Fundamental Redesign of Evaluation

MathPad/MPElementaryFunctionTerm.h

@@ -0,0 +1,20 @@
+//
+//  MPFunctionValue.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 11.10.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+@class MPElementaryFunctionTerm, MPValueGroup;
+
+@interface MPElementaryFunctionTerm : MPTerm
+
+- (instancetype)initWithFunctionIdentifier:(NSString *)function
+                                      term:(MPTerm *)term; /* designated initializer */
+
+@property (readonly, nonatomic, strong) MPTerm *term;
+
+@end

MathPad/MPElementaryFunctionTerm.m

@@ -0,0 +1,109 @@
+//
+//  MPFunctionValue.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 11.10.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPElementaryFunctionTerm.h"
+
+#import "MPParsedExpression.h"
+#import "MPPowerFunction.h"
+#import "MPProductTerm.h"
+#import "MPTokenStream.h"
+#import "MPToken.h"
+
+#import "MPExpression.h"
+#import "MPMathRules.h"
+
+@implementation MPElementaryFunctionTerm {
+    NSDecimalNumber *(^_function)(NSDecimalNumber *);
+}
+
+- (instancetype)initWithFunctionIdentifier:(NSString *)function
+                                      term:(MPTerm *)term
+{
+    self = [super init];
+    if (self) {
+        NSAssert(function != nil, @"function must not be nil.");
+        NSAssert(term != nil, @"term must not be nil.");
+        double (*func)(double);
+        BOOL takesArc = NO;
+        BOOL returnsArc = NO;
+        if ([function isEqualToString:@"sin"]) {
+            func = &sin;
+            takesArc = YES;
+        } else if ([function isEqualToString:@"cos"]) {
+            func = &cos;
+            takesArc = YES;
+        } else if ([function isEqualToString:@"tan"]) {
+            func = &tan;
+            takesArc = YES;
+        } else if ([function isEqualToString:@"asin"]) {
+            func = &asin;
+            returnsArc = YES;
+        } else if ([function isEqualToString:@"acos"]) {
+            func = &acos;
+            returnsArc = YES;
+        } else if ([function isEqualToString:@"atan"]) {
+            func = &atan;
+            returnsArc = YES;
+        } else {
+            NSAssert(true, @"function must be one of (sin, cos, tan, asin, acos, atan).");
+        }
+        [self setFunction:func
+            takesArcValue:takesArc
+          returnsArcValue:returnsArc];
+        _term = term;
+    }
+    return self;
+}
+
+- (void)setFunction:(double (*)(double))function
+      takesArcValue:(BOOL)takesArc
+    returnsArcValue:(BOOL)returnsArc
+{
+    id __weak weakSelf = self;
+    _function = ^(NSDecimalNumber *value){
+        if (takesArc) {
+            value = [weakSelf convertToRadiantsIfNecessary:value];
+        }
+        NSDecimalNumber *returnValue = [[NSDecimalNumber alloc] initWithDouble:function(value.doubleValue)];
+        if (returnsArc) {
+            returnValue = [weakSelf convertToDegreesIfNecessary:returnValue];
+        }
+        return returnValue;
+    };
+}
+
+- (NSDecimalNumber *)convertToRadiantsIfNecessary:(NSDecimalNumber *)degrees
+{
+    if ([MPMathRules sharedRules].isUsingDegrees) {
+        // * M_PI / 180
+        return [[degrees decimalNumberByMultiplyingBy:[[NSDecimalNumber alloc] initWithDouble:M_PI]] decimalNumberByDividingBy:[[NSDecimalNumber alloc] initWithInteger:180]];
+    } else {
+        return degrees;
+    }
+}
+
+- (NSDecimalNumber *)convertToDegreesIfNecessary:(NSDecimalNumber *)radiants
+{
+    if ([MPMathRules sharedRules].isUsingDegrees) {
+        // * 180 / M_PI
+        return [[radiants decimalNumberByMultiplyingBy:[[NSDecimalNumber alloc] initWithInteger:180]] decimalNumberByDividingBy:[[NSDecimalNumber alloc] initWithDouble:M_PI]];
+    } else {
+        return radiants;
+    }
+}
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *value = [self.term evaluate:error];
+    if (!value) {
+        return nil;
+    }
+    return _function(value);
+}
+
+@end

