableAsExpectedType.kt");
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/InferenceComponents.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/InferenceComponents.kt
index cb1df83b5c1..ec132d66375 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/InferenceComponents.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/InferenceComponents.kt
@@ -14,7 +14,7 @@ import org.jetbrains.kotlin.types.AbstractTypeApproximator
 
 @NoMutableState
 class InferenceComponents(val session: FirSession) : FirSessionComponent {
-    val ctx: ConeTypeCheckerContext = ConeTypeCheckerContext(isErrorTypeEqualsToAnything = false, isStubTypeEqualsToAnything = false, session)
+    val ctx: ConeTypeCheckerContext = ConeTypeCheckerContext(isErrorTypeEqualsToAnything = false, isStubTypeEqualsToAnything = true, session)
 
     val approximator: AbstractTypeApproximator = object : AbstractTypeApproximator(ctx) {}
     val trivialConstraintTypeInferenceOracle = TrivialConstraintTypeInferenceOracle.create(ctx)
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/types/ConeTypeContext.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/types/ConeTypeContext.kt
index fdb35bc8da0..b6905baca37 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/types/ConeTypeContext.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/types/ConeTypeContext.kt
@@ -584,7 +584,7 @@ class ConeTypeCheckerContext(
         errorTypesEqualToAnything: Boolean,
         stubTypesEqualToAnything: Boolean
     ): AbstractTypeCheckerContext =
-        if (this.isErrorTypeEqualsToAnything == errorTypesEqualToAnything)
+        if (this.isErrorTypeEqualsToAnything == errorTypesEqualToAnything && this.isStubTypeEqualsToAnything == stubTypesEqualToAnything)
             this
         else
             ConeTypeCheckerContext(errorTypesEqualToAnything, stubTypesEqualToAnything, session)
diff --git a/compiler/testData/diagnostics/tests/callableReference/generic/argumentAndReturnExpectedType.fir.kt b/compiler/testData/diagnostics/tests/callableReference/generic/argumentAndReturnExpectedType.fir.kt
index fc710a64a4f..c43049f5469 100644
--- a/compiler/testData/diagnostics/tests/callableReference/generic/argumentAndReturnExpectedType.fir.kt
+++ b/compiler/testData/diagnostics/tests/callableReference/generic/argumentAndReturnExpectedType.fir.kt
@@ -27,9 +27,9 @@ fun <T> listOf(): List<T> = TODO()
 fun <T> setOf(): Set<T> = TODO()
 
 fun <T> test2(x: T) {
-    bar(x, x, ::foo).checkType { <!INAPPLICABLE_CANDIDATE!>_<!><Pair<T, T>>() }
+    bar(x, x, ::foo).checkType { _<Pair<T, T>>() }
     bar(x, 1, ::foo).checkType { _<Pair<T, Int>>() }
-    bar(1, x, ::foo).checkType { <!INAPPLICABLE_CANDIDATE!>_<!><Pair<Int, T>>() }
+    bar(1, x, ::foo).checkType { _<Pair<Int, T>>() }
 
     bar(listOf<T>(), setOf<T>(), ::foo).checkType { _<Pair<List<T>, Set<T>>> () }
     bar(listOf<T>(), 1, ::foo).checkType { _<Pair<List<T>, Int>>() }
diff --git a/compiler/testData/ir/irText/expressions/kt30796.fir.kt.txt b/compiler/testData/ir/irText/expressions/kt30796.fir.kt.txt
index f45cf10a60b..92347743b7d 100644
--- a/compiler/testData/ir/irText/expressions/kt30796.fir.kt.txt
+++ b/compiler/testData/ir/irText/expressions/kt30796.fir.kt.txt
@@ -70,7 +70,7 @@ fun <T : Any?> test(value: T, value2: T) {
     }
   }
   val x7: Any = { // BLOCK
-    val <elvis>: T? = { // BLOCK
+    val <elvis>: T = { // BLOCK
       val <elvis>: T? = magic<T?>()
       when {
         EQEQ(arg0 = <elvis>, arg1 = null) -> value
@@ -79,7 +79,7 @@ fun <T : Any?> test(value: T, value2: T) {
