feat(frontends/lean/bultin_cmds): add 'print axioms <declname>' command that prints axioms a giving declaration depends on

src/frontends/lean/builtin_cmds.cpp

@@ -11,6 +11,7 @@ Author: Leonardo de Moura
 #include "kernel/type_checker.h"
 #include "kernel/abstract.h"
 #include "kernel/instantiate.h"
+#include "kernel/for_each_fn.h"
 #include "kernel/inductive/inductive.h"
 #include "kernel/quotient/quotient.h"
 #include "kernel/hits/hits.h"
@@ -68,7 +69,49 @@ static void print_coercions(parser & p, optional<name> const & C) {
         });
 }
 
+struct print_axioms_deps {
+    environment     m_env;
+    io_state_stream m_ios;
+    name_set        m_visited;
+    bool            m_use_axioms;
+    print_axioms_deps(environment const & env, io_state_stream const & ios):
+        m_env(env), m_ios(ios), m_use_axioms(false) {}
+
+    void visit(name const & n) {
+        if (m_visited.contains(n))
+            return;
+        m_visited.insert(n);
+        declaration const & d = m_env.get(n);
+        if (!d.is_definition() && !m_env.is_builtin(n)) {
+            m_use_axioms = true;
+            m_ios << d.get_name() << "\n";
+        }
+        visit(d.get_type());
+        if (d.is_definition())
+            visit(d.get_value());
+    }
+
+    void visit(expr const & e) {
+        for_each(e, [&](expr const & e, unsigned) {
+                if (is_constant(e))
+                    visit(const_name(e));
+                return true;
+            });
+    }
+
+    void operator()(name const & n) {
+        visit(n);
+        if (!m_use_axioms)
+            m_ios << "no axioms" << endl;
+    }
+
+};
+
 static void print_axioms(parser & p) {
+    if (p.curr_is_identifier()) {
+        name c = p.check_constant_next("invalid 'print axioms', constant expected");
+        print_axioms_deps(p.env(), p.regular_stream())(c);
+    } else {
         bool has_axioms = false;
         environment const & env = p.env();
         env.for_each_declaration([&](declaration const & d) {
@@ -81,6 +124,7 @@ static void print_axioms(parser & p) {
         if (!has_axioms)
             p.regular_stream() << "no axioms" << endl;
     }
+}
 
 static void print_prefix(parser & p) {
     name prefix = p.check_id_next("invalid 'print prefix' command, identifier expected");

tests/lean/axioms_of.lean

@@ -0,0 +1,13 @@
+import data.finset data.rat
+
+print axioms nat.add
+print "-----"
+print axioms int.add
+print "-----"
+print axioms rat.add
+print "-----"
+print axioms finset.union
+print "-----"
+print axioms finset.mem
+print "-----"
+print axioms finset.union.comm

tests/lean/axioms_of.lean.expected.out

@@ -0,0 +1,12 @@
+no axioms
+-----
+no axioms
+-----
+quot.sound
+-----
+quot.sound
+-----
+propext
+-----
+quot.sound
+propext