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

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 Tactics.
Import Check.

Goal True.

idtac "-------------------  apply_exercise1  --------------------".
idtac " ".

idtac "#> rev_exercise1".
idtac "Possible points: 2".
check_type @rev_exercise1 (
(forall (l l' : list nat) (_ : @eq (list nat) l (@rev nat l')),
 @eq (list nat) l' (@rev nat l))).
idtac "Assumptions:".
Abort.
Print Assumptions rev_exercise1.
Goal True.
idtac " ".

idtac "-------------------  injection_ex3  --------------------".
idtac " ".

idtac "#> injection_ex3".
idtac "Possible points: 3".
check_type @injection_ex3 (
(forall (X : Type) (x y z : X) (l j : list X)
   (_ : @eq (list X) (@cons X x (@cons X y l)) (@cons X z j))
   (_ : @eq (list X) j (@cons X z l)),
 @eq X x y)).
idtac "Assumptions:".
Abort.
Print Assumptions injection_ex3.
Goal True.
idtac " ".

idtac "-------------------  discriminate_ex3  --------------------".
idtac " ".

idtac "#> discriminate_ex3".
idtac "Possible points: 1".
check_type @discriminate_ex3 (
(forall (X : Type) (x y z : X) (l _ : list X)
   (_ : @eq (list X) (@cons X x (@cons X y l)) (@nil X)),
 @eq X x z)).
idtac "Assumptions:".
Abort.
Print Assumptions discriminate_ex3.
Goal True.
idtac " ".

idtac "-------------------  nth_error_always_none  --------------------".
idtac " ".

idtac "#> nth_error_always_none".
idtac "Possible points: 3".
check_type @nth_error_always_none (
(forall (l : list nat)
   (_ : forall i : nat, @eq (option nat) (@nth_error nat l i) (@None nat)),
 @eq (list nat) l (@nil nat))).
idtac "Assumptions:".
Abort.
Print Assumptions nth_error_always_none.
Goal True.
idtac " ".

idtac "-------------------  eqb_true  --------------------".
idtac " ".

idtac "#> eqb_true".
idtac "Possible points: 2".
check_type @eqb_true ((forall (n m : nat) (_ : @eq bool (eqb n m) true), @eq nat n m)).
idtac "Assumptions:".
Abort.
Print Assumptions eqb_true.
Goal True.
idtac " ".

idtac "-------------------  plus_n_n_injective  --------------------".
idtac " ".

idtac "#> plus_n_n_injective".
idtac "Possible points: 3".
check_type @plus_n_n_injective (
(forall (n m : nat) (_ : @eq nat (Nat.add n n) (Nat.add m m)), @eq nat n m)).
idtac "Assumptions:".
Abort.
Print Assumptions plus_n_n_injective.
Goal True.
idtac " ".

idtac "-------------------  gen_dep_practice  --------------------".
idtac " ".

idtac "#> nth_error_after_last".
idtac "Possible points: 3".
check_type @nth_error_after_last (
(forall (n : nat) (X : Type) (l : list X) (_ : @eq nat (@length X l) n),
 @eq (option X) (@nth_error X l n) (@None X))).
idtac "Assumptions:".
Abort.
Print Assumptions nth_error_after_last.
Goal True.
idtac " ".

idtac "-------------------  combine_split  --------------------".
idtac " ".

idtac "#> combine_split".
idtac "Possible points: 3".
check_type @combine_split (
(forall (X Y : Type) (l : list (prod X Y)) (l1 : list X)
   (l2 : list Y)
   (_ : @eq (prod (list X) (list Y)) (@split X Y l)
          (@pair (list X) (list Y) l1 l2)),
 @eq (list (prod X Y)) (@combine X Y l1 l2) l)).
idtac "Assumptions:".
Abort.
Print Assumptions combine_split.
Goal True.
idtac " ".

idtac "-------------------  destruct_eqn_practice  --------------------".
idtac " ".

idtac "#> bool_fn_applied_thrice".
idtac "Possible points: 2".
check_type @bool_fn_applied_thrice (
(forall (f : forall _ : bool, bool) (b : bool), @eq bool (f (f (f b))) (f b))).
idtac "Assumptions:".
Abort.
Print Assumptions bool_fn_applied_thrice.
Goal True.
idtac " ".

idtac "-------------------  eqb_sym  --------------------".
idtac " ".

idtac "#> eqb_sym".
idtac "Possible points: 3".
check_type @eqb_sym ((forall n m : nat, @eq bool (eqb n m) (eqb m n))).
idtac "Assumptions:".
Abort.
Print Assumptions eqb_sym.
Goal True.
idtac " ".

idtac "-------------------  split_combine  --------------------".
idtac " ".

idtac "#> Manually graded: split_combine".
idtac "Advanced".
idtac "Possible points: 3".
print_manual_grade manual_grade_for_split_combine.
idtac " ".

idtac "-------------------  filter_exercise  --------------------".
idtac " ".

idtac "#> filter_exercise".
idtac "Advanced".
idtac "Possible points: 3".
check_type @filter_exercise (
(forall (X : Type) (test : forall _ : X, bool) (x : X)
   (l lf : list X) (_ : @eq (list X) (@filter X test l) (@cons X x lf)),
 @eq bool (test x) true)).
idtac "Assumptions:".
Abort.
Print Assumptions filter_exercise.
Goal True.
idtac " ".

idtac "-------------------  forall_exists_challenge  --------------------".
idtac " ".

idtac "#> existsb_existsb'".
idtac "Advanced".
idtac "Possible points: 6".
check_type @existsb_existsb' (
(forall (X : Type) (test : forall _ : X, bool) (l : list X),
 @eq bool (@existsb X test l) (@existsb' X test l))).
idtac "Assumptions:".
Abort.
Print Assumptions existsb_existsb'.
Goal True.
idtac " ".

idtac " ".

idtac "Max points - standard: 25".
idtac "Max points - advanced: 37".
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 "---------- rev_exercise1 ---------".
Print Assumptions rev_exercise1.
idtac "---------- injection_ex3 ---------".
Print Assumptions injection_ex3.
idtac "---------- discriminate_ex3 ---------".
Print Assumptions discriminate_ex3.
idtac "---------- nth_error_always_none ---------".
Print Assumptions nth_error_always_none.
idtac "---------- eqb_true ---------".
Print Assumptions eqb_true.
idtac "---------- plus_n_n_injective ---------".
Print Assumptions plus_n_n_injective.
idtac "---------- nth_error_after_last ---------".
Print Assumptions nth_error_after_last.
idtac "---------- combine_split ---------".
Print Assumptions combine_split.
idtac "---------- bool_fn_applied_thrice ---------".
Print Assumptions bool_fn_applied_thrice.
idtac "---------- eqb_sym ---------".
Print Assumptions eqb_sym.
idtac "".
idtac "********** Advanced **********".
idtac "---------- split_combine ---------".
idtac "MANUAL".
idtac "---------- filter_exercise ---------".
Print Assumptions filter_exercise.
idtac "---------- existsb_existsb' ---------".
Print Assumptions existsb_existsb'.
Abort.

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

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