Add test-case for #9840

2 files changed, 594 insertions, 0 deletions

diff --git a/test-suite/output/NumeralNotations.out b/test-suite/output/NumeralNotations.out
new file mode 100644
index 0000000000..cb49e66ed7
--- /dev/null
+++ b/test-suite/output/NumeralNotations.out
@@ -0,0 +1,186 @@
+The command has indeed failed with message:
+Unexpected term (nat -> nat) while parsing a numeral notation.
+The command has indeed failed with message:
+Unexpected non-option term opaque4 while parsing a numeral notation.
+The command has indeed failed with message:
+Unexpected term (fun (A : Type) (x : A) => x) while parsing a numeral
+notation.
+let v := 0%ppp in v : punit
+     : punit
+let v := 0%ppp in v : punit
+     : punit
+let v := 0%ppp in v : punit
+     : punit
+let v := 0%ppp in v : punit
+     : punit
+let v := 0%uto in v : unit
+     : unit
+The command has indeed failed with message:
+Cannot interpret this number as a value of type unit
+The command has indeed failed with message:
+Cannot interpret this number as a value of type unit
+let v := 0%upp in v : unit
+     : unit
+let v := 0%upp in v : unit
+     : unit
+let v := 0%upp in v : unit
+     : unit
+let v := 0%ppps in v : punit
+     : punit
+File "stdin", line 91, characters 2-46:
+Warning: To avoid stack overflow, large numbers in punit are interpreted as
+applications of pto_punits. [abstract-large-number,numbers]
+The command has indeed failed with message:
+In environment
+v := pto_punits (Decimal.D1 Decimal.Nil) : punit
+The term "v" has type "punit@{Set}" while it is expected to have type
+ "punit@{u}".
+S
+     : nat -> nat
+S (ack 4 4)
+     : nat
+let v := 0%wnat in v : wnat
+     : wnat
+0%wnat
+     : wnat
+{| unwrap := ack 4 4 |}
+     : wnat
+{| Test6.unwrap := 0 |}
+     : Test6.wnat
+let v := 0%wnat in v : Test6.wnat
+     : Test6.wnat
+let v := 0%wuint in v : wuint
+     : wuint
+let v := 1%wuint in v : wuint
+     : wuint
+let v := 0%wuint8 in v : wuint
+     : wuint
+let v := 0 in v : nat
+     : nat
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "wuint".
+     = {| unwrap := Decimal.D0 Decimal.Nil |}
+     : wuint
+let v := 0%wuint8' in v : wuint
+     : wuint
+let v := 0%wuint9 in v : wuint
+     : wuint
+let v := 0%wuint9' in v : wuint
+     : wuint
+let v := 0 in v : nat
+     : nat
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "wuint".
+File "stdin", line 202, characters 2-72:
+Warning: The 'abstract after' directive has no effect when the parsing
+function (of_uint) targets an option type.
+[abstract-large-number-no-op,numbers]
+The command has indeed failed with message:
+The 'abstract after' directive has no effect when the parsing function
+(of_uint) targets an option type. [abstract-large-number-no-op,numbers]
+The command has indeed failed with message:
+The reference of_uint was not found in the current environment.
+The command has indeed failed with message:
+The reference of_uint was not found in the current environment.
+let v := of_uint (Decimal.D1 Decimal.Nil) in v : unit
+     : unit
+let v := 0%test13 in v : unit
+     : unit
+The command has indeed failed with message:
+to_uint' is bound to a notation that does not denote a reference.
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+The command has indeed failed with message:
+to_uint'' is bound to a notation that does not denote a reference.
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+let v := 0%test14' in v : unit
+     : unit
+let v := 0%test14' in v : unit
+     : unit
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+let v := 0%test14' in v : unit
+     : unit
+The command has indeed failed with message:
+This command does not support the Global option in sections.
+let v := 0%test14'' in v : unit
+     : unit
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+The command has indeed failed with message:
+In environment
+v := 0 : nat
+The term "v" has type "nat" while it is expected to have type "unit".
