check impossible clauses

Also clean up some comments.

We now have types in constraints, but are still using values from
context.

tests/Problem.newt

@@ -0,0 +1,48 @@
+module Problem
+
+-- partial finished translation of "A correct-by-construction conversion from lambda calculus to combinatory logic", by Wouter Swierstra
+-- added as a test of impossible clauses (in `lookup` below)
+-- prj/menagerie/papers/combinatory
+
+data Unit : U where
+  MkUnit : Unit
+
+infixr 7 _::_
+data List : U → U where
+  Nil : {A : U} → List A
+  _::_ : {A : U} → A → List A → List A
+
+infixr 6 _~>_
+data Type : U where
+  ι : Type
+  _~>_ : Type → Type → Type
+
+A : U
+A = Unit
+
+Val : Type → U
+Val ι = A
+Val (x ~> y) = Val x → Val y
+
+Ctx : U
+Ctx = List Type
+
+data Ref : Type → Ctx → U where
+  Z : {σ : Type} {Γ : Ctx} → Ref σ (σ :: Γ)
+  S : {σ τ : Type} {Γ : Ctx} → Ref σ Γ → Ref σ (τ :: Γ)
+
+data Term : Ctx → Type → U where
+  App : {Γ : Ctx} {σ τ : Type} → Term Γ (σ ~> τ) → Term Γ σ → Term Γ τ
+  Lam : {Γ : Ctx} {σ τ : Type} → Term (σ :: Γ) τ → Term Γ (σ ~> τ)
+  Var : {Γ : Ctx} {σ : Type} → Ref σ Γ → Term Γ σ
+
+infixr 7 _:::_
+data Env : Ctx → U where
+  ENil : Env Nil
+  _:::_ : {Γ : Ctx} {σ : Type} → Val σ → Env Γ → Env (σ :: Γ)
+
+-- due to the order that we match constructors, we need the impossible clause here
+lookup : {σ : Type} {Γ : Ctx} → Ref σ Γ → Env Γ → Val σ
+lookup Z (x ::: y) = x
+lookup () ENil
+lookup (S i) (x ::: env) = lookup i env