58 lines
2 KiB
C++
58 lines
2 KiB
C++
/*
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Copyright (c) 2016 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 "library/type_context.h"
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namespace lean {
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/** \brief If 'a' and 'b' are two distinct natural number values, then return a proof
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they are disequal. Otherwise return none.
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\remark This function assumes 'a' and 'b' have type nat.
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\remark A natural number value is any expression built using
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bit0, bit1, zero, one and nat.zero */
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optional<expr> mk_nat_val_ne_proof(expr const & a, expr const & b);
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/** \brief If 'a' and 'b' are two natural number values s.t. a < b,
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then return a proof for a < b. Otherwise return none.
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\remark This function assumes 'a' and 'b' have type nat.
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\remark A natural number value is any expression built using
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bit0, bit1, zero, one and nat.zero */
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optional<expr> mk_nat_val_lt_proof(expr const & a, expr const & b);
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/* Same for a <= b */
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optional<expr> mk_nat_val_le_proof(expr const & a, expr const & b);
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/* Similar to mk_nat_val_ne_proof, but for fin type */
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optional<expr> mk_fin_val_ne_proof(expr const & a, expr const & b);
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/* Similar to mk_nat_val_ne_proof, but for char type */
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optional<expr> mk_char_val_ne_proof(expr const & a, expr const & b);
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/* Similar to mk_nat_val_ne_proof, but for string type */
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optional<expr> mk_string_val_ne_proof(expr a, expr b);
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/* Return a proof for e >= 0 if e is a nonnegative int numeral.
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\pre typeof(e) is int. */
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optional<expr> mk_int_val_nonneg_proof(expr const & e);
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/* Return a proof for e > 0 if e is a nonnegative int numeral.
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\pre typeof(e) is int. */
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optional<expr> mk_int_val_pos_proof(expr const & a);
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/* Similar to mk_nat_val_ne_proof, but for int type */
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optional<expr> mk_int_val_ne_proof(expr const & a, expr const & b);
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/* Return a proof for a != b, a/b has type nat/int/char/string, and they are distinct values. */
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optional<expr> mk_val_ne_proof(type_context & ctx, expr const & a, expr const & b);
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void initialize_comp_val();
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void finalize_comp_val();
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}
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