diff --git a/Changelog.md b/Changelog.md
index 58cec4fe..d2e196f5 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -7,6 +7,15 @@
    a class that is known to have no instance (for the given type)
  - **Speedup** `toposort` on `gref` uses OCaml's maps and sets rather than lists
 
+- **Change** For a structure `S` on a subject of type `T`, declares `S.sort` as
+	an Elpi coercion from `S.type` to `T` and `S.pack` as an Elpi coercion from
+	`T` to `S.type` whenever `T` is not a global type (e.g. a variable). Note
+	that `S.pack` can cast a `t : T` to `S.type` only if an instance of the
+	class `S` on `t` is found by type class inference
+- **New** Attribute `#[typeclass]` to declare the class of a
+	structure (`axioms_`) as a type class on the subject with all arguments in
+	output mode but for the subject that is in input mode.
+
 ## [1.7.0] - 2024-01-10
 
 Compatible with
diff --git a/HB/common/synthesis.elpi b/HB/common/synthesis.elpi
index c596fc5c..cef3d186 100644
--- a/HB/common/synthesis.elpi
+++ b/HB/common/synthesis.elpi
@@ -154,7 +154,7 @@ infer-coercion-tgt (w-params.cons ID Ty F) CoeClass :-
   @pi-parameter ID Ty x\ infer-coercion-tgt (F x) CoeClass.
 infer-coercion-tgt (w-params.nil _ {{ Type }} _) sortclass.
 infer-coercion-tgt (w-params.nil _ {{ _ -> _ }} _) funclass.
-infer-coercion-tgt (w-params.nil _ T _) (grefclass GR) :- coq.term->gref T GR.
+infer-coercion-tgt (w-params.nil _ T _) (grefclass GR) :- coq.term-is-gref? T GR.
 
 pred w-args.check-key i:list term, i:term, i:list (w-args A), o:prop.
 w-args.check-key _PS _T [] true :- !.
diff --git a/HB/common/utils-synterp.elpi b/HB/common/utils-synterp.elpi
index 73932c1a..82962ad8 100644
--- a/HB/common/utils-synterp.elpi
+++ b/HB/common/utils-synterp.elpi
@@ -24,6 +24,7 @@ with-attributes P :-
     att "primitive" bool,
     att "non_forgetful_inheritance" bool,
     att "hnf" bool,
+	 att "typeclass" bool,
   ] Opts, !,
   Opts => (save-docstring, P).
 
diff --git a/HB/structure.elpi b/HB/structure.elpi
index be549496..e730c787 100644
--- a/HB/structure.elpi
+++ b/HB/structure.elpi
@@ -105,10 +105,14 @@ declare Module BSkel Sort :- std.do! [
   %]),
 
   if-verbose (coq.say {header} "making coercion from type to target"),
-  synthesis.infer-coercion-tgt MLwP CoeClass,
-  if-arg-sort (private.declare-sort-coercion CoeClass Structure
-    (global (const ArgSortCst))),
-  private.declare-sort-coercion CoeClass Structure SortProjection,
+  if (synthesis.infer-coercion-tgt MLwP CoeClass)
+    (if-arg-sort (private.declare-sort-coercion CoeClass Structure
+      (global (const ArgSortCst))),
+    private.declare-sort-coercion CoeClass Structure SortProjection)
+    (if-arg-sort (private.declare-sort-coercion-elpi (global Structure) (global (const ArgSortCst))),
+    private.declare-sort-coercion-elpi (global Structure) SortProjection),
+
+  private.declare-reverse-coercion-elpi Structure,
 
   if-verbose (coq.say {header} "exporting unification hints"),
   ClassAlias => Factories => GRDepsClauses =>
@@ -123,6 +127,11 @@ declare Module BSkel Sort :- std.do! [
     ])
     (coq.say "declare:" ClassName "should be an inductive", fail),
 
