diff --git a/src/parser/PrismParser.cpp b/src/parser/PrismParser.cpp
index 6039c2c11..9679168b6 100644
--- a/src/parser/PrismParser.cpp
+++ b/src/parser/PrismParser.cpp
@@ -585,7 +585,7 @@ namespace storm {
                     auto const& renamingPair = renaming.find(variable.getName());
                     LOG_THROW(renamingPair != renaming.end(), storm::exceptions::WrongFormatException, "Boolean variable '" << variable.getName() << " was not renamed.");
                     
-                    booleanVariables.push_back(storm::prism::BooleanVariable(renamingPair->second, variable.getInitialValueExpression().substitute<std::map>(expressionRenaming), this->getFilename(), get_line(qi::_1)));
+                    booleanVariables.push_back(storm::prism::BooleanVariable(renamingPair->second, variable.getInitialValueExpression().substitute(expressionRenaming), this->getFilename(), get_line(qi::_1)));
                 }
                 
                 // Rename the integer variables.
@@ -594,7 +594,7 @@ namespace storm {
                     auto const& renamingPair = renaming.find(variable.getName());
                     LOG_THROW(renamingPair != renaming.end(), storm::exceptions::WrongFormatException, "Integer variable '" << variable.getName() << " was not renamed.");
                     
-                    integerVariables.push_back(storm::prism::IntegerVariable(renamingPair->second, variable.getLowerBoundExpression().substitute<std::map>(expressionRenaming), variable.getUpperBoundExpression().substitute<std::map>(expressionRenaming), variable.getInitialValueExpression().substitute<std::map>(expressionRenaming), this->getFilename(), get_line(qi::_1)));
+                    integerVariables.push_back(storm::prism::IntegerVariable(renamingPair->second, variable.getLowerBoundExpression().substitute(expressionRenaming), variable.getUpperBoundExpression().substitute(expressionRenaming), variable.getInitialValueExpression().substitute(expressionRenaming), this->getFilename(), get_line(qi::_1)));
                 }
                 
                 // Rename commands.
@@ -606,12 +606,12 @@ namespace storm {
                         for (auto const& assignment : update.getAssignments()) {
                             auto const& renamingPair = renaming.find(assignment.getVariableName());
                             if (renamingPair != renaming.end()) {
-                                assignments.emplace_back(renamingPair->second, assignment.getExpression().substitute<std::map>(expressionRenaming), this->getFilename(), get_line(qi::_1));
+                                assignments.emplace_back(renamingPair->second, assignment.getExpression().substitute(expressionRenaming), this->getFilename(), get_line(qi::_1));
                             } else {
-                                assignments.emplace_back(assignment.getVariableName(), assignment.getExpression().substitute<std::map>(expressionRenaming), this->getFilename(), get_line(qi::_1));
+                                assignments.emplace_back(assignment.getVariableName(), assignment.getExpression().substitute(expressionRenaming), this->getFilename(), get_line(qi::_1));
                             }
                         }
-                        updates.emplace_back(globalProgramInformation.currentUpdateIndex, update.getLikelihoodExpression().substitute<std::map>(expressionRenaming), assignments, this->getFilename(), get_line(qi::_1));
+                        updates.emplace_back(globalProgramInformation.currentUpdateIndex, update.getLikelihoodExpression().substitute(expressionRenaming), assignments, this->getFilename(), get_line(qi::_1));
                         ++globalProgramInformation.currentUpdateIndex;
                     }
                     
@@ -621,7 +621,7 @@ namespace storm {
                         newActionName = renamingPair->second;
                     }
                     
