diff --git a/src/extra/DeBruijn.lagda b/src/extra/DeBruijn.lagda
deleted file mode 100644
index 60a4ad76..00000000
--- a/src/extra/DeBruijn.lagda
+++ /dev/null
@@ -1,59 +0,0 @@
-## DeBruijn encodings in Agda
-
-\begin{code}
-module DeBruijn where
-\end{code}
-
-## Imports
-
-\begin{code}
-import Relation.Binary.PropositionalEquality as Eq
-open Eq using (_≡_; refl; sym; trans; cong)
-open Eq.≡-Reasoning
-open import Data.Nat using (ℕ; zero; suc)
-open import Data.Product using (_×_; proj₁; proj₂) renaming (_,_ to ⟨_,_⟩)
-open import Data.Sum using (_⊎_; inj₁; inj₂)
-open import Relation.Nullary using (¬_)
-open import Relation.Nullary.Negation using (contraposition)
-open import Data.Unit using (⊤; tt)
-open import Data.Empty using (⊥; ⊥-elim)
-open import Function using (_∘_)
-\end{code}
-
-## Representation
-
-\begin{code}
-data Type : Set where
-  `ℕ : Type
-  _`→_ : Type → Type → Type
-
-data Env : Set where
-  ε : Env
-  _,_ : Env → Type → Env
-
-data Var : Env → Type → Set where
-  zero : ∀ {Γ : Env} {A : Type} → Var (Γ , A) A
-  suc : ∀ {Γ : Env} {A B : Type} → Var Γ B → Var (Γ , A) B
-
-data Exp : Env → Type → Set where
-  var : ∀ {Γ : Env} {A : Type} → Var Γ A → Exp Γ A
-  abs : ∀ {Γ : Env} {A B : Type} → Exp (Γ , A) B → Exp Γ (A `→ B)
-  app : ∀ {Γ : Env} {A B : Type} → Exp Γ (A `→ B) → Exp Γ A → Exp Γ B
-
-type : Type → Set
-type `ℕ = ℕ
-type (A `→ B) = type A → type B
-
-env : Env → Set
-env ε = ⊤
-env (Γ , A) = env Γ × type A
-
-lookup : ∀ {Γ : Env} {A : Type} → Var Γ A → env Γ → type A
-lookup zero ⟨ ρ , v ⟩ = v
-lookup (suc n) ⟨ ρ , v ⟩ = lookup n ρ
-
-eval : ∀ {Γ : Env} {A : Type} → Exp Γ A → env Γ → type A
-eval (var n) ρ  = lookup n ρ
-eval (abs N) ρ  = λ{ v → eval N ⟨ ρ , v ⟩ }
-eval (app L M) ρ  =  eval L ρ (eval M ρ)
-\end{code}
diff --git a/src/extra/DeBruijn2.lagda b/src/extra/DeBruijn2.lagda
new file mode 100644
index 00000000..00e44870
--- /dev/null
+++ b/src/extra/DeBruijn2.lagda
@@ -0,0 +1,75 @@
+## DeBruijn encodings in Agda
+
+\begin{code}
+module DeBruijn where
+\end{code}
+
+## Imports
+
+\begin{code}
+import Relation.Binary.PropositionalEquality as Eq
+open Eq using (_≡_; refl; sym; trans; cong)
+open Eq.≡-Reasoning
+open import Data.Nat using (ℕ; zero; suc)
+open import Data.Product using (_×_; proj₁; proj₂) renaming (_,_ to ⟨_,_⟩)
+open import Data.Sum using (_⊎_; inj₁; inj₂)
+open import Relation.Nullary using (¬_)
+open import Relation.Nullary.Negation using (contraposition)
+open import Data.Unit using (⊤; tt)
+open import Data.Empty using (⊥; ⊥-elim)
+open import Function using (_∘_)
+\end{code}
+
+## Representation
+
+\begin{code}
+infixr 4 _,_
+
+data TEnv : Set where
+  ε : TEnv
+  _,* : TEnv → TEnv
+
+data Type : TEnv → Set where
+  `ℕ : ∀ {Δ : TEnv} → Type Δ
+  _`→_ : ∀ {Δ : TEnv} → Type Δ → Type Δ → Type Δ
+  `∀ : ∀ {Δ : TEnv} → Type (Δ ,*) → Type Δ
+
+data Env : TEnv → Set where
+  ε : {Δ : TEnv} → Env Δ
+  _,_ : {Δ : TEnv} → Env Δ → Type Δ → Env Δ
+
+data TVar : TEnv → Set where
+  zero : ∀ {Δ : TEnv} → TVar (Δ ,*)
+  suc : ∀ {Δ : TEnv} → TVar Δ → TVar (Δ ,*)
+
+data Var : (Δ : TEnv) → Env Δ → Type Δ → Set where
+  zero : ∀ {Δ : TEnv} {Γ : Env Δ} {A : Type Δ} → Var Δ (Γ , A) A
+  suc : ∀ {Δ : TEnv} {Γ : Env Δ} {A B : Type Δ} → Var Δ Γ B → Var Δ (Γ , A) B
+
+sub : ∀ {Δ : TEnv} → Type (Δ ,*) → TVar (Δ ,*) → Type Δ → Type Δ
+sub = ?
+
+data Exp : (Δ : TEnv) → Env Δ → Type Δ → Set where
+  var : ∀ {Δ : TEnv} {Γ : Env Δ} {A : Type Δ} → Var Δ Γ A → Exp Δ Γ A
+  abs : ∀ {Δ : TEnv} {Γ : Env Δ} {A B : Type Δ} → Exp Δ (Γ , A) B → Exp Δ Γ (A `→ B)
+  app : ∀ {Δ : TEnv} {Γ : Env Δ} {A B : Type Δ} → Exp Δ Γ (A `→ B) → Exp Δ Γ A → Exp Δ Γ B
+  tabs : ∀ {Δ : TEnv} {Γ : Env Δ} {B : Type Δ} → Exp (Δ ,*) Γ B → Exp Δ Γ (`∀ B)
+  tapp : ∀ {Δ : TEnv} {Γ : Env Δ} {B : Type Δ} → Exp Δ Γ (`∀ B) → (A : Type Δ) → Exp Δ Γ (sub B zero A)
+
+type : Type → Set
+type `ℕ = ℕ
+type (A `→ B) = type A → type B
+
+env : Env → Set
+env ε = ⊤
+env (Γ , A) = env Γ × type A
+
+lookup : ∀ {Γ : Env} {A : Type} → Var Γ A → env Γ → type A
+lookup zero ⟨ ρ , v ⟩ = v
+lookup (suc n) ⟨ ρ , v ⟩ = lookup n ρ
+
+eval : ∀ {Γ : Env} {A : Type} → Exp Γ A → env Γ → type A
+eval (var n) ρ  = lookup n ρ
+eval (abs N) ρ  = λ{ v → eval N ⟨ ρ , v ⟩ }
+eval (app L M) ρ  =  eval L ρ (eval M ρ)
+\end{code}