Start working on exercise sheet 4

theories/type_systems/systemf/exercises04.v

@@ -14,17 +14,26 @@ Module dbterm.
   .
 
   (** Formalize substitutions and renamings as functions. *)
-  Definition subt := nat → expr.
+  Definition sub_t := nat → expr.
-  Definition rent := nat → nat.
+  Definition ren_t := nat → nat.
 
   Implicit Types
-    (σ : subt)
+    (σ : sub_t)
-    (δ : rent)
+    (δ : ren_t)
     (n x : nat)
     (e : expr).
 
   Fixpoint subst σ e :=
-    (* FIXME *) e.
+    match e with
+    | Lit l => Lit l
+    | Var i => σ i
+    | Lam e => Lam (subst (λ n, match n with
+      | 0 => Var 0
+      | S n => σ n
+    ))
+    | Plus e1 e2 => Plus (subst σ a) (subst σ b)
+    | App e_fn e_arg =>
+    end.