-                    commands.emplace_back(globalProgramInformation.currentCommandIndex, newActionName, command.getGuardExpression().substitute<std::map>(expressionRenaming), updates, this->getFilename(), get_line(qi::_1));
+                    commands.emplace_back(globalProgramInformation.currentCommandIndex, newActionName, command.getGuardExpression().substitute(expressionRenaming), updates, this->getFilename(), get_line(qi::_1));
                     ++globalProgramInformation.currentCommandIndex;
                 }
                 
diff --git a/src/storage/expressions/Expression.cpp b/src/storage/expressions/Expression.cpp
index 7eb94966b..93e356009 100644
--- a/src/storage/expressions/Expression.cpp
+++ b/src/storage/expressions/Expression.cpp
@@ -27,15 +27,21 @@ namespace storm {
             // Intentionally left empty.
         }
         
-        template<template<typename... Arguments> class MapType>
-        Expression Expression::substitute(MapType<std::string, Expression> const& identifierToExpressionMap) const {
-            return SubstitutionVisitor<MapType>(identifierToExpressionMap).substitute(this->getBaseExpressionPointer().get());
+		Expression Expression::substitute(std::map<std::string, Expression> const& identifierToExpressionMap) const {
+            return SubstitutionVisitor< std::map<std::string, Expression> >(identifierToExpressionMap).substitute(this->getBaseExpressionPointer().get());
         }
+
+		Expression Expression::substitute(std::unordered_map<std::string, Expression> const& identifierToExpressionMap) const {
+			return SubstitutionVisitor< std::unordered_map<std::string, Expression> >(identifierToExpressionMap).substitute(this->getBaseExpressionPointer().get());
+		}
         
-        template<template<typename... Arguments> class MapType>
-        Expression Expression::substitute(MapType<std::string, std::string> const& identifierToIdentifierMap) const {
-            return IdentifierSubstitutionVisitor<MapType>(identifierToIdentifierMap).substitute(this->getBaseExpressionPointer().get());
+		Expression Expression::substitute(std::map<std::string, std::string> const& identifierToIdentifierMap) const {
+			return IdentifierSubstitutionVisitor< std::map<std::string, std::string> >(identifierToIdentifierMap).substitute(this->getBaseExpressionPointer().get());
         }
+
+		Expression Expression::substitute(std::unordered_map<std::string, std::string> const& identifierToIdentifierMap) const {
+			return IdentifierSubstitutionVisitor< std::unordered_map<std::string, std::string> >(identifierToIdentifierMap).substitute(this->getBaseExpressionPointer().get());
+		}
         
         bool Expression::evaluateAsBool(Valuation const* valuation) const {
             return this->getBaseExpression().evaluateAsBool(valuation);
@@ -247,11 +253,6 @@ namespace storm {
             return Expression(std::shared_ptr<BaseExpression>(new UnaryNumericalFunctionExpression(ExpressionReturnType::Int, this->getBaseExpressionPointer(), UnaryNumericalFunctionExpression::OperatorType::Ceil)));
         }
         
-        template Expression Expression::substitute<std::map>(std::map<std::string, storm::expressions::Expression> const&) const;
-        template Expression Expression::substitute<std::unordered_map>(std::unordered_map<std::string, storm::expressions::Expression> const&) const;
-        template Expression Expression::substitute<std::map>(std::map<std::string, std::string> const&) const;
-        template Expression Expression::substitute<std::unordered_map>(std::unordered_map<std::string, std::string> const&) const;
-        
         std::ostream& operator<<(std::ostream& stream, Expression const& expression) {
             stream << expression.getBaseExpression();
             return stream;
diff --git a/src/storage/expressions/Expression.h b/src/storage/expressions/Expression.h
index ea7d99572..3001def0a 100644
--- a/src/storage/expressions/Expression.h
+++ b/src/storage/expressions/Expression.h
@@ -2,6 +2,8 @@
 #define STORM_STORAGE_EXPRESSIONS_EXPRESSION_H_
 
