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

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 AltAuto.
Import Check.

Goal True.

idtac "-------------------  try_sequence  --------------------".
idtac " ".

idtac "#> andb_eq_orb".
idtac "Possible points: 1".
check_type @andb_eq_orb (
(forall (b c : Basics.bool)
   (_ : @eq Basics.bool (Basics.andb b c) (Basics.orb b c)),
 @eq Basics.bool b c)).
idtac "Assumptions:".
Abort.
Print Assumptions andb_eq_orb.
Goal True.
idtac " ".

idtac "#> add_assoc".
idtac "Possible points: 1".
check_type @add_assoc (
(forall n m p : nat,
 @eq nat (Nat.add n (Nat.add m p)) (Nat.add (Nat.add n m) p))).
idtac "Assumptions:".
Abort.
Print Assumptions add_assoc.
Goal True.
idtac " ".

idtac "#> nonzeros_app".
idtac "Possible points: 1".
check_type @nonzeros_app (
(forall lst1 lst2 : Poly.list nat,
 @eq (Poly.list nat) (nonzeros (@Poly.app nat lst1 lst2))
   (@Poly.app nat (nonzeros lst1) (nonzeros lst2)))).
idtac "Assumptions:".
Abort.
Print Assumptions nonzeros_app.
Goal True.
idtac " ".

idtac "-------------------  notry_sequence  --------------------".
idtac " ".

idtac "#> add_assoc'".
idtac "Possible points: 1".
check_type @add_assoc' (
(forall n m p : nat,
 @eq nat (Nat.add n (Nat.add m p)) (Nat.add (Nat.add n m) p))).
idtac "Assumptions:".
Abort.
Print Assumptions add_assoc'.
Goal True.
idtac " ".

idtac "-------------------  ev100  --------------------".
idtac " ".

idtac "#> ev100".
idtac "Possible points: 1".
check_type @ev100 ((IndProp.ev 100)).
idtac "Assumptions:".
Abort.
Print Assumptions ev100.
Goal True.
idtac " ".

idtac "-------------------  re_opt  --------------------".
idtac " ".

idtac "#> Manually graded: re_opt".
idtac "Possible points: 6".
print_manual_grade manual_grade_for_re_opt.
idtac " ".

idtac "-------------------  automatic_solvers  --------------------".
idtac " ".

idtac "#> plus_id_exercise_from_basics".
idtac "Possible points: 0.5".
check_type @plus_id_exercise_from_basics (
(forall (n m o : nat) (_ : @eq nat n m) (_ : @eq nat m o),
 @eq nat (Nat.add n m) (Nat.add m o))).
idtac "Assumptions:".
Abort.
Print Assumptions plus_id_exercise_from_basics.
Goal True.
idtac " ".

idtac "#> add_assoc_from_induction".
idtac "Possible points: 0.5".
check_type @add_assoc_from_induction (
(forall n m p : nat,
 @eq nat (Nat.add n (Nat.add m p)) (Nat.add (Nat.add n m) p))).
idtac "Assumptions:".
Abort.
Print Assumptions add_assoc_from_induction.
Goal True.
idtac " ".

idtac "#> S_injective_from_tactics".
idtac "Possible points: 0.5".
check_type @S_injective_from_tactics (
(forall (n m : nat) (_ : @eq nat (S n) (S m)), @eq nat n m)).
idtac "Assumptions:".
Abort.
Print Assumptions S_injective_from_tactics.
Goal True.
idtac " ".

idtac "#> or_distributes_over_and_from_logic".
idtac "Possible points: 0.5".
check_type @or_distributes_over_and_from_logic (
(forall P Q R : Prop, iff (or P (and Q R)) (and (or P Q) (or P R)))).
idtac "Assumptions:".
Abort.
Print Assumptions or_distributes_over_and_from_logic.
Goal True.
idtac " ".

idtac "-------------------  re_opt_match_auto  --------------------".
idtac " ".

idtac "#> Manually graded: re_opt_match''".
idtac "Possible points: 3".
print_manual_grade manual_grade_for_re_opt_match''.
idtac " ".

idtac "-------------------  andb3_exchange  --------------------".
idtac " ".

idtac "#> andb3_exchange".
idtac "Possible points: 1".
check_type @andb3_exchange (
(forall b c d : Basics.bool,
 @eq Basics.bool (Basics.andb (Basics.andb b c) d)
   (Basics.andb (Basics.andb b d) c))).
idtac "Assumptions:".
Abort.
Print Assumptions andb3_exchange.
Goal True.
idtac " ".

idtac "-------------------  andb_true_elim2  --------------------".
idtac " ".

idtac "#> andb_true_elim2'".
idtac "Possible points: 1.5".
check_type @andb_true_elim2' (
(forall (b c : Basics.bool)
   (_ : @eq Basics.bool (Basics.andb b c) Basics.true),
 @eq Basics.bool c Basics.true)).
idtac "Assumptions:".
Abort.
Print Assumptions andb_true_elim2'.
Goal True.
idtac " ".

idtac "#> andb3_exchange'".
idtac "Possible points: 0.5".
check_type @andb3_exchange' (
(forall b c d : Basics.bool,
 @eq Basics.bool (Basics.andb (Basics.andb b c) d)
   (Basics.andb (Basics.andb b d) c))).
idtac "Assumptions:".
Abort.
Print Assumptions andb3_exchange'.
Goal True.
idtac " ".

idtac "-------------------  nor_intuition  --------------------".
idtac " ".

idtac "#> Manually graded: nor_intuition".
idtac "Advanced".
idtac "Possible points: 6".
print_manual_grade manual_grade_for_nor_intuition.
idtac " ".

idtac " ".

idtac "Max points - standard: 19".
idtac "Max points - advanced: 25".
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 "---------- andb_eq_orb ---------".
Print Assumptions andb_eq_orb.
idtac "---------- add_assoc ---------".
Print Assumptions add_assoc.
idtac "---------- nonzeros_app ---------".
Print Assumptions nonzeros_app.
idtac "---------- add_assoc' ---------".
Print Assumptions add_assoc'.
idtac "---------- ev100 ---------".
Print Assumptions ev100.
idtac "---------- re_opt ---------".
idtac "MANUAL".
idtac "---------- plus_id_exercise_from_basics ---------".
Print Assumptions plus_id_exercise_from_basics.
idtac "---------- add_assoc_from_induction ---------".
Print Assumptions add_assoc_from_induction.
idtac "---------- S_injective_from_tactics ---------".
Print Assumptions S_injective_from_tactics.
idtac "---------- or_distributes_over_and_from_logic ---------".
Print Assumptions or_distributes_over_and_from_logic.
idtac "---------- re_opt_match'' ---------".
idtac "MANUAL".
idtac "---------- andb3_exchange ---------".
Print Assumptions andb3_exchange.
idtac "---------- andb_true_elim2' ---------".
Print Assumptions andb_true_elim2'.
idtac "---------- andb3_exchange' ---------".
Print Assumptions andb3_exchange'.
idtac "".
idtac "********** Advanced **********".
idtac "---------- nor_intuition ---------".
idtac "MANUAL".
Abort.

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

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