bedrock.prelude.elpi.derive_test

(*
 * Copyright (c) 2023 BedRock Systems, Inc.
 * This software is distributed under the terms of the BedRock Open-Source
 * License. See the LICENSE-BedRock file in the repository root for details.
 *)


Require Import bedrock.prelude.prelude.
Require Import bedrock.prelude.finite.
Require Import bedrock.prelude.elpi.derive.

Module Type Alias.
  Variant T := A | B.
  Definition t1 := T.
  Definition t2 := t1.

  Module Import Cmd.
    Elpi Command assert_type.
    Elpi Accumulate lp:{{/*(*/
      pred main i:argument list.
      main trm (global (const C)), (trm Ty) :- std.do!  coq.env.const C _ CTy, Ty = CTy .
    /*)
*/}}.
    Elpi Typecheck.
    Elpi Export assert_type.
  End Cmd.

  Module Eq_Dec.
    Module Type OnVariant.
      #[only(eq_dec)] derive T.
      assert_type (T_eq_dec) (EqDecision T).
    End OnVariant.

    Module Type OnAliasDirect.
      #[only(eq_dec)] derive t1.
      Fail assert_type (t1_eq_dec) (EqDecision T).
      assert_type (t1_eq_dec) (EqDecision t1).
    End OnAliasDirect.

    Module Type OnAliasIndirect.
      #[only(eq_dec)] derive t2.
      Fail assert_type (t2_eq_dec) (EqDecision T).
      Fail assert_type (t2_eq_dec) (EqDecision t1).
      assert_type (t2_eq_dec) (EqDecision t2).
    End OnAliasIndirect.
  End Eq_Dec.

  Module Inhabited.
    Module Type OnVariant.
      #[only(inhabited)] derive T.
      assert_type (T_inhabited) (Inhabited T).
    End OnVariant.

    Module Type OnAliasDirect.
      #[only(inhabited)] derive t1.
      Fail assert_type (t1_inhabited) (Inhabited T).
      assert_type (t1_inhabited) (Inhabited t1).
    End OnAliasDirect.

    Module Type OnAliasIndirect.
      #[only(inhabited)] derive t2.
      Fail assert_type (t2_inhabited) (Inhabited T).
      Fail assert_type (t2_inhabited) (Inhabited t1).
      assert_type (t2_inhabited) (Inhabited t2).
    End OnAliasIndirect.
  End Inhabited.

  Module Countable.
    Module Type OnVariant.
      #[only(countable)] derive T.
      assert_type (T_countable) (Countable T).
    End OnVariant.

    Module Type OnAliasDirect.
      #[only(countable)] derive t1.
      Fail assert_type (t1_countable) (Countable T).
      assert_type (t1_countable) (Countable t1).
    End OnAliasDirect.

    Module Type OnAliasIndirect.
      #[only(countable)] derive t2.
      Fail assert_type (t2_countable) (Countable T).
      Fail assert_type (t2_countable) (Countable t1).
      assert_type (t2_countable) (Countable t2).
    End OnAliasIndirect.
  End Countable.

  Module Finite.
    Module Type OnVariant.
      #[only(finite)] derive T.
      assert_type (T_finite) (Finite T).
    End OnVariant.

    Module Type OnAliasDirect.
      #[only(finite)] derive t1.
      Fail assert_type (t1_finite) (Finite T).
      assert_type (t1_finite) (Finite t1).
    End OnAliasDirect.

    Module Type OnAliasIndirect.
      #[only(finite)] derive t2.
      Fail assert_type (t2_finite) (Finite T).
      Fail assert_type (t2_finite) (Finite t1).
      assert_type (t2_finite) (Finite t2).
    End OnAliasIndirect.
  End Finite.
End Alias.

Module Type BasicTests.
  Variant T1 := A1 | B1 | C1.
  #[only(eq_dec)] derive T1.
  #[only(inhabited)] derive T1.
  #[only(countable)] derive T1.
  #[only(finite)] derive T1.

  Succeed #[only(finite)] derive
  Variant T2 := A2 | B2 | C2.

  #[only(eq_dec,inhabited)] derive
  Variant T2 := A2 | B2 | C2.
  #[only(countable)] derive T2.
  #[only(finite)] derive T2.
End BasicTests.

(*Test interop of manual and generated definitions*)
Module Type InteropTests.
  Variant T1 := A1 | B1 | C1.
  (*Test: Manual EqDecision + generated Finite:*)
  #[local] Instance T1_eq_dec : EqDecision T1.
  Proof. solve_decision. Defined.
  #[only(finite)] derive T1.
  (*Search T1. (*Should give one instance T1_eq_dec (plus a finite instance)*)*)

  Variant T2 := A2 | B2 | C2.
  (*Test: Generated EqDecision + manual Finite + generated Finite:
    Should yield only one Finite instance*)

  #[only(eq_dec)] derive T2.
  #[local] Instance manual_T2_finite : Finite T2.
  Proof. solve_finite [A2;B2;C2]. Qed.
  #[only(finite)] derive T2.
  (*Search T2. (*Should give one instance manual_T2_finite*)*)
End InteropTests.

(*** Test derivation using Countable. *)
#[local] Ltac assert_True :=
  match goal with
  | |- True => idtac
  | |- _ => fail
  end.

