forked from oysteikt/sf1-template
293 lines
8.1 KiB
Coq
293 lines
8.1 KiB
Coq
Set Warnings "-notation-overridden,-parsing".
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From Stdlib Require Export String.
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From LF Require Import Imp.
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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 Imp.
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Import Check.
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Goal True.
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idtac "------------------- optimize_0plus_b_sound --------------------".
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idtac " ".
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idtac "#> AExp.optimize_0plus_b_test1".
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idtac "Possible points: 0.5".
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check_type @AExp.optimize_0plus_b_test1 (
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(@eq AExp.bexp
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(AExp.optimize_0plus_b
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(AExp.BNot
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(AExp.BGt (AExp.APlus (AExp.ANum 0) (AExp.ANum 4)) (AExp.ANum 8))))
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(AExp.BNot (AExp.BGt (AExp.ANum 4) (AExp.ANum 8))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions AExp.optimize_0plus_b_test1.
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Goal True.
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idtac " ".
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idtac "#> AExp.optimize_0plus_b_test2".
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idtac "Possible points: 0.5".
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check_type @AExp.optimize_0plus_b_test2 (
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(@eq AExp.bexp
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(AExp.optimize_0plus_b
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(AExp.BAnd
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(AExp.BLe (AExp.APlus (AExp.ANum 0) (AExp.ANum 4)) (AExp.ANum 5))
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AExp.BTrue))
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(AExp.BAnd (AExp.BLe (AExp.ANum 4) (AExp.ANum 5)) AExp.BTrue))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions AExp.optimize_0plus_b_test2.
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Goal True.
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idtac " ".
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idtac "#> AExp.optimize_0plus_b_sound".
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idtac "Possible points: 2".
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check_type @AExp.optimize_0plus_b_sound (
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(forall b : AExp.bexp,
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@eq bool (AExp.beval (AExp.optimize_0plus_b b)) (AExp.beval b))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions AExp.optimize_0plus_b_sound.
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Goal True.
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idtac " ".
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idtac "------------------- bevalR --------------------".
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idtac " ".
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idtac "#> AExp.bevalR_iff_beval".
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idtac "Possible points: 3".
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check_type @AExp.bevalR_iff_beval (
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(forall (b : AExp.bexp) (bv : bool),
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iff (AExp.bevalR b bv) (@eq bool (AExp.beval b) bv))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions AExp.bevalR_iff_beval.
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Goal True.
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idtac " ".
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idtac "------------------- ceval_example2 --------------------".
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idtac " ".
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idtac "#> ceval_example2".
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idtac "Possible points: 2".
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check_type @ceval_example2 (
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(ceval (CSeq (CAsgn X (ANum 0)) (CSeq (CAsgn Y (ANum 1)) (CAsgn Z (ANum 2))))
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empty_st
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(@Maps.t_update nat
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(@Maps.t_update nat (@Maps.t_update nat empty_st X 0) Y 1) Z 2))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions ceval_example2.
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Goal True.
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idtac " ".
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idtac "------------------- loop_never_stops --------------------".
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idtac " ".
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idtac "#> loop_never_stops".
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idtac "Possible points: 3".
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check_type @loop_never_stops ((forall st st' : state, not (ceval loop st st'))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions loop_never_stops.
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Goal True.
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idtac " ".
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idtac "------------------- no_whiles_eqv --------------------".
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idtac " ".
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idtac "#> no_whiles_eqv".
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idtac "Possible points: 3".
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check_type @no_whiles_eqv (
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(forall c : com, iff (@eq bool (no_whiles c) true) (no_whilesR c))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions no_whiles_eqv.
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Goal True.
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idtac " ".
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idtac "------------------- no_whiles_terminating --------------------".
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idtac " ".
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idtac "#> Manually graded: no_whiles_terminating".
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idtac "Possible points: 6".
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print_manual_grade manual_grade_for_no_whiles_terminating.
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idtac " ".
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idtac "------------------- stack_compiler --------------------".
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idtac " ".
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idtac "#> s_execute1".
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idtac "Possible points: 1".
