Implemented Expression Evaluation/Parsing with Proper Error Handling

MathPad.xcodeproj/project.pbxproj

@@ -8,6 +8,16 @@
 
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+		3B52CED019BE509C00CEDCFC /* MPParseError.h in Headers */ = {isa = PBXBuildFile; fileRef = 3B52CECE19BE509C00CEDCFC /* MPParseError.h */; };
+		3B52CED119BE509C00CEDCFC /* MPParseError.m in Sources */ = {isa = PBXBuildFile; fileRef = 3B52CECF19BE509C00CEDCFC /* MPParseError.m */; };
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+		3B52CEE219C070B900CEDCFC /* MPParsedProduct.h in Headers */ = {isa = PBXBuildFile; fileRef = 3B52CEE019C070B900CEDCFC /* MPParsedProduct.h */; };
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+		3B52CEE619C0755300CEDCFC /* MPElementParser.h in Headers */ = {isa = PBXBuildFile; fileRef = 3B52CEE419C0755300CEDCFC /* MPElementParser.h */; };
+		3B52CEE719C0755300CEDCFC /* MPElementParser.m in Sources */ = {isa = PBXBuildFile; fileRef = 3B52CEE519C0755300CEDCFC /* MPElementParser.m */; };
+		3B71432D19C0A1FC005A184E /* MPParsedFactor.h in Headers */ = {isa = PBXBuildFile; fileRef = 3B71432B19C0A1FC005A184E /* MPParsedFactor.h */; };
+		3B71432E19C0A1FC005A184E /* MPParsedFactor.m in Sources */ = {isa = PBXBuildFile; fileRef = 3B71432C19C0A1FC005A184E /* MPParsedFactor.m */; };
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@@ -19,8 +29,6 @@
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-		3B85834019BB651400D76A8D /* MPParsedElement.h in Headers */ = {isa = PBXBuildFile; fileRef = 3BE9C4B119B9CC70002CC508 /* MPParsedElement.h */; };
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@@ -37,8 +45,6 @@
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 		3BBEA93619BB79A700133766 /* MPFunction.m in Sources */ = {isa = PBXBuildFile; fileRef = 3B87E35F19009D5F00259938 /* MPFunction.m */; };
 		3BBEA93719BB79A700133766 /* MPExpressionEvaluator.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BC46B4819B38C980033F13A /* MPExpressionEvaluator.m */; };
-		3BBEA93819BB79A700133766 /* MPElementParser.m in Sources */ = {isa = PBXBuildFile; fileRef = 3B85830619BB573A00D76A8D /* MPElementParser.m */; };
-		3BBEA93919BB79A700133766 /* MPParsedElement.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BE9C4B219B9CC70002CC508 /* MPParsedElement.m */; };
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@@ -52,8 +58,6 @@
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@@ -114,10 +118,18 @@
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 		3B528D11199417E90054DB5F /* MPFunctionLayout.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPFunctionLayout.h; sourceTree = "<group>"; };
 		3B528D12199417E90054DB5F /* MPFunctionLayout.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPFunctionLayout.m; sourceTree = "<group>"; };
+		3B52CECE19BE509C00CEDCFC /* MPParseError.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPParseError.h; sourceTree = "<group>"; };
+		3B52CECF19BE509C00CEDCFC /* MPParseError.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPParseError.m; sourceTree = "<group>"; };
+		3B52CEDA19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = "NSRegularExpression+MPParsingAdditions.h"; sourceTree = "<group>"; };
+		3B52CEDB19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = "NSRegularExpression+MPParsingAdditions.m"; sourceTree = "<group>"; };
+		3B52CEE019C070B900CEDCFC /* MPParsedProduct.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPParsedProduct.h; sourceTree = "<group>"; };
+		3B52CEE119C070B900CEDCFC /* MPParsedProduct.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPParsedProduct.m; sourceTree = "<group>"; };
+		3B52CEE419C0755300CEDCFC /* MPElementParser.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPElementParser.h; sourceTree = "<group>"; };
+		3B52CEE519C0755300CEDCFC /* MPElementParser.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPElementParser.m; sourceTree = "<group>"; };
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+		3B71432B19C0A1FC005A184E /* MPParsedFactor.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPParsedFactor.h; sourceTree = "<group>"; };
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@@ -365,6 +373,8 @@
 				3BFAC39B1997BC7600B3EF67 /* NSString+MPExpressionElement.m */,
 				3BB09EDC190728220080A5ED /* NSIndexPath+MPAdditions.h */,
 				3BB09EDD190728220080A5ED /* NSIndexPath+MPAdditions.m */,
+				3B52CEDA19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.h */,
+				3B52CEDB19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.m */,
 			);
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 			sourceTree = "<group>";
@@ -374,12 +384,14 @@
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 				3BC46B4719B38C980033F13A /* MPExpressionEvaluator.h */,
 				3BC46B4819B38C980033F13A /* MPExpressionEvaluator.m */,
-				3B85830519BB573A00D76A8D /* MPElementParser.h */,
+				3B52CEE419C0755300CEDCFC /* MPElementParser.h */,
-				3B85830619BB573A00D76A8D /* MPElementParser.m */,
+				3B52CEE519C0755300CEDCFC /* MPElementParser.m */,
-				3BBEA95319BB9B3500133766 /* MPParseError.h */,
+				3B52CEE019C070B900CEDCFC /* MPParsedProduct.h */,
-				3BBEA95419BB9B3500133766 /* MPParseError.m */,
+				3B52CEE119C070B900CEDCFC /* MPParsedProduct.m */,
-				3BE9C4B119B9CC70002CC508 /* MPParsedElement.h */,
+				3B71432B19C0A1FC005A184E /* MPParsedFactor.h */,
-				3BE9C4B219B9CC70002CC508 /* MPParsedElement.m */,
+				3B71432C19C0A1FC005A184E /* MPParsedFactor.m */,
+				3B52CECE19BE509C00CEDCFC /* MPParseError.h */,
+				3B52CECF19BE509C00CEDCFC /* MPParseError.m */,
 			);
 			name = Evaluation;
 			sourceTree = "<group>";
@@ -481,21 +493,23 @@
 				3B85833819BB63BD00D76A8D /* MPExpression.h in Headers */,
 				3B85833919BB63C500D76A8D /* MPExpressionElement.h in Headers */,
 				3B85834419BB654D00D76A8D /* NSString+MPExpressionElement.h in Headers */,
-				3BBEA95519BB9B3500133766 /* MPParseError.h in Headers */,
+				3B52CEDC19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.h in Headers */,
 				3B85833A19BB63D400D76A8D /* MPFunction.h in Headers */,
 				3B85834319BB653700D76A8D /* MPSumFunction.h in Headers */,
 				3B85834119BB651E00D76A8D /* MPRangePath.h in Headers */,
 				3B85834219BB652900D76A8D /* MPException.h in Headers */,
 				3B85834519BB655200D76A8D /* NSIndexPath+MPAdditions.h in Headers */,
+				3B52CED019BE509C00CEDCFC /* MPParseError.h in Headers */,
 				3B85834619BB655C00D76A8D /* MPExpressionView.h in Headers */,
 				3B85834719BB655F00D76A8D /* MPExpressionStorage.h in Headers */,
+				3B52CEE219C070B900CEDCFC /* MPParsedProduct.h in Headers */,
 				3B85833E19BB651400D76A8D /* MPExpressionEvaluator.h in Headers */,
-				3B85833F19BB651400D76A8D /* MPElementParser.h in Headers */,
+				3B71432D19C0A1FC005A184E /* MPParsedFactor.h in Headers */,
-				3B85834019BB651400D76A8D /* MPParsedElement.h in Headers */,
 				3B85834819BB65B600D76A8D /* MPLayout.h in Headers */,
 				3B85834919BB65B600D76A8D /* MPExpressionLayout.h in Headers */,
 				3B85834A19BB65B600D76A8D /* MPFunctionLayout.h in Headers */,
 				3B85834B19BB65B600D76A8D /* MPSumFunctionLayout.h in Headers */,
+				3B52CEE619C0755300CEDCFC /* MPElementParser.h in Headers */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -660,23 +674,25 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				3B52CEE719C0755300CEDCFC /* MPElementParser.m in Sources */,
 				3BBEA94219BB79A700133766 /* MPExpressionLayout.m in Sources */,
 				3BBEA94119BB79A700133766 /* MPLayout.m in Sources */,
 				3BBEA93D19BB79A700133766 /* NSString+MPExpressionElement.m in Sources */,
-				3BBEA93819BB79A700133766 /* MPElementParser.m in Sources */,
 				3BBEA94019BB79A700133766 /* MPExpressionStorage.m in Sources */,
 				3BBEA93F19BB79A700133766 /* MPExpressionView.m in Sources */,
 				3BBEA94419BB79A700133766 /* MPSumFunctionLayout.m in Sources */,
+				3B71432E19C0A1FC005A184E /* MPParsedFactor.m in Sources */,
 				3BBEA93719BB79A700133766 /* MPExpressionEvaluator.m in Sources */,
 				3BBEA93A19BB79A700133766 /* MPSumFunction.m in Sources */,
-				3BBEA93919BB79A700133766 /* MPParsedElement.m in Sources */,
 				3BBEA93E19BB79A700133766 /* NSIndexPath+MPAdditions.m in Sources */,
-				3BBEA95619BB9B3500133766 /* MPParseError.m in Sources */,
+				3B52CEDD19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.m in Sources */,
 				3BBEA93C19BB79A700133766 /* MPException.m in Sources */,
+				3B52CED119BE509C00CEDCFC /* MPParseError.m in Sources */,
 				3BBEA93619BB79A700133766 /* MPFunction.m in Sources */,
 				3BBEA93519BB79A700133766 /* MPExpression.m in Sources */,
 				3BBEA93B19BB79A700133766 /* MPRangePath.m in Sources */,
 				3BBEA94319BB79A700133766 /* MPFunctionLayout.m in Sources */,
+				3B52CEE319C070B900CEDCFC /* MPParsedProduct.m in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};

