Set Warnings "-notation-overridden,-parsing".
From Stdlib Require Export String.
From LF Require Import Poly.

Parameter MISSING: Type.

Module Check.

Ltac check_type A B :=
    match type of A with
    | context[MISSING] => idtac "Missing:" A
    | ?T => first [unify T B; idtac "Type: ok" | idtac "Type: wrong - should be (" B ")"]
    end.

Ltac print_manual_grade A :=
    match eval compute in A with
    | Some (_ ?S ?C) =>
        idtac "Score:"  S;
        match eval compute in C with
          | ""%string => idtac "Comment: None"
          | _ => idtac "Comment:" C
        end
    | None =>
        idtac "Score: Ungraded";
        idtac "Comment: None"
    end.

End Check.

From LF Require Import Poly.
Import Check.

Goal True.

idtac "-------------------  poly_exercises  --------------------".
idtac " ".

idtac "#> app_nil_r".
idtac "Possible points: 0.5".
check_type @app_nil_r (
(forall (X : Type) (l : list X), @eq (list X) (@app X l (@nil X)) l)).
idtac "Assumptions:".
Abort.
Print Assumptions app_nil_r.
Goal True.
idtac " ".

idtac "#> app_assoc".
idtac "Possible points: 1".
check_type @app_assoc (
(forall (A : Type) (l m n : list A),
 @eq (list A) (@app A l (@app A m n)) (@app A (@app A l m) n))).
idtac "Assumptions:".
Abort.
Print Assumptions app_assoc.
Goal True.
idtac " ".

idtac "#> app_length".
idtac "Possible points: 0.5".
check_type @app_length (
(forall (X : Type) (l1 l2 : list X),
 @eq nat (@length X (@app X l1 l2)) (Nat.add (@length X l1) (@length X l2)))).
idtac "Assumptions:".
Abort.
Print Assumptions app_length.
Goal True.
idtac " ".

idtac "-------------------  more_poly_exercises  --------------------".
idtac " ".

idtac "#> rev_app_distr".
idtac "Possible points: 1".
check_type @rev_app_distr (
(forall (X : Type) (l1 l2 : list X),
 @eq (list X) (@rev X (@app X l1 l2)) (@app X (@rev X l2) (@rev X l1)))).
idtac "Assumptions:".
Abort.
Print Assumptions rev_app_distr.
Goal True.
idtac " ".

idtac "#> rev_involutive".
idtac "Possible points: 1".
check_type @rev_involutive (
(forall (X : Type) (l : list X), @eq (list X) (@rev X (@rev X l)) l)).
idtac "Assumptions:".
Abort.
Print Assumptions rev_involutive.
Goal True.
idtac " ".

idtac "-------------------  split  --------------------".
idtac " ".

idtac "#> split".
idtac "Possible points: 1".
check_type @split ((forall (X Y : Type) (_ : list (prod X Y)), prod (list X) (list Y))).
idtac "Assumptions:".
Abort.
Print Assumptions split.
Goal True.
idtac " ".

idtac "#> test_split".
idtac "Possible points: 1".
check_type @test_split (
(@eq (prod (list nat) (list bool))
   (@split nat bool
      (@cons (prod nat bool) (@pair nat bool 1 false)
         (@cons (prod nat bool) (@pair nat bool 2 false)
            (@nil (prod nat bool)))))
   (@pair (list nat) (list bool) (@cons nat 1 (@cons nat 2 (@nil nat)))
      (@cons bool false (@cons bool false (@nil bool)))))).
idtac "Assumptions:".
Abort.
Print Assumptions test_split.
Goal True.
idtac " ".

idtac "-------------------  filter_even_gt7  --------------------".
idtac " ".

idtac "#> test_filter_even_gt7_1".
idtac "Possible points: 1".
check_type @test_filter_even_gt7_1 (
(@eq (list nat)
   (filter_even_gt7
      (@cons nat 1
         (@cons nat 2
            (@cons nat 6
               (@cons nat 9
                  (@cons nat 10
                     (@cons nat 3 (@cons nat 12 (@cons nat 8 (@nil nat))))))))))
   (@cons nat 10 (@cons nat 12 (@cons nat 8 (@nil nat)))))).
idtac "Assumptions:".
Abort.
Print Assumptions test_filter_even_gt7_1.
Goal True.
idtac " ".

