# Narrowing for `!=` and `==` conditionals

## `x != None`

```py
def _(flag: bool):
    x = None if flag else 1

    if x != None:
        reveal_type(x)  # revealed: Literal[1]
    else:
        reveal_type(x)  # revealed: None
```

## `None != x` (reversed operands)

```py
def _(flag: bool):
    x = None if flag else 1

    if None != x:
        reveal_type(x)  # revealed: Literal[1]
    else:
        reveal_type(x)  # revealed: None
```

This also works for `==` with reversed operands:

```py
def _(flag: bool):
    x = None if flag else 1

    if None == x:
        reveal_type(x)  # revealed: None
    else:
        reveal_type(x)  # revealed: Literal[1]
```

## `!=` for other singleton types

### Bool

```py
def _(x: bool):
    if x != False:
        reveal_type(x)  # revealed: Literal[True]
    else:
        reveal_type(x)  # revealed: Literal[False]

def _(x: bool):
    if x == False:
        reveal_type(x)  # revealed: Literal[False]
    else:
        reveal_type(x)  # revealed: Literal[True]
```

### Enums

```py
from enum import Enum

class Answer(Enum):
    NO = 0
    YES = 1

def _(answer: Answer):
    if answer != Answer.NO:
        reveal_type(answer)  # revealed: Literal[Answer.YES]
    else:
        reveal_type(answer)  # revealed: Literal[Answer.NO]

def _(answer: Answer):
    if answer == Answer.NO:
        reveal_type(answer)  # revealed: Literal[Answer.NO]
    else:
        reveal_type(answer)  # revealed: Literal[Answer.YES]

class Single(Enum):
    VALUE = 1

def _(x: Single | int):
    if x != Single.VALUE:
        reveal_type(x)  # revealed: int
    else:
        # `int` is not eliminated here because there could be subclasses of `int` with custom `__eq__`/`__ne__` methods
        reveal_type(x)  # revealed: Single | int

def _(x: Single | int):
    if x == Single.VALUE:
        reveal_type(x)  # revealed: Single | int
    else:
        reveal_type(x)  # revealed: int
```

This narrowing behavior is only safe if the enum has no custom `__eq__`/`__ne__` method:

```py
from enum import Enum

class AmbiguousEnum(Enum):
    NO = 0
    YES = 1

    def __ne__(self, other) -> bool:
        return True

def _(answer: AmbiguousEnum):
    if answer != AmbiguousEnum.NO:
        reveal_type(answer)  # revealed: AmbiguousEnum
    else:
        reveal_type(answer)  # revealed: AmbiguousEnum
```

Similar if that method is inherited from a base class:

```py
from enum import Enum

class Mixin:
    def __eq__(self, other) -> bool:
        return True

class AmbiguousEnum(Mixin, Enum):
    NO = 0
    YES = 1

def _(answer: AmbiguousEnum):
    if answer == AmbiguousEnum.NO:
        reveal_type(answer)  # revealed: AmbiguousEnum
    else:
        reveal_type(answer)  # revealed: AmbiguousEnum
```

## `x != y` where `y` is of literal type

```py
def _(flag: bool):
    x = 1 if flag else 2

    if x != 1:
        reveal_type(x)  # revealed: Literal[2]
```

## `x != y` where `y` is a single-valued type

```py
def _(flag: bool):
    class A: ...
    class B: ...
    C = A if flag else B

    if C != A:
        reveal_type(C)  # revealed: <class 'B'>
    else:
        reveal_type(C)  # revealed: <class 'A'>
```

## `x != y` where `y` has multiple single-valued options

```py
def _(flag1: bool, flag2: bool):
    x = 1 if flag1 else 2
    y = 2 if flag2 else 3

    if x != y:
        reveal_type(x)  # revealed: Literal[1, 2]
    else:
        reveal_type(x)  # revealed: Literal[2]
```

## `!=` for non-single-valued types

Only single-valued types should narrow the type:

```py
def _(flag: bool, a: int, y: int):
    x = a if flag else None

    if x != y:
        reveal_type(x)  # revealed: int | None
```

## Mix of single-valued and non-single-valued types

```py
def _(flag1: bool, flag2: bool, a: int):
    x = 1 if flag1 else 2
    y = 2 if flag2 else a

    if x != y:
        reveal_type(x)  # revealed: Literal[1, 2]
    else:
        reveal_type(x)  # revealed: Literal[1, 2]
```

## `==` / `!=` with two narrowable operands

Both operands should be narrowed when both are narrowable expressions.

```py
from typing import Literal

def _(x: Literal[1], y: Literal[1, 2]):
    if x == y:
        reveal_type(y)  # revealed: Literal[1]
    if y == x:
        reveal_type(y)  # revealed: Literal[1]
    if x != y:
        reveal_type(y)  # revealed: Literal[2]
    if y != x:
        reveal_type(y)  # revealed: Literal[2]
```

## Assignment expressions

```py
from typing import Literal

def f() -> Literal[1, 2, 3]:
    return 1

if (x := f()) != 1:
    reveal_type(x)  # revealed: Literal[2, 3]
else:
    reveal_type(x)  # revealed: Literal[1]
```

## Union with `Any`

```py
from typing import Any

def _(x: Any | None, y: Any | None):
    if x != 1:
        reveal_type(x)  # revealed: (Any & ~Literal[1]) | None
    if y == 1:
        reveal_type(y)  # revealed: Any & ~None
```

## Booleans and integers

```py
from typing import Literal

def _(b: bool, i: Literal[1, 2]):
    if b == 1:
        reveal_type(b)  # revealed: Literal[True]
    else:
        reveal_type(b)  # revealed: Literal[False]

    if b == 6:
        reveal_type(b)  # revealed: Never
    else:
        reveal_type(b)  # revealed: bool

    if b == 0:
        reveal_type(b)  # revealed: Literal[False]
    else:
        reveal_type(b)  # revealed: Literal[True]

    if i == True:
        reveal_type(i)  # revealed: Literal[1]
    else:
        reveal_type(i)  # revealed: Literal[2]
```

## Narrowing `LiteralString` in union

```py
from typing_extensions import Literal, LiteralString, Any

def _(s: LiteralString | None, t: LiteralString | Any):
    if s == "foo":
        reveal_type(s)  # revealed: Literal["foo"]

    if s == 1:
        reveal_type(s)  # revealed: Never

    if t == "foo":
        # TODO could be `Literal["foo"] | Any`
        reveal_type(t)  # revealed: LiteralString | Any
```

## Narrowing with tuple types

We assume that tuple subclasses don't override `tuple.__eq__`, which only returns True for other
tuples. So they are excluded from the narrowed type when comparing to non-tuple values.

```py
from typing import Literal

def _(x: Literal["a", "b"] | tuple[int, int]):
    if x == "a":
        # tuple type is excluded because it's disjoint from the string literal
        reveal_type(x)  # revealed: Literal["a"]
    else:
        # tuple type remains in the else branch
        reveal_type(x)  # revealed: Literal["b"] | tuple[int, int]
```
