diff --git a/src/parser/ast_term.ml b/src/parser/ast_term.ml
index 615fc572..63e40f05 100644
--- a/src/parser/ast_term.ml
+++ b/src/parser/ast_term.ml
@@ -15,11 +15,15 @@ and term_view =
   | Int of string
   | App of term * term list
   | Let of let_binding list * term
-  | Lambda of var list * term
-  | Pi of var list * term
+  | Lambda of ty_var_group list * term
+  | Pi of ty_var_group list * term
   | Arrow of term list * term
   | Error_node of string
 
+and ty_var_group =
+  | VG_untyped of string
+  | VG_typed of { names: string list; ty: term }
+
 and let_binding = var * term
 
 and var = { name: string; ty: term option }
@@ -30,7 +34,12 @@ type decl = decl_view with_loc
 
 (* TODO: axiom *)
 and decl_view =
-  | D_def of { name: string; args: var list; ty_ret: term option; rhs: term }
+  | D_def of {
+      name: string;
+      args: ty_var_group list;
+      ty_ret: term option;
+      rhs: term;
+    }
   | D_hash of string * term
   | D_theorem of { name: string; goal: term; proof: proof }
 
@@ -131,19 +140,34 @@ let rec pp_term out (e : term) : unit =
     let ppb out ((x, t) : let_binding) =
       Fmt.fprintf out "@[<2>%s :=@ %a@]" x.name pp t
     in
-    Fmt.fprintf out "@[@[<2>let@ @[<hv>%a@]@] in@ %a@]"
-      (Util.pp_list ~sep:" and " ppb)
-      bs pp bod
+    let ppbs out l =
+      List.iteri
+        (fun i x ->
+          if i > 0 then Fmt.fprintf out "@ and ";
+          ppb out x)
+        l
+    in
+    Fmt.fprintf out "@[@[<hv>let %a@] in@ %a@]" ppbs bs pp bod
   | Lambda (args, bod) ->
-    Fmt.fprintf out "@[lam %a.@ %a@]" (Util.pp_list pp_tyvar) args pp_sub bod
+    Fmt.fprintf out "@[lam%a.@ %a@]"
+      (Util.pp_list ~sep:"" pp_ty_var_group)
+      args pp_sub bod
   | Pi (args, bod) ->
-    Fmt.fprintf out "@[pi %a.@ %a@]" (Util.pp_list pp_tyvar) args pp_sub bod
+    Fmt.fprintf out "@[pi%a.@ %a@]"
+      (Util.pp_list ~sep:"" pp_ty_var_group)
+      args pp_sub bod
 
 and pp_tyvar out (x : var) : unit =
   match x.ty with
   | None -> Fmt.string out x.name
   | Some ty -> Fmt.fprintf out "(@[%s : %a@])" x.name pp_term ty
 
+and pp_ty_var_group out (x : ty_var_group) : unit =
+  match x with
+  | VG_untyped x -> Fmt.fprintf out "@ %s" x
+  | VG_typed { names; ty } ->
+    Fmt.fprintf out "@ (@[%a : %a@])" (Util.pp_list Fmt.string) names pp_term ty
+
 let rec pp_proof out (p : proof) : unit =
   match p.view with
   | P_by t -> Fmt.fprintf out "@[by@ %a@]" pp_term t
@@ -166,7 +190,8 @@ let pp_decl out (d : decl) =
       | None -> ()
       | Some ty -> Fmt.fprintf out " @[: %a@]" pp_term ty
     in
-    Fmt.fprintf out "@[<2>def %s%a%a :=@ %a@];" name (Util.pp_list pp_tyvar)
+    Fmt.fprintf out "@[<2>def %s%a%a :=@ %a@];" name
+      (Util.pp_list ~sep:"" pp_ty_var_group)
       args pp_tyret () pp_term rhs
   | D_hash (name, t) -> Fmt.fprintf out "@[<2>#%s@ %a@];" name pp_term t
   | D_theorem { name; goal; proof } ->
diff --git a/src/parser/lex.mll b/src/parser/lex.mll
index 34994989..be33a831 100644
--- a/src/parser/lex.mll
+++ b/src/parser/lex.mll
@@ -32,6 +32,7 @@ rule token = parse
 | "let" { LET }
 | "in" { IN }
 | "and" { AND }
+| "def" { DEF }
 | "have" { HAVE }
 | "theorem" { THEOREM }
 | "by" { BY }
diff --git a/src/parser/parse.mly b/src/parser/parse.mly
index 8b7c382c..0e44316d 100644
--- a/src/parser/parse.mly
+++ b/src/parser/parse.mly
@@ -53,11 +53,11 @@ top_term: t=term EOF { t }
 decl:
 | h=HASH t=term SEMICOLON {
   let loc = Loc.of_lexloc $loc in
+  let h = String.sub h 1 (String.length h-1) in
   A.decl_hash ~loc h t
 }
-| DEF name=name args=tyvars* ty_ret=optional_ty EQDEF rhs=term SEMICOLON {
+| DEF name=name args=ty_var_group* ty_ret=optional_ty EQDEF rhs=term SEMICOLON {
   let loc = Loc.of_lexloc $loc in
-  let args = List.flatten args in
   A.decl_def ~loc name args ?ty_ret rhs
 }
 | THEOREM name=name EQDEF goal=term proof=proof SEMICOLON {
@@ -88,10 +88,10 @@ proof_step:
 tyvar:
 | name=name ty=optional_ty { A.var ?ty name }
 