MathPad/MPEvaluationContext.h

@@ -15,9 +15,11 @@
 - (void)push;
 - (void)pop;
 
-- (void)defineVariable:(NSString *)variable withValue:(NSDecimalNumber *)value;
+- (BOOL)defineVariable:(NSString *)variable
+                 value:(NSDecimalNumber *)value;
+- (BOOL)redefineVariable:(NSString *)variable
+                   value:(NSDecimalNumber *)value;
 - (void)undefineVariable:(NSString *)variable;
-- (BOOL)isVariableDefined:(NSString *)variable;
 
 - (NSDecimalNumber *)valueForVariable:(NSString *)variable;
 

MathPad/MPEvaluationContext.m

@@ -32,8 +32,10 @@ static MPEvaluationContext *sharedContext;
     if (self) {
         _stack = [[NSMutableArray alloc] init];
         [self push];
-        [self defineVariable:@"e" withValue:[[NSDecimalNumber alloc] initWithDouble:M_E]];
-        [self defineVariable:@"π" withValue:[[NSDecimalNumber alloc] initWithDouble:M_PI]];
+        [self defineVariable:@"e"
+                       value:[[NSDecimalNumber alloc] initWithDouble:M_E]];
+        [self defineVariable:@"π"
+                       value:[[NSDecimalNumber alloc] initWithDouble:M_PI]];
     }
     return self;
 }
@@ -48,10 +50,23 @@ static MPEvaluationContext *sharedContext;
     [self.stack removeLastObject];
 }
 
-- (void)defineVariable:(NSString *)variable withValue:(NSDecimalNumber *)value
+- (BOOL)defineVariable:(NSString *)variable
+                 value:(NSDecimalNumber *)value
 {
+    if ([self isVariableDefined:variable]) {
+        return NO;
+    }
     NSMutableDictionary *currentBindings = self.stack.lastObject;
     currentBindings[variable] = value;
+    return YES;
+}
+
+- (BOOL)redefineVariable:(NSString *)variable
+                   value:(NSDecimalNumber *)value
+{
+    [self undefineVariable:variable];
+    return [self defineVariable:variable
+                          value:value];
 }
 
 - (void)undefineVariable:(NSString *)variable
@@ -60,6 +75,11 @@ static MPEvaluationContext *sharedContext;
     [currentBindings removeObjectForKey:variable];
 }
 
+- (BOOL)isVariableDefined:(NSString *)variable
+{
+    return [self valueForVariable:variable] != nil;
+}
+
 - (NSDecimalNumber *)valueForVariable:(NSString *)variable
 {
     NSUInteger currentIndex = self.stack.count;
@@ -72,9 +92,4 @@ static MPEvaluationContext *sharedContext;
     return value;
 }
 
-- (BOOL)isVariableDefined:(NSString *)variable
-{
-    return [self valueForVariable:variable] != nil;
-}
-
 @end

MathPad/MPExpression.h

@@ -31,57 +31,6 @@ FOUNDATION_EXPORT NSString *const MPIllegalElementException;
 FOUNDATION_EXPORT NSString *const MPIllegalElementExceptionElementKey;
 
