f9dc77673b
This PR lets recursive functions defined by well-founded recursion use a different `fix` function when the termination measure is of type `Nat`. This fix-point operator use structural recursion on “fuel”, initialized by the given measure, and is thus reasonable to reduce, e.g. in `by decide` proofs. Extra provisions are in place that the fixpoint operator only starts reducing when the fuel is fully known, to prevent “accidential” defeqs when the remaining fuel for the recursive calls match the initial fuel for that recursive argument. To opt-out, the idiom `termination_by (n,0)` can be used. We still use `@[irreducible]` as the default for such recursive definitions, to avoid unexpected `defeq` lemmas. Making these functions `@[semireducible]` by default showed performance regressions in lean. When the measure is of type `Nat`, the system will accept an explicit `@[semireducible]` without the usual warning. Fixes #5234. Fixes: #11181.
102 lines
2.7 KiB
Text
102 lines
2.7 KiB
Text
import Lean
|
|
|
|
open Lean Meta
|
|
|
|
/-!
|
|
Testing Elab and Kernel reduction behavior with regards to Nat.shiftRight.
|
|
-/
|
|
|
|
example : [x].ctorIdx = 1 := rfl
|
|
|
|
example : Nat.land 1 (Nat.shiftRight 8 1) = 0 := rfl
|
|
|
|
-- The WHNF reduction does not reduce here:
|
|
|
|
/--
|
|
error: Type mismatch
|
|
Eq.refl 0
|
|
has type
|
|
0 = 0
|
|
but is expected to have type
|
|
Nat.land 1 (Nat.shiftRight 8 [x].ctorIdx) = 0
|
|
-/
|
|
#guard_msgs in
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 := Eq.refl 0
|
|
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 :=
|
|
@id (Nat.land 1 (Nat.shiftRight 8 1) = 0) (Eq.refl 0)
|
|
|
|
elab "refl0" : tactic =>
|
|
Lean.Elab.Tactic.closeMainGoalUsing `refl0 fun _ _ =>
|
|
Lean.Meta.mkEqRefl (Lean.mkRawNatLit 0)
|
|
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 := by
|
|
refl0
|
|
|
|
|
|
elab "eagerrefl0" : tactic =>
|
|
Lean.Elab.Tactic.closeMainGoalUsing `refl0 fun _ _ => do
|
|
Lean.Meta.mkAppM `eagerReduce #[← Lean.Meta.mkEqRefl (Lean.mkRawNatLit 0)]
|
|
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 := by
|
|
eagerrefl0
|
|
|
|
-- A variant that uses the expected (unreduced) type as the first argument to eagerReduce
|
|
elab "eagerrefl0'" : tactic =>
|
|
Lean.Elab.Tactic.closeMainGoalUsing `refl0 fun goal _ => do
|
|
let u ← getLevel goal
|
|
return mkApp2 (mkConst ``eagerReduce [u]) goal (← mkEqRefl (mkRawNatLit 0))
|
|
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 := by
|
|
eagerrefl0'
|
|
|
|
/--
|
|
error: Application type mismatch: The argument
|
|
Eq.refl true
|
|
has type
|
|
true = true
|
|
but is expected to have type
|
|
(Nat.land 1 (Nat.shiftRight 8 [x].ctorIdx)).beq 0 = true
|
|
in the application
|
|
Nat.eq_of_beq_eq_true (Eq.refl true)
|
|
-/
|
|
#guard_msgs in
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 :=
|
|
Nat.eq_of_beq_eq_true (Eq.refl true)
|
|
|
|
/--
|
|
error: Application type mismatch: The argument
|
|
Eq.refl true
|
|
has type
|
|
true = true
|
|
but is expected to have type
|
|
(Nat.land 1 (Nat.shiftRight 8 [x].ctorIdx)).beq 0 = true
|
|
in the application
|
|
eagerReduce (Eq.refl true)
|
|
-/
|
|
#guard_msgs in
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 :=
|
|
Nat.eq_of_beq_eq_true (eagerReduce (Eq.refl true))
|
|
|
|
elab "reflTrue" : tactic =>
|
|
Lean.Elab.Tactic.closeMainGoalUsing `refl0 fun _ _ =>
|
|
Lean.Meta.mkEqRefl (Lean.mkConst ``Bool.true)
|
|
|
|
-- This works! (But why?)
|
|
example : Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx)) = 0 :=
|
|
Nat.eq_of_beq_eq_true (by reflTrue)
|
|
|
|
|
|
/--
|
|
error: Type mismatch
|
|
Eq.refl true
|
|
has type
|
|
true = true
|
|
but is expected to have type
|
|
(Nat.land 1 (Nat.shiftRight 8 [x].ctorIdx)).beq 0 = true
|
|
-/
|
|
#guard_msgs in
|
|
example : Nat.beq (Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx))) 0 := Eq.refl true
|
|
|
|
-- This also works (But why?)
|
|
example : Nat.beq (Nat.land 1 (Nat.shiftRight 8 ([x].ctorIdx))) 0 := by reflTrue
|