+let v := 0%test15 in v : unit
+     : unit
+let v := 0%test15 in v : unit
+     : unit
+let v := 0%test15 in v : unit
+     : unit
+let v := foo a.t in v : Foo
+     : Foo
+The command has indeed failed with message:
+Cannot interpret in test16_scope because NumeralNotations.Test16.F.Foo could not be found in the current environment.
+let v := 0%test17 in v : myint63
+     : myint63
+let v := 0%Q in v : Q
+     : Q
+let v := 1%Q in v : Q
+     : Q
+let v := 2%Q in v : Q
+     : Q
+let v := 3%Q in v : Q
+     : Q
+let v := 4%Q in v : Q
+     : Q
+     = (0, 1)
+     : nat * nat
+     = (1, 1)
+     : nat * nat
+     = (2, 1)
+     : nat * nat
+     = (3, 1)
+     : nat * nat
+     = (4, 1)
+     : nat * nat
+let v := (-1)%Zlike in v : Zlike
+     : Zlike
+let v := 0%Zlike in v : Zlike
+     : Zlike
+let v := 1%Zlike in v : Zlike
+     : Zlike
+let v := 2%Zlike in v : Zlike
+     : Zlike
+let v := 3%Zlike in v : Zlike
+     : Zlike
+let v := 4%Zlike in v : Zlike
+     : Zlike
+2%Zlike
+     : Zlike
+0%Zlike
+     : Zlike
diff --git a/test-suite/output/NumeralNotations.v b/test-suite/output/NumeralNotations.v
new file mode 100644
index 0000000000..fcfdd82dcc
--- /dev/null
+++ b/test-suite/output/NumeralNotations.v
@@ -0,0 +1,408 @@
+(* Test that we fail, rather than raising anomalies, on opaque terms during interpretation *)
+
+Declare Scope opaque_scope.
+
+(* https://github.com/coq/coq/pull/8064#discussion_r202497516 *)
+Module Test1.
+  Axiom hold : forall {A B C}, A -> B -> C.
+  Definition opaque3 (x : Decimal.int) : Decimal.int := hold x (fix f (x : nat) : nat := match x with O => O | S n => S (f n) end).
+  Numeral Notation Decimal.int opaque3 opaque3 : opaque_scope.
+  Delimit Scope opaque_scope with opaque.
+  Fail Check 1%opaque.
+End Test1.
+
+(* https://github.com/coq/coq/pull/8064#discussion_r202497990 *)
+Module Test2.
+  Axiom opaque4 : option Decimal.int.
+  Definition opaque6 (x : Decimal.int) : option Decimal.int := opaque4.
+  Numeral Notation Decimal.int opaque6 opaque6 : opaque_scope.
+  Delimit Scope opaque_scope with opaque.
+  Open Scope opaque_scope.
+  Fail Check 1%opaque.
+End Test2.
+
+Declare Scope silly_scope.
+
+Module Test3.
+  Inductive silly := SILLY (v : Decimal.uint) (f : forall A, A -> A).
+  Definition to_silly (v : Decimal.uint) := SILLY v (fun _ x => x).
+  Definition of_silly (v : silly) := match v with SILLY v _ => v end.
+  Numeral Notation silly to_silly of_silly : silly_scope.
+  Delimit Scope silly_scope with silly.
+  Fail Check 1%silly.
+End Test3.
+
+Module Test4.
+  Declare Scope opaque_scope.
+  Declare Scope silly_scope.
+  Declare Scope pto.
+  Declare Scope ppo.
+  Declare Scope ptp.
+  Declare Scope ppp.
+  Declare Scope uto.
+  Declare Scope upo.
+  Declare Scope utp.
+  Declare Scope upp.
+  Declare Scope ppps.
+  Polymorphic NonCumulative Inductive punit := ptt.
+  Polymorphic Definition pto_punit (v : Decimal.uint) : option punit := match Nat.of_uint v with O => Some ptt | _ => None end.
+  Polymorphic Definition pto_punit_all (v : Decimal.uint) : punit := ptt.
+  Polymorphic Definition pof_punit (v : punit) : Decimal.uint := Nat.to_uint 0.
+  Definition to_punit (v : Decimal.uint) : option punit := match Nat.of_uint v with O => Some ptt | _ => None end.
+  Definition of_punit (v : punit) : Decimal.uint := Nat.to_uint 0.