Module Type DerivingTest.
  (*This example uses the default unfolding rule.
    It's motivated by functor use cases.*)

  Variant _t := A | B | C.
  Definition t := _t.
  #[only(eq_dec,countable)] derive t.
  Goal forall x y : t, if bool_decide (x = y) then True else True.
  Proof. by move => x y; case (bool_decide_reflect (x = y)). Qed.
  Goal forall x y : t, encode x = encode y -> x = y.
  Proof. by move => x y X; apply encode_inj in X. Qed.
  Goal match Pos.compare (encode A) (encode B) with
       | Eq => True
       | Lt => True
       | Gt => True
       end.
  Proof.
    Succeed by vm_compute.
    (* Even simpl normalizes this goal - that's nice! *)
    by simpl; assert_True.
  Qed.
End DerivingTest.

(*** Test derivation using Finite. *)
Module Type Deriving2Test.
  Variant _t := A | B | C (_ : bool) | D (_ : option bool) (_ : bool).
  Definition t := _t.
  #[global] Instance: EqDecision t.
  Proof. solve_decision. Defined.
  #[only(inhabited,eq_dec,finite)] derive t.

  (*
  Print Assumptions t_inhabited.
  Print t_inhabited.
  Print Assumptions t_finite.
  Print t_finite.
  Print t_finite_subproof_nodup.
  Print t_finite_subproof_elem_of.
  *)


  (* Test the tactic in isolation. *)
  Definition t_finite2 : Finite t.
  Proof. solve_finite ([A; B] ++ (C <$> enum _) ++ (D <$> enum _ <*> enum _)). Defined.
  (*
  Print Assumptions t_finite2.
  Print t_finite2_subproof.
  *)

  Variant _t2 := E | F | G.
  Definition t2 := _t2.
  #[only(inhabited,eq_dec)] derive t2.
  #[only(finite)] derive t2.
  (* [global] Instance: EqDecision t. Proof. solve_decision. Defined. *)
  Section test.
    Context (x : nat).
    Variant t3 := H.
    #[only(inhabited,eq_dec,finite)] derive t3.
  End test.

  Goal forall x y : t, if bool_decide (x = y) then True else True.
  Proof. by move => x y; case (bool_decide_reflect (x = y)). Qed.
  Goal forall x y : t, encode x = encode y -> x = y.
  Proof. by move => x y X; apply encode_inj in X. Qed.

  (* Eval vm_compute in enum t. *)

  Goal match Pos.compare (encode A) (encode B) with
       | Eq => True
       | Lt => True
       | Gt => True
       end.
  Proof.
    Succeed by vm_compute.
    (* simpl normalizes this goal too! *)
    by simpl; assert_True.
  Qed.
End Deriving2Test.

Module Type SimpleFiniteTest.
  Succeed #[only(finite_type)] derive
  Variant feature := A | B | C | D.

  Variant feature := A | B | C | D.
  #[only(finite_type)] derive feature.
  Goal feature.of_N (feature.to_N A) = Some A.
  Proof. reflexivity. Qed.
  Goal feature.of_N (feature.to_N B) = Some B.
  Proof. by rewrite feature.of_to_N. Qed.
End SimpleFiniteTest.

(* TODO: this cannot work due to the synterp phase. *)
Module Type FiniteTest.
  Variant feature := A | B | C | D.
  #[local] Instance: ToN feature (fun (x : feature) =>
    match x with
    | A => 0
    | B => 1
    | C => 3
    | D => 5
    end)%N := {}.
  #[only(finite_type_to_N)] derive feature.
  #[export] Instance feature_to_N_inj : Inj eq eq feature.to_N.
  Proof. case; case => //. Qed.
  Goal feature.of_N (feature.to_N C) = Some C.
  Proof. reflexivity. Qed.
  Goal feature.of_N (feature.to_N D) = Some D.
  Proof. by rewrite feature.of_to_N. Qed.
  Goal feature.of_N 3 = Some C.
  Proof. reflexivity. Qed.
End FiniteTest.

Module Type SimpleBitsetTest.
  Variant feature := A | B | C | D.
  #[only(bitset)] derive feature.
  Goal feature_set.to_bits {[ A ]} = 1%N.
  Proof. reflexivity. Qed.
  Goal feature_set.to_bits {[ C ]} = 4%N.
  Proof. reflexivity. Qed.
  Goal feature_set.to_bits {[ A; C ]} = 5%N.
  Proof. reflexivity. Qed.
End SimpleBitsetTest.

Module Type BitsetTest.
  Variant feature := A | B | C | D.
  #[local] Instance: ToBit feature (fun (x : feature) =>
    match x with
    | A => 0
    | B => 1
    | C => 3
    | D => 5
    end)%N := {}.
  #[only(bitset_to_bit)] derive feature.
  Goal feature_set.to_bits {[ A ]} = 1%N.
  Proof. reflexivity. Qed.
  Goal feature_set.to_bits {[ C ]} = 8%N.
  Proof. reflexivity. Qed.
  Goal feature_set.to_bits {[ A; C ]} = 9%N.
  Proof. reflexivity. Qed.
End BitsetTest.