diff --git a/.coveragerc b/.coveragerc
index ed33143..188cbaf 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -1,6 +1,8 @@
 [run]
 source =
     result
+omit =
+    result/typetests.py
 
 [report]
 # Regexes for lines to exclude from consideration
diff --git a/.travis.yml b/.travis.yml
index 2a7e8eb..d80972c 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,6 +11,12 @@ install:
 script:
   - pip install -e .
   - py.test
-  - mypy result/result.py
+  - if [ $(python -c 'import sys; print(sys.version_info.minor)') -gt 4 ]; then
+      mypy result/result.py;
+      mypy result/typetests.py;
+      echo "Mypy tests done";
+    else
+      echo "Skipping mypy";
+    fi
 after_success:
   - coveralls
diff --git a/CHANGELOG.md b/CHANGELOG.md
index bc5bf97..10378c6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,6 +11,11 @@ Possible log types:
 - `[fixed]` for any bug fixes.
 - `[security]` to invite users to upgrade in case of vulnerabilities.
 
+## Unreleased
+
+ - [changed] Type annotations: Change parameter order
+   from `Result[E, T]` to `Result[T, E]` to match Rust/OCaml/F# (#7)
+
 ## [0.4.1] - 2020-02-17
 
  - [added] Add `py.typed` for PEP561 package compliance (#16)
diff --git a/README.rst b/README.rst
index f88a9b5..d5a7648 100644
--- a/README.rst
+++ b/README.rst
@@ -9,7 +9,8 @@ Result
     :alt: Coverage
     :target: https://coveralls.io/github/dbrgn/result
 
-A simple Result type for Python 3 `inspired by Rust <https://doc.rust-lang.org/std/result/>`__.
+A simple Result type for Python 3 `inspired by Rust
+<https://doc.rust-lang.org/std/result/>`__, fully type annotated.
 
 The idea is that a ``Result`` value can be either ``Ok(value)`` or ``Err(error)``,
 with a way to differentiate between the two. It will change code like this:
@@ -62,8 +63,8 @@ side, you don't have to return semantically unclear tuples anymore.
 
 Not all methods (https://doc.rust-lang.org/std/result/enum.Result.html) have
 been implemented, only the ones that make sense in the Python context. You still
-don't get any type safety, but some easier handling of types that can be OK or
-not, without resorting to custom exceptions.
+don't get any type safety at runtime, but some easier handling of types that can
+be OK or not, without resorting to custom exceptions.
 
 
 API
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 8598ef4..f023f7b 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -1,4 +1,4 @@
 pytest==2.8.5
 pytest-cov==2.2.0
 pytest-pep8==1.0.6
--e git+https://github.com/python/mypy@005fd6b357b995f13e3d90293cabf3c8c8c2a952#egg=mypy
+mypy==0.720
diff --git a/result/result.py b/result/result.py
index 2490609..1c7983b 100644
--- a/result/result.py
+++ b/result/result.py
@@ -1,29 +1,33 @@
 from typing import Callable, Generic, TypeVar, Union, Any, Optional, cast, overload
 
 
-E = TypeVar("E")
+T = TypeVar("T")  # Success type
+E = TypeVar("E")  # Error type
 F = TypeVar("F")
-T = TypeVar("T")
 U = TypeVar("U")
 
 
-class Result(Generic[E, T]):
+class Result(Generic[T, E]):
     """
     A simple `Result` type inspired by Rust.
 
     Not all methods (https://doc.rust-lang.org/std/result/enum.Result.html)
     have been implemented, only the ones that make sense in the Python context.
     """
-    def __init__(self, is_ok: bool, value: Union[E, T], force: bool = False) -> None:
+    def __init__(self, is_ok: bool, value: Union[T, E], force: bool = False) -> None:
         """Do not call this constructor, use the Ok or Err class methods instead.
 
         There are no type guarantees on the value if this is called directly.
 
