diff --git a/pkg/compiler/lib/src/inferrer/builder.dart b/pkg/compiler/lib/src/inferrer/builder.dart
index 900f45376e5..c5df0f707c1 100644
--- a/pkg/compiler/lib/src/inferrer/builder.dart
+++ b/pkg/compiler/lib/src/inferrer/builder.dart
@@ -2798,17 +2798,9 @@ class ElementGraphBuilder extends ast.Visitor<TypeInformation>
       }
     }
 
-    return inferrer.registerCalledSelector(
-        callType,
-        node,
-        selector,
-        mask,
-        receiverType,
-        outermostElement,
-        arguments,
-        sideEffects,
-        inLoop,
-        isConditional);
+    return inferrer.registerCalledSelector(callType, node, selector, mask,
+        receiverType, outermostElement, arguments, sideEffects,
+        inLoop: inLoop, isConditional: isConditional);
   }
 
   TypeInformation handleDynamicInvoke(ast.Send node) {
diff --git a/pkg/compiler/lib/src/inferrer/builder_kernel.dart b/pkg/compiler/lib/src/inferrer/builder_kernel.dart
index a2739301b5b..ac087dd97d7 100644
--- a/pkg/compiler/lib/src/inferrer/builder_kernel.dart
+++ b/pkg/compiler/lib/src/inferrer/builder_kernel.dart
@@ -12,6 +12,9 @@ import '../elements/types.dart';
 import '../kernel/element_map.dart';
 import '../options.dart';
 import '../types/constants.dart';
+import '../types/types.dart';
+import '../universe/selector.dart';
+import '../universe/side_effects.dart';
 import '../world.dart';
 import 'inferrer_engine.dart';
 import 'locals_handler.dart';
@@ -35,6 +38,8 @@ class KernelTypeGraphBuilder extends ir.Visitor<TypeInformation> {
   final KernelToElementMapForBuilding _elementMap;
   final KernelToLocalsMap _localsMap;
   LocalsHandler _locals;
+  final GlobalTypeInferenceElementData<ir.Node> _memberData;
+  SideEffects _sideEffects = new SideEffects.empty();
 
   TypeInformation _returnType;
 
@@ -48,7 +53,8 @@ class KernelTypeGraphBuilder extends ir.Visitor<TypeInformation> {
       this._elementMap,
       this._localsMap,
       [this._locals])
-      : this._types = _inferrer.types {
+      : this._types = _inferrer.types,
+        this._memberData = _inferrer.dataOfMember(_analyzedMember) {
     if (_locals != null) return;
 
     FieldInitializationScope<ir.Node> fieldScope =
@@ -59,6 +65,10 @@ class KernelTypeGraphBuilder extends ir.Visitor<TypeInformation> {
         _inferrer, _types, _options, _analyzedNode, fieldScope);
   }
 
+  int _loopLevel = 0;
+
+  bool get inLoop => _loopLevel > 0;
+
   TypeInformation run() {
     if (_analyzedMember.isField) {
       if (_analyzedNode == null || _analyzedNode is ir.NullLiteral) {
@@ -254,4 +264,62 @@ class KernelTypeGraphBuilder extends ir.Visitor<TypeInformation> {
     _locals.update(local, rhsType, node, type);
     return rhsType;
   }
+
+  ArgumentsTypes analyzeArguments(ir.Arguments arguments) {
+    List<TypeInformation> positional = <TypeInformation>[];
+    Map<String, TypeInformation> named;
+    for (ir.Expression argument in arguments.positional) {
+      positional.add(argument.accept(this));
+    }
+    for (ir.NamedExpression argument in arguments.named) {
+      named ??= <String, TypeInformation>{};
+      named[argument.name] = argument.value.accept(this);
+    }
+
+    /// TODO(johnniwinther): Track `isThisExposed`.
+    return new ArgumentsTypes(positional, named);
+  }
+
+  @override
+  TypeInformation visitMethodInvocation(ir.MethodInvocation node) {
+    TypeInformation receiverType = visit(node.receiver);
+    Selector selector = _elementMap.getSelector(node);
+    TypeMask mask = _memberData.typeOfSend(node);
+
+    ArgumentsTypes arguments = analyzeArguments(node.arguments);
+    if (selector.name == '==' || selector.name == '!=') {
+      if (_types.isNull(receiverType)) {
+        // TODO(johnniwinther): Add null check.
+        return _types.boolType;
+      } else if (_types.isNull(arguments.positional[0])) {
+        // TODO(johnniwinther): Add null check.
+        return _types.boolType;
+      }
+    }
+    return handleDynamicInvoke(
+        CallType.access, node, selector, mask, receiverType, arguments);
+  }
+
+  TypeInformation handleDynamicInvoke(
+      CallType callType,
+      ir.Node node,
+      Selector selector,
+      TypeMask mask,
+      TypeInformation receiverType,
+      ArgumentsTypes arguments) {
+    assert(receiverType != null);
+    if (_types.selectorNeedsUpdate(receiverType, mask)) {
+      mask = receiverType == _types.dynamicType
+          ? null
+          : _types.newTypedSelector(receiverType, mask);
+      _inferrer.updateSelectorInMember(
+          _analyzedMember, callType, node, selector, mask);
+    }
+
+    // TODO(johnniwinther): Refine receiver on non-captured locals.
+
+    return _inferrer.registerCalledSelector(callType, node, selector, mask,
+        receiverType, _analyzedMember, arguments, _sideEffects,
+        inLoop: inLoop, isConditional: false);
+  }
 }
diff --git a/pkg/compiler/lib/src/inferrer/inferrer_engine.dart b/pkg/compiler/lib/src/inferrer/inferrer_engine.dart
index b04c4ab7124..085ac470f30 100644
--- a/pkg/compiler/lib/src/inferrer/inferrer_engine.dart
+++ b/pkg/compiler/lib/src/inferrer/inferrer_engine.dart
@@ -123,9 +123,9 @@ abstract class InferrerEngine<T> {
   Iterable<MemberEntity> getCallersOf(MemberEntity element);
 
