feat(frontends/lean): default for inductive types, closes #32

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/frontends/lean/inductive_cmd.cpp

@@ -136,10 +136,16 @@ struct inductive_cmd_fn {
         expr type;
         buffer<expr> ps;
         m_pos = m_p.pos();
-        if (!m_p.curr_is_token(g_colon)) {
+        if (m_p.curr_is_token(g_assign)) {
+            type = mk_sort(mk_level_placeholder());
+        } else if (!m_p.curr_is_token(g_colon)) {
             m_p.parse_binders(ps);
-            m_p.check_token_next(g_colon, "invalid inductive declaration, ':' expected");
-            type = m_p.parse_scoped_expr(ps);
+            if (m_p.curr_is_token(g_colon)) {
+                m_p.next();
+                type = m_p.parse_scoped_expr(ps);
+            } else {
+                type = mk_sort(mk_level_placeholder());
+            }
             type = Pi(ps, type, m_p);
         } else {
             m_p.next();

tests/lean/run/indimp.lean

@@ -0,0 +1,21 @@
+abbreviation Prop := Type.{0}
+
+inductive nat :=
+| zero : nat
+| succ : nat → nat
+
+inductive list (A : Type) :=
+| nil {} : list A
+| cons   : A → list A → list A
+
+inductive list2 (A : Type) : Type :=
+| nil2 {} : list2 A
+| cons2   : A → list2 A → list2 A
+
+inductive and (A B : Prop) : Prop :=
+| and_intro : A → B → and A B
+
+inductive class {T1 : Type} (R1 : T1 → T1 → Prop) {T2 : Type} (R2 : T2 → T2 → Prop) (f : T1 → T2) :=
+| mk : (∀x y : T1, R1 x y → R2 (f x) (f y)) → class R1 R2 f
+
+