296 lines
7.3 KiB
Coq
296 lines
7.3 KiB
Coq
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Set Warnings "-notation-overridden,-parsing".
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From Coq Require Export String.
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From LF Require Import IndProp.
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Parameter MISSING: Type.
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Module Check.
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Ltac check_type A B :=
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match type of A with
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| context[MISSING] => idtac "Missing:" A
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| ?T => first [unify T B; idtac "Type: ok" | idtac "Type: wrong - should be (" B ")"]
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end.
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Ltac print_manual_grade A :=
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match eval compute in A with
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| Some (_ ?S ?C) =>
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idtac "Score:" S;
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match eval compute in C with
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| ""%string => idtac "Comment: None"
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| _ => idtac "Comment:" C
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end
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| None =>
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idtac "Score: Ungraded";
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idtac "Comment: None"
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end.
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End Check.
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From LF Require Import IndProp.
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Import Check.
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Goal True.
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idtac "------------------- ev_double --------------------".
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idtac " ".
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idtac "#> ev_double".
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idtac "Possible points: 1".
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check_type @ev_double ((forall n : nat, even (double n))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions ev_double.
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Goal True.
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idtac " ".
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idtac "------------------- inversion_practice --------------------".
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idtac " ".
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idtac "#> SSSSev__even".
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idtac "Possible points: 1".
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check_type @SSSSev__even ((forall n : nat, even (S (S (S (S n)))) -> even n)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions SSSSev__even.
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Goal True.
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idtac " ".
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idtac "------------------- even5_nonsense --------------------".
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idtac " ".
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idtac "#> even5_nonsense".
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idtac "Possible points: 1".
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check_type @even5_nonsense ((even 5 -> 2 + 2 = 9)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions even5_nonsense.
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Goal True.
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idtac " ".
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idtac "------------------- ev_sum --------------------".
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idtac " ".
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idtac "#> ev_sum".
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idtac "Possible points: 2".
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check_type @ev_sum ((forall n m : nat, even n -> even m -> even (n + m))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions ev_sum.
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Goal True.
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idtac " ".
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idtac "------------------- ev_ev__ev --------------------".
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idtac " ".
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idtac "#> ev_ev__ev".
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idtac "Advanced".
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idtac "Possible points: 3".
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check_type @ev_ev__ev ((forall n m : nat, even (n + m) -> even n -> even m)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions ev_ev__ev.
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Goal True.
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idtac " ".
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idtac "------------------- R_provability --------------------".
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idtac " ".
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idtac "#> Manually graded: R.R_provability".
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idtac "Possible points: 3".
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print_manual_grade R.manual_grade_for_R_provability.
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idtac " ".
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idtac "------------------- subsequence --------------------".
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idtac " ".
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idtac "#> subseq_refl".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @subseq_refl ((forall l : list nat, subseq l l)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions subseq_refl.
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Goal True.
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idtac " ".
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idtac "#> subseq_app".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @subseq_app (
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(forall l1 l2 l3 : list nat, subseq l1 l2 -> subseq l1 (l2 ++ l3))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions subseq_app.
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Goal True.
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idtac " ".
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idtac "------------------- exp_match_ex1 --------------------".
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idtac " ".
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idtac "#> empty_is_empty".
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idtac "Possible points: 1".
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check_type @empty_is_empty ((forall (T : Type) (s : list T), ~ (s =~ @EmptySet T))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions empty_is_empty.
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Goal True.
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idtac " ".
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idtac "#> MUnion'".
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idtac "Possible points: 1".
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check_type @MUnion' (
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(forall (T : Type) (s : list T) (re1 re2 : @reg_exp T),
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s =~ re1 \/ s =~ re2 -> s =~ @Union T re1 re2)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions MUnion'.
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Goal True.
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idtac " ".
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idtac "#> MStar'".
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idtac "Possible points: 1".
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check_type @MStar' (
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(forall (T : Type) (ss : list (list T)) (re : @reg_exp T),
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(forall s : list T, @In (list T) s ss -> s =~ re) ->
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@fold (list T) (list T) (@app T) ss [ ] =~ @Star T re)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions MStar'.
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Goal True.
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idtac " ".
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idtac "------------------- re_not_empty --------------------".
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idtac " ".