 #include <memory>
+#include <map>
+#include <unordered_map>
 
 #include "src/storage/expressions/BaseExpression.h"
 #include "src/utility/OsDetection.h"
@@ -76,8 +78,18 @@ namespace storm {
              * @return An expression in which all identifiers in the key set of the mapping are replaced by the
              * expression they are mapped to.
              */
-            template<template<typename... Arguments> class MapType>
-            Expression substitute(MapType<std::string, Expression> const& identifierToExpressionMap) const;
+			Expression substitute(std::map<std::string, Expression> const& identifierToExpressionMap) const;
+
+			/*!
+			* Substitutes all occurrences of identifiers according to the given map. Note that this substitution is
+			* done simultaneously, i.e., identifiers appearing in the expressions that were "plugged in" are not
+			* substituted.
+			*
+			* @param identifierToExpressionMap A mapping from identifiers to the expression they are substituted with.
+			* @return An expression in which all identifiers in the key set of the mapping are replaced by the
+			* expression they are mapped to.
+			*/
+			Expression substitute(std::unordered_map<std::string, Expression> const& identifierToExpressionMap) const;
             
             /*!
              * Substitutes all occurrences of identifiers with different names given by a mapping.
@@ -86,8 +98,16 @@ namespace storm {
              * @return An expression in which all identifiers in the key set of the mapping are replaced by the
              * identifiers they are mapped to.
              */
-            template<template<typename... Arguments> class MapType>
-            Expression substitute(MapType<std::string, std::string> const& identifierToIdentifierMap) const;
+			Expression substitute(std::map<std::string, std::string> const& identifierToIdentifierMap) const;
+
+			/*!
+			* Substitutes all occurrences of identifiers with different names given by a mapping.
+			*
+			* @param identifierToIdentifierMap A mapping from identifiers to identifiers they are substituted with.
+			* @return An expression in which all identifiers in the key set of the mapping are replaced by the
+			* identifiers they are mapped to.
+			*/
+			Expression substitute(std::unordered_map<std::string, std::string> const& identifierToIdentifierMap) const;
             
             /*!
              * Evaluates the expression under the valuation of unknowns (variables and constants) given by the
diff --git a/src/storage/expressions/IdentifierSubstitutionVisitor.cpp b/src/storage/expressions/IdentifierSubstitutionVisitor.cpp
index 17161775a..1b058bed2 100644
--- a/src/storage/expressions/IdentifierSubstitutionVisitor.cpp
+++ b/src/storage/expressions/IdentifierSubstitutionVisitor.cpp
@@ -1,5 +1,6 @@
 #include <map>
 #include <unordered_map>
+#include <string>
 
 #include "src/storage/expressions/IdentifierSubstitutionVisitor.h"
 