+  Polymorphic Definition pto_unit (v : Decimal.uint) : option unit := match Nat.of_uint v with O => Some tt | _ => None end.
+  Polymorphic Definition pof_unit (v : unit) : Decimal.uint := Nat.to_uint 0.
+  Definition to_unit (v : Decimal.uint) : option unit := match Nat.of_uint v with O => Some tt | _ => None end.
+  Definition of_unit (v : unit) : Decimal.uint := Nat.to_uint 0.
+  Numeral Notation punit to_punit of_punit : pto.
+  Numeral Notation punit pto_punit of_punit : ppo.
+  Numeral Notation punit to_punit pof_punit : ptp.
+  Numeral Notation punit pto_punit pof_punit : ppp.
+  Numeral Notation unit to_unit of_unit : uto.
+  Delimit Scope pto with pto.
+  Delimit Scope ppo with ppo.
+  Delimit Scope ptp with ptp.
+  Delimit Scope ppp with ppp.
+  Delimit Scope uto with uto.
+  Check let v := 0%pto in v : punit.
+  Check let v := 0%ppo in v : punit.
+  Check let v := 0%ptp in v : punit.
+  Check let v := 0%ppp in v : punit.
+  Check let v := 0%uto in v : unit.
+  Fail Check 1%uto.
+  Fail Check (-1)%uto.
+  Numeral Notation unit pto_unit of_unit : upo.
+  Numeral Notation unit to_unit pof_unit : utp.
+  Numeral Notation unit pto_unit pof_unit : upp.
+  Delimit Scope upo with upo.
+  Delimit Scope utp with utp.
+  Delimit Scope upp with upp.
+  Check let v := 0%upo in v : unit.
+  Check let v := 0%utp in v : unit.
+  Check let v := 0%upp in v : unit.
+
+  Polymorphic Definition pto_punits := pto_punit_all@{Set}.
+  Polymorphic Definition pof_punits := pof_punit@{Set}.
+  Numeral Notation punit pto_punits pof_punits : ppps (abstract after 1).
+  Delimit Scope ppps with ppps.
+  Universe u.
+  Constraint Set < u.
+  Check let v := 0%ppps in v : punit@{u}. (* Check that universes are refreshed *)
+  Fail Check let v := 1%ppps in v : punit@{u}. (* Note that universes are not refreshed here *)
+End Test4.
+
+Module Test5.
+  Check S. (* At one point gave Error: Anomaly "Uncaught exception Pretype_errors.PretypeError(_, _, _)." Please report at http://coq.inria.fr/bugs/. *)
+End Test5.
+
+Module Test6.
+  (* Check that numeral notations on enormous terms don't take forever to print/parse *)
+  (* Ackerman definition from https://stackoverflow.com/a/10303475/377022 *)
+  Fixpoint ack (n m : nat) : nat :=
+    match n with
+    | O => S m
+    | S p => let fix ackn (m : nat) :=
+                 match m with
+                 | O => ack p 1
+                 | S q => ack p (ackn q)
+                 end
+             in ackn m
+    end.
+
+  Timeout 1 Check (S (ack 4 4)). (* should be instantaneous *)
+
+  Local Set Primitive Projections.
+  Record > wnat := wrap { unwrap :> nat }.
+  Definition to_uint (x : wnat) : Decimal.uint := Nat.to_uint x.
+  Definition of_uint (x : Decimal.uint) : wnat := Nat.of_uint x.
+  Module Export Scopes.
+    Declare Scope wnat_scope.
+    Delimit Scope wnat_scope with wnat.
+  End Scopes.
+  Module Export Notations.
+    Export Scopes.
+    Numeral Notation wnat of_uint to_uint : wnat_scope (abstract after 5000).
+  End Notations.
+  Check let v := 0%wnat in v : wnat.
+  Check wrap O.
+  Timeout 1 Check wrap (ack 4 4). (* should be instantaneous *)
+End Test6.
+
+Module Test6_2.
+  Import Test6.Scopes.
+  Check Test6.wrap 0.
+  Import Test6.Notations.
+  Check let v := 0%wnat in v : Test6.wnat.
+End Test6_2.
+
+Module Test7.
