diff --git a/libyul/optimiser/CommonSubexpressionEliminator.cpp b/libyul/optimiser/CommonSubexpressionEliminator.cpp
index 16cdfd893..d25beb6bd 100644
--- a/libyul/optimiser/CommonSubexpressionEliminator.cpp
+++ b/libyul/optimiser/CommonSubexpressionEliminator.cpp
@@ -95,10 +95,10 @@ void CommonSubexpressionEliminator::visit(Expression& _e)
 	if (Identifier const* identifier = get_if<Identifier>(&_e))
 	{
 		YulString identifierName = identifier->name;
-		if (m_value.count(identifierName))
+		if (AssignedValue const* assignedValue = variableValue(identifierName))
 		{
-			assertThrow(m_value.at(identifierName).value, OptimizerException, "");
-			if (Identifier const* value = get_if<Identifier>(m_value.at(identifierName).value))
+			assertThrow(assignedValue->value, OptimizerException, "");
+			if (Identifier const* value = get_if<Identifier>(assignedValue->value))
 				if (inScope(value->name))
 					_e = Identifier{debugDataOf(_e), value->name};
 		}
@@ -106,7 +106,7 @@ void CommonSubexpressionEliminator::visit(Expression& _e)
 	else
 	{
 		// TODO this search is rather inefficient.
-		for (auto const& [variable, value]: m_value)
+		for (auto const& [variable, value]: allValues())
 		{
 			assertThrow(value.value, OptimizerException, "");
 			// Prevent using the default value of return variables
diff --git a/libyul/optimiser/DataFlowAnalyzer.cpp b/libyul/optimiser/DataFlowAnalyzer.cpp
index c1ad2116a..34622e738 100644
--- a/libyul/optimiser/DataFlowAnalyzer.cpp
+++ b/libyul/optimiser/DataFlowAnalyzer.cpp
@@ -24,6 +24,7 @@
 
 #include <libyul/optimiser/NameCollector.h>
 #include <libyul/optimiser/Semantics.h>
+#include <libyul/optimiser/KnowledgeBase.h>
 #include <libyul/AST.h>
 #include <libyul/Dialect.h>
 #include <libyul/Exceptions.h>
@@ -47,7 +48,7 @@ DataFlowAnalyzer::DataFlowAnalyzer(
 ):
 	m_dialect(_dialect),
 	m_functionSideEffects(std::move(_functionSideEffects)),
-	m_knowledgeBase(_dialect, m_value)
+	m_knowledgeBase(_dialect, [this](YulString _var) { return variableValue(_var); })
 {
 	if (auto const* builtin = _dialect.memoryStoreFunction(YulString{}))
 		m_storeFunctionName[static_cast<unsigned>(StoreLoadLocation::Memory)] = builtin->name;
@@ -218,6 +219,22 @@ void DataFlowAnalyzer::operator()(Block& _block)
 	assertThrow(numScopes == m_variableScopes.size(), OptimizerException, "");
 }
 
+optional<YulString> DataFlowAnalyzer::storageValue(YulString _key) const
+{
+	if (YulString const* value = util::valueOrNullptr(m_storage, _key))
+		return *value;
+	else
+		return nullopt;
+}
+
+optional<YulString> DataFlowAnalyzer::memoryValue(YulString _key) const
+{
+	if (YulString const* value = util::valueOrNullptr(m_memory, _key))
+		return *value;
+	else
+		return nullopt;
+}
+
 void DataFlowAnalyzer::handleAssignment(set<YulString> const& _variables, Expression* _value, bool _isDeclaration)
 {
 	if (!_isDeclaration)
@@ -386,8 +403,8 @@ bool DataFlowAnalyzer::inScope(YulString _variableName) const
 
 optional<u256> DataFlowAnalyzer::valueOfIdentifier(YulString const& _name)
 {
-	if (m_value.count(_name))
-		if (Literal const* literal = get_if<Literal>(m_value.at(_name).value))
+	if (AssignedValue const* value = variableValue(_name))
+		if (Literal const* literal = get_if<Literal>(value->value))
 			return valueOfLiteral(*literal);
 	return nullopt;
 }
@@ -416,3 +433,4 @@ std::optional<YulString> DataFlowAnalyzer::isSimpleLoad(
 				return key->name;
 	return {};
 }
+
diff --git a/libyul/optimiser/DataFlowAnalyzer.h b/libyul/optimiser/DataFlowAnalyzer.h
index deaa71f89..56e48fed5 100644
--- a/libyul/optimiser/DataFlowAnalyzer.h
+++ b/libyul/optimiser/DataFlowAnalyzer.h
@@ -29,6 +29,7 @@
 #include <libyul/AST.h> // Needed for m_zero below.
 #include <libyul/SideEffects.h>
 