         Args:
-            is_ok: If this represents an ok result
-            value: The value inside the result
-            force: Force creation of the object. This is false by default to prevent
+            is_ok:
+                If this represents an ok result
+            value:
+                The value inside the result
+            force:
+                Force creation of the object. This is false by default to prevent
                 accidentally creating instance of a Result in an unsafe way.
+
         """
         if force is not True:
             raise RuntimeError("Don't instantiate a Result directly. "
@@ -51,20 +55,20 @@ def __repr__(self) -> str:
 
     @classmethod
     @overload
-    def Ok(cls) -> 'Result[E, bool]':
+    def Ok(cls) -> 'Result[bool, Any]':
         pass
 
     @classmethod
     @overload
-    def Ok(cls, value: T) -> 'Result[E, T]':
+    def Ok(cls, value: T) -> 'Result[T, Any]':
         pass
 
     @classmethod
-    def Ok(cls, value: Any = True) -> 'Result[E, Any]':
+    def Ok(cls, value: Any = True) -> 'Result[Any, Any]':
         return cls(is_ok=True, value=value, force=True)
 
     @classmethod
-    def Err(cls, error: E) -> 'Result[E, T]':
+    def Err(cls, error: E) -> 'Result[Any, E]':
         return cls(is_ok=False, value=error, force=True)
 
     def is_ok(self) -> bool:
@@ -87,7 +91,7 @@ def err(self) -> Optional[E]:
         return cast(E, self._value) if self.is_err() else None
 
     @property
-    def value(self) -> Union[E, T]:
+    def value(self) -> Union[T, E]:
         """
         Return the inner value. This might be either the ok or the error type.
         """
@@ -120,14 +124,14 @@ def unwrap_or(self, default: T) -> T:
         else:
             return default
 
-    def map(self, op: Callable[[T], U]) -> 'Result[E, U]':
+    def map(self, op: Callable[[T], U]) -> 'Result[U, E]':
         """
         If contained result is `Ok`, return `Ok` with original value mapped to
         a new value using the passed in function. Otherwise return `Err` with
         same value.
         """
         if not self._is_ok:
-            return cast(Result[E, U], self)
+            return cast(Result[U, E], self)
         return Ok(op(cast(T, self._value)))
 
     def map_or(self, default: U, op: Callable[[T], U]) -> U:
@@ -153,35 +157,35 @@ def map_or_else(
             return default_op()
         return op(cast(T, self._value))
 
-    def map_err(self, op: Callable[[E], F]) -> 'Result[F, T]':
+    def map_err(self, op: Callable[[E], F]) -> 'Result[T, F]':
         """
         If contained result is `Err`, return `Err` with original value mapped
         to a new value using the passed in `op` function. Otherwise return `Ok`
         with the same value.
         """
         if self._is_ok:
-            return cast(Result[F, T], self)
+            return cast(Result[T, F], self)
         return Err(op(cast(E, self._value)))
 
 
 @overload
-def Ok() -> Result[E, bool]:
+def Ok() -> Result[bool, Any]:
     pass
 
 
 @overload
-def Ok(value: T) -> Result[E, T]:
+def Ok(value: T) -> Result[T, Any]:
     pass
 
 
-def Ok(value: Any = True) -> Result[E, Any]:
+def Ok(value: Any = True) -> Result[Any, Any]:
     """
     Shortcut function to create a new Result.
     """
     return Result.Ok(value)
 
 
-def Err(error: E) -> Result[E, T]:
+def Err(error: E) -> Result[Any, E]:
     """
     Shortcut function to create a new Result.
     """
diff --git a/result/typetests.py b/result/typetests.py
new file mode 100644
index 0000000..ba0ee86
--- /dev/null
+++ b/result/typetests.py
@@ -0,0 +1,20 @@
+from typing import List, Optional
+
+from .result import Result, Ok, Err
+
+
+res1 = Result.Ok('hello')  # type: Result[str, int]
+if res1.is_ok():
+    ok = res1.ok()  # type: Optional[str]
+    mapped_to_float = res1.map_or(1.0, lambda s: len(s) * 1.5)  # type: float
+else:
+    err = res1.err()  # type: Optional[int]
+    mapped_to_list = res1.map_err(lambda e: [e]).err()  # type: Optional[List[int]]
+
+# Test constructor functions
+res2 = Ok()
+res3 = Result.Ok()
+res4 = Ok(42)
+res5 = Result.Ok(23)
+res6 = Err(1)
+res7 = Result.Err(2)