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check_type @s_execute1 (
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(@eq (list nat)
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(s_execute empty_st (@nil nat)
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(@cons sinstr (SPush 5)
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(@cons sinstr (SPush 3)
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(@cons sinstr (SPush 1) (@cons sinstr SMinus (@nil sinstr))))))
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(@cons nat 2 (@cons nat 5 (@nil nat))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions s_execute1.
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Goal True.
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idtac " ".
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idtac "#> s_execute2".
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idtac "Possible points: 0.5".
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check_type @s_execute2 (
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(@eq (list nat)
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(s_execute (@Maps.t_update nat empty_st X 3)
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(@cons nat 3 (@cons nat 4 (@nil nat)))
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(@cons sinstr (SPush 4)
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(@cons sinstr (SLoad X)
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(@cons sinstr SMult (@cons sinstr SPlus (@nil sinstr))))))
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(@cons nat 15 (@cons nat 4 (@nil nat))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions s_execute2.
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Goal True.
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idtac " ".
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idtac "#> s_compile1".
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idtac "Possible points: 1.5".
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check_type @s_compile1 (
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(@eq (list sinstr) (s_compile (AMinus (AId X) (AMult (ANum 2) (AId Y))))
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(@cons sinstr (SLoad X)
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(@cons sinstr (SPush 2)
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(@cons sinstr (SLoad Y)
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(@cons sinstr SMult (@cons sinstr SMinus (@nil sinstr)))))))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions s_compile1.
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Goal True.
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idtac " ".
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idtac "------------------- execute_app --------------------".
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idtac " ".
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idtac "#> execute_app".
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idtac "Possible points: 3".
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check_type @execute_app (
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(forall (st : state) (p1 p2 : list sinstr) (stack : list nat),
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@eq (list nat) (s_execute st stack (@app sinstr p1 p2))
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(s_execute st (s_execute st stack p1) p2))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions execute_app.
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Goal True.
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idtac " ".
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idtac "------------------- stack_compiler_correct --------------------".
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idtac " ".
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idtac "#> s_compile_correct_aux".
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idtac "Possible points: 2.5".
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check_type @s_compile_correct_aux (
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(forall (st : state) (e : aexp) (stack : list nat),
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@eq (list nat) (s_execute st stack (s_compile e))
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(@cons nat (aeval st e) stack))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions s_compile_correct_aux.
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Goal True.
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idtac " ".
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idtac "#> s_compile_correct".
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idtac "Possible points: 0.5".
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check_type @s_compile_correct (
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(forall (st : state) (e : aexp),
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@eq (list nat) (s_execute st (@nil nat) (s_compile e))
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(@cons nat (aeval st e) (@nil nat)))).
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idtac "Assumptions:".
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Abort.
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Print Assumptions s_compile_correct.
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Goal True.
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idtac " ".
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idtac " ".
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idtac "Max points - standard: 29".
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idtac "Max points - advanced: 29".
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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 "---------- AExp.optimize_0plus_b_test1 ---------".
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Print Assumptions AExp.optimize_0plus_b_test1.
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idtac "---------- AExp.optimize_0plus_b_test2 ---------".
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Print Assumptions AExp.optimize_0plus_b_test2.
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idtac "---------- AExp.optimize_0plus_b_sound ---------".
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Print Assumptions AExp.optimize_0plus_b_sound.
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idtac "---------- AExp.bevalR_iff_beval ---------".
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Print Assumptions AExp.bevalR_iff_beval.
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idtac "---------- ceval_example2 ---------".
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Print Assumptions ceval_example2.
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idtac "---------- loop_never_stops ---------".
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Print Assumptions loop_never_stops.
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idtac "---------- no_whiles_eqv ---------".
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Print Assumptions no_whiles_eqv.
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idtac "---------- no_whiles_terminating ---------".
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idtac "MANUAL".
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idtac "---------- s_execute1 ---------".
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Print Assumptions s_execute1.
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idtac "---------- s_execute2 ---------".
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Print Assumptions s_execute2.
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idtac "---------- s_compile1 ---------".
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Print Assumptions s_compile1.
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idtac "---------- execute_app ---------".
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Print Assumptions execute_app.
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idtac "---------- s_compile_correct_aux ---------".
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Print Assumptions s_compile_correct_aux.
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idtac "---------- s_compile_correct ---------".
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Print Assumptions s_compile_correct.
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idtac "".
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idtac "********** Advanced **********".
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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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