diff --git a/compiler/dcalc/typing.ml b/compiler/dcalc/typing.ml
index 1b3bec0f..6d764771 100644
--- a/compiler/dcalc/typing.ml
+++ b/compiler/dcalc/typing.ml
@@ -107,7 +107,7 @@ let rec format_typ
   | TArray t1 -> Format.fprintf fmt "@[%a@ array@]" format_typ t1
   | TAny d -> Format.fprintf fmt "any[%d]" (Any.hash d)
 
-exception Type_error of A.any_marked_expr * unionfind_typ * unionfind_typ
+exception Type_error of A.any_expr * unionfind_typ * unionfind_typ
 
 type mark = { pos : Pos.t; uf : unionfind_typ }
 
diff --git a/compiler/shared_ast/definitions.ml b/compiler/shared_ast/definitions.ml
index fecff430..df91a91d 100644
--- a/compiler/shared_ast/definitions.ml
+++ b/compiler/shared_ast/definitions.ml
@@ -148,8 +148,6 @@ type scopelang = [ `Scopelang ]
 type dcalc = [ `Dcalc ]
 type lcalc = [ `Lcalc ]
 
-(* type scalc = [ `Scalc ] *)
-
 type 'a any = [< desugared | scopelang | dcalc | lcalc ] as 'a
 
 (** Literals are the same throughout compilation except for the [LEmptyError]
@@ -194,16 +192,15 @@ and ('a, 't) naked_gexpr =
   | EApp : ('a, 't) gexpr * ('a, 't) gexpr list -> ('a any, 't) naked_gexpr
   | EOp : operator -> ('a any, 't) naked_gexpr
   | EArray : ('a, 't) gexpr list -> ('a any, 't) naked_gexpr
-  (* All but statement calculus *)
   | EVar :
       ('a, 't) naked_gexpr Bindlib.var
-      -> (([< desugared | scopelang | dcalc | lcalc ] as 'a), 't) naked_gexpr
+      -> ('a any, 't) naked_gexpr
   | EAbs :
       (('a, 't) naked_gexpr, ('a, 't) gexpr) Bindlib.mbinder * typ list
-      -> (([< desugared | scopelang | dcalc | lcalc ] as 'a), 't) naked_gexpr
+      -> ('a any, 't) naked_gexpr
   | EIfThenElse :
       ('a, 't) gexpr * ('a, 't) gexpr * ('a, 't) gexpr
-      -> (([< desugared | scopelang | dcalc | lcalc ] as 'a), 't) naked_gexpr
+      -> ('a any, 't) naked_gexpr
   (* Early stages *)
   | ELocation :
       'a glocation
@@ -254,16 +251,6 @@ type ('e, 'b) binder = (('a, 't) naked_gexpr, 'b) Bindlib.binder
 (** The expressions use the {{:https://lepigre.fr/ocaml-bindlib/} Bindlib}
     library, based on higher-order abstract syntax *)
 
-(* (\* Statement calculus *\)
- * | ESVar: LocalName.t -> (scalc as 'a, 't) naked_gexpr
- * | ESStruct: ('a, 't) gexpr list * StructName.t -> (scalc as 'a, 't) naked_gexpr
- * | ESStructFieldAccess: ('a, 't) gexpr * StructFieldName.t * StructName.t -> (scalc as 'a, 't) naked_gexpr
- * | ESInj: ('a, 't) gexpr * EnumConstructor.t * EnumName.t -> (scalc as 'a, 't) naked_gexpr
- * | ESFunc: TopLevelName.t -> (scalc as 'a, 't) naked_gexpr *)
-
-type 'e anyexpr = 'e constraint 'e = (_ any, _) gexpr
-(** Shorter alias for functions taking any kind of expression *)
-
 (** {2 Markings} *)
 
 type untyped = { pos : Pos.t } [@@ocaml.unboxed]
@@ -277,7 +264,7 @@ type typed = { pos : Pos.t; ty : typ }
 type _ mark = Untyped : untyped -> untyped mark | Typed : typed -> typed mark
 
 (** Useful for errors and printing, for example *)
-type any_marked_expr = AnyExpr : (_ any, _ mark) gexpr -> any_marked_expr
+type any_expr = AnyExpr : (_ any, _ mark) gexpr -> any_expr
 
 (** {2 Higher-level program structure} *)
 
@@ -308,7 +295,7 @@ type 'e scope_let = {
   scope_let_next : ('e, 'e scope_body_expr) binder;
   scope_let_pos : Pos.t;
 }
-  constraint 'e = ('a, 'm mark) gexpr
+  constraint 'e = (_ any, _ mark) gexpr
 (** This type is parametrized by the expression type so it can be reused in
     later intermediate representations. *)
 
@@ -318,14 +305,14 @@ type 'e scope_let = {
 and 'e scope_body_expr =
   | Result of 'e
   | ScopeLet of 'e scope_let
-  constraint 'e = (_, _ mark) gexpr
+  constraint 'e = (_ any, _ mark) gexpr
 
 type 'e scope_body = {
   scope_body_input_struct : StructName.t;
   scope_body_output_struct : StructName.t;
   scope_body_expr : ('e, 'e scope_body_expr) binder;
 }
-  constraint 'e = (_, _ mark) gexpr
+  constraint 'e = (_ any, _ mark) gexpr
 (** Instead of being a single expression, we give a little more ad-hoc structure
     to the scope body by decomposing it in an ordered list of let-bindings, and
     a result expression that uses the let-binded variables. The first binder is
@@ -336,14 +323,14 @@ type 'e scope_def = {
   scope_body : 'e scope_body;
   scope_next : ('e, 'e scopes) binder;
 }
-  constraint 'e = (_, _ mark) gexpr
+  constraint 'e = (_ any, _ mark) gexpr
 
 (** Finally, we do the same transformation for the whole program for the kinded
     lets. This permit us to use bindlib variables for scopes names. *)
 and 'e scopes =
   | Nil
   | ScopeDef of 'e scope_def
-  constraint 'e = (_, _ mark) gexpr
+  constraint 'e = (_ any, _ mark) gexpr
 
 type struct_ctx = (StructFieldName.t * typ) list StructMap.t
 type enum_ctx = (EnumConstructor.t * typ) list EnumMap.t
diff --git a/compiler/shared_ast/scope.mli b/compiler/shared_ast/scope.mli
index bdc22a43..54e3e10f 100644
--- a/compiler/shared_ast/scope.mli
+++ b/compiler/shared_ast/scope.mli
@@ -85,7 +85,7 @@ val format :
   ?debug:bool (** [true] for debug printing *) ->
   decl_ctx ->
   Format.formatter ->
-  ScopeName.t * 'e anyexpr scope_body ->
+  ScopeName.t * 'e scope_body ->
   unit
 
 val to_expr :
@@ -112,6 +112,6 @@ val build_typ_from_sig :
 
 (** {2 Analysis and tests} *)
 
-val free_vars_body_expr : 'e anyexpr scope_body_expr -> 'e Var.Set.t
-val free_vars_body : 'e anyexpr scope_body -> 'e Var.Set.t
-val free_vars : 'e anyexpr scopes -> 'e Var.Set.t
+val free_vars_body_expr : 'e scope_body_expr -> 'e Var.Set.t
+val free_vars_body : 'e scope_body -> 'e Var.Set.t
+val free_vars : 'e scopes -> 'e Var.Set.t