idtac "#> test_filter_even_gt7_2".
idtac "Possible points: 1".
check_type @test_filter_even_gt7_2 (
(@eq (list nat)
   (filter_even_gt7
      (@cons nat 5
         (@cons nat 2 (@cons nat 6 (@cons nat 19 (@cons nat 129 (@nil nat)))))))
   (@nil nat))).
idtac "Assumptions:".
Abort.
Print Assumptions test_filter_even_gt7_2.
Goal True.
idtac " ".

idtac "-------------------  partition  --------------------".
idtac " ".

idtac "#> partition".
idtac "Possible points: 1".
check_type @partition (
(forall (X : Type) (_ : forall _ : X, bool) (_ : list X),
 prod (list X) (list X))).
idtac "Assumptions:".
Abort.
Print Assumptions partition.
Goal True.
idtac " ".

idtac "#> test_partition1".
idtac "Possible points: 1".
check_type @test_partition1 (
(@eq (prod (list nat) (list nat))
   (@partition nat odd
      (@cons nat 1
         (@cons nat 2 (@cons nat 3 (@cons nat 4 (@cons nat 5 (@nil nat)))))))
   (@pair (list nat) (list nat)
      (@cons nat 1 (@cons nat 3 (@cons nat 5 (@nil nat))))
      (@cons nat 2 (@cons nat 4 (@nil nat)))))).
idtac "Assumptions:".
Abort.
Print Assumptions test_partition1.
Goal True.
idtac " ".

idtac "#> test_partition2".
idtac "Possible points: 1".
check_type @test_partition2 (
(@eq (prod (list nat) (list nat))
   (@partition nat (fun _ : nat => false)
      (@cons nat 5 (@cons nat 9 (@cons nat 0 (@nil nat)))))
   (@pair (list nat) (list nat) (@nil nat)
      (@cons nat 5 (@cons nat 9 (@cons nat 0 (@nil nat))))))).
idtac "Assumptions:".
Abort.
Print Assumptions test_partition2.
Goal True.
idtac " ".

idtac "-------------------  map_rev  --------------------".
idtac " ".

idtac "#> map_rev".
idtac "Possible points: 3".
check_type @map_rev (
(forall (X Y : Type) (f : forall _ : X, Y) (l : list X),
 @eq (list Y) (@map X Y f (@rev X l)) (@rev Y (@map X Y f l)))).
idtac "Assumptions:".
Abort.
Print Assumptions map_rev.
Goal True.
idtac " ".

idtac "-------------------  flat_map  --------------------".
idtac " ".

idtac "#> flat_map".
idtac "Possible points: 1".
check_type @flat_map (
(forall (X Y : Type) (_ : forall _ : X, list Y) (_ : list X), list Y)).
idtac "Assumptions:".
Abort.
Print Assumptions flat_map.
Goal True.
idtac " ".

idtac "#> test_flat_map1".
idtac "Possible points: 1".
check_type @test_flat_map1 (
(@eq (list nat)
   (@flat_map nat nat
      (fun n : nat => @cons nat n (@cons nat n (@cons nat n (@nil nat))))
      (@cons nat 1 (@cons nat 5 (@cons nat 4 (@nil nat)))))
   (@cons nat 1
      (@cons nat 1
         (@cons nat 1
            (@cons nat 5
               (@cons nat 5
                  (@cons nat 5
                     (@cons nat 4 (@cons nat 4 (@cons nat 4 (@nil nat)))))))))))).
idtac "Assumptions:".
Abort.
Print Assumptions test_flat_map1.
Goal True.
idtac " ".

idtac "-------------------  fold_length  --------------------".
idtac " ".

idtac "#> Exercises.fold_length_correct".
idtac "Possible points: 2".
check_type @Exercises.fold_length_correct (
(forall (X : Type) (l : list X),
 @eq nat (@Exercises.fold_length X l) (@length X l))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.fold_length_correct.
Goal True.
idtac " ".

idtac "-------------------  fold_map  --------------------".
idtac " ".

idtac "#> Manually graded: Exercises.fold_map".
idtac "Possible points: 3".
print_manual_grade Exercises.manual_grade_for_fold_map.
idtac " ".

idtac "-------------------  currying  --------------------".
idtac " ".