+  Local Set Primitive Projections.
+  Record wuint := wrap { unwrap : Decimal.uint }.
+  Declare Scope wuint_scope.
+  Delimit Scope wuint_scope with wuint.
+  Numeral Notation wuint wrap unwrap : wuint_scope.
+  Check let v := 0%wuint in v : wuint.
+  Check let v := 1%wuint in v : wuint.
+End Test7.
+
+Module Test8.
+  Local Set Primitive Projections.
+  Record wuint := wrap { unwrap : Decimal.uint }.
+  Declare Scope wuint8_scope.
+  Declare Scope wuint8'_scope.
+  Delimit Scope wuint8_scope with wuint8.
+  Delimit Scope wuint8'_scope with wuint8'.
+  Section with_var.
+    Context (dummy : unit).
+    Definition wrap' := let __ := dummy in wrap.
+    Definition unwrap' := let __ := dummy in unwrap.
+    Numeral Notation wuint wrap' unwrap' : wuint8_scope.
+    Check let v := 0%wuint8 in v : wuint.
+  End with_var.
+  Check let v := 0%wuint8 in v : nat.
+  Fail Check let v := 0%wuint8 in v : wuint.
+  Compute wrap (Nat.to_uint 0).
+
+  Notation wrap'' := wrap.
+  Notation unwrap'' := unwrap.
+  Numeral Notation wuint wrap'' unwrap'' : wuint8'_scope.
+  Check let v := 0%wuint8' in v : wuint.
+End Test8.
+
+Module Test9.
+  Declare Scope wuint9_scope.
+  Declare Scope wuint9'_scope.
+  Delimit Scope wuint9_scope with wuint9.
+  Delimit Scope wuint9'_scope with wuint9'.
+  Section with_let.
+    Local Set Primitive Projections.
+    Record wuint := wrap { unwrap : Decimal.uint }.
+    Let wrap' := wrap.
+    Let unwrap' := unwrap.
+    Local Notation wrap'' := wrap.
+    Local Notation unwrap'' := unwrap.
+    Numeral Notation wuint wrap' unwrap' : wuint9_scope.
+    Check let v := 0%wuint9 in v : wuint.
+    Numeral Notation wuint wrap'' unwrap'' : wuint9'_scope.
+    Check let v := 0%wuint9' in v : wuint.
+  End with_let.
+  Check let v := 0%wuint9 in v : nat.
+  Fail Check let v := 0%wuint9 in v : wuint.
+End Test9.
+
+Module Test10.
+  (* Test that it is only a warning to add abstract after to an optional parsing function *)
+  Definition to_uint (v : unit) := Nat.to_uint 0.
+  Definition of_uint (v : Decimal.uint) := match Nat.of_uint v with O => Some tt | _ => None end.
+  Definition of_any_uint (v : Decimal.uint) := tt.
+  Declare Scope unit_scope.
+  Declare Scope unit2_scope.
+  Delimit Scope unit_scope with unit.
+  Delimit Scope unit2_scope with unit2.
+  Numeral Notation unit of_uint to_uint : unit_scope (abstract after 1).
+  Local Set Warnings Append "+abstract-large-number-no-op".
+  (* Check that there is actually a warning here *)
+  Fail Numeral Notation unit of_uint to_uint : unit2_scope (abstract after 1).
+  (* Check that there is no warning here *)
+  Numeral Notation unit of_any_uint to_uint : unit2_scope (abstract after 1).
+End Test10.
+
+Module Test11.
+  (* Test that numeral notations don't work on proof-local variables, especially not ones containing evars *)
+  Inductive unit11 := tt11.
+  Declare Scope unit11_scope.
+  Delimit Scope unit11_scope with unit11.
+  Goal True.
+    evar (to_uint : unit11 -> Decimal.uint).
+    evar (of_uint : Decimal.uint -> unit11).
+    Fail Numeral Notation unit11 of_uint to_uint : uint11_scope.
+    exact I.
+    Unshelve.
+    all: solve [ constructor ].
+  Qed.
+End Test11.
+
+Module Test12.
+  (* Test for numeral notations on context variables *)
+  Declare Scope test12_scope.
+  Delimit Scope test12_scope with test12.