MathPad/MPElementParser.h

@@ -2,17 +2,36 @@
 //  MPElementParser.h
 //  MathPad
 //
-//  Created by Kim Wittenburg on 06.09.14.
+//  Created by Kim Wittenburg on 10.09.14.
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
 #import <Foundation/Foundation.h>
-#import "MPParsedElement.h"
+#import "MPParsedProduct.h"
 #import "MPParseError.h"
 
+#define MPMaximumOperatorChainLength NSUIntegerMax
+
 @interface MPElementParser : NSObject
 
-- (MPParsedElement *)parseElement:(NSString *)string error:(MPParseError *__autoreleasing *)error;
++ (BOOL)isUsingDefaultValuesFromUserDefaults;
++ (void)setUsingDefaultValuesFromUserDefaults:(BOOL)flag;
+
+@property (nonatomic) BOOL allowsImplicitMultiplications; // wether 2 3 is equal to 6 or error
+// Default value uses the key "..." in NSUserDefaults or ... if the key does not exist.
+@property (nonatomic) NSUInteger maximumOperatorChainLength; // +--++-5 -> Chain length: 6, 2 default (sign of number and operator) (0 is invalid?)
+@property (nonatomic) NSUInteger maximumOperatorChainLengthInMultiplication; // Default: 1, 0 means actually 0
+@property (nonatomic) NSUInteger maximumOperatorChainLengthInFunction; // For sin, cos, tan. Default: 1
+
+- (NSArray *)parseElement:(NSString *)string
+          previousProduct:(MPParsedProduct *)previousProduct
+               nextFactor:(MPParsedFactor *)nextFactor
+          definesVariable:(BOOL)flag
+          definedVariable:(NSString *__autoreleasing *)variableName
+                    error:(out MPParseError *__autoreleasing *)error;
+- (NSArray *)parseElement:(NSString *)string
+          previousProduct:(MPParsedProduct *)previousProduct
+               nextFactor:(MPParsedFactor *)nextFactor
+                    error:(out MPParseError *__autoreleasing *)error;
 
