lean2/src/kernel/abstract.h

/*
Copyright (c) 2013 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 "kernel/expr.h"

namespace lean {
/**
   \brief Replace the expressions s[0], ..., s[n-1] in e with var(n-1), ..., var(0).

   Structural equality is used to compare subexpressions of e with the s[i]'s.

   \pre s[0], ..., s[n-1] must be closed expressions (i.e., no free variables).
*/
expr abstract(expr const & e, unsigned n, expr const * s);
inline expr abstract(expr const & e, expr const & s) { return abstract(e, 1, &s); }
inline expr abstract(expr const & e, std::initializer_list<expr> const & l) { return abstract(e, l.size(), l.begin()); }
/** \brief Replace s with variable #i in the given expression. \pre s is closed */
expr abstract(expr const & e, expr const & s, unsigned i);

/**
   \brief Replace the expressions s[0], ..., s[n-1] in e with var(n-1), ..., var(0).

   Pointer comparison is used to compare subexpressions of e with the s[i]'s.

   \pre s[0], ..., s[n-1] must be closed expressions (i.e., no free variables).
*/
expr abstract_p(expr const & e, unsigned n, expr const * s);
inline expr abstract_p(expr const & e, expr const & s) { return abstract_p(e, 1, &s); }

/**
   \brief Create a lambda expression (lambda (x : t) b), the term b is abstracted using abstract(b, constant(x)).
*/
inline expr Fun(name const & n, expr const & t, expr const & b, binder_info const & bi = binder_info()) {
    return mk_lambda(n, t, abstract(b, mk_constant(n)), bi);
}
inline expr Fun(expr const & n, expr const & t, expr const & b, binder_info const & bi = binder_info()) {
    return mk_lambda(named_expr_name(n), t, abstract(b, n), bi);
}
inline expr Fun(std::pair<expr const &, expr const &> const & p, expr const & b) { return Fun(p.first, p.second, b); }
expr Fun(std::initializer_list<std::pair<expr const &, expr const &>> const & l, expr const & b);
/** \brief Create a lambda-expression by abstracting the given local constants over b */
expr Fun(unsigned num, expr const * locals, expr const & b);
template<typename T> expr Fun(T const & locals, expr const & b) { return Fun(locals.size(), locals.data(), b); }
inline expr Fun(expr const & local, expr const & b, binder_info const & bi = binder_info()) {
    return Fun(local_pp_name(local), mlocal_type(local), abstract(b, local), bi);
}

/**
   \brief Create a Pi expression (pi (x : t) b), the term b is abstracted using abstract(b, constant(x)).
*/
inline expr Pi(name const & n, expr const & t, expr const & b, binder_info const & bi = binder_info()) {
    return mk_pi(n, t, abstract(b, mk_constant(n)), bi);
}
inline expr Pi(expr const & n, expr const & t, expr const & b, binder_info const & bi = binder_info()) {
    return mk_pi(named_expr_name(n), t, abstract(b, n), bi);
}
inline expr Pi(std::pair<expr const &, expr const &> const & p, expr const & b) { return Pi(p.first, p.second, b); }
expr Pi(std::initializer_list<std::pair<expr const &, expr const &>> const & l, expr const & b);
/** \brief Create a Pi-expression by abstracting the given local constants over b */
expr Pi(unsigned num, expr const * locals, expr const & b);
template<typename T> expr Pi(T const & locals, expr const & b) { return Pi(locals.size(), locals.data(), b); }
inline expr Pi(expr const & local, expr const & b, binder_info const & bi = binder_info()) {
    return Pi(local_pp_name(local), mlocal_type(local), abstract(b, local), bi);
}
/**
-   \brief Create a Let expression (Let x := v in b), the term b is abstracted using abstract(b, x).
-*/
inline expr Let(name const & x, expr const & t, expr const & v, expr const & b) { return mk_let(x, t, v, abstract(b, mk_constant(x))); }
inline expr Let(expr const & x, expr const & t, expr const & v, expr const & b) { return mk_let(named_expr_name(x), t, v, abstract(b, x)); }
}