     }
     when {
       EQEQ(arg0 = <elvis>, arg1 = null) -> 42
-      else -> <elvis> /*as T */
+      else -> <elvis>
     }
   }
 }
diff --git a/compiler/testData/ir/irText/expressions/kt30796.fir.txt b/compiler/testData/ir/irText/expressions/kt30796.fir.txt
index 0b70ed16ffd..344efa7f284 100644
--- a/compiler/testData/ir/irText/expressions/kt30796.fir.txt
+++ b/compiler/testData/ir/irText/expressions/kt30796.fir.txt
@@ -137,12 +137,12 @@ FILE fqName:<root> fileName:/kt30796.kt
               then: GET_VAR 'val tmp_8: T of <root>.test [val] declared in <root>.test' type=T of <root>.test origin=null
       VAR name:x7 type:kotlin.Any [val]
         BLOCK type=kotlin.Any origin=ELVIS
-          VAR IR_TEMPORARY_VARIABLE name:tmp_10 type:T of <root>.test? [val]
-            BLOCK type=T of <root>.test? origin=ELVIS
+          VAR IR_TEMPORARY_VARIABLE name:tmp_10 type:T of <root>.test [val]
+            BLOCK type=T of <root>.test origin=ELVIS
               VAR IR_TEMPORARY_VARIABLE name:tmp_11 type:T of <root>.test? [val]
                 CALL 'public final fun magic <T> (): T of <root>.magic declared in <root>' type=T of <root>.test? origin=null
                   <T>: T of <root>.test?
-              WHEN type=T of <root>.test? origin=ELVIS
+              WHEN type=T of <root>.test origin=ELVIS
                 BRANCH
                   if: CALL 'public final fun EQEQ (arg0: kotlin.Any?, arg1: kotlin.Any?): kotlin.Boolean declared in kotlin.internal.ir' type=kotlin.Boolean origin=EQEQ
                     arg0: GET_VAR 'val tmp_11: T of <root>.test? [val] declared in <root>.test' type=T of <root>.test? origin=null
@@ -155,10 +155,9 @@ FILE fqName:<root> fileName:/kt30796.kt
           WHEN type=kotlin.Any origin=ELVIS
             BRANCH
               if: CALL 'public final fun EQEQ (arg0: kotlin.Any?, arg1: kotlin.Any?): kotlin.Boolean declared in kotlin.internal.ir' type=kotlin.Boolean origin=EQEQ
-                arg0: GET_VAR 'val tmp_10: T of <root>.test? [val] declared in <root>.test' type=T of <root>.test? origin=null
+                arg0: GET_VAR 'val tmp_10: T of <root>.test [val] declared in <root>.test' type=T of <root>.test origin=null
                 arg1: CONST Null type=kotlin.Nothing? value=null
               then: CONST Int type=kotlin.Int value=42
             BRANCH
               if: CONST Boolean type=kotlin.Boolean value=true
-              then: TYPE_OP type=T of <root>.test origin=IMPLICIT_CAST typeOperand=T of <root>.test
-                GET_VAR 'val tmp_10: T of <root>.test? [val] declared in <root>.test' type=T of <root>.test? origin=null
+              then: GET_VAR 'val tmp_10: T of <root>.test [val] declared in <root>.test' type=T of <root>.test origin=null
diff --git a/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.kt.txt b/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.kt.txt
index df40c6ff4e0..35d4f744505 100644
--- a/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.kt.txt
+++ b/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.kt.txt
@@ -1,5 +1,5 @@
 fun <T : Any?> problematic(lss: List<List<T>>): List<T> {
-  return lss.flatMap<List<T>, T>(transform = local fun <anonymous>(it: List<T>): Iterable<T> {
+  return lss.flatMap<List<T>, T?>(transform = local fun <anonymous>(it: List<T>): Iterable<T?> {
     return id<T?>(v = it) /*!! List<T?> */
   }
 )
diff --git a/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.txt b/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.txt