 @end
-

MathPad/MPElementParser.m

@@ -2,184 +2,335 @@
 //  MPElementParser.m
 //  MathPad
 //
-//  Created by Kim Wittenburg on 06.09.14.
+//  Created by Kim Wittenburg on 10.09.14.
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
 #import "MPElementParser.h"
+#import "NSRegularExpression+MPParsingAdditions.h"
+
+#define MPMultiplicationSymbol @"*"
+
+@interface MPElementParser ()
+
+@property (nonatomic) NSString *input;
+@property (nonatomic) NSUInteger parsePosition;
+
+- (void)setError:(MPParseError *)error;
+
+- (BOOL)isAtEnd;
+
+- (NSRange)parseVariableDefinition:(NSString *__autoreleasing *)variableName;
+
+- (NSRange)parseWhitespaces;
+- (NSRange)parseMultiplicationSymbol;
+- (NSRange)parseOperators;
+- (NSUInteger)countOperatorsInRange:(NSRange)range
+                      multiplicator:(out NSDecimalNumber *__autoreleasing *)multiplicator;
+- (NSRange)parseNumber;
+- (NSDecimalNumber *)numberInRange:(NSRange)range;
+
+@end
 
 @implementation MPElementParser {
-    NSScanner *scanner;
+    MPParseError *__autoreleasing *outError;
 }
 
-- (MPParsedElement *)parseElement:(NSString *)string error:(MPParseError *__autoreleasing *)error
+static BOOL useUserDefaults;
-{
-    // Setup the Scanner
-    scanner = [[NSScanner alloc] initWithString:string];
-    scanner.charactersToBeSkipped = [NSCharacterSet whitespaceAndNewlineCharacterSet];
-    scanner.caseSensitive = YES;
-    
-    MPParsedElement *parsedElement = [[MPParsedElement alloc] init];
-    
-    // Scan the defined variable
-    NSString *firstCharacters = nil;
-    BOOL hasLettersInFront = [scanner scanCharactersFromSet:[NSCharacterSet letterCharacterSet]
-                                                 intoString:&firstCharacters];
-    BOOL foundEquals = [scanner scanString:@"="
-                                intoString:NULL];
-    
-    if (hasLettersInFront && firstCharacters.length == 1 && foundEquals) {
-        // Found variable definition
-        parsedElement.definedVariable = firstCharacters;
-        parsedElement.afterVariableDefinitionIndex = scanner.scanLocation;
-    } else {
-        // No variable definition found, reset the scanner
-        parsedElement.definedVariable = nil;
-        scanner.scanLocation = 0;
-    }
-    
-    // Scan the Prefix
-    BOOL startsWithAsterisk = [scanner scanString:@"*"
-                                       intoString:NULL];
-    BOOL productClosed;
-    NSDecimalNumber *prefix = [self scanClosedProduct:&productClosed
-                                                error:NULL];
-    
-    // Simple Factor
-    if (scanner.isAtEnd) {
-        parsedElement.isFactor = YES;
-        parsedElement.value = prefix == nil ? [NSDecimalNumber one] : prefix;
-        parsedElement.prefixOperatorExplicit = startsWithAsterisk;
-        parsedElement.suffixOperatorExplicit = !productClosed;
-        parsedElement.suffixIndex = scanner.scanLocation;
-        return parsedElement;
-    } else if (!productClosed) {
-        if (error) {
-            *error = MPParseError(scanner.scanLocation, @"Missing Number");
-        }
-        return nil;
-    }
-    
-    parsedElement.prefixOperatorExplicit = startsWithAsterisk;
-    parsedElement.prefixValueExplicit = YES;
-    parsedElement.prefixMultiplicator = prefix;
-    
-    parsedElement.suffixValueExplicit = YES;
-    
-    // Scan Summands
-    NSDecimalNumber *value = [NSDecimalNumber zero];
-    NSDecimalNumber *currentSummand;
-    while (!scanner.isAtEnd) {
 