idtac "#> Exercises.uncurry_curry".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.uncurry_curry (
(forall (X Y Z : Type) (f : forall (_ : X) (_ : Y), Z) (x : X) (y : Y),
 @eq Z (@Exercises.prod_curry X Y Z (@Exercises.prod_uncurry X Y Z f) x y)
   (f x y))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.uncurry_curry.
Goal True.
idtac " ".

idtac "#> Exercises.curry_uncurry".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.curry_uncurry (
(forall (X Y Z : Type) (f : forall _ : prod X Y, Z) (p : prod X Y),
 @eq Z (@Exercises.prod_uncurry X Y Z (@Exercises.prod_curry X Y Z f) p)
   (f p))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.curry_uncurry.
Goal True.
idtac " ".

idtac "-------------------  church_scc  --------------------".
idtac " ".

idtac "#> Exercises.Church.scc_2".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.scc_2 (
(@eq Exercises.Church.cnat (Exercises.Church.scc Exercises.Church.one)
   Exercises.Church.two)).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.scc_2.
Goal True.
idtac " ".

idtac "#> Exercises.Church.scc_3".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.scc_3 (
(@eq Exercises.Church.cnat (Exercises.Church.scc Exercises.Church.two)
   Exercises.Church.three)).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.scc_3.
Goal True.
idtac " ".

idtac "-------------------  church_plus  --------------------".
idtac " ".

idtac "#> Exercises.Church.plus_1".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.plus_1 (
(@eq Exercises.Church.cnat
   (Exercises.Church.plus Exercises.Church.zero Exercises.Church.one)
   Exercises.Church.one)).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.plus_1.
Goal True.
idtac " ".

idtac "#> Exercises.Church.plus_2".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.plus_2 (
(@eq Exercises.Church.cnat
   (Exercises.Church.plus Exercises.Church.two Exercises.Church.three)
   (Exercises.Church.plus Exercises.Church.three Exercises.Church.two))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.plus_2.
Goal True.
idtac " ".

idtac "#> Exercises.Church.plus_3".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.plus_3 (
(@eq Exercises.Church.cnat
   (Exercises.Church.plus
      (Exercises.Church.plus Exercises.Church.two Exercises.Church.two)
      Exercises.Church.three)
   (Exercises.Church.plus Exercises.Church.one
      (Exercises.Church.plus Exercises.Church.three Exercises.Church.three)))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.plus_3.
Goal True.
idtac " ".

idtac "-------------------  church_mult  --------------------".
idtac " ".

idtac "#> Exercises.Church.mult_1".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.mult_1 (
(@eq Exercises.Church.cnat
   (Exercises.Church.mult Exercises.Church.one Exercises.Church.one)
   Exercises.Church.one)).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.mult_1.
Goal True.
idtac " ".

idtac "#> Exercises.Church.mult_2".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.mult_2 (
(@eq Exercises.Church.cnat
   (Exercises.Church.mult Exercises.Church.zero
      (Exercises.Church.plus Exercises.Church.three Exercises.Church.three))
   Exercises.Church.zero)).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.mult_2.
Goal True.
idtac " ".

idtac "#> Exercises.Church.mult_3".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.mult_3 (
(@eq Exercises.Church.cnat
   (Exercises.Church.mult Exercises.Church.two Exercises.Church.three)
   (Exercises.Church.plus Exercises.Church.three Exercises.Church.three))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.mult_3.
Goal True.
idtac " ".

idtac "-------------------  church_exp  --------------------".
idtac " ".

idtac "#> Exercises.Church.exp_1".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.exp_1 (
(@eq Exercises.Church.cnat
   (Exercises.Church.exp Exercises.Church.two Exercises.Church.two)
   (Exercises.Church.plus Exercises.Church.two Exercises.Church.two))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.exp_1.
Goal True.
idtac " ".

idtac "#> Exercises.Church.exp_2".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.exp_2 (
(@eq Exercises.Church.cnat
   (Exercises.Church.exp Exercises.Church.three Exercises.Church.zero)
   Exercises.Church.one)).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.exp_2.
Goal True.
idtac " ".

idtac "#> Exercises.Church.exp_3".
idtac "Advanced".
idtac "Possible points: 1".
check_type @Exercises.Church.exp_3 (
(@eq Exercises.Church.cnat
   (Exercises.Church.exp Exercises.Church.three Exercises.Church.two)
   (Exercises.Church.plus
      (Exercises.Church.mult Exercises.Church.two
         (Exercises.Church.mult Exercises.Church.two Exercises.Church.two))
      Exercises.Church.one))).
idtac "Assumptions:".
Abort.
Print Assumptions Exercises.Church.exp_3.
Goal True.
idtac " ".

