Require Import List.
Import ListNotations.

Fixpoint hlist (l:list Type):Type :=
  match l with
  | [] => unit
  | t::ts => t * (hlist ts)
  end.

Definition hd {t:Type} {ts:list Type}
    (l:hlist (t::ts)) : t := fst l.
Definition tl {t:Type} {ts:list Type}
    (l:hlist (t::ts)) : hlist ts := snd l.

Definition hnil : hlist [] := tt.

Definition hcons {t:Type} {ts:list Type} (a:t)
  : hlist ts -> hlist (t::ts) :=
  match ts with
  | [] => fun _ => (a, tt)
  | (x::xs) => fun hl => (a, hl)
  end.

Fixpoint append {ts1 ts2:list Type} :
    hlist ts1 -> hlist ts2 -> hlist (ts1 ++ ts2) :=
  match ts1 with
  | [] => fun _ => fun hl2 => hl2
  | t::ts => fun hl1 => fun hl2 =>
      (*hcons (hd hl1) (append (tl hl1) hl2)*)
      (hd hl1, append (tl hl1) hl2)
  end.

Example foo0 : hlist [nat:Type] := (2,tt).
Compute hcons 3 foo0.
(*
     = (3, (2, tt))
     : hlist [nat; nat : Type]
*)

Compute hcons true (hcons 3 foo0).
(*
     = (true, (3, (2, tt)))
     : hlist [bool; nat; nat : Type]
*)

Example foo1 : hlist [nat:Type; bool:Type] := (2,(true,tt)).
Compute append foo1 foo0.
(*
     = (2, (true, (2, tt)))
     : hlist ([nat : Type; bool : Type] ++ [nat : Type])
*)

Compute append foo1 (hcons 3 foo0).
(*
     = (2, (true, (3, (2, tt))))
     : hlist ([nat : Type; bool : Type] ++ [nat; nat : Type])
*)