 
-/*!
-    @const      MPMathKitErrorDomain
-    @brief      Predefined error domain for errors from the MathKit framework.
- 
-    @discussion Errors in MathKit can occur during parsing of expressions or
-                during evaluation of expressions. These two can be distinguished
-                by the error code. Parsing errors have lower error codes.
-                Evaluation errors (math errors) have error codes from @c 100 upwards.
- */
-FOUNDATION_EXPORT NSString *const MPMathKitErrorDomain;
-
-
-// TODO: Deal with this:
-// FOUNDATION_EXPORT NSString *const MPPathToExpressionKey;
-// FOUNDATION_EXPORT NSString *const MPRangeKey;
-
-
-/*!
-    @function   MPParseError
-    @brief      Creates an @c NSError object in the @c MPMathKitErrorDomain.
- 
-    @discussion The created error is filled with the passed data if present.
- 
-    @param      errorCode
-                The error code of the created error.
- 
-    @param      errorDescription
-                The localized description of the created error. May be @c nil.
- 
-    @param      underlyingError
-                The underlying error of the created error. May be @c nil.
- 
-    @return     An @c NSError object initialized with the given data.
- */
-NS_INLINE NSError * MPParseError(NSInteger errorCode,
-                                 NSString *errorDescription,
-                                 NSError *underlyingError) {
-    NSMutableDictionary *userInfo = [[NSMutableDictionary alloc] init];
-    if (errorDescription) {
-        userInfo[NSLocalizedDescriptionKey] = errorDescription;
-    }
-    if (underlyingError) {
-        userInfo[NSUnderlyingErrorKey] = underlyingError;
-    }
-    NSError *error = [NSError errorWithDomain:MPMathKitErrorDomain
-                                         code:errorCode
-                                     userInfo:userInfo.copy];
-    return error;
-}
-
-
 /*!
     @typedef    MPReferenceFrame
     @brief      A reference frame describes what an @em item is.
@@ -116,7 +65,7 @@ typedef NS_ENUM(NSUInteger, MPReferenceFrame) {
 
 
 
-@class MPExpression, MPFunction, MPRangePath, MPExpressionTree, MPExpressionEvaluator;
+@class MPExpression, MPFunction, MPRangePath, MPParsedExpression;
 @protocol MPExpressionElement, MPToken;
 
 /*!
@@ -630,7 +579,7 @@ typedef NS_ENUM(NSUInteger, MPReferenceFrame) {
                 want more control over the evaluation process use @c -parse
                 instead.
  
-    @param      error
+    @param      errors
                 If the receiver (or any of its elements) contains a syntax error
                 or can not be evaluated this parameter is set to an appropriate
                 value. Pass @c NULL if you are not interested in any errors that
@@ -642,7 +591,7 @@ typedef NS_ENUM(NSUInteger, MPReferenceFrame) {
                 math error. In most cases the error parameter contains an
                 appropriate description of the problem.
  */
-- (NSDecimalNumber *)evaluateWithError:(NSError *__autoreleasing *)error;
+- (NSDecimalNumber *)evaluateWithErrors:(NSArray *__autoreleasing *)errors;
 
 
 /*!
@@ -657,7 +606,10 @@ typedef NS_ENUM(NSUInteger, MPReferenceFrame) {
  
     @return     A @c MPExpressionTree object that can evaluate the receiver.
  */
-- (MPExpressionTree *)parse;
+- (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors;
+
+- (MPParsedExpression *)parseExpectingVariable:(BOOL)flag
+                                        errors:(NSArray *__autoreleasing *)errors;
 
 
 #pragma mark Notifications

MathPad/MPExpression.m

@@ -14,9 +14,9 @@
 #import "MPRangePath.h"
 
 #import "MPExpressionTokenizer.h"
-#import "MPTokenStream.h"
 #import "MPToken.h"
-#import "MPExpressionTree.h"
+#import "MPExpressionParser.h"
+#import "MPParsedExpression.h"
 
 #import "NSIndexPath+MPAdditions.h"
 
@@ -25,10 +25,6 @@
 NSString *const MPIllegalElementException = @"MPIllegalElementException";
 NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptionElementKey";
 
-NSString *const MPMathKitErrorDomain = @"MPMathKitErrorDomain";
-NSString *const MPExpressionPathErrorKey = @"MPExpressionPathErrorKey";
-
-
 
 @interface MPExpression () {
     NSMutableArray * _elements;
@@ -328,7 +324,11 @@ NSString *const MPExpressionPathErrorKey = @"MPExpressionPathErrorKey";
             break;
             
         case MPTokenReferenceFrame:
-            symbolIndex = [self.tokens[anIndex] range].location;
+            [self.tokens enumerateObjectsUsingBlock:^(id<MPToken> obj, NSUInteger idx, BOOL *stop) {
+                symbolIndex += obj.range.length;
+                *stop = idx >= anIndex - 1;
+            }];
+//            symbolIndex = [self.tokens[anIndex] range].location;
             break;
     }
     