-        // Add every summand but the last one
+#pragma mark Creation Methods
-        if (currentSummand != nil) {
+
-            value = [value decimalNumberByAdding:currentSummand];
++ (void)initialize
-        }
+{
-        
+    useUserDefaults = YES;
-        // Find the operator (+ or -)
+}
-        NSString *operator;
+
-        BOOL found = [scanner scanString:@"+"
+- (instancetype)init
-                              intoString:&operator];
+{
-        if (!found) {
+    self = [super init];
-            found = [scanner scanString:@"-"
+    if (self) {
-                             intoString:&operator];
+        self.allowsImplicitMultiplications = NO;
-        }
+        self.maximumOperatorChainLength = 2;
-        if (!found && !scanner.isAtEnd) {
+        self.maximumOperatorChainLengthInMultiplication = 1;
-            // Two numbers separated by just a space
+    }
-            if (error) {
+    return self;
-                *error = MPParseError(scanner.scanLocation, @"Missing Operator");
+}
-            }
+
+#pragma mark Properties
+
++ (BOOL)isUsingDefaultValuesFromUserDefaults
+{
+    return useUserDefaults;
+}
+
++ (void)setUsingDefaultValuesFromUserDefaults:(BOOL)flag
+{
+    useUserDefaults = flag;
+}
+
+#pragma mark Parsing Methods
+
+- (BOOL)isAtEnd
+{
+    return self.parsePosition >= self.input.length;
+}
+
+- (void)setError:(MPParseError *)error
+{
+    if (outError != NULL) {
+        *outError = error;
+    }
+}
+
+- (NSArray *)parseElement:(NSString *)string
+          previousProduct:(MPParsedProduct *)previousProduct
+               nextFactor:(MPParsedFactor *)nextFactor
+                    error:(out MPParseError *__autoreleasing *)error
+{
+    return [self parseElement:string
+              previousProduct:previousProduct
+                   nextFactor:nextFactor
+              definesVariable:NO
+              definedVariable:NULL
+                        error:error];
+}
+
+- (NSArray *)parseElement:(NSString *)string
+          previousProduct:(MPParsedProduct *)previousProduct
+               nextFactor:(MPParsedFactor *)nextFactor
+          definesVariable:(BOOL)flag
+          definedVariable:(NSString *__autoreleasing *)variableName
+                    error:(out MPParseError *__autoreleasing *)error
+{
+    self.input = string;
+    outError = error;
+    self.parsePosition = 0;
+    
+    NSString *definedVariable;
+    NSRange variableDefinitionRange = [self parseVariableDefinition:&definedVariable];
+    if (flag) {
+        if (!definedVariable) {
+            self.error = MPParseError(NSMakeRange(0, 0), @"Expected Variable Definition");
             return nil;
-        } else if (!found) {
+        } else if (variableName) {
-            // Reached end of string
+            *variableName = definedVariable;
-            break;
-        }
-        
-        currentSummand = [self scanClosedProduct:&productClosed
-                                           error:error];
-        
-        // No number was found
-        if (currentSummand == nil) {
-            // The string ends wit + or -
-            if (scanner.isAtEnd) {
-                productClosed = NO;
-                parsedElement.suffixValueExplicit = NO;
-                NSInteger suffix = [operator isEqualToString:@"+"] ? 1 : -1;
-                currentSummand = [[NSDecimalNumber alloc] initWithInteger:suffix];
-                if (error) {
-                    *error = nil;
-                }
-                break;
-            // Something else instead of a number
-            } else {
-                if (error) {
-                    *error = MPParseError(scanner.scanLocation, @"Expected Number");
-                }
-                return nil;
-            }
-        }
-        
-        // Process the current summand
-        if ([operator isEqualToString:@"-"]) {
-            currentSummand = [currentSummand decimalNumberByMultiplyingBy:[[NSDecimalNumber alloc] initWithInteger:-1]];
-        }
-        
-        // The summand ends with a *
-        if (!productClosed) {
-            // The string ends with a *
-            if (scanner.isAtEnd) {
-                parsedElement.suffixValueExplicit = YES;
-                break;
-            // After a * followed something else than a number
-            } else {
-                if (error) {
-                    *error = MPParseError(scanner.scanLocation, @"Unexpected Symbol");
-                }
-                return nil;
-            }
-        }
-    }
-    
-    parsedElement.value = value;
-    parsedElement.suffixOperatorExplicit = !productClosed;
-    parsedElement.suffixMultiplicator = currentSummand;
-    parsedElement.suffixIndex = scanner.scanLocation;
-
-    return parsedElement;
-}
-
-- (NSDecimalNumber *)scanClosedProduct:(BOOL *)closed error:(MPParseError **)error
-{
-    NSDecimal decimal;
-    BOOL found = [scanner scanDecimal:&decimal];
-    if (!found) {
-        if (error != NULL) {
-            *error = MPParseError(scanner.scanLocation, @"Unexpected Symbol");
         }
+    } else if (definedVariable) {
+        self.error = MPParseError(variableDefinitionRange, @"Unexpected Variable Definition");
         return nil;
     }
-    NSDecimalNumber *product = [NSDecimalNumber decimalNumberWithDecimal:decimal];
+        
-    while (true) {
+    NSMutableArray *products = [[NSMutableArray alloc] init];
-        found = [scanner scanString:@"*"
+    MPParsedProduct *currentProduct = previousProduct;
-                         intoString:NULL];
+    
-        if (found) {
+    while (![self isAtEnd]) {
-            found = [scanner scanDecimal:&decimal];
+        [self parseWhitespaces];
-            if (found) {
+        
-                product = [product decimalNumberByMultiplyingBy:[NSDecimalNumber decimalNumberWithDecimal:decimal]];
+        NSRange multiplicationSymbolRange = [self parseMultiplicationSymbol];
-            } else {
+        BOOL hasMultiplicationSymbol = multiplicationSymbolRange.location != NSNotFound;
-                if (closed != NULL) {
+        
-                    *closed = NO;
+        NSRange operatorsRange = [self parseOperators];
+        BOOL hasOperators = operatorsRange.location != NSNotFound;
+        
+        // NSRange functionRange = ...
+        // BOOL hasFunction = functionRange.location != NSNotFound;
+        
+        NSRange numberRange = [self parseNumber];
+        BOOL hasNumber = numberRange.location != NSNotFound;
+        
+        
+        NSDecimalNumber *operatorMultiplicator;
+        NSUInteger operatorCount = [self countOperatorsInRange:operatorsRange
+                                                     multiplicator:&operatorMultiplicator];
+
+        if (!hasNumber) {
+            if ([self isAtEnd] && nextFactor != nil) {
+                if (hasMultiplicationSymbol) {
+                    if (operatorCount > self.maximumOperatorChainLengthInFunction) {
+                        self.error = MPParseError(operatorsRange, @"Too many operators in multiplication.");
+                        return nil;
+                    }
+                    [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:operatorMultiplicator]];
+                } else if (hasOperators) {
+                    if (operatorCount > self.maximumOperatorChainLength) {
+                        self.error = MPParseError(operatorsRange, @"Too many operators.");
+                        return nil;
+                    }
+                    [products addObject:currentProduct];
+                    currentProduct = [[MPParsedProduct alloc] init];
+                    [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:[[NSDecimalNumber alloc] initWithUnsignedInteger:operatorCount]]];
+                } else if (self.allowsImplicitMultiplications) {
+                    if (!currentProduct) {
+                        currentProduct = [[MPParsedProduct alloc] init];
+                    }
+                } else {
+                    self.error = MPParseError(NSMakeRange(self.parsePosition, 0), @"Implicit Multiplication not allowed.");