+#include <libsolutil/Numeric.h>
 #include <libsolutil/Common.h>
 
 #include <map>
@@ -38,6 +39,7 @@ namespace solidity::yul
 {
 struct Dialect;
 struct SideEffects;
+class KnowledgeBase;
 
 /// Value assigned to a variable.
 struct AssignedValue
@@ -98,6 +100,13 @@ public:
 	void operator()(ForLoop&) override;
 	void operator()(Block& _block) override;
 
+	/// @returns the current value of the given variable, if known - always movable.
+	AssignedValue const* variableValue(YulString _variable) const { return util::valueOrNullptr(m_value, _variable); }
+	std::set<YulString> const* references(YulString _variable) const { return util::valueOrNullptr(m_references, _variable); }
+	std::map<YulString, AssignedValue> const& allValues() const { return m_value; }
+	std::optional<YulString> storageValue(YulString _key) const;
+	std::optional<YulString> memoryValue(YulString _key) const;
+
 protected:
 	/// Registers the assignment.
 	void handleAssignment(std::set<YulString> const& _names, Expression* _value, bool _isDeclaration);
diff --git a/libyul/optimiser/EqualStoreEliminator.cpp b/libyul/optimiser/EqualStoreEliminator.cpp
index 56f9902f8..542d8d50b 100644
--- a/libyul/optimiser/EqualStoreEliminator.cpp
+++ b/libyul/optimiser/EqualStoreEliminator.cpp
@@ -54,13 +54,13 @@ void EqualStoreEliminator::visit(Statement& _statement)
 	{
 		if (auto vars = isSimpleStore(StoreLoadLocation::Storage, *expression))
 		{
-			if (auto const* currentValue = util::valueOrNullptr(m_storage, vars->first))
+			if (optional<YulString> currentValue = storageValue(vars->first))
 				if (*currentValue == vars->second)
 					m_pendingRemovals.insert(&_statement);
 		}
 		else if (auto vars = isSimpleStore(StoreLoadLocation::Memory, *expression))
 		{
-			if (auto const* currentValue = util::valueOrNullptr(m_memory, vars->first))
+			if (optional<YulString> currentValue = memoryValue(vars->first))
 				if (*currentValue == vars->second)
 					m_pendingRemovals.insert(&_statement);
 		}
diff --git a/libyul/optimiser/ExpressionSimplifier.cpp b/libyul/optimiser/ExpressionSimplifier.cpp
index 736ebe4b9..8c3a038f1 100644
--- a/libyul/optimiser/ExpressionSimplifier.cpp
+++ b/libyul/optimiser/ExpressionSimplifier.cpp
@@ -38,6 +38,10 @@ void ExpressionSimplifier::visit(Expression& _expression)
 {
 	ASTModifier::visit(_expression);
 
-	while (auto const* match = SimplificationRules::findFirstMatch(_expression, m_dialect, m_value))
+	while (auto const* match = SimplificationRules::findFirstMatch(
+		_expression,
+		m_dialect,
+		[this](YulString _var) { return variableValue(_var); }
+	))
 		_expression = match->action().toExpression(debugDataOf(_expression));
 }
diff --git a/libyul/optimiser/KnowledgeBase.cpp b/libyul/optimiser/KnowledgeBase.cpp
index 5b5c07dda..460f6707f 100644
--- a/libyul/optimiser/KnowledgeBase.cpp
+++ b/libyul/optimiser/KnowledgeBase.cpp
@@ -80,8 +80,8 @@ bool KnowledgeBase::knownToBeZero(YulString _a)
 
 optional<u256> KnowledgeBase::valueIfKnownConstant(YulString _a)
 {
-	if (m_variableValues.count(_a))
-		if (Literal const* literal = get_if<Literal>(m_variableValues.at(_a).value))
+	if (AssignedValue const* value = m_variableValues(_a))
+		if (Literal const* literal = get_if<Literal>(value->value))
 			return valueOfLiteral(*literal);
 	return {};
 }
diff --git a/libyul/optimiser/KnowledgeBase.h b/libyul/optimiser/KnowledgeBase.h
index 75e060eb1..999d0e312 100644
--- a/libyul/optimiser/KnowledgeBase.h
+++ b/libyul/optimiser/KnowledgeBase.h
@@ -28,6 +28,7 @@
 #include <libsolutil/Numeric.h>
 
