lean2/src/library/coercion.h

/*
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 <utility>
#include "util/lua.h"
#include "kernel/environment.h"
#include "library/expr_pair.h"
#include "library/io_state.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.

   \remark \c ios is used to report warning messages.
*/
environment add_coercion(environment const & env, name const & f, io_state const & ios);
environment add_coercion(environment const & env, name const & f, name const & C, io_state const & ios);
bool is_coercion(environment const & env, name const & f);
bool is_coercion(environment const & env, expr const & f);
/** \brief Return true iff the given environment has coercions from a user-class named \c C. */
bool has_coercions_from(environment const & env, name const & C);
bool has_coercions_from(environment const & env, expr const & C);
/** \brief Return true iff the given environment has coercions to a user-class named \c D. */
bool has_coercions_to(environment const & env, name const & D);
/**
   \brief Return a coercion (if it exists) from (C_name.{l1 lk} t_1 ... t_n) to the class named D.
   The coercion is a unary function that takes a term of type (C_name.{l1 lk} t_1 ... t_n) and returns
   and element of type (D.{L_1  L_o} s_1 ... s_m)
*/
optional<expr> get_coercion(environment const & env, expr const & C, name const & D);
optional<expr> get_coercion_to_sort(environment const & env, expr const & C);
optional<expr> get_coercion_to_fun(environment const & env, expr const & C);
/**
   \brief Return all user coercions C >-> D for the type C of the form (C_name.{l1 ... lk} t_1 ... t_n)
   The result is a pair (user-class D, coercion, coercion type), and is stored in the result buffer \c result.
   The Boolean result is true if at least one pair is added to \c result.

   \remark The most recent coercions occur first.
*/
bool get_user_coercions(environment const & env, expr const & C, buffer<std::tuple<name, expr, expr>> & result);

void for_each_coercion_user(environment const & env,
                            std::function<void(name const &, name const &, expr const &, level_param_names const &, unsigned)> const & f);
void for_each_coercion_sort(environment const & env,
                            std::function<void(name const &, expr const &, level_param_names const &, unsigned)> const & f);
void for_each_coercion_fun(environment const & env,
                           std::function<void(name const &, expr const &, level_param_names const &, unsigned)> const & f);

void open_coercion(lua_State * L);
}