@@ -19,18 +20,18 @@
 
 namespace storm {
     namespace expressions  {
-        template<template<typename... Arguments> class MapType>
-        IdentifierSubstitutionVisitor<MapType>::IdentifierSubstitutionVisitor(MapType<std::string, std::string> const& identifierToIdentifierMap) : identifierToIdentifierMap(identifierToIdentifierMap) {
+		template<typename MapType>
+        IdentifierSubstitutionVisitor<MapType>::IdentifierSubstitutionVisitor(MapType const& identifierToIdentifierMap) : identifierToIdentifierMap(identifierToIdentifierMap) {
             // Intentionally left empty.
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         Expression IdentifierSubstitutionVisitor<MapType>::substitute(BaseExpression const* expression) {
             expression->accept(this);
             return Expression(this->expressionStack.top());
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(IfThenElseExpression const* expression) {
             expression->getCondition()->accept(this);
             std::shared_ptr<BaseExpression const> conditionExpression = expressionStack.top();
@@ -52,7 +53,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(BinaryBooleanFunctionExpression const* expression) {
             expression->getFirstOperand()->accept(this);
             std::shared_ptr<BaseExpression const> firstExpression = expressionStack.top();
@@ -70,7 +71,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(BinaryNumericalFunctionExpression const* expression) {
             expression->getFirstOperand()->accept(this);
             std::shared_ptr<BaseExpression const> firstExpression = expressionStack.top();
@@ -88,7 +89,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(BinaryRelationExpression const* expression) {
             expression->getFirstOperand()->accept(this);
             std::shared_ptr<BaseExpression const> firstExpression = expressionStack.top();
@@ -106,7 +107,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(BooleanConstantExpression const* expression) {
             // If the boolean constant is in the key set of the substitution, we need to replace it.
             auto const& namePair = this->identifierToIdentifierMap.find(expression->getConstantName());
@@ -117,7 +118,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(DoubleConstantExpression const* expression) {
             // If the double constant is in the key set of the substitution, we need to replace it.
             auto const& namePair = this->identifierToIdentifierMap.find(expression->getConstantName());
@@ -128,7 +129,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(IntegerConstantExpression const* expression) {
             // If the integer constant is in the key set of the substitution, we need to replace it.
             auto const& namePair = this->identifierToIdentifierMap.find(expression->getConstantName());
@@ -139,7 +140,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(VariableExpression const* expression) {
             // If the variable is in the key set of the substitution, we need to replace it.
             auto const& namePair = this->identifierToIdentifierMap.find(expression->getVariableName());
@@ -150,7 +151,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(UnaryBooleanFunctionExpression const* expression) {
             expression->getOperand()->accept(this);
             std::shared_ptr<BaseExpression const> operandExpression = expressionStack.top();
@@ -164,7 +165,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(UnaryNumericalFunctionExpression const* expression) {
             expression->getOperand()->accept(this);
             std::shared_ptr<BaseExpression const> operandExpression = expressionStack.top();
@@ -178,23 +179,23 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(BooleanLiteralExpression const* expression) {
             this->expressionStack.push(expression->getSharedPointer());
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(IntegerLiteralExpression const* expression) {
             this->expressionStack.push(expression->getSharedPointer());
         }
         
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         void IdentifierSubstitutionVisitor<MapType>::visit(DoubleLiteralExpression const* expression) {
             this->expressionStack.push(expression->getSharedPointer());
         }
         
         // Explicitly instantiate the class with map and unordered_map.
-        template class IdentifierSubstitutionVisitor<std::map>;
-        template class IdentifierSubstitutionVisitor<std::unordered_map>;
+		template class IdentifierSubstitutionVisitor< std::map<std::string, std::string> >;
+		template class IdentifierSubstitutionVisitor< std::unordered_map<std::string, std::string> >;
     }
 }
diff --git a/src/storage/expressions/IdentifierSubstitutionVisitor.h b/src/storage/expressions/IdentifierSubstitutionVisitor.h
index 6be7aa9ca..e8412d949 100644
--- a/src/storage/expressions/IdentifierSubstitutionVisitor.h
+++ b/src/storage/expressions/IdentifierSubstitutionVisitor.h
@@ -8,7 +8,7 @@
 
 namespace storm {
     namespace expressions {
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         class IdentifierSubstitutionVisitor : public ExpressionVisitor {
         public:
             /*!
@@ -16,7 +16,7 @@ namespace storm {
              *
              * @param identifierToExpressionMap A mapping from identifiers to expressions.
              */
-            IdentifierSubstitutionVisitor(MapType<std::string, std::string> const& identifierToExpressionMap);
+            IdentifierSubstitutionVisitor(MapType const& identifierToExpressionMap);
             
             /*!
              * Substitutes the identifiers in the given expression according to the previously given map and returns the
@@ -47,7 +47,7 @@ namespace storm {
             std::stack<std::shared_ptr<BaseExpression const>> expressionStack;
             
