Documentation

Lean.Meta.ACLt

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def Lean.Expr.ctorWeight:
Lean.Expr → UInt8
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unsafe def Lean.Meta.ACLt.lt (a : Lean.Expr) (b : Lean.Expr) :
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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unsafe def Lean.Meta.ACLt.lt.ltPair (a₁ : Lean.Expr) (a₂ : Lean.Expr) (b₁ : Lean.Expr) (b₂ : Lean.Expr) :
Lean.MetaM Bool
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unsafe def Lean.Meta.ACLt.lt.ltApp (a : Lean.Expr) (b : Lean.Expr) :
Lean.MetaM Bool
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unsafe def Lean.Meta.ACLt.lt.lexSameCtor (a : Lean.Expr) (b : Lean.Expr) :
Lean.MetaM Bool
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unsafe def Lean.Meta.ACLt.lt.allChildrenLt (a : Lean.Expr) (b : Lean.Expr) :
Lean.MetaM Bool
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unsafe def Lean.Meta.ACLt.lt.someChildGe (a : Lean.Expr) (b : Lean.Expr) :
Lean.MetaM Bool
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unsafe def Lean.Meta.ACLt.lt.lpo (a : Lean.Expr) (b : Lean.Expr) :
Lean.MetaM Bool
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@[implementedBy Lean.Meta.ACLt.lt]
opaque Lean.Meta.Expr.acLt:
Lean.Expr → Lean.Expr → Lean.MetaM Bool