   // TODO(johnniwinther): Make this private again.
-  GlobalTypeInferenceElementData dataOfMember(MemberEntity element);
+  GlobalTypeInferenceElementData<T> dataOfMember(MemberEntity element);
 
-  GlobalTypeInferenceElementData lookupDataOfMember(MemberEntity element);
+  GlobalTypeInferenceElementData<T> lookupDataOfMember(MemberEntity element);
 
   bool checkIfExposesThis(ConstructorEntity element);
 
@@ -194,8 +194,8 @@ abstract class InferrerEngine<T> {
       MemberEntity caller,
       ArgumentsTypes arguments,
       SideEffects sideEffects,
-      bool inLoop,
-      bool isConditional);
+      {bool inLoop,
+      bool isConditional});
 
   /// Update the assignments to parameters in the graph. [remove] tells whether
   /// assignments must be added or removed. If [init] is false, parameters are
@@ -1004,8 +1004,8 @@ abstract class InferrerEngineImpl<T> extends InferrerEngine<T> {
       MemberEntity caller,
       ArgumentsTypes arguments,
       SideEffects sideEffects,
-      bool inLoop,
-      bool isConditional) {
+      {bool inLoop,
+      bool isConditional}) {
     if (selector.isClosureCall) {
       return registerCalledClosure(node, selector, mask, receiverType, caller,
           arguments, sideEffects, inLoop);
@@ -1105,7 +1105,7 @@ abstract class InferrerEngineImpl<T> extends InferrerEngine<T> {
   }
 
   TypeInformation typeOfMemberWithSelector(
-      covariant MemberElement element, Selector selector) {
+      MemberEntity element, Selector selector) {
     if (element.name == Identifiers.noSuchMethod_ &&
         selector.name != element.name) {
       // An invocation can resolve to a [noSuchMethod], in which case
@@ -1119,11 +1119,11 @@ abstract class InferrerEngineImpl<T> extends InferrerEngine<T> {
             : types.functionType;
       } else if (element.isField) {
         return typeOfMember(element);
-      } else if (Elements.isUnresolved(element)) {
-        return types.dynamicType;
-      } else {
-        assert(element.isGetter);
+      } else if (element.isGetter) {
         return returnTypeOfMember(element);
+      } else {
+        assert(element is MemberElement && Elements.isUnresolved(element));
+        return types.dynamicType;
       }
     } else if (element.isGetter || element.isField) {
       assert(selector.isCall || selector.isSetter);
diff --git a/pkg/compiler/lib/src/inferrer/kernel_inferrer_engine.dart b/pkg/compiler/lib/src/inferrer/kernel_inferrer_engine.dart
index 21dc8ec5feb..bee3b4d2e48 100644
--- a/pkg/compiler/lib/src/inferrer/kernel_inferrer_engine.dart
+++ b/pkg/compiler/lib/src/inferrer/kernel_inferrer_engine.dart
@@ -205,7 +205,7 @@ class KernelInferrerEngine extends InferrerEngineImpl<ir.Node> {
 