             // A mapping of identifier names to expressions with which they shall be replaced.
-            MapType<std::string, std::string> const& identifierToIdentifierMap;
+            MapType const& identifierToIdentifierMap;
         };
     }
 }
diff --git a/src/storage/expressions/SubstitutionVisitor.cpp b/src/storage/expressions/SubstitutionVisitor.cpp
index c3f2ea0a8..54b533d49 100644
--- a/src/storage/expressions/SubstitutionVisitor.cpp
+++ b/src/storage/expressions/SubstitutionVisitor.cpp
@@ -1,5 +1,6 @@
 #include <map>
 #include <unordered_map>
+#include <string>
 
 #include "src/storage/expressions/SubstitutionVisitor.h"
 
@@ -19,18 +20,18 @@
 
 namespace storm {
     namespace expressions  {
-        template<template<typename... Arguments> class MapType>
-        SubstitutionVisitor<MapType>::SubstitutionVisitor(MapType<std::string, Expression> const& identifierToExpressionMap) : identifierToExpressionMap(identifierToExpressionMap) {
+        template<typename MapType>
+        SubstitutionVisitor<MapType>::SubstitutionVisitor(MapType const& identifierToExpressionMap) : identifierToExpressionMap(identifierToExpressionMap) {
             // Intentionally left empty.
         }
 
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         Expression SubstitutionVisitor<MapType>::substitute(BaseExpression const* expression) {
             expression->accept(this);
             return Expression(this->expressionStack.top());
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(IfThenElseExpression const* expression) {
             expression->getCondition()->accept(this);
             std::shared_ptr<BaseExpression const> conditionExpression = expressionStack.top();
@@ -52,7 +53,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(BinaryBooleanFunctionExpression const* expression) {
             expression->getFirstOperand()->accept(this);
             std::shared_ptr<BaseExpression const> firstExpression = expressionStack.top();
@@ -70,7 +71,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(BinaryNumericalFunctionExpression const* expression) {
             expression->getFirstOperand()->accept(this);
             std::shared_ptr<BaseExpression const> firstExpression = expressionStack.top();
@@ -88,7 +89,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(BinaryRelationExpression const* expression) {
             expression->getFirstOperand()->accept(this);
             std::shared_ptr<BaseExpression const> firstExpression = expressionStack.top();
@@ -106,7 +107,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(BooleanConstantExpression const* expression) {
             // If the boolean constant is in the key set of the substitution, we need to replace it.
             auto const& nameExpressionPair = this->identifierToExpressionMap.find(expression->getConstantName());
@@ -117,7 +118,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(DoubleConstantExpression const* expression) {
             // If the double constant is in the key set of the substitution, we need to replace it.
             auto const& nameExpressionPair = this->identifierToExpressionMap.find(expression->getConstantName());
@@ -128,7 +129,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(IntegerConstantExpression const* expression) {
             // If the integer constant is in the key set of the substitution, we need to replace it.
             auto const& nameExpressionPair = this->identifierToExpressionMap.find(expression->getConstantName());
@@ -139,7 +140,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(VariableExpression const* expression) {
             // If the variable is in the key set of the substitution, we need to replace it.
             auto const& nameExpressionPair = this->identifierToExpressionMap.find(expression->getVariableName());
@@ -150,7 +151,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(UnaryBooleanFunctionExpression const* expression) {
             expression->getOperand()->accept(this);
             std::shared_ptr<BaseExpression const> operandExpression = expressionStack.top();
@@ -164,7 +165,7 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(UnaryNumericalFunctionExpression const* expression) {
             expression->getOperand()->accept(this);
             std::shared_ptr<BaseExpression const> operandExpression = expressionStack.top();
@@ -178,23 +179,23 @@ namespace storm {
             }
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(BooleanLiteralExpression const* expression) {
             this->expressionStack.push(expression->getSharedPointer());
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(IntegerLiteralExpression const* expression) {
             this->expressionStack.push(expression->getSharedPointer());
         }
         
-        template<template<typename... Arguments> class MapType>
+		template<typename MapType>
         void SubstitutionVisitor<MapType>::visit(DoubleLiteralExpression const* expression) {
             this->expressionStack.push(expression->getSharedPointer());
         }
         
