e0a266780b
This PR adds the instances `Grind.CommRing (Fin n)` and `Grind.IsCharP
(Fin n) n`. New tests:
```lean
example (x y z : Fin 13) :
(x + y + z) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 * (x * y + y * z + z * x) := by
grind +ring
example (x y : Fin 17) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * x * y * (x + y) := by
grind +ring
example (x y : Fin 19) : (x - y) * (x ^ 2 + x * y + y ^ 2) = x ^ 3 - y ^ 3 := by
grind +ring
```
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
126 lines
2.5 KiB
Text
126 lines
2.5 KiB
Text
import Lean
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/-!
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# Testing the `delabAppMatch` delaborator
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-/
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/-!
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Basic functionality
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-/
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/--
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info: def Nat.pred : Nat → Nat :=
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fun x =>
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match x with
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| 0 => 0
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| a.succ => a
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-/
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#guard_msgs in
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#print Nat.pred
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/--
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info: def List.head?.{u} : {α : Type u} → List α → Option α :=
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fun {α} x =>
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match x with
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| [] => none
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| a :: tail => some a
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-/
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#guard_msgs in
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#print List.head?
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/-!
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`h :` annotations
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-/
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/--
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info: fun x =>
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let_fun this :=
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match h : ↑x + 1 with
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| 0 => Nat.noConfusion h
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| n.succ => Exists.intro n (Nat.succ.inj h);
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this : ∀ (x : Fin 1), ∃ n, ↑x = n
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-/
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#guard_msgs in
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#check fun (x : Fin 1) => show ∃ (n : Nat), ↑x = n from
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match h : x.1 + 1 with
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| 0 => Nat.noConfusion h
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| n + 1 => ⟨n, Nat.succ.inj h⟩
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/-!
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Shadowing with `h :` annotations
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-/
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/--
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info: fun h =>
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let_fun this :=
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match h_1 : ↑h + 1 with
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| 0 => Nat.noConfusion h_1
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| n.succ => Exists.intro n (Nat.succ.inj h_1);
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this : ∀ (h : Fin 1), ∃ n, ↑h = n
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-/
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#guard_msgs in
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#check fun (h : Fin 1) => show ∃ (n : Nat), ↑h = n from
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match h : h.1 + 1 with
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| 0 => Nat.noConfusion h
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| n + 1 => ⟨n, Nat.succ.inj h⟩
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/-!
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Even more shadowing with `h :` annotations
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-/
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set_option linter.unusedVariables false in
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/--
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info: fun h =>
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let_fun this :=
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match h_1 : ↑h + 1 with
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| 0 => Nat.noConfusion h_1
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| h_2.succ => Exists.intro h_2 (Nat.succ.inj h_1);
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this : ∀ (h : Fin 1), ∃ n, ↑h = n
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-/
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#guard_msgs in
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#check fun (h : Fin 1) => show ∃ (n : Nat), ↑h = n from
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match h : h.1 + 1 with
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| 0 => Nat.noConfusion h
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| h + 1 => ⟨_, Nat.succ.inj ‹_›⟩
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/-!
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Overapplication
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-/
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/--
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info: fun b =>
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(match (motive := Bool → Bool → Bool) b with
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| false => fun x => x
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| true => fun x => !x)
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b : Bool → Bool
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-/
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#guard_msgs in
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#check (fun b : Bool => (match b with | false => fun x => x | true => fun x => !x) b)
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namespace WithFoo
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def foo (b : Bool) : Bool := match b with | false => false | _ => b
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/-!
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Follows the names from the functions
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-/
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set_option linter.unusedVariables false in
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/--
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info: fun b =>
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match b with
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| false => false
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| a => b : Bool → Bool
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-/
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#guard_msgs in
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#check fun b => foo.match_1 (fun _ => Bool) b (fun _ => false) fun a => b
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/-!
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Underapplied, no `match` notation
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-/
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set_option linter.unusedVariables false in
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/-- info: fun b => foo.match_1 (fun x => Bool) b fun x => false : Bool → (Bool → Bool) → Bool -/
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#guard_msgs in
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#check fun b => foo.match_1 (fun _ => Bool) b (fun _ => false)
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end WithFoo
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