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 {
enum class coercion_class_kind { User, Sort, Fun };
/**
   \brief A coercion is a mapping between classes.
   We support three kinds of classes: User, Sort, Function.
*/
class coercion_class {
    coercion_class_kind m_kind;
    name                m_name; // relevant only if m_kind == User
    coercion_class(coercion_class_kind k, name const & n = name()):m_kind(k), m_name(n) {}
public:
    coercion_class():m_kind(coercion_class_kind::Sort) {}
    static coercion_class mk_user(name n);
    static coercion_class mk_sort();
    static coercion_class mk_fun();
    friend bool operator==(coercion_class const & c1, coercion_class const & c2);
    friend bool operator!=(coercion_class const & c1, coercion_class const & c2);
    coercion_class_kind kind() const { return m_kind; }
    name get_name() const { return m_name; }
};

/**
   \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.

   \remark if persistent == true, then coercion is saved in .olean files
*/
environment add_coercion(environment const & env, name const & f, io_state const & ios, bool persistent = true);
environment add_coercion(environment const & env, name const & f, name const & C, io_state const & ios,
                         bool persistent = true);
/** \brief If \c f is a coercion, then return the name of the 'from-class' and the number of
    class parameters.
*/
optional<pair<name, unsigned>> is_coercion(environment const & env, name const & f);
optional<pair<name, unsigned>> 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);
bool has_coercions_to_sort(environment const & env);
bool has_coercions_to_fun(environment const & env);
/**
   \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)
*/
list<expr> get_coercions(environment const & env, expr const & C, name const & D);
list<expr> get_coercions_to_sort(environment const & env, expr const & C);
list<expr> get_coercions_to_fun(environment const & env, expr const & C);
/**
   \brief Return all coercions C >-> D for the type C of the form (C_name.{l1 ... lk} t_1 ... t_n)
   The result is a tuple (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_coercions_from(environment const & env, expr const & C, buffer<std::tuple<coercion_class, expr, expr>> & result);

typedef std::function<void(name const &, name const &, expr const &, level_param_names const &, unsigned)> coercion_user_fn;
typedef std::function<void(name const &, expr const &, level_param_names const &, unsigned)> coercion_sort_fn;
typedef std::function<void(name const &, expr const &, level_param_names const &, unsigned)> coercion_fun_fn;
void for_each_coercion_user(environment const & env, coercion_user_fn const & f);
void for_each_coercion_sort(environment const & env, coercion_sort_fn const & f);
void for_each_coercion_fun(environment const & env, coercion_fun_fn const & f);
void open_coercion(lua_State * L);
}