forked from oysteikt/sf1-template
553 lines
15 KiB
Coq
553 lines
15 KiB
Coq
Set Warnings "-notation-overridden,-parsing".
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From Stdlib Require Export String.
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From LF Require Import Poly.
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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 Poly.
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Import Check.
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Goal True.
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idtac "------------------- poly_exercises --------------------".
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idtac " ".
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idtac "#> app_nil_r".
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idtac "Possible points: 0.5".
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check_type @app_nil_r (
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(forall (X : Type) (l : list X), @eq (list X) (@app X l (@nil X)) l)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions app_nil_r.
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Goal True.
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idtac " ".
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idtac "#> app_assoc".
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idtac "Possible points: 1".
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check_type @app_assoc (
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(forall (A : Type) (l m n : list A),
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@eq (list A) (@app A l (@app A m n)) (@app A (@app A l m) n))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions app_assoc.
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Goal True.
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idtac " ".
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idtac "#> app_length".
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idtac "Possible points: 0.5".
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check_type @app_length (
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(forall (X : Type) (l1 l2 : list X),
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@eq nat (@length X (@app X l1 l2)) (Nat.add (@length X l1) (@length X l2)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions app_length.
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Goal True.
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idtac " ".
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idtac "------------------- more_poly_exercises --------------------".
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idtac " ".
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idtac "#> rev_app_distr".
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idtac "Possible points: 1".
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check_type @rev_app_distr (
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(forall (X : Type) (l1 l2 : list X),
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@eq (list X) (@rev X (@app X l1 l2)) (@app X (@rev X l2) (@rev X l1)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions rev_app_distr.
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Goal True.
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idtac " ".
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idtac "#> rev_involutive".
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idtac "Possible points: 1".
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check_type @rev_involutive (
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(forall (X : Type) (l : list X), @eq (list X) (@rev X (@rev X l)) l)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions rev_involutive.
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Goal True.
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idtac " ".
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idtac "------------------- split --------------------".
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idtac " ".
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idtac "#> split".
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idtac "Possible points: 1".
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check_type @split ((forall (X Y : Type) (_ : list (prod X Y)), prod (list X) (list Y))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions split.
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Goal True.
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idtac " ".
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idtac "#> test_split".
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idtac "Possible points: 1".
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check_type @test_split (
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(@eq (prod (list nat) (list bool))
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(@split nat bool
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(@cons (prod nat bool) (@pair nat bool 1 false)
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(@cons (prod nat bool) (@pair nat bool 2 false)
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(@nil (prod nat bool)))))
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(@pair (list nat) (list bool) (@cons nat 1 (@cons nat 2 (@nil nat)))
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(@cons bool false (@cons bool false (@nil bool)))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions test_split.
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Goal True.
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idtac " ".
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idtac "------------------- filter_even_gt7 --------------------".
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idtac " ".
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idtac "#> test_filter_even_gt7_1".
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idtac "Possible points: 1".
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check_type @test_filter_even_gt7_1 (
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(@eq (list nat)
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(filter_even_gt7
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(@cons nat 1
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(@cons nat 2
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(@cons nat 6
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(@cons nat 9
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(@cons nat 10
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(@cons nat 3 (@cons nat 12 (@cons nat 8 (@nil nat))))))))))
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(@cons nat 10 (@cons nat 12 (@cons nat 8 (@nil nat)))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions test_filter_even_gt7_1.
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Goal True.
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idtac " ".
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idtac "#> test_filter_even_gt7_2".
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idtac "Possible points: 1".
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check_type @test_filter_even_gt7_2 (
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(@eq (list nat)
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(filter_even_gt7
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(@cons nat 5
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(@cons nat 2 (@cons nat 6 (@cons nat 19 (@cons nat 129 (@nil nat)))))))
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(@nil nat))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions test_filter_even_gt7_2.
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Goal True.
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idtac " ".
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idtac "------------------- partition --------------------".
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idtac " ".
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idtac "#> partition".
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idtac "Possible points: 1".
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check_type @partition (
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(forall (X : Type) (_ : forall _ : X, bool) (_ : list X),
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prod (list X) (list X))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions partition.
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Goal True.
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idtac " ".
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idtac "#> test_partition1".
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idtac "Possible points: 1".
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check_type @test_partition1 (
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(@eq (prod (list nat) (list nat))
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(@partition nat odd
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(@cons nat 1
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(@cons nat 2 (@cons nat 3 (@cons nat 4 (@cons nat 5 (@nil nat)))))))
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(@pair (list nat) (list nat)
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(@cons nat 1 (@cons nat 3 (@cons nat 5 (@nil nat))))
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(@cons nat 2 (@cons nat 4 (@nil nat)))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions test_partition1.
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Goal True.
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idtac " ".
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idtac "#> test_partition2".
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idtac "Possible points: 1".