 #include <map>
+#include <functional>
 
 namespace solidity::yul
 {
@@ -37,15 +38,16 @@ struct AssignedValue;
 
 /**
  * Class that can answer questions about values of variables and their relations.
- *
- * The reference to the map of values provided at construction is assumed to be updating.
  */
 class KnowledgeBase
 {
 public:
-	KnowledgeBase(Dialect const& _dialect, std::map<YulString, AssignedValue> const& _variableValues):
+	KnowledgeBase(
+		Dialect const& _dialect,
+		std::function<AssignedValue const*(YulString)> _variableValues
+	):
 		m_dialect(_dialect),
-		m_variableValues(_variableValues)
+		m_variableValues(std::move(_variableValues))
 	{}
 
 	bool knownToBeDifferent(YulString _a, YulString _b);
@@ -60,7 +62,7 @@ private:
 	Expression simplifyRecursively(Expression _expression);
 
 	Dialect const& m_dialect;
-	std::map<YulString, AssignedValue> const& m_variableValues;
+	std::function<AssignedValue const*(YulString)> m_variableValues;
 	size_t m_counter = 0;
 };
 
diff --git a/libyul/optimiser/LoadResolver.cpp b/libyul/optimiser/LoadResolver.cpp
index 550ca6fb3..abcfbaabb 100644
--- a/libyul/optimiser/LoadResolver.cpp
+++ b/libyul/optimiser/LoadResolver.cpp
@@ -82,12 +82,12 @@ void LoadResolver::tryResolve(
 	YulString key = std::get<Identifier>(_arguments.at(0)).name;
 	if (_location == StoreLoadLocation::Storage)
 	{
-		if (auto value = util::valueOrNullptr(m_storage, key))
+		if (auto value = storageValue(key))
 			if (inScope(*value))
 				_e = Identifier{debugDataOf(_e), *value};
 	}
 	else if (!m_containsMSize && _location == StoreLoadLocation::Memory)
-		if (auto value = util::valueOrNullptr(m_memory, key))
+		if (auto value = memoryValue(key))
 			if (inScope(*value))
 				_e = Identifier{debugDataOf(_e), *value};
 }
@@ -129,10 +129,10 @@ void LoadResolver::tryEvaluateKeccak(
 	if (costOfLiteral > costOfKeccak)
 		return;
 
