58 lines
2.1 KiB
C++
58 lines
2.1 KiB
C++
/*
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Copyright (c) 2013 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#pragma once
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#include "expr.h"
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#include "builtin.h"
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#include "mpz.h"
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namespace lean {
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/** \brief Natural numbers type */
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expr mk_nat_type();
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extern expr const Nat;
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/** \brief Return the value of type Natural number that represents \c v. */
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expr mk_nat_value(mpz const & v);
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inline expr mk_nat_value(unsigned v) { return mk_nat_value(mpz(v)); }
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inline expr nVal(unsigned v) { return mk_nat_value(v); }
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bool is_nat_value(expr const & e);
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mpz const & nat_value_numeral(expr const & e);
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/** \brief Addition, Nat::add : Nat -> Nat -> Nat */
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expr mk_nat_add_fn();
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inline expr nAdd(expr const & e1, expr const & e2) { return mk_app(mk_nat_add_fn(), e1, e2); }
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/** \brief Multiplication, Nat::mul : Nat -> Nat -> Nat */
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expr mk_nat_mul_fn();
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inline expr nMul(expr const & e1, expr const & e2) { return mk_app(mk_nat_mul_fn(), e1, e2); }
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/** \brief Less than or equal to, Nat::le : Nat -> Nat -> Bool */
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expr mk_nat_le_fn();
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inline expr nLe(expr const & e1, expr const & e2) { return mk_app(mk_nat_le_fn(), e1, e2); }
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/** \brief Greater than or equal to, Nat::ge : Nat -> Nat -> Bool */
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expr mk_nat_ge_fn();
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inline expr nGe(expr const & e1, expr const & e2) { return mk_app(mk_nat_ge_fn(), e1, e2); }
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/** \brief Less than, Nat::lt : Nat -> Nat -> Bool */
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expr mk_nat_lt_fn();
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inline expr nLt(expr const & e1, expr const & e2) { return mk_app(mk_nat_lt_fn(), e1, e2); }
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/** \brief Greater than, Nat::gt : Nat -> Nat -> Bool */
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expr mk_nat_gt_fn();
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inline expr nGt(expr const & e1, expr const & e2) { return mk_app(mk_nat_gt_fn(), e1, e2); }
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/** \brief Identity function for natural numbers, Nat::id : Nat -> Nat */
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expr mk_nat_id_fn();
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inline expr nId(expr const & e) { return mk_app(mk_nat_id_fn(), e); }
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/** \brief If-then-else for natural numbers */
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inline expr nIf(expr const & c, expr const & t, expr const & e) { return mk_if(Nat, c, t, e); }
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class environment;
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/** \brief Import Natural number library in the given environment (if it has not been imported already). */
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void import_natlib(environment & env);
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}
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