def Lean.Expr.ctorWeight : Lean.Expr → UInt8

inductive Lean.Meta.ACLt.ReduceMode : Type

• reduce: Lean.Meta.ACLt.ReduceMode
• reduceSimpleOnly: Lean.Meta.ACLt.ReduceMode
• none: Lean.Meta.ACLt.ReduceMode

def Lean.Meta.ACLt.main (a b : Lean.Expr) (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) : Lean.MetaM Bool

An AC-compatible ordering.

Recall that an AC-compatible ordering if it is monotonic, well-founded, and total. Both KBO and LPO are AC-compatible. KBO is faster, but we do not cache the weight of each expression in Lean 4. Even if we did, we would need to have a weight where implicit instance arguments are ignored. So, we use a LPO-like term ordering.

Remark: this method is used to implement ordered rewriting. We ignore implicit instance arguments to address an issue reported at issue #972.

Remark: the order is not really total on terms since

• We instance implicit arguments.
• We ignore metadata.
• We ignore universe parameterst at constants.

Equations

• Lean.Meta.ACLt.main a b mode = Lean.Meta.ACLt.main.lt mode a b

def Lean.Meta.ACLt.main.reduce (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (e : Lean.Expr) : Lean.MetaM Lean.Expr

Equations

• One or more equations did not get rendered due to their size.
• Lean.Meta.ACLt.main.reduce Lean.Meta.ACLt.ReduceMode.reduce e = if e.hasLooseBVars = true then pure e else Lean.Meta.DiscrTree.reduce e
• Lean.Meta.ACLt.main.reduce Lean.Meta.ACLt.ReduceMode.none e = if e.hasLooseBVars = true then pure e else pure e

partial def Lean.Meta.ACLt.main.lt (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a b : Lean.Expr) : Lean.MetaM Bool

partial def Lean.Meta.ACLt.main.ltPair (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a₁ a₂ b₁ b₂ : Lean.Expr) : Lean.MetaM Bool

def Lean.Meta.ACLt.main.getParamsInfo (f : Lean.Expr) (numArgs : Nat) : Lean.MetaM (Array Lean.Meta.ParamInfo)

partial def Lean.Meta.ACLt.main.ltApp (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a b : Lean.Expr) : Lean.MetaM Bool

partial def Lean.Meta.ACLt.main.lexSameCtor (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a b : Lean.Expr) : Lean.MetaM Bool

partial def Lean.Meta.ACLt.main.allChildrenLt (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a b : Lean.Expr) : Lean.MetaM Bool

partial def Lean.Meta.ACLt.main.someChildGe (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a b : Lean.Expr) : Lean.MetaM Bool

partial def Lean.Meta.ACLt.main.lpo (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) (a b : Lean.Expr) : Lean.MetaM Bool

def Lean.Meta.acLt (a b : Lean.Expr) (mode : Lean.Meta.ACLt.ReduceMode := Lean.Meta.ACLt.ReduceMode.none) : Lean.MetaM Bool

An AC-compatible ordering.

Recall that an AC-compatible ordering if it is monotonic, well-founded, and total. Both KBO and LPO are AC-compatible. KBO is faster, but we do not cache the weight of each expression in Lean 4. Even if we did, we would need to have a weight where implicit instance arguments are ignored. So, we use a LPO-like term ordering.

Remark: this method is used to implement ordered rewriting. We ignore implicit instance arguments to address an issue reported at issue #972.

Remark: the order is not really total on terms since

• We instance implicit arguments.
• We ignore metadata.
• We ignore universe parameterst at constants.

Equations

• Lean.Meta.acLt a b mode = Lean.Meta.ACLt.main a b mode