   @override
   GlobalTypeInferenceElementData<ir.Node> createElementData() {
-    throw new UnimplementedError('KernelInferrerEngine.createElementData');
+    return new KernelGlobalTypeInferenceElementData();
   }
 }
 
@@ -343,3 +343,81 @@ class KernelTypeSystemStrategy implements TypeSystemStrategy<ir.Node> {
     }
   }
 }
+
+class KernelGlobalTypeInferenceElementData
+    extends GlobalTypeInferenceElementData<ir.Node> {
+  // TODO(johnniwinther): Rename this together with [typeOfSend].
+  Map<ir.Node, TypeMask> _sendMap;
+
+  @override
+  TypeMask typeOfSend(ir.Node node) {
+    if (_sendMap == null) return null;
+    return _sendMap[node];
+  }
+
+  @override
+  void setCurrentTypeMask(ir.Node node, TypeMask mask) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.setCurrentTypeMask');
+  }
+
+  @override
+  void setMoveNextTypeMask(ir.Node node, TypeMask mask) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.setMoveNextTypeMask');
+  }
+
+  @override
+  void setIteratorTypeMask(ir.Node node, TypeMask mask) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.setIteratorTypeMask');
+  }
+
+  @override
+  TypeMask typeOfIteratorCurrent(ir.Node node) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.typeOfIteratorCurrent');
+  }
+
+  @override
+  TypeMask typeOfIteratorMoveNext(ir.Node node) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.typeOfIteratorMoveNext');
+  }
+
+  @override
+  TypeMask typeOfIterator(ir.Node node) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.typeOfIterator');
+  }
+
+  @override
+  void setOperatorTypeMaskInComplexSendSet(ir.Node node, TypeMask mask) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.setOperatorTypeMaskInComplexSendSet');
+  }
+
+  @override
+  void setGetterTypeMaskInComplexSendSet(ir.Node node, TypeMask mask) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.setGetterTypeMaskInComplexSendSet');
+  }
+
+  @override
+  void setTypeMask(ir.Node node, TypeMask mask) {
+    _sendMap ??= <ir.Node, TypeMask>{};
+    _sendMap[node] = mask;
+  }
+
+  @override
+  TypeMask typeOfOperator(ir.Node node) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.typeOfOperator');
+  }
+
+  @override
+  TypeMask typeOfGetter(ir.Node node) {
+    throw new UnsupportedError(
+        'KernelGlobalTypeInferenceElementData.typeOfGetter');
+  }
+}
diff --git a/pkg/compiler/lib/src/inferrer/type_graph_nodes.dart b/pkg/compiler/lib/src/inferrer/type_graph_nodes.dart
index 25632dbe81d..3e5635ae185 100644
--- a/pkg/compiler/lib/src/inferrer/type_graph_nodes.dart
+++ b/pkg/compiler/lib/src/inferrer/type_graph_nodes.dart
@@ -6,6 +6,8 @@ library compiler.src.inferrer.type_graph_nodes;
 
 import 'dart:collection' show IterableBase;
 
+import 'package:kernel/ast.dart' as ir;
+
 import '../common.dart';
 import '../common/names.dart' show Identifiers;
 import '../constants/values.dart';
@@ -382,12 +384,13 @@ abstract class MemberTypeInformation extends ElementTypeInformation
    * to enable counting the global number of call sites of [element].
    *
    * A call site is either an AST [ast.Node], an [Element] (see uses of
-   * [synthesizeForwardingCall] in [SimpleTypeInferrerVisitor]).
+   * [synthesizeForwardingCall] in [SimpleTypeInferrerVisitor]) or an IR
+   * [ir.Node].
    *
    * The global information is summarized in [cleanup], after which [_callers]
    * is set to `null`.
    */
-  Map<MemberEntity, Setlet<Spannable>> _callers;
+  Map<MemberEntity, Setlet<Object>> _callers;
 
   MemberTypeInformation._internal(this._member) : super._internal(null) {
     assert(_checkMember(_member));
@@ -401,12 +404,12 @@ abstract class MemberTypeInformation extends ElementTypeInformation
 
   String get debugName => '$member';
 
-  void addCall(MemberEntity caller, Spannable node) {
-    _callers ??= <MemberEntity, Setlet<Spannable>>{};
+  void addCall(MemberEntity caller, Object node) {
+    _callers ??= <MemberEntity, Setlet<Object>>{};
     _callers.putIfAbsent(caller, () => new Setlet()).add(node);
   }
 
