376 lines
10 KiB
Coq
376 lines
10 KiB
Coq
Set Warnings "-notation-overridden,-parsing".
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From Stdlib Require Export String.
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From LF Require Import ProofObjects.
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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 ProofObjects.
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Import Check.
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Goal True.
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idtac "------------------- eight_is_even --------------------".
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idtac " ".
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idtac "#> ev_8".
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idtac "Possible points: 1".
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check_type @ev_8 ((ev 8)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions ev_8.
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Goal True.
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idtac " ".
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idtac "#> ev_8'".
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idtac "Possible points: 1".
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check_type @ev_8' ((ev 8)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions ev_8'.
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Goal True.
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idtac " ".
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idtac "------------------- conj_fact --------------------".
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idtac " ".
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idtac "#> Props.conj_fact".
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idtac "Possible points: 2".
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check_type @Props.conj_fact (
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(forall (P Q R : Prop) (_ : and P Q) (_ : and Q R), and P R)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Props.conj_fact.
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Goal True.
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idtac " ".
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idtac "------------------- or_commut' --------------------".
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idtac " ".
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idtac "#> Props.or_commut'".
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idtac "Possible points: 2".
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check_type @Props.or_commut' ((forall (P Q : Prop) (_ : or P Q), or Q P)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Props.or_commut'.
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Goal True.
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idtac " ".
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idtac "------------------- ex_ev_Sn --------------------".
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idtac " ".
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idtac "#> Props.ex_ev_Sn".
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idtac "Possible points: 2".
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check_type @Props.ex_ev_Sn ((@ex nat (fun n : nat => ev (S n)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Props.ex_ev_Sn.
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Goal True.
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idtac " ".
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idtac "------------------- ex_match --------------------".
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idtac " ".
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idtac "#> Props.ex_match".
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idtac "Possible points: 2".
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check_type @Props.ex_match (
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(forall (A : Type) (P Q : forall _ : A, Prop)
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(_ : forall (x : A) (_ : P x), Q x) (_ : @ex A (fun x : A => P x)),
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@ex A (fun x : A => Q x))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Props.ex_match.
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Goal True.
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idtac " ".
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idtac "------------------- p_implies_true --------------------".
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idtac " ".
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idtac "#> Props.p_implies_true".
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idtac "Possible points: 1".
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check_type @Props.p_implies_true ((forall (P : Type) (_ : P), Props.True)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Props.p_implies_true.
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Goal True.
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idtac " ".
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idtac "------------------- ex_falso_quodlibet' --------------------".
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idtac " ".
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idtac "#> Props.ex_falso_quodlibet'".
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idtac "Possible points: 1".
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check_type @Props.ex_falso_quodlibet' ((forall (P : Type) (_ : Props.False), P)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Props.ex_falso_quodlibet'.
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Goal True.
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idtac " ".
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idtac "------------------- eq_cons --------------------".
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idtac " ".
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idtac "#> EqualityPlayground.eq_cons".
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idtac "Possible points: 2".
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check_type @EqualityPlayground.eq_cons (
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(forall (X : Type) (h1 h2 : X) (t1 t2 : list X)
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(_ : @EqualityPlayground.eq X h1 h2)
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(_ : @EqualityPlayground.eq (list X) t1 t2),
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@EqualityPlayground.eq (list X) (@cons X h1 t1) (@cons X h2 t2))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions EqualityPlayground.eq_cons.
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Goal True.
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idtac " ".
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idtac "------------------- equality__leibniz_equality --------------------".
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idtac " ".
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idtac "#> EqualityPlayground.equality__leibniz_equality".
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idtac "Possible points: 2".
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check_type @EqualityPlayground.equality__leibniz_equality (
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(forall (X : Type) (x y : X) (_ : @EqualityPlayground.eq X x y)
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(P : forall _ : X, Prop) (_ : P x),
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P y)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions EqualityPlayground.equality__leibniz_equality.
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Goal True.
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idtac " ".
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idtac "------------------- equality__leibniz_equality_term --------------------".
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idtac " ".
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idtac "#> EqualityPlayground.equality__leibniz_equality_term".
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idtac "Possible points: 2".
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check_type @EqualityPlayground.equality__leibniz_equality_term (
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(forall (X : Type) (x y : X) (_ : @EqualityPlayground.eq X x y)
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(P : forall _ : X, Prop) (_ : P x),
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P y)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions EqualityPlayground.equality__leibniz_equality_term.
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Goal True.
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idtac " ".
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idtac "------------------- and_assoc --------------------".
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idtac " ".
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idtac "#> and_assoc".
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idtac "Possible points: 2".
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check_type @and_assoc ((forall (P Q R : Prop) (_ : and P (and Q R)), and (and P Q) R)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions and_assoc.
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Goal True.
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idtac " ".
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idtac "------------------- or_distributes_over_and --------------------".
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idtac " ".
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idtac "#> or_distributes_over_and".
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idtac "Possible points: 3".
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check_type @or_distributes_over_and (
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(forall P Q R : Prop, iff (or P (and Q R)) (and (or P Q) (or P R)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions or_distributes_over_and.
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Goal True.
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idtac " ".
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idtac "------------------- negations --------------------".
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idtac " ".
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idtac "#> double_neg".
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idtac "Possible points: 1".
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check_type @double_neg ((forall (P : Prop) (_ : P), not (not P))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions double_neg.
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Goal True.
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idtac " ".
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idtac "#> contradiction_implies_anything".