+  Section test12.
+    Context (to_uint : unit -> Decimal.uint) (of_uint : Decimal.uint -> unit).
+
+    Numeral Notation unit of_uint to_uint : test12_scope.
+    Check let v := 1%test12 in v : unit.
+  End test12.
+End Test12.
+
+Module Test13.
+  (* Test for numeral notations on notations which do not denote references *)
+  Declare Scope test13_scope.
+  Declare Scope test13'_scope.
+  Declare Scope test13''_scope.
+  Delimit Scope test13_scope with test13.
+  Delimit Scope test13'_scope with test13'.
+  Delimit Scope test13''_scope with test13''.
+  Definition to_uint (x y : unit) : Decimal.uint := Nat.to_uint O.
+  Definition of_uint (x : Decimal.uint) : unit := tt.
+  Definition to_uint_good := to_uint tt.
+  Notation to_uint' := (to_uint tt).
+  Notation to_uint'' := (to_uint _).
+  Numeral Notation unit of_uint to_uint_good : test13_scope.
+  Check let v := 0%test13 in v : unit.
+  Fail Numeral Notation unit of_uint to_uint' : test13'_scope.
+  Fail Check let v := 0%test13' in v : unit.
+  Fail Numeral Notation unit of_uint to_uint'' : test13''_scope.
+  Fail Check let v := 0%test13'' in v : unit.
+End Test13.
+
+Module Test14.
+  (* Test that numeral notations follow [Import], not [Require], and
+     also test that [Local Numeral Notation]s do not escape modules
+     nor sections. *)
+  Declare Scope test14_scope.
+  Declare Scope test14'_scope.
+  Declare Scope test14''_scope.
+  Declare Scope test14'''_scope.
+  Delimit Scope test14_scope with test14.
+  Delimit Scope test14'_scope with test14'.
+  Delimit Scope test14''_scope with test14''.
+  Delimit Scope test14'''_scope with test14'''.
+  Module Inner.
+    Definition to_uint (x : unit) : Decimal.uint := Nat.to_uint O.
+    Definition of_uint (x : Decimal.uint) : unit := tt.
+    Local Numeral Notation unit of_uint to_uint : test14_scope.
+    Global Numeral Notation unit of_uint to_uint : test14'_scope.
+    Check let v := 0%test14 in v : unit.
+    Check let v := 0%test14' in v : unit.
+  End Inner.
+  Fail Check let v := 0%test14 in v : unit.
+  Fail Check let v := 0%test14' in v : unit.
+  Import Inner.
+  Fail Check let v := 0%test14 in v : unit.
+  Check let v := 0%test14' in v : unit.
+  Section InnerSection.
+    Definition to_uint (x : unit) : Decimal.uint := Nat.to_uint O.
+    Definition of_uint (x : Decimal.uint) : unit := tt.
+    Local Numeral Notation unit of_uint to_uint : test14''_scope.
+    Fail Global Numeral Notation unit of_uint to_uint : test14'''_scope.
+    Check let v := 0%test14'' in v : unit.
+    Fail Check let v := 0%test14''' in v : unit.
+  End InnerSection.
+  Fail Check let v := 0%test14'' in v : unit.
+  Fail Check let v := 0%test14''' in v : unit.
+End Test14.
+
+Module Test15.
+  (** Test module include *)
+  Declare Scope test15_scope.
+  Delimit Scope test15_scope with test15.
+  Module Inner.
+    Definition to_uint (x : unit) : Decimal.uint := Nat.to_uint O.
+    Definition of_uint (x : Decimal.uint) : unit := tt.
+    Numeral Notation unit of_uint to_uint : test15_scope.
+    Check let v := 0%test15 in v : unit.
+  End Inner.
+  Module Inner2.
+    Include Inner.
+    Check let v := 0%test15 in v : unit.
+  End Inner2.
+  Import Inner Inner2.
+  Check let v := 0%test15 in v : unit.
+End Test15.
+
+Module Test16.
+  (** Test functors *)
+  Declare Scope test16_scope.
+  Delimit Scope test16_scope with test16.
+  Module Type A.
+    Axiom T : Set.
+    Axiom t : T.
+  End A.
+  Module F (a : A).
