feat(library): add new coercion API

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

src/library/coercion.h

@@ -0,0 +1,38 @@
+/*
+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/environment.h"
+namespace lean {
+/**
+   \brief Add an new coercion in the given environment.
+
+   There are three kinds of coercions supported
+   1- From type C to type D
+        type of f must have the form:
+        {l1 ... lk} Pi (x1 : A1) ... (xn : An) (y: C.{l1 ... lk} x1 ... xn), D.{L1 ... Lr} t1 ... tm
+            - C and D are constants.
+            - l1 ... lk are universe level parameters
+            - L1 ... Lr are universe level expressions
+            - t1 ... tm are level expressions
+
+   2- From type to sort
+        type of f must have the form:
+        {l1 ... lk}  Pi (x1 : A1) ... (xn : An) (y: C.{l1 ... lk} x1 ... xn) (x : A), B
+
+   3- From type to function type
+        type of f must have the form:
+        {l1 ... lk}  Pi (x1 : A1) ... (xn : An) (y: C.{l1 ... lk} x1 ... xn), Type.{L}
+
+   \pre \c f is a constant defined in \c env.
+*/
+environment add_coercion(environment const & env, expr const & f);
+bool is_coercion(environment const & env, expr const & f);
+list<expr_pair> get_coercions(environment const & env, expr const & from, expr const & from_type);
+optional<expr> get_coercion(environment const & env, expr const & from, expr const & from_type, expr const & to_type);
+optional<expr> get_coercion_to_sort(environment const & env, expr const & from, expr const & from_type);
+optional<expr> get_coercion_to_fun(environment const & env, expr const & from, expr const & from_type);
+}