/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module

prelude
public import Init.Core

public section

/--
The `BEq α` and `Hashable α` instances on `α` are compatible. This means that that `a == b` implies
`hash a = hash b`.

This is automatic if the `BEq` instance is lawful.
-/
class LawfulHashable (α : Type u) [BEq α] [Hashable α] where
  /-- If `a == b`, then `hash a = hash b`. -/
  hash_eq (a b : α) : a == b → hash a = hash b

/--
A lawful hash function respects its Boolean equality test.
-/
theorem hash_eq [BEq α] [Hashable α] [LawfulHashable α] {a b : α} : a == b → hash a = hash b :=
  LawfulHashable.hash_eq a b

instance (priority := low) [BEq α] [Hashable α] [LawfulBEq α] : LawfulHashable α where
  hash_eq _ _ h := eq_of_beq h ▸ rfl