         // Explicitly instantiate the class with map and unordered_map.
-        template class SubstitutionVisitor<std::map>;
-        template class SubstitutionVisitor<std::unordered_map>;
+		template class SubstitutionVisitor< std::map<std::string, Expression> >;
+		template class SubstitutionVisitor< std::unordered_map<std::string, Expression> >;
     }
 }
diff --git a/src/storage/expressions/SubstitutionVisitor.h b/src/storage/expressions/SubstitutionVisitor.h
index ad29ad6ab..d46d62cee 100644
--- a/src/storage/expressions/SubstitutionVisitor.h
+++ b/src/storage/expressions/SubstitutionVisitor.h
@@ -8,7 +8,7 @@
 
 namespace storm {
     namespace expressions {
-        template<template<typename... Arguments> class MapType>
+        template<typename MapType>
         class SubstitutionVisitor : public ExpressionVisitor {
         public:
             /*!
@@ -16,7 +16,7 @@ namespace storm {
              *
              * @param identifierToExpressionMap A mapping from identifiers to expressions.
              */
-            SubstitutionVisitor(MapType<std::string, Expression> const& identifierToExpressionMap);
+            SubstitutionVisitor(MapType const& identifierToExpressionMap);
             
             /*!
              * Substitutes the identifiers in the given expression according to the previously given map and returns the
@@ -47,7 +47,7 @@ namespace storm {
             std::stack<std::shared_ptr<BaseExpression const>> expressionStack;
             
             // A mapping of identifier names to expressions with which they shall be replaced.
-            MapType<std::string, Expression> const& identifierToExpressionMap;
+            MapType const& identifierToExpressionMap;
         };
     }
 }
diff --git a/src/storage/prism/Assignment.cpp b/src/storage/prism/Assignment.cpp
index f15797e6d..3b63703ed 100644
--- a/src/storage/prism/Assignment.cpp
+++ b/src/storage/prism/Assignment.cpp
@@ -15,7 +15,7 @@ namespace storm {
         }
         
         Assignment Assignment::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return Assignment(this->getVariableName(), this->getExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return Assignment(this->getVariableName(), this->getExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, Assignment const& assignment) {
diff --git a/src/storage/prism/BooleanVariable.cpp b/src/storage/prism/BooleanVariable.cpp
index 478b9322d..ef88cefc4 100644
--- a/src/storage/prism/BooleanVariable.cpp
+++ b/src/storage/prism/BooleanVariable.cpp
@@ -11,7 +11,7 @@ namespace storm {
         }
         
         BooleanVariable BooleanVariable::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return BooleanVariable(this->getName(), this->getInitialValueExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return BooleanVariable(this->getName(), this->getInitialValueExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, BooleanVariable const& variable) {
diff --git a/src/storage/prism/Command.cpp b/src/storage/prism/Command.cpp
index f075ff6c6..4b36942df 100644
--- a/src/storage/prism/Command.cpp
+++ b/src/storage/prism/Command.cpp
@@ -37,7 +37,7 @@ namespace storm {
                 newUpdates.emplace_back(update.substitute(substitution));
             }
             
-            return Command(this->getGlobalIndex(), this->getActionName(), this->getGuardExpression().substitute<std::map>(substitution), newUpdates, this->getFilename(), this->getLineNumber());
+            return Command(this->getGlobalIndex(), this->getActionName(), this->getGuardExpression().substitute(substitution), newUpdates, this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, Command const& command) {
diff --git a/src/storage/prism/Constant.cpp b/src/storage/prism/Constant.cpp
index 160e9ad22..3df0a26bc 100644
--- a/src/storage/prism/Constant.cpp
+++ b/src/storage/prism/Constant.cpp
@@ -27,7 +27,7 @@ namespace storm {
         }
         
