refactor(library): add type_util module, and move get_expect_num_args to it

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

src/library/CMakeLists.txt

@@ -8,6 +8,6 @@ add_library(library deep_copy.cpp expr_lt.cpp io_state.cpp occurs.cpp
   unifier.cpp unifier_plugin.cpp inductive_unifier_plugin.cpp
   explicit.cpp num.cpp string.cpp opaque_hints.cpp head_map.cpp
   match.cpp definition_cache.cpp declaration_index.cpp
-  print.cpp annotation.cpp typed_expr.cpp let.cpp)
+  print.cpp annotation.cpp typed_expr.cpp let.cpp type_util.cpp)
 
 target_link_libraries(library ${LEAN_LIBS})

src/library/tactic/apply_tactic.cpp

@@ -16,6 +16,7 @@ Author: Leonardo de Moura
 #include "library/kernel_bindings.h"
 #include "library/unifier.h"
 #include "library/occurs.h"
+#include "library/type_util.h"
 #include "library/tactic/apply_tactic.h"
 
 namespace lean {
@@ -41,17 +42,6 @@ bool collect_simple_metas(expr const & e, buffer<expr> & result) {
     return !failed;
 }
 
-unsigned get_expect_num_args(type_checker & tc, expr e) {
-    unsigned r = 0;
-    while (true) {
-        e = tc.whnf(e).first;
-        if (!is_pi(e))
-            return r;
-        e = binding_body(e);
-        r++;
-    }
-}
-
 void collect_simple_meta(expr const & e, buffer<expr> & metas) {
     for_each(e, [&](expr const & e, unsigned) {
             if (is_meta(e)) {

src/library/type_util.cpp

@@ -0,0 +1,24 @@
+/*
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include "kernel/instantiate.h"
+#include "library/type_util.h"
+
+namespace lean {
+unsigned get_expect_num_args(type_checker & tc, expr e) {
+    name_generator ngen = tc.mk_ngen();
+    unsigned r = 0;
+    while (true) {
+        e = tc.whnf(e).first;
+        if (!is_pi(e))
+            return r;
+        // TODO(Leo): try to avoid the following instantiate.
+        expr local = mk_local(ngen.next(), binding_name(e), binding_domain(e), binding_info(e));
+        e = instantiate(binding_body(e), local);
+        r++;
+    }
+}
+}

src/library/type_util.h

@@ -0,0 +1,18 @@
+/*
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#pragma once
+#include "kernel/type_checker.h"
+
+namespace lean {
+/** \brief Given an expression \c e, return the number of arguments expected arguments.
+
+    \remark This function computes the type of \c e, and then counts the number of nested
+    Pi's. Weak-head-normal-forms are computed for the type of \c e.
+    \remark The type and whnf are computed using \c tc.
+*/
+unsigned get_expect_num_args(type_checker & tc, expr e);
+}