Universe level error when defining dependent types in one metacoq call.

[DeLectionnes]

When defining new objects and inductive types in one MetaCoq Run call from their term AST, if your definitions are dependent, it can lead to a universe level error not present when defining them with multiple calls.

We provide a better MWE in the posts below.

[MathisBD]

I have a MWE for this bug (or a related one) : Actually it's a different bug, see https://github.com/MetaCoq/metacoq/issues/1115

[DeLectionnes]

Here is a MWE with the same error as my previous message. It's a different error message from what MathisBD got :

MWE

```coq From MetaCoq.Utils Require Import utils. From MetaCoq.Template Require Import All. From MetaCoq.Template Require Import Checker. Import MCMonadNotation. Notation nameAnon := {| binder_name := nAnon; binder_relevance := Relevant |}. Definition AST_Ind := {| ind_finite := Finite; ind_npars := 1; ind_params := []; ind_bodies := [{| ind_name := "Ind"; ind_indices := []; ind_sort := sProp; ind_type := tProd {| binder_name := nNamed "T"; binder_relevance := Relevant |} (tSort (sType {| t_set := {| LevelExprSet.this := [(Level.level "__metacoq_fresh_level__", 0)]; LevelExprSet.is_ok := LevelExprSet.Raw.singleton_ok (Level.level "__metacoq_fresh_level__", 0) |}; t_ne := eq_refl |})) (tProd nameAnon (tRel 0) (tSort sProp)); ind_kelim := IntoPropSProp; ind_ctors :=[]; ind_projs := []; ind_relevance := Relevant |}]; ind_universes := Monomorphic_ctx; ind_variance := None |}. Definition AST_match := tLambda {| binder_name := nNamed "T"; binder_relevance := Relevant |} (tSort (sType {| t_set := {| LevelExprSet.this := [(Level.level "__metacoq_fresh_level__", 0)]; LevelExprSet.is_ok := LevelExprSet.Raw.singleton_ok (Level.level "__metacoq_fresh_level__", 0) |}; t_ne := eq_refl |})) (tCase {| ci_ind := {| inductive_mind :=(MPfile ["Logic"; "Init"; "Coq"], "True"); inductive_ind := 0 |}; ci_npar := 0; ci_relevance := Relevant |} {| puinst := []; pparams := []; pcontext := [nameAnon]; preturn := tProd nameAnon (tRel 1) (tSort sProp) |} (tConstruct {| inductive_mind := (MPfile ["Logic"; "Init"; "Coq"], "True"); inductive_ind := 0 |} 0 []) [{| bcontext := []; bbody := tLambda nameAnon (tRel 0) (tApp (tInd {| inductive_mind := (MPfile ["recherche"; "tests"], "Ind"); inductive_ind := 0 |} []) [tRel 1; tRel 0]) |} ]). Definition define_ind : TemplateMonad unit := tmMkInductive true (mind_body_to_entry AST_Ind). Definition define_dispatch : TemplateMonad unit := tmMkDefinition "dispatch" AST_match. Unset MetaCoq Strict Unquote Universe Mode. Fail MetaCoq Run (_ <- define_ind;; define_dispatch). MetaCoq Run (define_ind). MetaCoq Run (define_dispatch). ``` These AST correspond to the definitions ```coq Inductive Ind (T:Type) : T -> Prop :=. Definition dispatch := fun (T:Type) => match I with I => fun t => Ind T t end. ```

The error message is

Illegal application: 
The term "Ind" of type "forall T : Type, T -> Prop"
cannot be applied to the terms
 "T" : "Type"
 "t" : "T"
The 1st term has type "Type@{tests.recherche.45}" which should be a subtype of "Type@{tests.recherche.43}".

[MathisBD]

It's a different error message from what MathisBD got :

Indeed, this now seems like two different bugs. I'll open a new issue.

[MathisBD]

Also I shortened your MWE a bit :

MWE

```Coq From MetaCoq.Utils Require Import utils. From MetaCoq.Template Require Import All. Import MCMonadNotation. (* Modify this based on the current file. *) Definition ind : term := tInd {| inductive_mind := (MPfile ["Bug1"], "Ind") ; inductive_ind := 0 |} []. (* AST of [Inductive Ind (T : Type) : Prop :=.]. *) Definition AST_Ind := {| ind_finite := Finite; ind_npars := 1; ind_params := [{| decl_name := {| binder_name := nNamed "T"; binder_relevance := Relevant |}; decl_body := None; decl_type := tSort (sType fresh_universe) |}]; ind_bodies := [{| ind_name := "Ind"; ind_indices := []; ind_sort := sProp; ind_type := tProd {| binder_name := nNamed "T"; binder_relevance := Relevant |} (tSort (sType fresh_universe)) (tSort sProp); ind_kelim := IntoPropSProp; ind_ctors :=[]; ind_projs := []; ind_relevance := Relevant |}]; ind_universes := Monomorphic_ctx; ind_variance := None |}. (* AST of [fun T : Type => Ind T]. *) Definition AST_fun := tLambda {| binder_name := nNamed "T"; binder_relevance := Relevant |} (tSort (sType fresh_universe)) (tApp ind [tRel 0]). Definition define_ind : TemplateMonad unit := tmMkInductive true (mind_body_to_entry AST_Ind). Definition define_fun : TemplateMonad unit := tmMkDefinition "def" AST_fun. Unset MetaCoq Strict Unquote Universe Mode. Fail MetaCoq Run (define_ind ;; define_fun). MetaCoq Run (define_ind). MetaCoq Run (define_fun). ```

The error message is still the same.