         Constant Constant::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return Constant(this->getType(), this->getName(), this->getExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return Constant(this->getType(), this->getName(), this->getExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, Constant const& constant) {
diff --git a/src/storage/prism/Formula.cpp b/src/storage/prism/Formula.cpp
index 3bf72a7de..fbda0c69d 100644
--- a/src/storage/prism/Formula.cpp
+++ b/src/storage/prism/Formula.cpp
@@ -19,7 +19,7 @@ namespace storm {
         }
         
         Formula Formula::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return Formula(this->getName(), this->getExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return Formula(this->getName(), this->getExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, Formula const& formula) {
diff --git a/src/storage/prism/IntegerVariable.cpp b/src/storage/prism/IntegerVariable.cpp
index a80b6394e..1968a07ca 100644
--- a/src/storage/prism/IntegerVariable.cpp
+++ b/src/storage/prism/IntegerVariable.cpp
@@ -19,7 +19,7 @@ namespace storm {
         }
         
         IntegerVariable IntegerVariable::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return IntegerVariable(this->getName(), this->getLowerBoundExpression().substitute<std::map>(substitution), this->getUpperBoundExpression().substitute<std::map>(substitution), this->getInitialValueExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return IntegerVariable(this->getName(), this->getLowerBoundExpression().substitute(substitution), this->getUpperBoundExpression().substitute(substitution), this->getInitialValueExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, IntegerVariable const& variable) {
diff --git a/src/storage/prism/Label.cpp b/src/storage/prism/Label.cpp
index a78f9079f..cb8a13f25 100644
--- a/src/storage/prism/Label.cpp
+++ b/src/storage/prism/Label.cpp
@@ -15,7 +15,7 @@ namespace storm {
         }
         
         Label Label::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return Label(this->getName(), this->getStatePredicateExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return Label(this->getName(), this->getStatePredicateExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, Label const& label) {
diff --git a/src/storage/prism/Program.cpp b/src/storage/prism/Program.cpp
index cdbba3e22..1c4118b8b 100644
--- a/src/storage/prism/Program.cpp
+++ b/src/storage/prism/Program.cpp
@@ -229,7 +229,7 @@ namespace storm {
                     LOG_THROW(constantDefinitions.find(constant.getName()) == constantDefinitions.end(), storm::exceptions::InvalidArgumentException, "Illegally defining already defined constant '" << constant.getName() << "'.");
                     
                     // Now replace the occurrences of undefined constants in its defining expression.
-                    newConstants.emplace_back(constant.getType(), constant.getName(), constant.getExpression().substitute<std::map>(constantDefinitions), constant.getFilename(), constant.getLineNumber());
+                    newConstants.emplace_back(constant.getType(), constant.getName(), constant.getExpression().substitute(constantDefinitions), constant.getFilename(), constant.getLineNumber());
                 } else {
                     auto const& variableExpressionPair = constantDefinitions.find(constant.getName());
                     
@@ -306,7 +306,7 @@ namespace storm {
                 newRewardModels.emplace_back(rewardModel.substitute(constantSubstitution));
             }
             
-            storm::expressions::Expression newInitialStateExpression = this->getInitialStatesExpression().substitute<std::map>(constantSubstitution);
+            storm::expressions::Expression newInitialStateExpression = this->getInitialStatesExpression().substitute(constantSubstitution);
             
             std::vector<Label> newLabels;
             newLabels.reserve(this->getNumberOfLabels());
diff --git a/src/storage/prism/StateReward.cpp b/src/storage/prism/StateReward.cpp
index ab2f0974b..a93729b52 100644
--- a/src/storage/prism/StateReward.cpp
+++ b/src/storage/prism/StateReward.cpp
@@ -15,7 +15,7 @@ namespace storm {
         }
         
