Implement inferrable index signatures for enum types

Author: ahejlsberg

src/compiler/checker.ts

@@ -7299,7 +7299,8 @@ namespace ts {
                         stringIndexInfo = createIndexInfo(anyType, /*isReadonly*/ false);
                     }
                 }
-                const numberIndexInfo = symbol.flags & SymbolFlags.Enum ? enumNumberIndexInfo : undefined;
+                const numberIndexInfo = symbol.flags & SymbolFlags.Enum && (getDeclaredTypeOfSymbol(symbol).flags & TypeFlags.Enum ||
+                    some(type.properties, prop => !!(getTypeOfSymbol(prop).flags & TypeFlags.NumberLike))) ? enumNumberIndexInfo : undefined;
                 setStructuredTypeMembers(type, members, emptyArray, emptyArray, stringIndexInfo, numberIndexInfo);
                 // We resolve the members before computing the signatures because a signature may use
                 // typeof with a qualified name expression that circularly references the type we are
@@ -8161,6 +8162,9 @@ namespace ts {
                         propTypes.push(getTypeOfSymbol(prop));
                     }
                 }
+                if (kind === IndexKind.String) {
+                    append(propTypes, getIndexTypeOfType(type, IndexKind.Number));
+                }
                 if (propTypes.length) {
                     return getUnionType(propTypes, UnionReduction.Subtype);
                 }
@@ -14498,7 +14502,7 @@ namespace ts {
          * with no call or construct signatures.
          */
         function isObjectTypeWithInferableIndex(type: Type) {
-            return type.symbol && (type.symbol.flags & (SymbolFlags.ObjectLiteral | SymbolFlags.TypeLiteral | SymbolFlags.ValueModule)) !== 0 &&
+            return type.symbol && (type.symbol.flags & (SymbolFlags.ObjectLiteral | SymbolFlags.TypeLiteral | SymbolFlags.Enum| SymbolFlags.ValueModule)) !== 0 &&
                 !typeHasCallOrConstructSignatures(type);
         }