-	auto memoryValue = util::valueOrNullptr(m_memory, memoryKey->name);
-	if (memoryValue && inScope(*memoryValue))
+	optional<YulString> value = memoryValue(memoryKey->name);
+	if (value && inScope(*value))
 	{
-		optional<u256> memoryContent = valueOfIdentifier(*memoryValue);
+		optional<u256> memoryContent = valueOfIdentifier(*value);
 		optional<u256> byteLength = valueOfIdentifier(length->name);
 		if (memoryContent && byteLength && *byteLength <= 32)
 		{
diff --git a/libyul/optimiser/Rematerialiser.cpp b/libyul/optimiser/Rematerialiser.cpp
index f1597a7f2..6e00fcd8a 100644
--- a/libyul/optimiser/Rematerialiser.cpp
+++ b/libyul/optimiser/Rematerialiser.cpp
@@ -79,16 +79,15 @@ void Rematerialiser::visit(Expression& _e)
 	{
 		Identifier& identifier = std::get<Identifier>(_e);
 		YulString name = identifier.name;
-		if (m_value.count(name))
+		if (AssignedValue const* value = variableValue(name))
 		{
-			assertThrow(m_value.at(name).value, OptimizerException, "");
-			AssignedValue const& value = m_value.at(name);
+			assertThrow(value->value, OptimizerException, "");
 			size_t refs = m_referenceCounts[name];
-			size_t cost = CodeCost::codeCost(m_dialect, *value.value);
+			size_t cost = CodeCost::codeCost(m_dialect, *value->value);
 			if (
 				(
 					!m_onlySelectedVariables && (
-						(refs <= 1 && value.loopDepth == m_loopDepth) ||
+						(refs <= 1 && value->loopDepth == m_loopDepth) ||
 						cost == 0 ||
 						(refs <= 5 && cost <= 1 && m_loopDepth == 0)
 					)
@@ -96,13 +95,14 @@ void Rematerialiser::visit(Expression& _e)
 			)
 			{
 				assertThrow(m_referenceCounts[name] > 0, OptimizerException, "");
-				if (ranges::all_of(m_references[name], [&](auto const& ref) { return inScope(ref); }))
+				auto variableReferences = references(name);
+				if (!variableReferences || ranges::all_of(*variableReferences, [&](auto const& ref) { return inScope(ref); }))
 				{
 					// update reference counts
 					m_referenceCounts[name]--;
-					for (auto const& ref: ReferencesCounter::countReferences(*value.value))
+					for (auto const& ref: ReferencesCounter::countReferences(*value->value))
 						m_referenceCounts[ref.first] += ref.second;
-					_e = (ASTCopier{}).translate(*value.value);
+					_e = (ASTCopier{}).translate(*value->value);
 				}
 			}
 		}
@@ -116,12 +116,11 @@ void LiteralRematerialiser::visit(Expression& _e)
 	{
 		Identifier& identifier = std::get<Identifier>(_e);
 		YulString name = identifier.name;
-		if (m_value.count(name))
+		if (AssignedValue const* value = variableValue(name))
 		{
-			Expression const* value = m_value.at(name).value;
-			assertThrow(value, OptimizerException, "");
-			if (holds_alternative<Literal>(*value))
-				_e = *value;
+			assertThrow(value->value, OptimizerException, "");
+			if (holds_alternative<Literal>(*value->value))
+				_e = *value->value;
 		}
 	}
 	DataFlowAnalyzer::visit(_e);
diff --git a/libyul/optimiser/SimplificationRules.cpp b/libyul/optimiser/SimplificationRules.cpp
index 3e906fcdf..9d0144750 100644
--- a/libyul/optimiser/SimplificationRules.cpp
+++ b/libyul/optimiser/SimplificationRules.cpp
@@ -41,7 +41,7 @@ using namespace solidity::yul;
 SimplificationRules::Rule const* SimplificationRules::findFirstMatch(
 	Expression const& _expr,
 	Dialect const& _dialect,
-	map<YulString, AssignedValue> const& _ssaValues
+	function<AssignedValue const*(YulString)> const& _ssaValues
 )
 {
 	auto instruction = instructionAndArguments(_dialect, _expr);
@@ -138,7 +138,7 @@ void Pattern::setMatchGroup(unsigned _group, map<unsigned, Expression const*>& _
 bool Pattern::matches(
 	Expression const& _expr,
 	Dialect const& _dialect,
-	map<YulString, AssignedValue> const& _ssaValues
+	function<AssignedValue const*(YulString)> const& _ssaValues
 ) const
 {
 	Expression const* expr = &_expr;
@@ -148,8 +148,8 @@ bool Pattern::matches(
 	if (m_kind != PatternKind::Any && holds_alternative<Identifier>(_expr))
 	{
 		YulString varName = std::get<Identifier>(_expr).name;
-		if (_ssaValues.count(varName))
-			if (Expression const* new_expr = _ssaValues.at(varName).value)
+		if (AssignedValue const* value = _ssaValues(varName))
+			if (Expression const* new_expr = value->value)
 				expr = new_expr;
 	}
 	assertThrow(expr, OptimizerException, "");
diff --git a/libyul/optimiser/SimplificationRules.h b/libyul/optimiser/SimplificationRules.h
index 77018bb38..7444c47fb 100644
--- a/libyul/optimiser/SimplificationRules.h
+++ b/libyul/optimiser/SimplificationRules.h
@@ -62,7 +62,7 @@ public:
 	static Rule const* findFirstMatch(
 		Expression const& _expr,
 		Dialect const& _dialect,
-		std::map<YulString, AssignedValue> const& _ssaValues
+		std::function<AssignedValue const*(YulString)> const& _ssaValues
 	);
 
