See file DiscrTree.lean for the actual implementation and documentation.

inductive Lean.Meta.DiscrTree.Key : Type

Discrimination tree key. See DiscrTree

• star : Key
• other : Key
• lit : Literal → Key
• fvar : FVarId → Nat → Key
• const : Name → Nat → Key
• arrow : Key
• proj : Name → Nat → Nat → Key

instance Lean.Meta.DiscrTree.instInhabitedKey : Inhabited Key

def Lean.Meta.DiscrTree.instInhabitedKey.default : Key

instance Lean.Meta.DiscrTree.instBEqKey : BEq Key

def Lean.Meta.DiscrTree.instBEqKey.beq : Key → Key → Bool

instance Lean.Meta.DiscrTree.instReprKey : Repr Key

def Lean.Meta.DiscrTree.instReprKey.repr : Key → Nat → Format

def Lean.Meta.DiscrTree.Key.hash : Key → UInt64

instance Lean.Meta.DiscrTree.instHashableKey : Hashable Key

instance Lean.Meta.DiscrTree.instToExprKey : ToExpr Key

inductive Lean.Meta.DiscrTree.Trie (α : Type) : Type

Discrimination tree trie. See DiscrTree.

• node {α : Type} (vs : Array α) (children : Array (Key × Trie α)) : Trie α

Notes regarding term reduction at the DiscrTree module.

• In simp, we want to have simp theorem such as

@[simp] theorem liftOn_mk (a : α) (f : α → γ) (h : ∀ a₁ a₂, r a₁ a₂ → f a₁ = f a₂) :
    Quot.liftOn (Quot.mk r a) f h = f a := rfl

If we enable iota, then the lhs is reduced to f a. Note that when retrieving terms, we may also disable beta and zeta reduction. See issue https://github.com/leanprover/lean4/issues/2669

• During type class resolution, we often want to reduce types using even iota and projection reduction. Example:

inductive Ty where
  | int
  | bool

@[reducible] def Ty.interp (ty : Ty) : Type :=
  Ty.casesOn (motive := fun _ => Type) ty Int Bool

def test {a b c : Ty} (f : a.interp → b.interp → c.interp) (x : a.interp) (y : b.interp) : c.interp :=
  f x y

def f (a b : Ty.bool.interp) : Ty.bool.interp :=
  -- We want to synthesize `BEq Ty.bool.interp` here, and it will fail
  -- if we do not reduce `Ty.bool.interp` to `Bool`.
  test (.==.) a b

structure Lean.Meta.DiscrTree (α : Type) : Type

Discrimination trees. It is an index from terms to values of type α.

• root : PersistentHashMap Key (Trie α)