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check_type @test_partition2 (
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(@eq (prod (list nat) (list nat))
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(@partition nat (fun _ : nat => false)
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(@cons nat 5 (@cons nat 9 (@cons nat 0 (@nil nat)))))
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(@pair (list nat) (list nat) (@nil nat)
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(@cons nat 5 (@cons nat 9 (@cons nat 0 (@nil nat))))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions test_partition2.
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Goal True.
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idtac " ".
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idtac "------------------- map_rev --------------------".
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idtac " ".
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idtac "#> map_rev".
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idtac "Possible points: 3".
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check_type @map_rev (
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(forall (X Y : Type) (f : forall _ : X, Y) (l : list X),
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@eq (list Y) (@map X Y f (@rev X l)) (@rev Y (@map X Y f l)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions map_rev.
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Goal True.
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idtac " ".
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idtac "------------------- flat_map --------------------".
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idtac " ".
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idtac "#> flat_map".
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idtac "Possible points: 1".
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check_type @flat_map (
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(forall (X Y : Type) (_ : forall _ : X, list Y) (_ : list X), list Y)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions flat_map.
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Goal True.
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idtac " ".
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idtac "#> test_flat_map1".
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idtac "Possible points: 1".
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check_type @test_flat_map1 (
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(@eq (list nat)
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(@flat_map nat nat
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(fun n : nat => @cons nat n (@cons nat n (@cons nat n (@nil nat))))
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(@cons nat 1 (@cons nat 5 (@cons nat 4 (@nil nat)))))
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(@cons nat 1
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(@cons nat 1
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(@cons nat 1
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(@cons nat 5
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(@cons nat 5
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(@cons nat 5
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(@cons nat 4 (@cons nat 4 (@cons nat 4 (@nil nat)))))))))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions test_flat_map1.
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Goal True.
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idtac " ".
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idtac "------------------- fold_length --------------------".
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idtac " ".
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idtac "#> Exercises.fold_length_correct".
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idtac "Possible points: 2".
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check_type @Exercises.fold_length_correct (
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(forall (X : Type) (l : list X),
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@eq nat (@Exercises.fold_length X l) (@length X l))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.fold_length_correct.
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Goal True.
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idtac " ".
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idtac "------------------- fold_map --------------------".
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idtac " ".
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idtac "#> Manually graded: Exercises.fold_map".
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idtac "Possible points: 3".
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print_manual_grade Exercises.manual_grade_for_fold_map.
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idtac " ".
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idtac "------------------- currying --------------------".
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idtac " ".
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idtac "#> Exercises.uncurry_curry".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.uncurry_curry (
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(forall (X Y Z : Type) (f : forall (_ : X) (_ : Y), Z) (x : X) (y : Y),
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@eq Z (@Exercises.prod_curry X Y Z (@Exercises.prod_uncurry X Y Z f) x y)
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(f x y))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.uncurry_curry.
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Goal True.
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idtac " ".
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idtac "#> Exercises.curry_uncurry".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.curry_uncurry (
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(forall (X Y Z : Type) (f : forall _ : prod X Y, Z) (p : prod X Y),
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@eq Z (@Exercises.prod_uncurry X Y Z (@Exercises.prod_curry X Y Z f) p)
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(f p))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.curry_uncurry.
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Goal True.
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idtac " ".
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idtac "------------------- church_scc --------------------".
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idtac " ".
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idtac "#> Exercises.Church.scc_2".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.scc_2 (
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(@eq Exercises.Church.cnat (Exercises.Church.scc Exercises.Church.one)
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Exercises.Church.two)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.scc_2.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.scc_3".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.scc_3 (
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(@eq Exercises.Church.cnat (Exercises.Church.scc Exercises.Church.two)
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Exercises.Church.three)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.scc_3.
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Goal True.
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idtac " ".
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idtac "------------------- church_plus --------------------".
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idtac " ".
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idtac "#> Exercises.Church.plus_1".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.plus_1 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.plus Exercises.Church.zero Exercises.Church.one)
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Exercises.Church.one)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.plus_1.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.plus_2".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.plus_2 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.plus Exercises.Church.two Exercises.Church.three)
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(Exercises.Church.plus Exercises.Church.three Exercises.Church.two))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.plus_2.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.plus_3".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.plus_3 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.plus
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(Exercises.Church.plus Exercises.Church.two Exercises.Church.two)
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Exercises.Church.three)
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(Exercises.Church.plus Exercises.Church.one
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(Exercises.Church.plus Exercises.Church.three Exercises.Church.three)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.plus_3.
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Goal True.
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idtac " ".
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idtac "------------------- church_mult --------------------".
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idtac " ".
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idtac "#> Exercises.Church.mult_1".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.mult_1 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.mult Exercises.Church.one Exercises.Church.one)
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Exercises.Church.one)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.mult_1.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.mult_2".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.mult_2 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.mult Exercises.Church.zero
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(Exercises.Church.plus Exercises.Church.three Exercises.Church.three))
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Exercises.Church.zero)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.mult_2.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.mult_3".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.mult_3 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.mult Exercises.Church.two Exercises.Church.three)
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(Exercises.Church.plus Exercises.Church.three Exercises.Church.three))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.mult_3.