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idtac "Possible points: 1".
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check_type @contradiction_implies_anything ((forall (P Q : Prop) (_ : and P (not P)), Q)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions contradiction_implies_anything.
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Goal True.
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idtac " ".
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idtac "#> de_morgan_not_or".
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idtac "Possible points: 1".
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check_type @de_morgan_not_or (
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(forall (P Q : Prop) (_ : not (or P Q)), and (not P) (not Q))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions de_morgan_not_or.
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Goal True.
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idtac " ".
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idtac "------------------- currying --------------------".
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idtac " ".
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idtac "#> curry".
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idtac "Possible points: 1".
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check_type @curry (
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(forall (P Q R : Prop) (_ : forall _ : and P Q, R) (_ : P) (_ : Q), R)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions curry.
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Goal True.
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idtac " ".
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idtac "#> uncurry".
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idtac "Possible points: 1".
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check_type @uncurry (
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(forall (P Q R : Prop) (_ : forall (_ : P) (_ : Q), R) (_ : and P Q), R)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions uncurry.
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Goal True.
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idtac " ".
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idtac "------------------- pe_implies_or_eq --------------------".
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idtac " ".
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idtac "#> pe_implies_or_eq".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @pe_implies_or_eq (
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(forall (_ : propositional_extensionality) (P Q : Prop),
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@eq Prop (or P Q) (or Q P))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions pe_implies_or_eq.
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Goal True.
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idtac " ".
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idtac "------------------- pe_implies_true_eq --------------------".
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idtac " ".
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idtac "#> pe_implies_true_eq".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @pe_implies_true_eq (
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(forall (_ : propositional_extensionality) (P : Prop) (_ : P),
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@eq Prop True P)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions pe_implies_true_eq.
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Goal True.
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idtac " ".
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idtac "------------------- pe_implies_pi --------------------".
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idtac " ".
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idtac "#> pe_implies_pi".
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idtac "Advanced".
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idtac "Possible points: 3".
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check_type @pe_implies_pi ((forall _ : propositional_extensionality, proof_irrelevance)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions pe_implies_pi.
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Goal True.
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idtac " ".
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idtac " ".
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idtac "Max points - standard: 28".
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idtac "Max points - advanced: 33".
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idtac "".
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idtac "Allowed Axioms:".
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idtac "functional_extensionality".
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idtac "FunctionalExtensionality.functional_extensionality_dep".
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idtac "plus_le".
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idtac "le_trans".
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idtac "le_plus_l".
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idtac "add_le_cases".
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idtac "Sn_le_Sm__n_le_m".
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idtac "O_le_n".
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idtac "".
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idtac "".
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idtac "********** Summary **********".
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idtac "".
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idtac "Below is a summary of the automatically graded exercises that are incomplete.".
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idtac "".
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idtac "The output for each exercise can be any of the following:".
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idtac " - 'Closed under the global context', if it is complete".
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idtac " - 'MANUAL', if it is manually graded".
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idtac " - A list of pending axioms, containing unproven assumptions. In this case".
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idtac " the exercise is considered complete, if the axioms are all allowed.".
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idtac "".
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idtac "********** Standard **********".
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idtac "---------- ev_8 ---------".
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Print Assumptions ev_8.
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idtac "---------- ev_8' ---------".
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Print Assumptions ev_8'.
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idtac "---------- Props.conj_fact ---------".
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Print Assumptions Props.conj_fact.
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idtac "---------- Props.or_commut' ---------".
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Print Assumptions Props.or_commut'.
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idtac "---------- Props.ex_ev_Sn ---------".
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Print Assumptions Props.ex_ev_Sn.
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idtac "---------- Props.ex_match ---------".
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Print Assumptions Props.ex_match.
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idtac "---------- Props.p_implies_true ---------".
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Print Assumptions Props.p_implies_true.
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idtac "---------- Props.ex_falso_quodlibet' ---------".
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Print Assumptions Props.ex_falso_quodlibet'.
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idtac "---------- EqualityPlayground.eq_cons ---------".
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Print Assumptions EqualityPlayground.eq_cons.
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idtac "---------- EqualityPlayground.equality__leibniz_equality ---------".
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Print Assumptions EqualityPlayground.equality__leibniz_equality.
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idtac "---------- EqualityPlayground.equality__leibniz_equality_term ---------".
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Print Assumptions EqualityPlayground.equality__leibniz_equality_term.
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idtac "---------- and_assoc ---------".
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Print Assumptions and_assoc.
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idtac "---------- or_distributes_over_and ---------".
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Print Assumptions or_distributes_over_and.
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idtac "---------- double_neg ---------".
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Print Assumptions double_neg.
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idtac "---------- contradiction_implies_anything ---------".
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Print Assumptions contradiction_implies_anything.
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idtac "---------- de_morgan_not_or ---------".
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Print Assumptions de_morgan_not_or.
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idtac "---------- curry ---------".
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Print Assumptions curry.
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idtac "---------- uncurry ---------".
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Print Assumptions uncurry.
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idtac "".
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idtac "********** Advanced **********".
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idtac "---------- pe_implies_or_eq ---------".
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Print Assumptions pe_implies_or_eq.
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idtac "---------- pe_implies_true_eq ---------".
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Print Assumptions pe_implies_true_eq.
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idtac "---------- pe_implies_pi ---------".
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Print Assumptions pe_implies_pi.
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Abort.
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(* 2026-01-07 13:18 *)
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(* 2026-01-07 13:18 *)
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