+    Inductive Foo := foo (_ : a.T).
+    Definition to_uint (x : Foo) : Decimal.uint := Nat.to_uint O.
+    Definition of_uint (x : Decimal.uint) : Foo := foo a.t.
+    Global Numeral Notation Foo of_uint to_uint : test16_scope.
+    Check let v := 0%test16 in v : Foo.
+  End F.
+  Module a <: A.
+    Definition T : Set := unit.
+    Definition t : T := tt.
+  End a.
+  Module Import f := F a.
+  (** Ideally this should work, but it should definitely not anomaly *)
+  Fail Check let v := 0%test16 in v : Foo.
+End Test16.
+
+Require Import Coq.Numbers.Cyclic.Int63.Int63.
+Module Test17.
+  (** Test int63 *)
+  Declare Scope test17_scope.
+  Declare Scope test17_scope.
+  Delimit Scope test17_scope with test17.
+  Local Set Primitive Projections.
+  Record myint63 := of_int { to_int : int }.
+  Numeral Notation myint63 of_int to_int : test17_scope.
+  Check let v := 0%test17 in v : myint63.
+End Test17.
+
+Module Test18.
+  (** Test https://github.com/coq/coq/issues/9840 *)
+  Record Q := { num : nat ; den : nat ; reduced : Nat.gcd num den = 1 }.
+  Declare Scope Q_scope.
+  Delimit Scope Q_scope with Q.
+
+  Definition nat_eq_dec (x y : nat) : {x = y} + {x <> y}.
+  Proof. decide equality. Defined.
+
+  Definition transparentify {A} (D : {A} + {not A}) (H : A) : A :=
+    match D with
+    | left pf => pf
+    | right npf => match npf H with end
+    end.
+
+  Axiom gcd_good : forall x, Nat.gcd x 1 = 1.
+
+  Definition Q_of_nat (x : nat) : Q := {| num := x ; den := 1 ; reduced := transparentify (nat_eq_dec _ _) (gcd_good _) |}.
+  Definition nat_of_Q (x : Q) : option nat
+    := if Nat.eqb x.(den) 1 then Some (x.(num)) else None.
+  Definition Q_of_uint (x : Decimal.uint) : Q := Q_of_nat (Nat.of_uint x).
+  Definition uint_of_Q (x : Q) : option Decimal.uint
+    := option_map Nat.to_uint (nat_of_Q x).
+
+  Numeral Notation Q Q_of_uint uint_of_Q : Q_scope.
+
+  Check let v := 0%Q in v : Q.
+  Check let v := 1%Q in v : Q.
+  Check let v := 2%Q in v : Q.
+  Check let v := 3%Q in v : Q.
+  Check let v := 4%Q in v : Q.
+  Compute let v := 0%Q in (num v, den v).
+  Compute let v := 1%Q in (num v, den v).
+  Compute let v := 2%Q in (num v, den v).
+  Compute let v := 3%Q in (num v, den v).
+  Compute let v := 4%Q in (num v, den v).
+End Test18.
+
+Require Import Coq.Lists.List.
+Require Import Coq.ZArith.ZArith.
+Module Test19.
+  (** Test another thing related to https://github.com/coq/coq/issues/9840 *)
+  Record Zlike := { summands : list Z }.
+  Declare Scope Zlike_scope.
+  Delimit Scope Zlike_scope with Zlike.
+
+  Definition Z_of_Zlike (x : Zlike) := List.fold_right Z.add 0%Z (summands x).
+  Definition Zlike_of_Z (x : Z) := {| summands := cons x nil |}.
+
+  Numeral Notation Zlike Zlike_of_Z Z_of_Zlike : Zlike_scope.
+
+  Check let v := (-1)%Zlike in v : Zlike.
+  Check let v := 0%Zlike in v : Zlike.
+  Check let v := 1%Zlike in v : Zlike.
+  Check let v := 2%Zlike in v : Zlike.
+  Check let v := 3%Zlike in v : Zlike.
+  Check let v := 4%Zlike in v : Zlike.
+  Check {| summands := (cons 1 (cons 2 (cons (-1) nil)))%Z |}.
+  Check {| summands := nil |}.
+End Test19.