80 lines
3.2 KiB
C++
80 lines
3.2 KiB
C++
/*
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Copyright (c) 2015 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 <memory>
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#include "library/app_builder.h"
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#include "library/fun_info_manager.h"
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namespace lean {
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enum class congr_arg_kind {
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/* It is a parameter for the congruence lemma, the parit occurs in the left and right hand sides. */
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Fixed,
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/* It is not a parameter for the congruence lemma, the lemma was specialized for this parameter.
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This only happens if the parameter is a subsingleton/proposition, and other parameters depend on it. */
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FixedNoParam,
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/* The lemma contains three parameters for this kind of argument a_i, b_i and (eq_i : a_i = b_i).
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a_i and b_i represent the left and right hand sides, and eq_i is a proof for their equality. */
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Eq,
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/* congr-simp lemma contains only one parameter for this kind of argument, and congr-lemmas contains two.
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They correspond to arguments that are subsingletons/propositions. */
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Cast,
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/* The lemma contains three parameters for this kind of argument a_i, b_i and (eq_i : a_i == b_i).
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a_i and b_i represent the left and right hand sides, and eq_i is a proof for their heterogeneous equality. */
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HEq
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};
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class congr_lemma {
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expr m_type;
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expr m_proof;
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list<congr_arg_kind> m_arg_kinds;
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public:
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congr_lemma(expr const & type, expr const & proof, list<congr_arg_kind> const & ks):
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m_type(type), m_proof(proof), m_arg_kinds(ks) {}
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expr const & get_type() const { return m_type; }
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expr const & get_proof() const { return m_proof; }
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list<congr_arg_kind> const & get_arg_kinds() const { return m_arg_kinds; }
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bool all_eq_kind() const;
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};
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class congr_lemma_manager {
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struct imp;
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std::unique_ptr<imp> m_ptr;
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public:
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congr_lemma_manager(app_builder & b, fun_info_manager & fm);
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~congr_lemma_manager();
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typedef congr_lemma result;
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type_context & ctx();
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unsigned get_specialization_prefix_size(expr const & fn, unsigned nargs);
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optional<result> mk_congr_simp(expr const & fn);
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optional<result> mk_congr_simp(expr const & fn, unsigned nargs);
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/* Create a specialized theorem using (a prefix of) the arguments of the given application. */
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optional<result> mk_specialized_congr_simp(expr const & a);
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optional<result> mk_congr(expr const & fn);
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optional<result> mk_congr(expr const & fn, unsigned nargs);
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/* Create a specialized theorem using (a prefix of) the arguments of the given application. */
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optional<result> mk_specialized_congr(expr const & a);
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optional<result> mk_hcongr(expr const & fn);
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optional<result> mk_hcongr(expr const & fn, unsigned nargs);
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/** \brief If R is an equivalence relation, construct the congruence lemma
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R a1 a2 -> R b1 b2 -> (R a1 b1) <-> (R a2 b2) */
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optional<result> mk_rel_iff_congr(expr const & R);
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/** \brief Similar to previous one.
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It returns none if propext is not available.
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R a1 a2 -> R b1 b2 -> (R a1 b1) = (R a2 b2) */
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optional<result> mk_rel_eq_congr(expr const & R);
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};
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void initialize_congr_lemma_manager();
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void finalize_congr_lemma_manager();
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}
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