         StateReward StateReward::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return StateReward(this->getStatePredicateExpression().substitute<std::map>(substitution), this->getRewardValueExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return StateReward(this->getStatePredicateExpression().substitute(substitution), this->getRewardValueExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, StateReward const& stateReward) {
diff --git a/src/storage/prism/TransitionReward.cpp b/src/storage/prism/TransitionReward.cpp
index 0034231d8..cef7bf654 100644
--- a/src/storage/prism/TransitionReward.cpp
+++ b/src/storage/prism/TransitionReward.cpp
@@ -19,7 +19,7 @@ namespace storm {
         }
         
         TransitionReward TransitionReward::substitute(std::map<std::string, storm::expressions::Expression> const& substitution) const {
-            return TransitionReward(this->getActionName(), this->getStatePredicateExpression().substitute<std::map>(substitution), this->getRewardValueExpression().substitute<std::map>(substitution), this->getFilename(), this->getLineNumber());
+            return TransitionReward(this->getActionName(), this->getStatePredicateExpression().substitute(substitution), this->getRewardValueExpression().substitute(substitution), this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, TransitionReward const& transitionReward) {
diff --git a/src/storage/prism/Update.cpp b/src/storage/prism/Update.cpp
index 2e01187c9..5d65e6dd5 100644
--- a/src/storage/prism/Update.cpp
+++ b/src/storage/prism/Update.cpp
@@ -44,7 +44,7 @@ namespace storm {
                 newAssignments.emplace_back(assignment.substitute(substitution));
             }
             
-            return Update(this->getGlobalIndex(), this->getLikelihoodExpression().substitute<std::map>(substitution), newAssignments, this->getFilename(), this->getLineNumber());
+            return Update(this->getGlobalIndex(), this->getLikelihoodExpression().substitute(substitution), newAssignments, this->getFilename(), this->getLineNumber());
         }
         
         std::ostream& operator<<(std::ostream& stream, Update const& update) {
diff --git a/src/storage/prism/Variable.cpp b/src/storage/prism/Variable.cpp
index e6c884813..4aabd548c 100644
--- a/src/storage/prism/Variable.cpp
+++ b/src/storage/prism/Variable.cpp
@@ -8,7 +8,7 @@ namespace storm {
             // Nothing to do here.
         }
         
-        Variable::Variable(Variable const& oldVariable, std::string const& newName, std::map<std::string, std::string> const& renaming, std::string const& filename, uint_fast64_t lineNumber) : LocatedInformation(filename, lineNumber), name(newName), initialValueExpression(oldVariable.getInitialValueExpression().substitute<std::map>(renaming)), defaultInitialValue(oldVariable.hasDefaultInitialValue()) {
+        Variable::Variable(Variable const& oldVariable, std::string const& newName, std::map<std::string, std::string> const& renaming, std::string const& filename, uint_fast64_t lineNumber) : LocatedInformation(filename, lineNumber), name(newName), initialValueExpression(oldVariable.getInitialValueExpression().substitute(renaming)), defaultInitialValue(oldVariable.hasDefaultInitialValue()) {
             // Intentionally left empty.
         }
         
diff --git a/test/functional/storage/ExpressionTest.cpp b/test/functional/storage/ExpressionTest.cpp
index 41556f6d6..d70cbd7d1 100644
--- a/test/functional/storage/ExpressionTest.cpp
+++ b/test/functional/storage/ExpressionTest.cpp
@@ -306,7 +306,7 @@ TEST(Expression, SubstitutionTest) {
 
     std::map<std::string, storm::expressions::Expression> substution = { std::make_pair("y", doubleConstExpression), std::make_pair("x", storm::expressions::Expression::createTrue()), std::make_pair("a", storm::expressions::Expression::createTrue()) };
     storm::expressions::Expression substitutedExpression;
-    ASSERT_NO_THROW(substitutedExpression = tempExpression.substitute<std::map>(substution));
+    ASSERT_NO_THROW(substitutedExpression = tempExpression.substitute(substution));
     EXPECT_TRUE(substitutedExpression.simplify().isTrue());
 }