+  if (get-option "typeclass" tt) (
+	 coq.TC.declare-class ClassName,
+	 coq.hints.add-mode ClassName "typeclass_instances" {std.append {std.map {std.iota {w-params.nparams MLwP}} (_\ r\ r = mode-output)} [mode-input]})
+	 (true),
+
   if-verbose (coq.say {header} "accumulating various props"),
   std.flatten [
       Factories, [ClassAlias], [is-structure Structure],
@@ -137,24 +146,26 @@ declare Module BSkel Sort :- std.do! [
 
   log.coq.env.import-module "Exports" Exports,
 
-  if-verbose (coq.say {header} "declaring on_ abbreviation"),
+  if (var CoeClass)
+    (if-verbose (coq.say {header} "could not declare the `on_`, `copy` and `on` abbreviations because the target of sort is not a coercion class"))
+    (if-verbose (coq.say {header} "declaring on_ abbreviation"),
 
-  private.mk-infer-key CoeClass ClassProjection NilwP (global Structure) PhClass,
+		private.mk-infer-key CoeClass ClassProjection NilwP (global Structure) PhClass,
 
-  phant.add-abbreviation "on_" PhClass _ ClassOfAbbrev,
-  (pi c\ coq.notation.abbreviation ClassOfAbbrev [c] (ClassOfAbbrev_ c)),
+		phant.add-abbreviation "on_" PhClass _ ClassOfAbbrev,
+		(pi c\ coq.notation.abbreviation ClassOfAbbrev [c] (ClassOfAbbrev_ c)),
 
-  if-verbose (coq.say {header} "declaring `copy` abbreviation"),
+		if-verbose (coq.say {header} "declaring `copy` abbreviation"),
 
-  coq.mk-app (global ClassName) {params->holes NilwP} AppClassHoles,
-  @global! => log.coq.notation.add-abbreviation "copy" 2
-    {{fun T C => (lp:(ClassOfAbbrev_ C) : (lp:AppClassHoles T)) }} tt _,
+		coq.mk-app (global ClassName) {params->holes NilwP} AppClassHoles,
+		@global! => log.coq.notation.add-abbreviation "copy" 2
+			{{fun T C => (lp:(ClassOfAbbrev_ C) : (lp:AppClassHoles T)) }} tt _,
 
-  if-verbose (coq.say {header} "declaring on abbreviation"),
+		if-verbose (coq.say {header} "declaring on abbreviation"),
 
-  @global! => log.coq.notation.add-abbreviation "on" 1
-    {{fun T => (lp:{{ ClassOfAbbrev_ {{_}} }} : (lp:AppClassHoles T)) }} tt
-    _OnAbbrev,
+		@global! => log.coq.notation.add-abbreviation "on" 1
+			{{fun T => (lp:{{ ClassOfAbbrev_ {{_}} }} : (lp:AppClassHoles T)) }} tt
+			_OnAbbrev),
 
   log.coq.env.end-module-name Module ModulePath,
 
@@ -276,6 +287,47 @@ export-operations Structure ProjSort ProjClass MLwP EX1 EX2 MLToExport :- std.do
   std.map LMwPToExport w-params_1 MLToExport,
 ].
 
+pred mk-sort-coercion-aux i:term, i:term, i:term, i:list term, o:prop.
+mk-sort-coercion-aux (prod _N _T Body) Structure P Args Clause :-
+  Clause = (pi x\ C x),
+  pi x\ mk-sort-coercion-aux (Body x) Structure P [x | Args] (C x).
+
+mk-sort-coercion-aux _ Structure P Args Clause :-
+  std.rev Args ArgsRev,
+  Clause =
+    (pi ctx v t e r argsAll w\ (coercion ctx v (app [Structure | ArgsRev]) e r :-
+		coq.say "try sort coercion",
+      std.append ArgsRev [v] argsAll,
+      coq.mk-app P argsAll w,
+		coq.say "find coercion from sort",
+      coq.elaborate-skeleton w e r ok,
+      coq.ltac.collect-goals r [] [],
+		coq.say "sort coercion succeeds")).
+
+pred mk-sort-coercion i:term, i:term, o:prop.
+mk-sort-coercion Structure P Clause :-
+  std.assert-ok! (coq.typecheck Structure T) "anomaly: mk-sort-coercion",
+  mk-sort-coercion-aux T Structure P [] Clause.
+
+pred mk-reverse-coercion-aux i:term, i:term, i:term, i:list term, o:prop.
+mk-reverse-coercion-aux (prod _N _T Body) Structure G Args (pi x\ C x) :-
+  pi x\ mk-reverse-coercion-aux (Body x) Structure G [x | Args] (C x).
+
+mk-reverse-coercion-aux _ Structure G Args Clause :-
+  std.rev Args ArgsRev,
+  Clause =
+    (pi ctx v t e r c argsAll w\ (coercion ctx v t (app [Structure | ArgsRev]) r :-
+      std.append ArgsRev [v, c] argsAll,
+      coq.mk-app G argsAll w,
+      coq.elaborate-skeleton w e r ok,
+      coq.ltac.collect-goals r [] [])).
+
+pred mk-reverse-coercion i:gref, o:prop.
+mk-reverse-coercion Structure Clause :-
+  coq.env.typeof Structure T,
+  get-constructor Structure G,
+  mk-reverse-coercion-aux T (global Structure) (global G) [] Clause.
+
 pred mk-coe-class-body
   i:factoryname, % From class
   i:factoryname, % To class
@@ -428,18 +480,23 @@ declare-unification-hints SortProj ClassProj CurrentClass NewJoins :- std.do! [
 