-  void removeCall(MemberEntity caller, node) {
+  void removeCall(MemberEntity caller, Object node) {
     if (_callers == null) return;
     Setlet calls = _callers[caller];
     if (calls == null) return;
@@ -831,7 +834,7 @@ bool validCallType(CallType callType, Object call) {
     case CallType.complex:
       return call is ast.SendSet;
     case CallType.access:
-      return call is ast.Send;
+      return call is ast.Send || call is ir.Node;
     case CallType.forIn:
       return call is ast.ForIn;
   }
@@ -863,7 +866,8 @@ abstract class CallSiteTypeInformation extends TypeInformation
     assert(_checkCaller(caller));
     // [_call] is either an AST node or a constructor element in case of a
     // a forwarding constructor _call.
-    assert(_call is ast.Node || _call is ConstructorElement);
+    assert(
+        _call is ast.Node || _call is ConstructorElement || _call is ir.Node);
   }
 
   bool _checkCaller(MemberEntity caller) {
diff --git a/pkg/compiler/lib/src/types/types.dart b/pkg/compiler/lib/src/types/types.dart
index 03d72ea2d9c..d950348f726 100644
--- a/pkg/compiler/lib/src/types/types.dart
+++ b/pkg/compiler/lib/src/types/types.dart
@@ -152,6 +152,7 @@ class GlobalTypeInferenceParameterResultImpl<T>
 /// Internal data used during type-inference to store intermediate results about
 /// a single element.
 abstract class GlobalTypeInferenceElementData<T> {
+  // TODO(johnniwinther): Remove this. Maybe split by access/invoke.
   TypeMask typeOfSend(T node);
   TypeMask typeOfGetter(T node);
   TypeMask typeOfOperator(T node);
diff --git a/tests/compiler/dart2js/equivalence/id_equivalence_helper.dart b/tests/compiler/dart2js/equivalence/id_equivalence_helper.dart
index b5b61af76e0..c9b36793c4e 100644
--- a/tests/compiler/dart2js/equivalence/id_equivalence_helper.dart
+++ b/tests/compiler/dart2js/equivalence/id_equivalence_helper.dart
@@ -133,17 +133,15 @@ class IdData {
       IdValue value = expectedMap[id];
       if (data.value != value || value == null && data.value.value != '') {
         String expected = value?.toString() ?? '';
+        int offset = getOffsetFromId(id);
         annotations
-            .putIfAbsent(data.sourceSpan.begin, () => [])
+            .putIfAbsent(offset, () => [])
             .add('${expected} | ${data.value}');
       }
     });
     expectedMap.forEach((Id id, IdValue expected) {
       if (!actualMap.containsKey(id)) {
-        int offset = compiler.reporter
-            .spanFromSpannable(
-                computeSpannable(elementEnvironment, mainUri, id))
-            .begin;
+        int offset = getOffsetFromId(id);
         annotations.putIfAbsent(offset, () => []).add('${expected} | ---');
       }
     });
@@ -171,6 +169,12 @@ class IdData {
     });
     return withAnnotations(annotations);
   }
+
+  int getOffsetFromId(Id id) {
+    return compiler.reporter
+        .spanFromSpannable(computeSpannable(elementEnvironment, mainUri, id))
+        .begin;
+  }
 }
 
 /// Check code for all test files int [data] using [computeFromAst] and
diff --git a/tests/compiler/dart2js/inference/data/locals.dart b/tests/compiler/dart2js/inference/data/locals.dart
index eefa25bc290..4ef0128215a 100644
--- a/tests/compiler/dart2js/inference/data/locals.dart
+++ b/tests/compiler/dart2js/inference/data/locals.dart
@@ -7,6 +7,8 @@ main() {
   uninitializedLocal();
   initializedLocal();
   updatedLocal();
+  invokeLocal();
+  postfixLocal();
 }
 
 /*element: uninitializedLocal:[null]*/
@@ -27,3 +29,18 @@ updatedLocal() {
   local2 = 0;
   return local2;
 }
+
+/*element: invokeLocal:[null]*/
+invokeLocal() {
+  var local2 = 0;
+  local2. /*invoke: [exact=JSUInt31]*/ toString();
+  return null;
+}
+
+/*element: postfixLocal:[null]*/
+postfixLocal() {
+  // ignore: UNUSED_LOCAL_VARIABLE
+  var local2 = 0;
+  local2 /*invoke: [exact=JSUInt31]*/ ++;
+  return null;
+}