Simplify abstract type structuring

proof.py

@@ -15,6 +15,16 @@ class App(Term):
     f : Term
     x : Term
 
+A0 = lambda fn : Const(fn)
+A1 = lambda fn, a : App(f=A0(fn), x=a)
+A2 = lambda fn, a, b : App(f=A1(fn, a), x=b)
+A3 = lambda fn, a, b, c : App(f=A2(fn, a, b), x=c)
+A4 = lambda fn, a, b, c, d : App(f=A3(fn, a, b, c), x=d)
+A5 = lambda fn, a, b, c, d, e : App(f=A4(fn, a, b, c, d), x=e)
+A6 = lambda fn, a, b, c, d, e, f : App(f=A5(fn, a, b, c, d, e), x=f)
+A7 = lambda fn, a, b, c, d, e, f, g : App(f=A6(fn, a, b, c, d, e, f), x=g)
+A8 = lambda fn, a, b, c, d, e, f, g, h : App(f=A7(fn, a, b, c, d, e, f, g), x=h)
+
 @dataclass(frozen=True)
 class Const(Term):
     name : str
@@ -22,18 +32,26 @@ class Const(Term):
 # --- Bool constructors ---
 
 def Truth() -> Term:
-    return Const("Bool.Truth")
+    return A0("Bool.Truth")
 
 def Contradiction() -> Term:
-    return Const("Bool.Contradiction")
+    return A0("Bool.Contradiction")
+
+# --- List constructors ---
+
+def Nil() -> Term:
+    return A0("List.Nil")
+
+def Cons(head : Term, tail : Term) -> Term:
+    return A2("List.Cons", head, tail)
 
 # --- Nat constructors ---
 
 def Zero() -> Term:
-    return Const("Nat.Zero")
+    return A0("Nat.Zero")
 
 def Succ(n : Term) -> Term:
-    return App(Const("Nat.Succ"), n)
+    return A1("Nat.Succ", n)
 
 def kernel_from_int(n : int) -> Term:
     if n == 0:
@@ -174,7 +192,7 @@ if __name__ == "__main__":
     # 2 + 3 == 5
     print(check(
         Eq(
-            lhs=App(f=App(f=Const("Nat.add"), x=kernel_from_int(2)), x=kernel_from_int(3)),
+            lhs=A2("Nat.add", kernel_from_int(2), kernel_from_int(3)),
             rhs=kernel_from_int(5),
         ),
         Refl(),
@@ -183,7 +201,7 @@ if __name__ == "__main__":
     # 0 + x == x
     print(check(
         Eq(
-            lhs=App(f=App(f=Const("Nat.add"), x=Zero()), x=Const("x")),
+            lhs=A2("Nat.add", Zero(), Const("x")),
             rhs=Const("x")
         ),
         Refl(),
@@ -192,7 +210,7 @@ if __name__ == "__main__":
     # x + 0 == x
     print(check(
         Eq(
-            lhs=App(f=App(f=Const("Nat.add"), x=Const("x")), x=Zero()),
+            lhs=A2("Nat.add", Const("x"), Zero()),
             rhs=Const("x")
         ),
         Refl(),