+                    return nil;
                 }
-                return product;
+                break;
+            } else if ([self isAtEnd]) {
+                self.error = MPParseError(NSMakeRange(self.parsePosition, 0), @"Unexpected End. Expected Number.");
+                return nil;
+            } else {
+                self.error = MPParseError(NSMakeRange(self.parsePosition, 1), @"Unexpected Symbol. Expected Number.");
+                return nil;
             }
         } else {
-            break;
+            NSDecimalNumber *number = [self numberInRange:numberRange];
+            NSDecimalNumber *value = [operatorMultiplicator decimalNumberByMultiplyingBy:number];
+            
+            if (hasMultiplicationSymbol) {
+                if (currentProduct) {
+                    if (operatorCount > self.maximumOperatorChainLengthInMultiplication) {
+                        self.error = MPParseError(operatorsRange, @"Too many operators in multiplication.");
+                        return nil;
+                    }
+                    [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:value]];
+                } else {
+                    self.error = MPParseError(multiplicationSymbolRange, @"Unexpected Symbol. Expected Number.");
+                    return nil;
+                }
+            } else if (hasOperators) {
+                if (operatorCount > self.maximumOperatorChainLength) {
+                    self.error = MPParseError(operatorsRange, @"Too many operators.");
+                    return nil;
+                }
+                if (currentProduct) {
+                    [products addObject:currentProduct];
+                }
+                currentProduct = [[MPParsedProduct alloc] init];
+                [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:value]];
+            } else if (!currentProduct) {
+                currentProduct = [[MPParsedProduct alloc] init];
+                [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:value]];
+            } else if (self.allowsImplicitMultiplications) {
+                [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:value]];
+            } else {
+                self.error = MPParseError(NSMakeRange(numberRange.location, 0), @"Implicit Multiplication not allowed.");
+                return nil;
+            }
         }
     }
-    if (closed != NULL) {
+    if (nextFactor) {
-        *closed = YES;
+        [currentProduct addFactor:nextFactor];
     }
-    return product;
+    [products addObject:currentProduct];
+    return products;
+}
+
+static NSRegularExpression *variableDefinitionRegex;
+- (NSRange)parseVariableDefinition:(NSString *__autoreleasing *)variableName
+{
+    if (!variableDefinitionRegex) {
+        variableDefinitionRegex = [NSRegularExpression regularExpressionWithPattern:@"\\A\\s*([A-Za-z])\\s*=\\s*"
+                                                                            options:0
+                                                                              error:NULL];
+    }
+    
+    NSTextCheckingResult *match = [variableDefinitionRegex firstMatchInString:self.input
+                                                                    fromIndex:self.parsePosition];
+    if (!match) {
+        return NSMakeRange(NSNotFound, 0);
+    }
+    self.parsePosition = NSMaxRange(match.range);
+    NSRange variableDefinitionRange = [match rangeAtIndex:1];
+    *variableName = [self.input substringWithRange:variableDefinitionRange];
+    return variableDefinitionRange;
+}
+
+static NSRegularExpression *whitespaceRegex;
+- (NSRange)parseWhitespaces
+{
+    if (!whitespaceRegex) {
+        whitespaceRegex = [NSRegularExpression regularExpressionWithPattern:@"\\A\\s*"
+                                                                    options:0
+                                                                      error:NULL];
+    }
+    NSTextCheckingResult *match = [whitespaceRegex firstMatchInString:self.input
+                                                            fromIndex:self.parsePosition];
+    if (match) {
+        self.parsePosition = NSMaxRange(match.range);
+        return match.range;
+    } else {
+        return NSMakeRange(NSNotFound, 0);
+    }
+}
+
+static NSRegularExpression *multiplicationSymbolRegex;
+- (NSRange)parseMultiplicationSymbol
+{
+    if (!multiplicationSymbolRegex) {
+        NSString *multiplicationSymbolString = [NSRegularExpression escapedPatternForString:MPMultiplicationSymbol];
+        NSString *multiplicationSymbolRegexString = [NSString stringWithFormat:@"\\A\\s*(%@)\\s*", multiplicationSymbolString];
+        multiplicationSymbolRegex = [NSRegularExpression regularExpressionWithPattern:multiplicationSymbolRegexString
+                                                                              options:0
+                                                                                error:NULL];
+    }
+    NSTextCheckingResult *match = [multiplicationSymbolRegex firstMatchInString:self.input
+                                                                      fromIndex:self.parsePosition];
+    if (!match) {
+        return NSMakeRange(NSNotFound, 0);
+    }
+    self.parsePosition = NSMaxRange(match.range);
+    return [match rangeAtIndex:1];
+}
+
+static NSRegularExpression *operatorsRegex;
+- (NSRange)parseOperators
+{
+    if (!operatorsRegex) {
+        operatorsRegex = [NSRegularExpression regularExpressionWithPattern:@"\\A\\s*([+-](?:\\s*[+-])*)\\s*"
+                                                                   options:0
+                                                                     error:NULL];
+    }
+    NSTextCheckingResult *match = [operatorsRegex firstMatchInString:self.input
+                                                           fromIndex:self.parsePosition];
+    if (match == nil) {
+        return NSMakeRange(NSNotFound, 0);
+    }
+    self.parsePosition = NSMaxRange(match.range);
+    return [match rangeAtIndex:1];
+}
+
+- (NSUInteger)countOperatorsInRange:(NSRange)range
+                      multiplicator:(out NSDecimalNumber *__autoreleasing *)outMultiplicator
+{
+    if (range.location == NSNotFound) {
+        *outMultiplicator = [NSDecimalNumber one];
+        return 0;
+    }
+    NSString *operatorsString = [self.input substringWithRange:range];
+    NSString *operators = [[operatorsString componentsSeparatedByCharactersInSet:[NSCharacterSet whitespaceAndNewlineCharacterSet]] componentsJoinedByString:@""];
+    NSInteger multiplicator = 1;
+    for (NSUInteger characterIndex; characterIndex < operators.length; characterIndex++) {
+        if ([[operators substringWithRange:NSMakeRange(characterIndex, 1)] isEqualToString:@"-"]) {
+            multiplicator *= -1;
+        }
+    }
+    *outMultiplicator = [[NSDecimalNumber alloc] initWithInteger:multiplicator];
+    return operators.length;
+}
+
+- (NSRange)parseNumber
+{
+    NSString *decimalSeparatorRegexString = [NSRegularExpression escapedPatternForString:[[NSLocale currentLocale] objectForKey:NSLocaleDecimalSeparator]];
+    NSString *numberRegexFormat = [NSString stringWithFormat:@"\\A\\s*((?:\\d+(?:%@\\d+)?)|(?:%@\\d+))\\s*", decimalSeparatorRegexString, decimalSeparatorRegexString];
+    NSRegularExpression *numberRegex = [NSRegularExpression regularExpressionWithPattern:numberRegexFormat
+                                                                                 options:0
+                                                                                   error:NULL];
+    NSTextCheckingResult *match = [numberRegex firstMatchInString:self.input
+                                                        fromIndex:self.parsePosition];
+    if (!match) {
+        return NSMakeRange(NSNotFound, 0);
+    }
+    self.parsePosition = NSMaxRange(match.range);
+    return [match rangeAtIndex:1];
+}
+
+- (NSDecimalNumber *)numberInRange:(NSRange)range
+{
+    NSString *numberString = [self.input substringWithRange:range];
+    return [NSDecimalNumber decimalNumberWithString:numberString];
 }
 