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Goal True.
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idtac " ".
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idtac "------------------- church_exp --------------------".
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idtac " ".
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idtac "#> Exercises.Church.exp_1".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.exp_1 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.exp Exercises.Church.two Exercises.Church.two)
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(Exercises.Church.plus Exercises.Church.two Exercises.Church.two))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.exp_1.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.exp_2".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.exp_2 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.exp Exercises.Church.three Exercises.Church.zero)
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Exercises.Church.one)).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.exp_2.
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Goal True.
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idtac " ".
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idtac "#> Exercises.Church.exp_3".
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idtac "Advanced".
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idtac "Possible points: 1".
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check_type @Exercises.Church.exp_3 (
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(@eq Exercises.Church.cnat
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(Exercises.Church.exp Exercises.Church.three Exercises.Church.two)
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(Exercises.Church.plus
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(Exercises.Church.mult Exercises.Church.two
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(Exercises.Church.mult Exercises.Church.two Exercises.Church.two))
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Exercises.Church.one))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions Exercises.Church.exp_3.
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Goal True.
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idtac " ".
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idtac " ".
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idtac "Max points - standard: 21".
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idtac "Max points - advanced: 34".
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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 "---------- app_nil_r ---------".
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Print Assumptions app_nil_r.
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idtac "---------- app_assoc ---------".
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|
Print Assumptions app_assoc.
|
|
idtac "---------- app_length ---------".
|
|
Print Assumptions app_length.
|
|
idtac "---------- rev_app_distr ---------".
|
|
Print Assumptions rev_app_distr.
|
|
idtac "---------- rev_involutive ---------".
|
|
Print Assumptions rev_involutive.
|
|
idtac "---------- split ---------".
|
|
Print Assumptions split.
|
|
idtac "---------- test_split ---------".
|
|
Print Assumptions test_split.
|
|
idtac "---------- test_filter_even_gt7_1 ---------".
|
|
Print Assumptions test_filter_even_gt7_1.
|
|
idtac "---------- test_filter_even_gt7_2 ---------".
|
|
Print Assumptions test_filter_even_gt7_2.
|
|
idtac "---------- partition ---------".
|
|
Print Assumptions partition.
|
|
idtac "---------- test_partition1 ---------".
|
|
Print Assumptions test_partition1.
|
|
idtac "---------- test_partition2 ---------".
|
|
Print Assumptions test_partition2.
|
|
idtac "---------- map_rev ---------".
|
|
Print Assumptions map_rev.
|
|
idtac "---------- flat_map ---------".
|
|
Print Assumptions flat_map.
|
|
idtac "---------- test_flat_map1 ---------".
|
|
Print Assumptions test_flat_map1.
|
|
idtac "---------- Exercises.fold_length_correct ---------".
|
|
Print Assumptions Exercises.fold_length_correct.
|
|
idtac "---------- fold_map ---------".
|
|
idtac "MANUAL".
|
|
idtac "".
|
|
idtac "********** Advanced **********".
|
|
idtac "---------- Exercises.uncurry_curry ---------".
|
|
Print Assumptions Exercises.uncurry_curry.
|
|
idtac "---------- Exercises.curry_uncurry ---------".
|
|
Print Assumptions Exercises.curry_uncurry.
|
|
idtac "---------- Exercises.Church.scc_2 ---------".
|
|
Print Assumptions Exercises.Church.scc_2.
|
|
idtac "---------- Exercises.Church.scc_3 ---------".
|
|
Print Assumptions Exercises.Church.scc_3.
|
|
idtac "---------- Exercises.Church.plus_1 ---------".
|
|
Print Assumptions Exercises.Church.plus_1.
|
|
idtac "---------- Exercises.Church.plus_2 ---------".
|
|
Print Assumptions Exercises.Church.plus_2.
|
|
idtac "---------- Exercises.Church.plus_3 ---------".
|
|
Print Assumptions Exercises.Church.plus_3.
|
|
idtac "---------- Exercises.Church.mult_1 ---------".
|
|
Print Assumptions Exercises.Church.mult_1.
|
|
idtac "---------- Exercises.Church.mult_2 ---------".
|
|
Print Assumptions Exercises.Church.mult_2.
|
|
idtac "---------- Exercises.Church.mult_3 ---------".
|
|
Print Assumptions Exercises.Church.mult_3.
|
|
idtac "---------- Exercises.Church.exp_1 ---------".
|
|
Print Assumptions Exercises.Church.exp_1.
|
|
idtac "---------- Exercises.Church.exp_2 ---------".
|
|
Print Assumptions Exercises.Church.exp_2.
|
|
idtac "---------- Exercises.Church.exp_3 ---------".
|
|
Print Assumptions Exercises.Church.exp_3.
|
|
Abort.
|
|
|
|
(* 2026-01-07 13:18 *)
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|
|
(* 2026-01-07 13:18 *)
|