diff --git a/mlir/docs/LangRef.md b/mlir/docs/LangRef.md
--- a/mlir/docs/LangRef.md
+++ b/mlir/docs/LangRef.md
@@ -929,15 +929,14 @@
 ```
 memref-type ::= ranked-memref-type | unranked-memref-type
 
-ranked-memref-type ::= `memref` `<` dimension-list-ranked tensor-memref-element-type
+ranked-memref-type ::= `memref` `<` dimension-list-ranked type
                       (`,` layout-specification)? (`,` memory-space)? `>`
 
-unranked-memref-type ::= `memref` `<*x` tensor-memref-element-type
-                         (`,` memory-space)? `>`
+unranked-memref-type ::= `memref` `<*x` type (`,` memory-space)? `>`
 
 stride-list ::= `[` (dimension (`,` dimension)*)? `]`
 strided-layout ::= `offset:` dimension `,` `strides: ` stride-list
-layout-specification ::= semi-affine-map | strided-layout
+layout-specification ::= semi-affine-map-composition | strided-layout
 memory-space ::= integer-literal /* | TODO: address-space-id */
 ```
 
@@ -1201,10 +1200,8 @@
 Syntax:
 
 ```
-tensor-type ::= `tensor` `<` dimension-list tensor-memref-element-type `>`
-tensor-memref-element-type ::= vector-element-type | vector-type | complex-type
+tensor-type ::= `tensor` `<` dimension-list type `>`
 
-// memref requires a known rank, but tensor does not.
 dimension-list ::= dimension-list-ranked | (`*` `x`)
 dimension-list-ranked ::= (dimension `x`)*
 dimension ::= `?` | decimal-literal
diff --git a/mlir/lib/Parser/TypeParser.cpp b/mlir/lib/Parser/TypeParser.cpp
--- a/mlir/lib/Parser/TypeParser.cpp
+++ b/mlir/lib/Parser/TypeParser.cpp
@@ -181,12 +181,13 @@
 ///   memref-type ::= ranked-memref-type | unranked-memref-type
 ///
 ///   ranked-memref-type ::= `memref` `<` dimension-list-ranked type
-///                          (`,` semi-affine-map-composition)? (`,`
-///                          memory-space)? `>`
+///                          (`,` layout-specification)? (`,` memory-space)? `>`
 ///
 ///   unranked-memref-type ::= `memref` `<*x` type (`,` memory-space)? `>`
 ///
-///   semi-affine-map-composition ::= (semi-affine-map `,` )* semi-affine-map
+///   stride-list ::= `[` (dimension (`,` dimension)*)? `]`
+///   strided-layout ::= `offset:` dimension `,` `strides: ` stride-list
+///   layout-specification ::= semi-affine-map-composition | strided-layout
 ///   memory-space ::= integer-literal /* | TODO: address-space-id */
 ///
 Type Parser::parseMemRefType() {