 @end

MathPad/MPExpressionElement.h

@@ -17,6 +17,4 @@
 
 - (NSUInteger)length;
 
-- (NSDecimalNumber *)evaluate:(MPParseError *__autoreleasing *)error;
-
 @end

MathPad/MPExpressionEvaluator.h

@@ -10,7 +10,7 @@
 #import "MPExpression.h"
 #import "MPElementParser.h"
 
-@class MPExpressionEvaluator, MPExpression, MPParsedElement;
+@class MPExpressionEvaluator, MPExpression, MPParsedElementOld;
 
 @interface MPExpressionEvaluator : NSObject
 
@@ -25,8 +25,9 @@
 - (void)bindValue:(NSDecimalNumber *)value toVariableName:(NSString *)name;
 - (void)unbindVariableName:(NSString *)name;
 
-- (NSDecimalNumber *)evaluateWithError:(MPParseError *__autoreleasing *)error;
-- (NSDecimalNumber *)evaluateVariableDefinition:(BOOL)flag error:(MPParseError *__autoreleasing *)error;
 @property (readonly, nonatomic, strong) NSString *definedVariable;
 
+- (NSDecimalNumber *)evaluateWithError:(MPParseError *__autoreleasing *)error;
+- (NSDecimalNumber *)evaluateVariableDefinition:(BOOL)flag error:(MPParseError *__autoreleasing *)error;
+
 @end

MathPad/MPExpressionEvaluator.m

@@ -8,9 +8,11 @@
 
 #import "MPExpressionEvaluator.h"
 #import "MPExpression.h"
+#import "MPFunction.h"
 
 @interface MPExpressionEvaluator ()
 @property (readwrite, nonatomic, strong) NSString *definedVariable;
+
 @end
 
 @implementation MPExpressionEvaluator {
@@ -52,146 +54,74 @@
 
 - (NSDecimalNumber *)evaluateVariableDefinition:(BOOL)flag error:(MPParseError *__autoreleasing *)error
 {
-#warning Implement Cache
     // Empty Expression
     if (self.expression.numberOfElements == 0) {
-        if (error) {
+        *error = MPParseError(NSMakeRange(0, 0), @"Expected Expression");
-            *error = MPParseError(0, @"Empty Expression");
-        }
         return nil;
     }
-    
-    // Expression of just one element
-    if (self.expression.numberOfElements == 1) {
-        id<MPExpressionElement> singleElement = [self.expression elementAtIndex:0];
-        if ([singleElement isString]) {
-            MPParsedElement *parseResult = [parser parseElement:(NSString *)singleElement
-                                                          error:error];
-            if ([parseResult isValidStandaloneElement:error]) {
-                if (flag && parseResult.definedVariable) {
-                    self.definedVariable = parseResult.definedVariable;
-                } else if (flag) {
-                    if (error) {
-                        *error = MPParseError(0, @"Expected Variable Definition");
-                    }
-                    return nil;
-                } else if (parseResult.definedVariable) {
-                    if (error) {
-                        *error = MPParseError(0, @"Unexpected Variable Definition");
-                    }
-                    return nil;
-                }
-                return parseResult.standaloneValue;
-            } else {
-                return nil;
-            }
-        } else {
-            return [singleElement evaluate:error];
-        }
-    }
 
-    // Expression with any number of elements
+    NSMutableArray *products = [[NSMutableArray alloc] init];
-    NSDecimalNumber *value = [NSDecimalNumber zero];
+    MPParsedProduct *currentProduct = nil;
-    NSDecimalNumber *currentSummand = nil;
     
-    // Process the first element
+    for (NSUInteger elementIndex = 0; elementIndex < self.expression.numberOfElements; elementIndex++) {
-    id<MPExpressionElement> firstElement = [self.expression elementAtIndex:0];
+        
-    if ([firstElement isString]) {
+        id<MPExpressionElement> element = [self.expression elementAtIndex:elementIndex];
-        MPParsedElement *parseResult = [parser parseElement:(NSString *)firstElement
+        
-                                                      error:error];
-        if (parseResult && [parseResult isValidElementAtBeginning:error]) {
-            if (flag && parseResult.definedVariable) {
-                self.definedVariable = parseResult.definedVariable;
-            } else if (flag) {
-                if (error) {
-                    *error = MPParseError(0, @"Expected Variable Definition");
-                }
-                return nil;
-            } else if (parseResult.definedVariable) {
-                if (error) {
-                    *error = MPParseError(0, @"Unexpected Variable Definition");
-                }
-                return nil;
-            }
-            if ([parseResult isFactor]) {
-                currentSummand = parseResult.value;
-            } else {
-                value = [parseResult valueAtBeginning];
-                currentSummand = parseResult.suffixMultiplicator;
-            }
-        }
-    } else {
-        currentSummand = [firstElement evaluate:error];
-    }
-    if (!currentSummand) {
-        return nil;
-    }
-    
-    // Process the elements between the first and last element
-    for (NSUInteger index = 1; index < self.expression.numberOfElements-1; index++) {
-        id<MPExpressionElement> element = [self.expression elementAtIndex:index];
         if ([element isString]) {
-            MPParsedElement *parseResult = [parser parseElement:(NSString *)element
+            MPParsedFactor *nextFactor = nil;
-                                                          error:error];
+            if (elementIndex < self.expression.numberOfElements - 1) {
-            if (parseResult) {
+                MPFunction *nextFunction = (MPFunction *)[self.expression elementAtIndex:elementIndex+1];
-                if (parseResult.definedVariable) {
+                NSDecimalNumber *functionValue = [nextFunction evaluate:error];
-                    if (error) {
+                if (!functionValue) {
-                        *error = MPParseError(index, @"Unexpected Variable Definition");
-                    }
                     return nil;
                 }
-                if ([parseResult isFactor]) {
+                nextFactor = [MPParsedFactor factorWithDecimalNumber:functionValue];
-                    currentSummand = [currentSummand decimalNumberByMultiplyingBy:parseResult.value];
+            }
-                } else {
+            
-                    currentSummand = [currentSummand decimalNumberByMultiplyingBy:parseResult.prefixMultiplicator];
+            NSArray *newProducts;
-                    value = [[value decimalNumberByAdding:currentSummand] decimalNumberByAdding:parseResult.value];
+            if (elementIndex == 0 && flag) {
-                    currentSummand = parseResult.suffixMultiplicator;
+                NSString *definedVariable;
-                }
+                newProducts = [parser parseElement:(NSString *)element
+                                   previousProduct:currentProduct
+                                        nextFactor:nextFactor
+                                   definesVariable:YES
+                                   definedVariable:&definedVariable
+                                             error:error];
+                self.definedVariable = definedVariable;
             } else {
+                newProducts = [parser parseElement:(NSString *)element
+                                   previousProduct:currentProduct
+                                        nextFactor:nextFactor
+                                             error:error];
+            }
+            if (!newProducts) {
                 return nil;
             }
+            
+            for (NSUInteger productIndex = 0; productIndex < newProducts.count-1; productIndex++) {
+                [products addObject:newProducts[productIndex]];
+            }
+            currentProduct = newProducts.lastObject;
+            
+            elementIndex++;
         } else {
-            NSDecimalNumber *result = [element evaluate:error];
+            NSDecimalNumber *functionValue = [(MPFunction *)element evaluate:error];
-            if (result) {
+            if (!functionValue) {
-                currentSummand = [currentSummand decimalNumberByMultiplyingBy:result];
-            } else {
                 return nil;
             }
+            if (!currentProduct) {
+                currentProduct = [[MPParsedProduct alloc] init];
+            }
+            [currentProduct addFactor:[MPParsedFactor factorWithDecimalNumber:functionValue]];
         }
     }
     