idtac " ".

idtac "Max points - standard: 21".
idtac "Max points - advanced: 34".
idtac "".
idtac "Allowed Axioms:".
idtac "functional_extensionality".
idtac "FunctionalExtensionality.functional_extensionality_dep".
idtac "plus_le".
idtac "le_trans".
idtac "le_plus_l".
idtac "add_le_cases".
idtac "Sn_le_Sm__n_le_m".
idtac "O_le_n".
idtac "".
idtac "".
idtac "********** Summary **********".
idtac "".
idtac "Below is a summary of the automatically graded exercises that are incomplete.".
idtac "".
idtac "The output for each exercise can be any of the following:".
idtac "  - 'Closed under the global context', if it is complete".
idtac "  - 'MANUAL', if it is manually graded".
idtac "  - A list of pending axioms, containing unproven assumptions. In this case".
idtac "    the exercise is considered complete, if the axioms are all allowed.".
idtac "".
idtac "********** Standard **********".
idtac "---------- app_nil_r ---------".
Print Assumptions app_nil_r.
idtac "---------- app_assoc ---------".
Print Assumptions app_assoc.
idtac "---------- app_length ---------".
Print Assumptions app_length.
idtac "---------- rev_app_distr ---------".
Print Assumptions rev_app_distr.
idtac "---------- rev_involutive ---------".
Print Assumptions rev_involutive.
idtac "---------- split ---------".
Print Assumptions split.
idtac "---------- test_split ---------".
Print Assumptions test_split.
idtac "---------- test_filter_even_gt7_1 ---------".
Print Assumptions test_filter_even_gt7_1.
idtac "---------- test_filter_even_gt7_2 ---------".
Print Assumptions test_filter_even_gt7_2.
idtac "---------- partition ---------".
Print Assumptions partition.
idtac "---------- test_partition1 ---------".
Print Assumptions test_partition1.
idtac "---------- test_partition2 ---------".
Print Assumptions test_partition2.
idtac "---------- map_rev ---------".
Print Assumptions map_rev.
idtac "---------- flat_map ---------".
Print Assumptions flat_map.
idtac "---------- test_flat_map1 ---------".
Print Assumptions test_flat_map1.
idtac "---------- Exercises.fold_length_correct ---------".
Print Assumptions Exercises.fold_length_correct.
idtac "---------- fold_map ---------".
idtac "MANUAL".
idtac "".
idtac "********** Advanced **********".
idtac "---------- Exercises.uncurry_curry ---------".
Print Assumptions Exercises.uncurry_curry.
idtac "---------- Exercises.curry_uncurry ---------".
Print Assumptions Exercises.curry_uncurry.
idtac "---------- Exercises.Church.scc_2 ---------".
Print Assumptions Exercises.Church.scc_2.
idtac "---------- Exercises.Church.scc_3 ---------".
Print Assumptions Exercises.Church.scc_3.
idtac "---------- Exercises.Church.plus_1 ---------".
Print Assumptions Exercises.Church.plus_1.
idtac "---------- Exercises.Church.plus_2 ---------".
Print Assumptions Exercises.Church.plus_2.
idtac "---------- Exercises.Church.plus_3 ---------".
Print Assumptions Exercises.Church.plus_3.
idtac "---------- Exercises.Church.mult_1 ---------".
Print Assumptions Exercises.Church.mult_1.
idtac "---------- Exercises.Church.mult_2 ---------".
Print Assumptions Exercises.Church.mult_2.
idtac "---------- Exercises.Church.mult_3 ---------".
Print Assumptions Exercises.Church.mult_3.
idtac "---------- Exercises.Church.exp_1 ---------".
Print Assumptions Exercises.Church.exp_1.
idtac "---------- Exercises.Church.exp_2 ---------".
Print Assumptions Exercises.Church.exp_2.
idtac "---------- Exercises.Church.exp_3 ---------".
Print Assumptions Exercises.Church.exp_3.
Abort.

(* 2026-01-07 13:18 *)

(* 2026-01-07 13:18 *)