index a21eafe3e68..2b7343b61d9 100644
--- a/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.txt
+++ b/compiler/testData/ir/irText/regressions/typeParametersInImplicitCast.fir.txt
@@ -4,15 +4,15 @@ FILE fqName:<root> fileName:/typeParametersInImplicitCast.kt
     VALUE_PARAMETER name:lss index:0 type:kotlin.collections.List<kotlin.collections.List<T of <root>.problematic>>
     BLOCK_BODY
       RETURN type=kotlin.Nothing from='public final fun problematic <T> (lss: kotlin.collections.List<kotlin.collections.List<T of <root>.problematic>>): kotlin.collections.List<T of <root>.problematic> declared in <root>'
-        CALL 'public final fun flatMap <T, R> (transform: kotlin.Function1<T of kotlin.collections.flatMap, kotlin.collections.Iterable<R of kotlin.collections.flatMap>>): kotlin.collections.List<R of kotlin.collections.flatMap> [inline] declared in kotlin.collections' type=kotlin.collections.List<T of <root>.problematic> origin=null
+        CALL 'public final fun flatMap <T, R> (transform: kotlin.Function1<T of kotlin.collections.flatMap, kotlin.collections.Iterable<R of kotlin.collections.flatMap>>): kotlin.collections.List<R of kotlin.collections.flatMap> [inline] declared in kotlin.collections' type=kotlin.collections.List<T of <root>.problematic?> origin=null
           <T>: kotlin.collections.List<T of <root>.problematic>
-          <R>: T of <root>.problematic
+          <R>: T of <root>.problematic?
           $receiver: GET_VAR 'lss: kotlin.collections.List<kotlin.collections.List<T of <root>.problematic>> declared in <root>.problematic' type=kotlin.collections.List<kotlin.collections.List<T of <root>.problematic>> origin=null
-          transform: FUN_EXPR type=kotlin.Function1<kotlin.collections.List<T of <root>.problematic>, kotlin.collections.Iterable<T of <root>.problematic>> origin=LAMBDA
-            FUN LOCAL_FUNCTION_FOR_LAMBDA name:<anonymous> visibility:local modality:FINAL <> (it:kotlin.collections.List<T of <root>.problematic>) returnType:kotlin.collections.Iterable<T of <root>.problematic>
+          transform: FUN_EXPR type=kotlin.Function1<kotlin.collections.List<T of <root>.problematic>, kotlin.collections.Iterable<T of <root>.problematic?>> origin=LAMBDA
+            FUN LOCAL_FUNCTION_FOR_LAMBDA name:<anonymous> visibility:local modality:FINAL <> (it:kotlin.collections.List<T of <root>.problematic>) returnType:kotlin.collections.Iterable<T of <root>.problematic?>
               VALUE_PARAMETER name:it index:0 type:kotlin.collections.List<T of <root>.problematic>
               BLOCK_BODY
-                RETURN type=kotlin.Nothing from='local final fun <anonymous> (it: kotlin.collections.List<T of <root>.problematic>): kotlin.collections.Iterable<T of <root>.problematic> declared in <root>.problematic'
+                RETURN type=kotlin.Nothing from='local final fun <anonymous> (it: kotlin.collections.List<T of <root>.problematic>): kotlin.collections.Iterable<T of <root>.problematic?> declared in <root>.problematic'
                   TYPE_OP type=kotlin.collections.List<T of <root>.problematic?> origin=IMPLICIT_NOTNULL typeOperand=kotlin.collections.List<T of <root>.problematic?>
                     CALL 'public/*package*/ open fun id <T> (v: kotlin.collections.List<T of <root>.ListId.id?>?): @[EnhancedNullability] kotlin.collections.List<T of <root>.ListId.id?> declared in <root>.ListId' type=@[EnhancedNullability] kotlin.collections.List<T of <root>.problematic?> origin=null
                       <T>: T of <root>.problematic?