-    // Process the last element
+    [products addObject:currentProduct];
-    id<MPExpressionElement> lastElement = [self.expression elementAtIndex:self.expression.numberOfElements-1];
-    if ([lastElement isString]) {
-        MPParsedElement *parseResult = [parser parseElement:(NSString *)lastElement
-                                                      error:error];
-        if (parseResult && [parseResult isValidElementAtEnd:error]) {
-            if (parseResult.definedVariable) {
-                if (error) {
-                    *error = MPParseError(0, @"Unexpected Variable Definition");
-                }
-                return nil;
-            }
-            if ([parseResult isFactor]) {
-                currentSummand = [currentSummand decimalNumberByMultiplyingBy:parseResult.value];
-            } else {
-                currentSummand = [currentSummand decimalNumberByMultiplyingBy:parseResult.prefixMultiplicator];
-                value = [[value decimalNumberByAdding:currentSummand] decimalNumberByAdding:parseResult.value];
-                currentSummand = parseResult.suffixMultiplicator;
-            }
-        } else {
-            return nil;
-        }
-    } else {
-        NSDecimalNumber *result = [lastElement evaluate:error];
-        if (result) {
-            currentSummand = [currentSummand decimalNumberByMultiplyingBy:result];
-        } else {
-            return nil;
-        }
-    }
-    value = [value decimalNumberByAdding:currentSummand];
     
+    NSDecimalNumber *value = [NSDecimalNumber zero];
+    for (MPParsedProduct *product in products) {
+        value = [value decimalNumberByAdding:product.value];
+    }
     return value;
 }
 

MathPad/MPParseError.h

@@ -2,20 +2,25 @@
 //  MPParseError.h
 //  MathPad
 //
-//  Created by Kim Wittenburg on 06.09.14.
+//  Created by Kim Wittenburg on 08.09.14.
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
 #import <Foundation/Foundation.h>
 
-#define MPParseError(index,key) [[MPParseError alloc] initWithErrorIndex:index errorMessageKey:key]
+#define MPParseError(range,key) [[MPParseError alloc] initWithErrorRange:range errorMessageKey:key]
 
 @interface MPParseError : NSObject
 
-- (instancetype)initWithErrorIndex:(NSUInteger)errorIndex
+- (instancetype)initWithErrorRange:(NSRange)errorRange
-                   errorMessageKey:(NSString *)errorMessageKey;
+                   errorMessageKey:(NSString *)key;
 
-@property (nonatomic) NSUInteger errorIndex;
+- (instancetype)initWithErrorRange:(NSRange)errorRange
-@property (nonatomic) NSString *localizedErrorMessage;
+             localizederrorMessage:(NSString *)errorMessage;
 
-@end
+@property (nonatomic, strong) NSIndexPath *pathToExpression;
+
+@property (nonatomic) NSRange errorRange;
+@property (nonatomic, copy) NSString *localizedErrorMessage;
+
+@end

MathPad/MPParseError.m

@@ -2,7 +2,7 @@
 //  MPParseError.m
 //  MathPad
 //
-//  Created by Kim Wittenburg on 06.09.14.
+//  Created by Kim Wittenburg on 08.09.14.
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
@@ -10,19 +10,29 @@
 
 @implementation MPParseError
 
-- (instancetype)initWithErrorIndex:(NSUInteger)errorIndex errorMessageKey:(NSString *)errorMessageKey
+- (instancetype)initWithErrorRange:(NSRange)errorRange errorMessageKey:(NSString *)key
 {
     self = [super init];
     if (self) {
-        _errorIndex = errorIndex;
+        _errorRange = errorRange;
-        _localizedErrorMessage = NSLocalizedString(errorMessageKey, nil);
+        _localizedErrorMessage = NSLocalizedString(key, nil);
+    }
+    return self;
+}
+
+- (instancetype)initWithErrorRange:(NSRange)errorRange localizederrorMessage:(NSString *)errorMessage
+{
+    self = [super init];
+    if (self) {
+        _errorRange = errorRange;
+        _localizedErrorMessage = errorMessage;
     }
     return self;
 }
 
 - (NSString *)description
 {
-    return [NSString stringWithFormat:@"MPParseError<at=%ld message=\"%@\">", self.errorIndex, self.localizedErrorMessage];
+    return [NSString stringWithFormat:@"MPParseError<at=(%ld, %ld) message=\"%@\">", self.errorRange.location, self.errorRange.length, self.localizedErrorMessage];
 }
 
 @end

MathPad/MPParsedFactor.h

@@ -0,0 +1,22 @@
+//
+//  MPParsedFactor.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 10.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import <Foundation/Foundation.h>
+
+@interface MPParsedFactor : NSObject
+
++ (MPParsedFactor *)factorWithDecimalNumber:(NSDecimalNumber *)number;
++ (MPParsedFactor *)sinFactorWithFactor:(MPParsedFactor *)factor;
++ (MPParsedFactor *)cosFactorWithFactor:(MPParsedFactor *)factor;
++ (MPParsedFactor *)tanFactorWithFactor:(MPParsedFactor *)factor;
+
+- (instancetype)initWithDecimalNumber:(NSDecimalNumber *)number;
+
+- (NSDecimalNumber *)value;
+
+@end