 	/// Checks whether the rulelist is non-empty. This is usually enforced
@@ -119,7 +119,7 @@ public:
 	bool matches(
 		Expression const& _expr,
 		Dialect const& _dialect,
-		std::map<YulString, AssignedValue> const& _ssaValues
+		std::function<AssignedValue const*(YulString)> const& _ssaValues
 	) const;
 
 	std::vector<Pattern> arguments() const { return m_arguments; }
diff --git a/libyul/optimiser/StackCompressor.cpp b/libyul/optimiser/StackCompressor.cpp
index 2deef5234..8b06d6625 100644
--- a/libyul/optimiser/StackCompressor.cpp
+++ b/libyul/optimiser/StackCompressor.cpp
@@ -67,7 +67,8 @@ public:
 			if (size_t const* cost = util::valueOrNullptr(m_expressionCodeCost, candidate))
 			{
 				size_t numRef = m_numReferences[candidate];
-				cand[*cost * numRef].emplace_back(candidate, m_references[candidate]);
+				set<YulString> const* ref = references(candidate);
+				cand[*cost * numRef].emplace_back(candidate, ref ? move(*ref) : set<YulString>{});
 			}
 		}
 		return cand;
@@ -80,11 +81,11 @@ public:
 		if (_varDecl.variables.size() == 1)
 		{
 			YulString varName = _varDecl.variables.front().name;
-			if (m_value.count(varName))
+			if (AssignedValue const* value = variableValue(varName))
 			{
 				yulAssert(!m_expressionCodeCost.count(varName), "");
 				m_candidates.emplace_back(varName);
-				m_expressionCodeCost[varName] = CodeCost::codeCost(m_dialect, *m_value[varName].value);
+				m_expressionCodeCost[varName] = CodeCost::codeCost(m_dialect, *value->value);
 			}
 		}
 	}
@@ -105,7 +106,7 @@ public:
 			YulString name = std::get<Identifier>(_e).name;
 			if (m_expressionCodeCost.count(name))
 			{
-				if (!m_value.count(name))
+				if (!variableValue(name))
 					rematImpossible(name);
 				else
 					++m_numReferences[name];
diff --git a/libyul/optimiser/UnusedStoreEliminator.cpp b/libyul/optimiser/UnusedStoreEliminator.cpp
index e3ff2d77a..343bd720a 100644
--- a/libyul/optimiser/UnusedStoreEliminator.cpp
+++ b/libyul/optimiser/UnusedStoreEliminator.cpp
@@ -238,7 +238,7 @@ bool UnusedStoreEliminator::knownUnrelated(
 	UnusedStoreEliminator::Operation const& _op2
 ) const
 {
-	KnowledgeBase knowledge(m_dialect, m_ssaValues);
+	KnowledgeBase knowledge(m_dialect, [this](YulString _var) { return util::valueOrNullptr(m_ssaValues, _var); });
 
 	if (_op1.location != _op2.location)
 		return true;
@@ -319,7 +319,7 @@ bool UnusedStoreEliminator::knownCovered(
 		return true;
 	if (_covered.location == Location::Memory)
 	{
-		KnowledgeBase knowledge(m_dialect, m_ssaValues);
+		KnowledgeBase knowledge(m_dialect, [this](YulString _var) { return util::valueOrNullptr(m_ssaValues, _var); });
 
 		if (_covered.length && knowledge.knownToBeZero(*_covered.length))
 			return true;
diff --git a/test/libyul/KnowledgeBaseTest.cpp b/test/libyul/KnowledgeBaseTest.cpp
index ac48f962f..ec2f0313d 100644
--- a/test/libyul/KnowledgeBaseTest.cpp
+++ b/test/libyul/KnowledgeBaseTest.cpp
@@ -58,7 +58,7 @@ protected:
 		for (auto const& [name, expression]: m_ssaValues.values())
 			m_values[name].value = expression;
 
-		return KnowledgeBase(m_dialect, m_values);
+		return KnowledgeBase(m_dialect, [this](YulString _var) { return util::valueOrNullptr(m_values, _var); });
 	}
 
 	EVMDialect m_dialect{EVMVersion{}, true};