196 lines
4.8 KiB
Coq
196 lines
4.8 KiB
Coq
Set Warnings "-notation-overridden,-parsing".
|
|
From Coq Require Export String.
|
|
From LF Require Import Basics.
|
|
|
|
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 Basics.
|
|
Import Check.
|
|
|
|
Goal True.
|
|
|
|
idtac "------------------- nandb --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> test_nandb4".
|
|
idtac "Possible points: 1".
|
|
check_type @test_nandb4 ((nandb true true = false)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions test_nandb4.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- andb3 --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> test_andb34".
|
|
idtac "Possible points: 1".
|
|
check_type @test_andb34 ((andb3 true true false = false)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions test_andb34.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- factorial --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> test_factorial2".
|
|
idtac "Possible points: 1".
|
|
check_type @test_factorial2 ((factorial 5 = 10 * 12)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions test_factorial2.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- ltb --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> test_ltb3".
|
|
idtac "Possible points: 1".
|
|
check_type @test_ltb3 (((4 <? 2) = false)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions test_ltb3.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- plus_id_exercise --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> plus_id_exercise".
|
|
idtac "Possible points: 1".
|
|
check_type @plus_id_exercise ((forall n m o : nat, n = m -> m = o -> n + m = m + o)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions plus_id_exercise.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- mult_S_1 --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> mult_S_1".
|
|
idtac "Possible points: 2".
|
|
check_type @mult_S_1 ((forall n m : nat, m = S n -> m * (1 + n) = m * m)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions mult_S_1.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- andb_true_elim2 --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> andb_true_elim2".
|
|
idtac "Possible points: 2".
|
|
check_type @andb_true_elim2 ((forall b c : bool, b && c = true -> c = true)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions andb_true_elim2.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- zero_nbeq_plus_1 --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> zero_nbeq_plus_1".
|
|
idtac "Possible points: 1".
|
|
check_type @zero_nbeq_plus_1 ((forall n : nat, (0 =? n + 1) = false)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions zero_nbeq_plus_1.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- indentity_fn_applied_twice --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> identity_fn_applied_twice".
|
|
idtac "Possible points: 1".
|
|
check_type @identity_fn_applied_twice (
|
|
(forall f : bool -> bool,
|
|
(forall x : bool, f x = x) -> forall b : bool, f (f b) = b)).
|
|
idtac "Assumptions:".
|
|
Abort.
|
|
Print Assumptions identity_fn_applied_twice.
|
|
Goal True.
|
|
idtac " ".
|
|
|
|
idtac "------------------- negation_fn_applied_twice --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> Manually graded: negation_fn_applied_twice".
|
|
idtac "Possible points: 1".
|
|
print_manual_grade manual_grade_for_negation_fn_applied_twice.
|
|
idtac " ".
|
|
|
|
idtac "------------------- binary --------------------".
|
|
idtac " ".
|
|
|
|
idtac "#> Manually graded: binary".
|
|
idtac "Possible points: 3".
|
|
print_manual_grade manual_grade_for_binary.
|
|
idtac " ".
|
|
|
|
idtac " ".
|
|
|
|
idtac "Max points - standard: 15".
|
|
idtac "Max points - advanced: 15".
|
|
idtac "".
|
|
idtac "********** Summary **********".
|
|
idtac "".
|
|
idtac "********** Standard **********".
|
|
idtac "---------- test_nandb4 ---------".
|
|
Print Assumptions test_nandb4.
|
|
idtac "---------- test_andb34 ---------".
|
|
Print Assumptions test_andb34.
|
|
idtac "---------- test_factorial2 ---------".
|
|
Print Assumptions test_factorial2.
|
|
idtac "---------- test_ltb3 ---------".
|
|
Print Assumptions test_ltb3.
|
|
idtac "---------- plus_id_exercise ---------".
|
|
Print Assumptions plus_id_exercise.
|
|
idtac "---------- mult_S_1 ---------".
|
|
Print Assumptions mult_S_1.
|
|
idtac "---------- andb_true_elim2 ---------".
|
|
Print Assumptions andb_true_elim2.
|
|
idtac "---------- zero_nbeq_plus_1 ---------".
|
|
Print Assumptions zero_nbeq_plus_1.
|
|
idtac "---------- identity_fn_applied_twice ---------".
|
|
Print Assumptions identity_fn_applied_twice.
|
|
idtac "---------- negation_fn_applied_twice ---------".
|
|
idtac "MANUAL".
|
|
idtac "---------- binary ---------".
|
|
idtac "MANUAL".
|
|
idtac "".
|
|
idtac "********** Advanced **********".
|
|
Abort.
|
|
|
|
(* Wed Jan 9 12:02:05 EST 2019 *)
|