MathPad/MPParsedFactor.m

@@ -0,0 +1,60 @@
+//
+//  MPParsedFactor.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 10.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPParsedFactor.h"
+
+@implementation MPParsedFactor {
+    NSDecimalNumber *_value;
+}
+
++ (MPParsedFactor *)factorWithDecimalNumber:(NSDecimalNumber *)number
+{
+    return [[MPParsedFactor alloc] initWithDecimalNumber:number];
+}
+
++ (MPParsedFactor *)sinFactorWithFactor:(MPParsedFactor *)factor
+{
+    double value = factor.value.doubleValue;
+    NSDecimalNumber *actualNumber = [[NSDecimalNumber alloc] initWithDouble:sin(value)];
+    return [[MPParsedFactor alloc] initWithDecimalNumber:actualNumber];
+}
+
++ (MPParsedFactor *)cosFactorWithFactor:(MPParsedFactor *)factor
+{
+    double value = factor.value.doubleValue;
+    NSDecimalNumber *actualNumber = [[NSDecimalNumber alloc] initWithDouble:cos(value)];
+    return [[MPParsedFactor alloc] initWithDecimalNumber:actualNumber];
+}
+
++ (MPParsedFactor *)tanFactorWithFactor:(MPParsedFactor *)factor
+{
+    double value = factor.value.doubleValue;
+    NSDecimalNumber *actualNumber = [[NSDecimalNumber alloc] initWithDouble:tan(value)];
+    return [[MPParsedFactor alloc] initWithDecimalNumber:actualNumber];
+}
+
+- (instancetype)initWithDecimalNumber:(NSDecimalNumber *)number
+{
+    self = [super init];
+    if (self) {
+        _value = number;
+    }
+    return self;
+}
+
+- (NSDecimalNumber *)value
+{
+    return _value;
+}
+
+- (NSString *)description
+{
+    return [NSString stringWithFormat:@"MPParsedFactor<%@>", _value];
+}
+
+@end

MathPad/MPParsedProduct.h

@@ -0,0 +1,20 @@
+//
+//  MPParsedSummand.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 10.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import <Foundation/Foundation.h>
+#import "MPParsedFactor.h"
+
+@interface MPParsedProduct : NSObject
+
+@property (readonly, nonatomic, strong) NSArray *factors;
+
+- (void)addFactor:(MPParsedFactor *)factor;
+
+- (NSDecimalNumber *)value;
+
+@end

MathPad/MPParsedProduct.m

@@ -0,0 +1,51 @@
+//
+//  MPParsedSummand.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 10.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPParsedProduct.h"
+
+@implementation MPParsedProduct {
+    NSMutableArray *_factors;
+}
+
+- (instancetype)init
+{
+    self = [super init];
+    if (self) {
+        _factors = [[NSMutableArray alloc] init];
+    }
+    return self;
+}
+
+- (NSArray *)factors
+{
+    return _factors;
+}
+
+- (void)addFactor:(MPParsedFactor *)factor
+{
+    [_factors addObject:factor];
+}
+
+- (NSDecimalNumber *)value
+{
+    if (_factors.count == 0) {
+        return [NSDecimalNumber zero];
+    }
+    NSDecimalNumber *value = [NSDecimalNumber one];
+    for (MPParsedFactor *factor in _factors) {
+        value = [value decimalNumberByMultiplyingBy:factor.value];
+    }
+    return value;
+}
+
+- (NSString *)description
+{
+    return [NSString stringWithFormat:@"MPParsedProduct<%@>", [_factors componentsJoinedByString:@"*"]];
+}
+
+@end

MathPad/MPSumFunctionLayout.m

@@ -33,6 +33,14 @@
     return 2;
 }
 
+- (NSUInteger)indexOfChildAfterChildAtIndex:(NSUInteger)index
+{
+    if (index != 2) {
+        return 2;
+    }
+    return [super indexOfChildAfterChildAtIndex:index];
+}
+
 - (CTLineRef)line
 {
     CTLineRef line = [self lineForPrivateCacheIndex:0 generator:^CTLineRef{

MathPad/NSRegularExpression+MPParsingAdditions.h

@@ -0,0 +1,21 @@
+//
+//  NSRegularExpression+MPParsingAdditions.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 09.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import <Foundation/Foundation.h>
+
+#define MPStringRange(string) NSMakeRange(0, [string length])
+#define MPStringRangeFrom(from, string) NSMakeRange(from, [string length]-from)
+
+@interface NSRegularExpression (MPParsingAdditions)
+
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string;
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string fromIndex:(NSUInteger)start;
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string options:(NSMatchingOptions)options;
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string options:(NSMatchingOptions)options fromIndex:(NSUInteger)start;
+
+@end

MathPad/NSRegularExpression+MPParsingAdditions.m

@@ -0,0 +1,33 @@
+//
+//  NSRegularExpression+MPParsingAdditions.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 09.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "NSRegularExpression+MPParsingAdditions.h"
+
+@implementation NSRegularExpression (MPParsingAdditions)
+
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string
+{
+    return [self firstMatchInString:string options:0 range:MPStringRange(string)];
+}
+
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string fromIndex:(NSUInteger)start
+{
+    return [self firstMatchInString:string options:0 range:NSMakeRange(start, [string length]-start)];
+}
+
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string options:(NSMatchingOptions)options
+{
+    return [self firstMatchInString:string options:options range:MPStringRange(string)];
+}
+
+- (NSTextCheckingResult *)firstMatchInString:(NSString *)string options:(NSMatchingOptions)options fromIndex:(NSUInteger)start
+{
+    return [self firstMatchInString:string options:options range:NSMakeRange(start, [string length]-start)];
+}
+
+@end

MathPad/NSString+MPExpressionElement.m

@@ -21,9 +21,4 @@
     return NO;
 }
 
-- (NSDecimalNumber *)evaluate:(MPParseError *__autoreleasing *)error
-{
-    return [[[MPElementParser alloc] init] parseElement:self error:error].standaloneValue;
-}
-
 @end