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

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inductive Lean.Meta.ACLt.ReduceMode : Type

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

unsafe def Lean.Meta.ACLt.main (a : Lean.Expr) (b : Lean.Expr) (mode : optParam 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 instace 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.

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

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

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

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

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

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

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

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

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• Lean.Meta.ACLt.main.someChildGe mode a b = do let __do_lift ← Lean.Meta.ACLt.main.allChildrenLt mode a b pure !__do_lift

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

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@[implemented_by Lean.Meta.ACLt.main]

opaque Lean.Meta.Expr.acLt : Lean.Expr → Lean.Expr → optParam 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 instace 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.