80 lines
3.1 KiB
C++
80 lines
3.1 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 "util/numerics/mpq.h"
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#include "kernel/expr.h"
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#include "kernel/builtin.h"
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namespace lean {
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/** \brief Real numbers type */
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expr mk_real_type();
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extern expr const Real;
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/** \brief Return the value of type Real that represents \c v. */
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expr mk_real_value(mpq const & v);
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inline expr mk_real_value(int v) { return mk_real_value(mpq(v)); }
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inline expr rVal(int v) { return mk_real_value(v); }
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bool is_real_value(expr const & e);
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mpq const & real_value_numeral(expr const & e);
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/** \brief Addition, Real::add : Real -> Real -> Real */
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expr mk_real_add_fn();
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inline expr rAdd(expr const & e1, expr const & e2) { return mk_app(mk_real_add_fn(), e1, e2); }
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/** \brief Subtraction, Real::sub : Real -> Real -> Real */
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expr mk_real_sub_fn();
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inline expr rSub(expr const & e1, expr const & e2) { return mk_app(mk_real_sub_fn(), e1, e2); }
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/** \brief Unary minus, Real::neg : Real -> Real */
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expr mk_real_neg_fn();
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inline expr rNeg(expr const & e) { return mk_app(mk_real_neg_fn(), e); }
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/** \brief Multiplication, Real::mul : Real -> Real -> Real */
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expr mk_real_mul_fn();
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inline expr rMul(expr const & e1, expr const & e2) { return mk_app(mk_real_mul_fn(), e1, e2); }
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/** \brief Division, Real::mul : Real -> Real -> Real */
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expr mk_real_div_fn();
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inline expr rDiv(expr const & e1, expr const & e2) { return mk_app(mk_real_div_fn(), e1, e2); }
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/** \brief Absolute value function, Real::abs : Real -> Real */
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expr mk_real_abs_fn();
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inline expr rAbs(expr const & e) { return mk_app(mk_real_abs_fn(), e); }
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/** \brief Less than or equal to, Real::le : Real -> Real -> Bool */
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expr mk_real_le_fn();
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inline expr rLe(expr const & e1, expr const & e2) { return mk_app(mk_real_le_fn(), e1, e2); }
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/** \brief Greater than or equal to, Real::ge : Real -> Real -> Bool */
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expr mk_real_ge_fn();
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inline expr rGe(expr const & e1, expr const & e2) { return mk_app(mk_real_ge_fn(), e1, e2); }
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/** \brief Less than, Real::lt : Real -> Real -> Bool */
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expr mk_real_lt_fn();
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inline expr rLt(expr const & e1, expr const & e2) { return mk_app(mk_real_lt_fn(), e1, e2); }
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/** \brief Greater than, Real::gt : Real -> Real -> Bool */
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expr mk_real_gt_fn();
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inline expr rGt(expr const & e1, expr const & e2) { return mk_app(mk_real_gt_fn(), e1, e2); }
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/** \brief If-then-else for reals */
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inline expr rIf(expr const & c, expr const & t, expr const & e) { return mk_if(Real, c, t, e); }
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class environment;
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/** \brief Import (basic) Real number library in the given environment (if it has not been imported already). */
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void import_real(environment & env);
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/** \brief Coercion from int to real */
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expr mk_int_to_real_fn();
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inline expr i2r(expr const & e) { return mk_app(mk_int_to_real_fn(), e); }
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/** \brief Coercion from nat to real */
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expr mk_nat_to_real_fn();
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inline expr n2r(expr const & e) { return mk_app(mk_nat_to_real_fn(), e); }
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/** \brief Import the coercions \c i2r and \c n2r. The Integer and (basic) Real libraries are also imported. */
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void import_int_to_real_coercions(environment & env);
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}
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