-tyvars:
-| name=name { [A.var name] }
+ty_var_group:
+| name=name { A.VG_untyped name }
 | LPAREN names=name+ COLON ty=term RPAREN {
-  List.map (fun name -> A.var ~ty name) names
+  A.VG_typed {names; ty}
 }
 
 %inline optional_ty:
@@ -114,14 +114,12 @@ let_bindings:
 
 binder_term:
 | t=sym_term { t }
-| FUNCTION vars=tyvars+ DOT rhs=binder_term {
+| FUNCTION vars=ty_var_group+ DOT rhs=binder_term {
   let loc = Loc.of_lexloc $loc in
-  let vars = List.flatten vars in
   A.mk_lam ~loc vars rhs
 }
-| PI vars=tyvars+ DOT rhs=binder_term {
+| PI vars=ty_var_group+ DOT rhs=binder_term {
   let loc = Loc.of_lexloc $loc in
-  let vars = List.flatten vars in
   A.mk_pi ~loc vars rhs
 }
 
diff --git a/unittest/parser/p1.expected b/unittest/parser/p1.expected
index e3305f97..259ab264 100644
--- a/unittest/parser/p1.expected
+++ b/unittest/parser/p1.expected
@@ -3,11 +3,13 @@ loc(t1): at line 1, column 0 - at line 1, column 9
 t2: let x := 1 in f (f x 2)
 loc(t2): at line 1, column 0 - at line 1, column 22
 t3: let l := map f (list 1 2 3) in let l2 := rev l in = (rev l2) l
-loc(t3): at line 1, column 1 - at line 1, column 61
+loc(t3): at line 1, column 0 - at line 1, column 60
 t4: let assm := ==> (is_foo p) (= (filter p l) nil) in true
 loc(t4): at line 1, column 0 - at line 1, column 51
-t5: let
-      f := lam (x : int) (y : int) (z : bool). (= (+ x y) z) and 
-      g := lam x. (f (f x)) in
-    is_g g
+t5: let f := lam (x y : int) (z : bool). (= (+ x y) z)
+    and g := lam x. (f (f x)) in is_g g
 loc(t5): at line 1, column 0 - at line 1, column 84
+d1:
+  def f (x y : list int) : list int := if (= x 0) y whatever;
+  #ty f;
+  #sledgehammer lam x y. (= (f x y) (f x y));
diff --git a/unittest/parser/p1.ml b/unittest/parser/p1.ml
index 6494c9ec..c10ce7fb 100644
--- a/unittest/parser/p1.ml
+++ b/unittest/parser/p1.ml
@@ -4,14 +4,13 @@ module A = Ast_term
 (*
 let () = Printexc.record_backtrace true
 *)
-let () = Printexc.record_backtrace true
 
 let () =
   Printexc.register_printer (function
     | P.Exn_parse_error e -> Some (P.Error.to_string e)
     | _ -> None)
 
-let test_str what s =
+let test_term_str what s =
   let t = P.term_of_string s in
   match t with
   | Ok t ->
@@ -20,22 +19,33 @@ let test_str what s =
   | Error err ->
     Fmt.printf "FAIL:@ error while parsing %S:@ %a@." what P.Error.pp err
 
-let () = test_str "t1" "f (g x) y"
-let () = test_str "t2" "let x:= 1 in f (f x 2)"
+let () = test_term_str "t1" "f (g x) y"
+let () = test_term_str "t2" "let x:= 1 in f (f x 2)"
 
 let () =
-  test_str "t3"
-    {|
-let l := map f (list 1 2 3) in
-let l2 := rev l in rev l2 = l
-    |}
+  test_term_str "t3"
+    {|let l := map f (list 1 2 3) in
+let l2 := rev l in rev l2 = l|}
 
 let () =
-  test_str "t4" {|let assm := is_foo p ==> (filter p l = nil) in true
-    |}
+  test_term_str "t4" {|let assm := is_foo p ==> (filter p l = nil) in true|}
 
 let () =
-  test_str "t5"
+  test_term_str "t5"
     {|let f := fn (x y : int) (z:bool). ( x+ y) = z
-      and g := fn x. f (f x) in is_g g
-    |}
+      and g := fn x. f (f x) in is_g g|}
+
+let test_decl what s =
+  let t = P.decls_of_string s in
+  match t with
+  | Ok l ->
+    Fmt.printf "@[<v2>%s:@ %a@]@." what (Util.pp_list ~sep:"" A.pp_decl) l
+  | Error err ->
+    Fmt.printf "FAIL:@ error while parsing %S:@ %a@." what P.Error.pp err
+
+let () =
+  test_decl "d1"
+    {|def f (x y:list int) : list int := if (x = 0) y whatever;
+    #ty f;
+    #sledgehammer fn x y. f x y = f x y;
+  |}