 % For each mixin we declare a field and apply the mixin to its dependencies
 % (that are previously declared fields recorded via field-for-mixin)
-pred synthesize-fields i:term, i:list (w-args mixinname), o:record-decl.
-synthesize-fields _T []     end-record.
-synthesize-fields T  [triple M Args _|ML] (field _ Name MTy Fields) :- std.do! [
+% Keeps track of whether every field is in Prop
+pred synthesize-fields i:term, i:list (w-args mixinname), o:record-decl, o:bool.
+synthesize-fields _T []     end-record tt.
+synthesize-fields T  [triple M Args V|ML] (field _ Name MTy Fields) B :- std.do! [
+  if (coq.typecheck {mk-app (global M) {std.append Args [V]} } {{ Prop }} ok)
+    (B = B2)
+    (B = ff),
   Name is {gref->modname M 2 "_"} ^ "_mixin",
   if-verbose (coq.say {header} "typing class field" M),
   std.assert! (synthesis.infer-all-gref-deps Args T M MTy) "anomaly: a field type cannot be solved",
-  @pi-decl `m` MTy m\ mixin-src T M m => synthesize-fields T ML (Fields m)
+  @pi-decl `m` MTy m\ mixin-src T M m => synthesize-fields T ML (Fields m) B2
 ].
 
 pred synthesize-fields.body i:list term, i:term, i:list (w-args mixinname), o:indt-decl.
-synthesize-fields.body _Params T ML (record "axioms_" {{ Type }} "Class" FS) :-
-  synthesize-fields T ML FS.
+synthesize-fields.body _Params T ML (record "axioms_" Ty "Class" FS) :-
+  synthesize-fields T ML FS B,
+  if (B = tt) (Ty = {{ Prop }}) (Ty = {{ Type }}).
 
 pred mk-record+sort-field i:sort, i:name, i:term, i:(term -> record-decl), o:indt-decl.
 pred mk-record+sort-field i:universe, i:name, i:term, i:(term -> record-decl), o:indt-decl.
@@ -495,6 +552,27 @@ declare-sort-coercion CoeClass StructureName (global Proj) :-
 
   log.coq.coercion.declare (coercion Proj 0 StructureName CoeClass).
 
+% Declares "sort" as a Coercion in elpi's coercion db Proj : Structurename >-> CoeClass.
+pred declare-sort-coercion-elpi i:term, i:term.
+declare-sort-coercion-elpi Structure Proj :-
+
+  if-verbose (coq.say {header} "declare sort coercion in elpi"),
+
+  %TODO: log.coq.coercion-elpi.declare 
+  mk-sort-coercion Structure Proj Clause,
+  coq.elpi.accumulate _ "coercion.db" (clause _ _ Clause).
+
+% Declares a reverse coercion for the sort projection in elpi's coercion db
+pred declare-reverse-coercion-elpi i:gref.
+declare-reverse-coercion-elpi Structure :-
+
+  if-verbose (coq.say {header} "declare reverse coercion in elpi"),
+
+  %TODO: log.coq.coercion-elpi.declare 
+  mk-reverse-coercion Structure Clause,
+  coq.elpi.accumulate _ "coercion.db" (clause _ _ Clause).
+
+
 pred if-class-already-exists-error i:id, i:list class, i:list mixinname.
 if-class-already-exists-error _ [] _.
 if-class-already-exists-error N [class _ S ML1wP|CS] ML2 :-
diff --git a/_CoqProject.test-suite b/_CoqProject.test-suite
index f59e999a..a7eea476 100644
--- a/_CoqProject.test-suite
+++ b/_CoqProject.test-suite
@@ -96,8 +96,9 @@ tests/unit/struct.v
 tests/factory_when_notation.v
 
