Set Warnings "-notation-overridden,-parsing".
From Coq Require Export String.
From PLF Require Import Records.

Parameter MISSING: Type.

Module Check.

Ltac check_type A B :=
    match type of A with
    | context[MISSING] => idtac "Missing:" A
    | ?T => first [unify T B; idtac "Type: ok" | idtac "Type: wrong - should be (" B ")"]
    end.

Ltac print_manual_grade A :=
    match eval compute in A with
    | Some (_ ?S ?C) =>
        idtac "Score:"  S;
        match eval compute in C with
          | ""%string => idtac "Comment: None"
          | _ => idtac "Comment:" C
        end
    | None =>
        idtac "Score: Ungraded";
        idtac "Comment: None"
    end.

End Check.

From PLF Require Import Records.
Import Check.

Goal True.

idtac "-------------------  examples  --------------------".
idtac " ".

idtac "#> STLCExtendedRecords.typing_example_2".
idtac "Possible points: 0.5".
check_type @STLCExtendedRecords.typing_example_2 (
(STLCExtendedRecords.has_type (@Maps.empty STLCExtendedRecords.ty)
   (STLCExtendedRecords.tm_app
      (STLCExtendedRecords.tm_abs STLCExtendedRecords.a
         (STLCExtendedRecords.Ty_RCons STLCExtendedRecords.i1
            (STLCExtendedRecords.Ty_Arrow STLCExtendedRecords.A
               STLCExtendedRecords.A)
            (STLCExtendedRecords.Ty_RCons STLCExtendedRecords.i2
               (STLCExtendedRecords.Ty_Arrow STLCExtendedRecords.B
                  STLCExtendedRecords.B) STLCExtendedRecords.Ty_RNil))
         (STLCExtendedRecords.tm_rproj
            (STLCExtendedRecords.tm_var STLCExtendedRecords.a)
            STLCExtendedRecords.i2))
      (STLCExtendedRecords.tm_rcons STLCExtendedRecords.i1
         (STLCExtendedRecords.tm_abs STLCExtendedRecords.a
            STLCExtendedRecords.A
            (STLCExtendedRecords.tm_var STLCExtendedRecords.a))
         (STLCExtendedRecords.tm_rcons STLCExtendedRecords.i2
            (STLCExtendedRecords.tm_abs STLCExtendedRecords.a
               STLCExtendedRecords.B
               (STLCExtendedRecords.tm_var STLCExtendedRecords.a))
            STLCExtendedRecords.tm_rnil)))
   (STLCExtendedRecords.Ty_Arrow STLCExtendedRecords.B STLCExtendedRecords.B))).
idtac "Assumptions:".
Abort.
Print Assumptions STLCExtendedRecords.typing_example_2.
Goal True.
idtac " ".

idtac "#> STLCExtendedRecords.typing_nonexample".
idtac "Possible points: 0.5".
check_type @STLCExtendedRecords.typing_nonexample (
(~
 (exists T : STLCExtendedRecords.ty,
    STLCExtendedRecords.has_type
      (@Maps.update STLCExtendedRecords.ty
         (@Maps.empty STLCExtendedRecords.ty) STLCExtendedRecords.a
         (STLCExtendedRecords.Ty_RCons STLCExtendedRecords.i2
            (STLCExtendedRecords.Ty_Arrow STLCExtendedRecords.A
               STLCExtendedRecords.A) STLCExtendedRecords.Ty_RNil))
      (STLCExtendedRecords.tm_rcons STLCExtendedRecords.i1
         (STLCExtendedRecords.tm_abs STLCExtendedRecords.a
            STLCExtendedRecords.B
            (STLCExtendedRecords.tm_var STLCExtendedRecords.a))
         (STLCExtendedRecords.tm_var STLCExtendedRecords.a)) T))).
idtac "Assumptions:".
Abort.
Print Assumptions STLCExtendedRecords.typing_nonexample.
Goal True.
idtac " ".

idtac "#> STLCExtendedRecords.typing_nonexample_2".
idtac "Possible points: 1".
check_type @STLCExtendedRecords.typing_nonexample_2 (
(forall y : String.string,
 ~
 (exists T : STLCExtendedRecords.ty,
    STLCExtendedRecords.has_type
      (@Maps.update STLCExtendedRecords.ty
         (@Maps.empty STLCExtendedRecords.ty) y STLCExtendedRecords.A)
      (STLCExtendedRecords.tm_app
         (STLCExtendedRecords.tm_abs STLCExtendedRecords.a
            (STLCExtendedRecords.Ty_RCons STLCExtendedRecords.i1
               STLCExtendedRecords.A STLCExtendedRecords.Ty_RNil)
            (STLCExtendedRecords.tm_rproj
               (STLCExtendedRecords.tm_var STLCExtendedRecords.a)
               STLCExtendedRecords.i1))
         (STLCExtendedRecords.tm_rcons STLCExtendedRecords.i1
            (STLCExtendedRecords.tm_var y)
            (STLCExtendedRecords.tm_rcons STLCExtendedRecords.i2
               (STLCExtendedRecords.tm_var y) STLCExtendedRecords.tm_rnil)))
      T))).
idtac "Assumptions:".
Abort.
Print Assumptions STLCExtendedRecords.typing_nonexample_2.
Goal True.
idtac " ".

idtac " ".

idtac "Max points - standard: 2".
idtac "Max points - advanced: 2".
idtac "".
idtac "Allowed Axioms:".
idtac "functional_extensionality".
idtac "FunctionalExtensionality.functional_extensionality_dep".
idtac "CSeq_congruence".
idtac "fold_constants_bexp_sound".
idtac "succ_hastype_nat__hastype_nat".
idtac "".
idtac "".
idtac "********** Summary **********".
idtac "".
idtac "Below is a summary of the automatically graded exercises that are incomplete.".
idtac "".
idtac "The output for each exercise can be any of the following:".
idtac "  - 'Closed under the global context', if it is complete".
idtac "  - 'MANUAL', if it is manually graded".
idtac "  - A list of pending axioms, containing unproven assumptions. In this case".
idtac "    the exercise is considered complete, if the axioms are all allowed.".
idtac "".
idtac "********** Standard **********".
idtac "---------- STLCExtendedRecords.typing_example_2 ---------".
Print Assumptions STLCExtendedRecords.typing_example_2.
idtac "---------- STLCExtendedRecords.typing_nonexample ---------".
Print Assumptions STLCExtendedRecords.typing_nonexample.
idtac "---------- STLCExtendedRecords.typing_nonexample_2 ---------".
Print Assumptions STLCExtendedRecords.typing_nonexample_2.
idtac "".
idtac "********** Advanced **********".
Abort.

(* 2024-08-25 08:24 *)

(* 2024-08-25 08:25 *)