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idtac "#> re_not_empty".
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idtac "Possible points: 2".
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check_type @re_not_empty ((forall T : Type, @reg_exp T -> bool)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions re_not_empty.
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Goal True.
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idtac " ".
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idtac "#> re_not_empty_correct".
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idtac "Possible points: 2".
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check_type @re_not_empty_correct (
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(forall (T : Type) (re : @reg_exp T),
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(exists s : list T, s =~ re) <-> @re_not_empty T re = true)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions re_not_empty_correct.
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Goal True.
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idtac " ".
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idtac "------------------- pumping --------------------".
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idtac " ".
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idtac "#> Pumping.pumping".
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idtac "Advanced".
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idtac "Possible points: 5".
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check_type @Pumping.pumping (
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(forall (T : Type) (re : @reg_exp T) (s : list T),
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s =~ re ->
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@Pumping.pumping_constant T re <= @length T s ->
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exists s1 s2 s3 : list T,
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s = s1 ++ s2 ++ s3 /\
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s2 <> [ ] /\ (forall m : nat, s1 ++ @Pumping.napp T m s2 ++ s3 =~ re))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Pumping.pumping.
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Goal True.
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idtac " ".
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idtac "------------------- reflect_iff --------------------".
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idtac " ".
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idtac "#> reflect_iff".
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idtac "Possible points: 2".
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check_type @reflect_iff ((forall (P : Prop) (b : bool), reflect P b -> P <-> b = true)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions reflect_iff.
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Goal True.
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idtac " ".
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idtac "------------------- eqbP_practice --------------------".
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idtac " ".
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idtac "#> eqbP_practice".
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idtac "Possible points: 3".
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check_type @eqbP_practice (
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(forall (n : nat) (l : list nat), count n l = 0 -> ~ @In nat n l)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions eqbP_practice.
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Goal True.
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idtac " ".
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idtac "------------------- nostutter_defn --------------------".
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idtac " ".
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idtac "#> Manually graded: nostutter".
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idtac "Possible points: 3".
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print_manual_grade manual_grade_for_nostutter.
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idtac " ".
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idtac "------------------- filter_challenge --------------------".
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idtac " ".
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idtac "#> Manually graded: filter_challenge".
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idtac "Advanced".
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idtac "Possible points: 4".
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print_manual_grade manual_grade_for_filter_challenge.
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idtac " ".
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idtac " ".
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idtac "Max points - standard: 23".
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idtac "Max points - advanced: 37".
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idtac "".
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idtac "********** Summary **********".
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idtac "".
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idtac "********** Standard **********".
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idtac "---------- ev_double ---------".
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Print Assumptions ev_double.
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idtac "---------- SSSSev__even ---------".
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Print Assumptions SSSSev__even.
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idtac "---------- even5_nonsense ---------".
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Print Assumptions even5_nonsense.
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idtac "---------- ev_sum ---------".
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Print Assumptions ev_sum.
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idtac "---------- R_provability ---------".
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idtac "MANUAL".
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idtac "---------- empty_is_empty ---------".
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Print Assumptions empty_is_empty.
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idtac "---------- MUnion' ---------".
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Print Assumptions MUnion'.
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idtac "---------- MStar' ---------".
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Print Assumptions MStar'.
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idtac "---------- re_not_empty ---------".
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Print Assumptions re_not_empty.
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idtac "---------- re_not_empty_correct ---------".
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Print Assumptions re_not_empty_correct.
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idtac "---------- reflect_iff ---------".
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Print Assumptions reflect_iff.
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idtac "---------- eqbP_practice ---------".
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Print Assumptions eqbP_practice.
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idtac "---------- nostutter ---------".
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idtac "MANUAL".
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idtac "".
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idtac "********** Advanced **********".
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idtac "---------- ev_ev__ev ---------".
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Print Assumptions ev_ev__ev.
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idtac "---------- subseq_refl ---------".
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Print Assumptions subseq_refl.
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idtac "---------- subseq_app ---------".
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Print Assumptions subseq_app.
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idtac "---------- Pumping.pumping ---------".
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Print Assumptions Pumping.pumping.
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idtac "---------- filter_challenge ---------".
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idtac "MANUAL".
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Abort.
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(* Wed Jan 9 12:02:15 EST 2019 *)
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