 tests/saturate_on.v
+tests/coercion.v
 
 -R tests HB.tests
 -R examples HB.examples
 
--Q . HB
\ No newline at end of file
+-Q . HB
diff --git a/structures.v b/structures.v
index 5a8a81e0..24f54271 100644
--- a/structures.v
+++ b/structures.v
@@ -16,6 +16,7 @@ Definition ignore_disabled {T T'} (x : T) (x' : T') := x'.
 
 (* ********************* structures ****************************** *)
 From elpi Require Import elpi.
+From elpi.apps Require Import coercion.
 
 Register unify as hb.unify.
 Register id_phant as hb.id.
@@ -618,6 +619,7 @@ HB.structure Definition StructureName params :=
 *)
 
 #[arguments(raw)] Elpi Command HB.structure.
+Elpi Accumulate Db coercion.db.
 Elpi Accumulate Db hb.db.
 Elpi Accumulate File "HB/common/stdpp.elpi".
 Elpi Accumulate File "HB/common/database.elpi".
diff --git a/tests/coercion.v b/tests/coercion.v
new file mode 100644
index 00000000..6eaf1e87
--- /dev/null
+++ b/tests/coercion.v
@@ -0,0 +1,65 @@
+From Coq Require Import ssreflect.
+From HB Require Import structures.
+
+HB.mixin Record isSigma (T : Type) (P : T -> Prop) (x : T) := {
+  _ : P x
+}.
+
+#[short(type="sigType"), typeclass]
+HB.structure Definition Sig (T : Type) (P : T -> Prop) := {x of isSigma T P x}.
+
+Section Sigma.
+
+Check fun (T : Type) (P : T -> Prop) (x : sigType T P) => x : T.
+Check fun (T : Type) (P : T -> Prop) (x : T) (Px : Sig T P x) => x : sigType T P.
+Fail Check fun (T : Type) (P : T -> Prop) (x : T) => x : sigType T P.
+
+Axioms (A B B' C : Type) (AtoB : A -> B) (BtoB' : B -> B').
+Axioms (P : A -> Prop) (CtoAP : C -> sigType A P). 
+Coercion AtoB : A >-> B.
+Coercion BtoB' : B >-> B'.
+(* does postcompose automatically with Coq coercions*) 
+Check fun (x : sigType A P) => x : B.
+Check fun (x : sigType A P) => x : B'.
+
+(* testing a Coq coercion to sigType *)
+Coercion CtoAP : C >-> sigType.
+Check fun (x : C) => x : sigType A P.
+
+(* does not precompose automatically with Coq coercions *)
+Fail Check fun (x : C) => x : A.
+Check fun (x : C) => (x : sigType A P) : A.
+Check fun (x : C) => (x : sigType A P) : B.
+
+Axioms (x : A) (Px : Sig A P x).
+
+(* should not work indeed *)
+Fail Check (x : sigType A P).
+
+(* this works though ...*)
+Succeed Check (let Px' := Px in x : sigType A P).
+
+HB.instance Definition _ := Px.
+Fail Check x : sigType A P.
+
+End Sigma.
+
+HB.mixin Record isSigmaT (P : Type -> Prop) (x : Type) := { _ : P x }.
+#[short(type="sigTType"), typeclass]
+HB.structure Definition SigT (P : Type -> Prop) := {x of isSigmaT P x}.
+
+Section SigmaT.
+
+Axioms (X : Type) (PT : Type -> Prop) (PX : SigT PT X).
+
+(* should not work indeed *)
+Fail Check (X : sigTType PT).
+
+(* this works though now ... cf my next point*)
+Succeed Check (let PX' := PX in X : sigTType PT).
+
+(* Now this works *)
+HB.instance Definition _ := PX.
+Succeed Check X : sigTType PT.
+
+End SigmaT.