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diff --git a/libyul/optimiser/SimplificationRules.h b/libyul/optimiser/SimplificationRules.h
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+/*
+	This file is part of solidity.
+
+	solidity is free software: you can redistribute it and/or modify
+	it under the terms of the GNU General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	solidity is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU General Public License for more details.
+
+	You should have received a copy of the GNU General Public License
+	along with solidity.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/**
+ * Module for applying replacement rules against Expressions.
+ */
+
+#pragma once
+
+#include <libevmasm/ExpressionClasses.h>
+#include <libevmasm/SimplificationRule.h>
+
+#include <libyul/ASTDataForward.h>
+
+#include <libsolidity/inlineasm/AsmData.h>
+
+#include <boost/noncopyable.hpp>
+
+#include <functional>
+#include <vector>
+
+namespace dev
+{
+namespace yul
+{
+
+class Pattern;
+
+/**
+ * Container for all simplification rules.
+ */
+class SimplificationRules: public boost::noncopyable
+{
+public:
+	SimplificationRules();
+
+	/// @returns a pointer to the first matching pattern and sets the match
+	/// groups accordingly.
+	static SimplificationRule<Pattern> const* findFirstMatch(Expression const& _expr);
+
+	/// Checks whether the rulelist is non-empty. This is usually enforced
+	/// by the constructor, but we had some issues with static initialization.
+	bool isInitialized() const;
+private:
+	void addRules(std::vector<SimplificationRule<Pattern>> const& _rules);
+	void addRule(SimplificationRule<Pattern> const& _rule);
+
+	void resetMatchGroups() { m_matchGroups.clear(); }
+
+	std::map<unsigned, Expression const*> m_matchGroups;
+	std::vector<SimplificationRule<Pattern>> m_rules[256];
+};
+
+enum class PatternKind
+{
+	Operation,
+	Constant,
+	Any
+};
+
+/**
+ * Pattern to match against an expression.
+ * Also stores matched expressions to retrieve them later, for constructing new expressions using
+ * ExpressionTemplate.
+ */
+class Pattern
+{
+public:
+	/// Matches any expression.
+	Pattern(PatternKind _kind = PatternKind::Any): m_kind(_kind) {}
+	// Matches a specific constant value.
+	Pattern(unsigned _value): Pattern(u256(_value)) {}
+	// Matches a specific constant value.
+	Pattern(u256 const& _value): m_kind(PatternKind::Constant), m_data(std::make_shared<u256>(_value)) {}
+	// Matches a given instruction with given arguments
+	Pattern(solidity::Instruction _instruction, std::vector<Pattern> const& _arguments = {});
+	/// Sets this pattern to be part of the match group with the identifier @a _group.
+	/// Inside one rule, all patterns in the same match group have to match expressions from the
+	/// same expression equivalence class.
+	void setMatchGroup(unsigned _group, std::map<unsigned, Expression const*>& _matchGroups);
+	unsigned matchGroup() const { return m_matchGroup; }
+	bool matches(Expression const& _expr) const;
+
+	std::vector<Pattern> arguments() const { return m_arguments; }
+
+	/// @returns the data of the matched expression if this pattern is part of a match group.
+	u256 d() const;
+
+	solidity::Instruction instruction() const;
+
+	/// Turns this pattern into an actual expression. Should only be called
+	/// for patterns resulting from an action, i.e. with match groups assigned.
+	Expression toExpression(SourceLocation const& _location) const;
+
+private:
+	Expression const& matchGroupValue() const;
+
+	PatternKind m_kind = PatternKind::Any;
+	solidity::Instruction m_instruction; ///< Only valid if m_kind is Operation
+	std::shared_ptr<u256> m_data; ///< Only valid if m_kind is Constant
+	std::vector<Pattern> m_arguments;
+	unsigned m_matchGroup = 0;
+	std::map<unsigned, Expression const*>* m_matchGroups = nullptr;
+};
+
+}
+}