@@ -556,17 +556,38 @@ NSString *const MPExpressionPathErrorKey = @"MPExpressionPathErrorKey";
 #pragma mark Evaluating Expressions
 
 
-- (NSDecimalNumber *)evaluateWithError:(NSError *__autoreleasing *)error
+- (NSDecimalNumber *)evaluateWithErrors:(NSArray *__autoreleasing *)errors
 {
-    MPExpressionTree *tree = [self parse];
-    return [tree validate:error] ? [tree evaluate] : nil;
+    NSArray *parsingErrors;
+    MPParsedExpression *parsedExpression = [self parse:&parsingErrors];
+    NSError *evaluationError;
+    NSDecimalNumber *result = parsedExpression ? [parsedExpression evaluate:&evaluationError] : nil;
+    if (errors) {
+        NSMutableArray *localErrors = [[NSMutableArray alloc] initWithCapacity:parsingErrors.count+1];
+        if (parsingErrors) {
+            [localErrors addObjectsFromArray:parsingErrors];
+        }
+        if (evaluationError) {
+            [localErrors addObject:evaluationError];
+        }
+        *errors = localErrors;
+    }
+    return result;
 }
 
 
-- (MPExpressionTree *)parse
+- (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors
 {
-    MPTokenStream *tokenStream = [[MPTokenStream alloc] initWithTokens:self.tokens];
-    return [[MPExpressionTree alloc] initWithTokenStream:tokenStream];
+    return [self parseExpectingVariable:NO
+                                 errors:errors];
+}
+
+
+- (MPParsedExpression *)parseExpectingVariable:(BOOL)flag
+                                        errors:(NSArray *__autoreleasing *)errors
+{
+    return [[[MPExpressionParser alloc] initWithExpression:self] parseExpectingVariableDefinition:flag
+                                                                                           errors:errors];
 }
 
 

MathPad/MPExpressionParser.h

@@ -0,0 +1,22 @@
+//
+//  MPExpressionParser.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 16.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPExpression.h"
+#import "MPParsedExpression.h"
+
+@interface MPExpressionParser : NSObject
+
+@property (readonly, nonatomic, strong) MPExpression *expression;
+
+- (instancetype)initWithExpression:(MPExpression *)expression;
+
+- (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors;
+- (MPParsedExpression *)parseExpectingVariableDefinition:(BOOL)flag
+                                                  errors:(NSArray *__autoreleasing *)errors;
+
+@end

MathPad/MPExpressionParser.m

@@ -0,0 +1,416 @@
+//
+//  MPExpressionParser.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 16.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPExpressionParser.h"
+
+#import "MPExpression.h"
+#import "MPTokenStream.h"
+#import "MPTerm.h"
+#import "MPToken.h"
+#import "MPSumTerm.h"
+#import "MPProductTerm.h"
+#import "MPFactorialTerm.h"
+#import "MPElementaryFunctionTerm.h"
+#import "MPFunctionTerm.h"
+#import "MPPowerTerm.h"
+#import "MPNegatedTerm.h"
+
+#import "MPNumber.h"
+#import "MPVariable.h"
+#import "MPFactorialTerm.h"
+
+#define success() state = 0
+#define fail() state = -1
+
+@interface MPExpressionParser ()
+
+@property (nonatomic, strong) NSArray *tokens;
+@property (nonatomic) NSUInteger currentTokenIndex;
+
+@property (nonatomic, strong) NSMutableArray *errors;
+
+@property (nonatomic, strong) NSMutableArray *summands;
+@property (nonatomic) BOOL summandNegative;
+@property (nonatomic, strong) NSMutableArray *factors;
+@property (nonatomic) BOOL factorNegative;
+@property (nonatomic, strong) NSMutableArray *functionStack;
+@property (nonatomic, strong) NSMutableArray *valueGroup;
+@property (nonatomic, strong) MPTerm *value;
+
+@property (nonatomic) NSUInteger errorTokenIndex;
+
+@end
+
+@implementation MPExpressionParser
+
+- (instancetype)initWithExpression:(MPExpression *)expression
+{
+    self = [super init];
+    if (self) {
+        _tokens = [expression allItemsInReferenceFrame:MPTokenReferenceFrame];
+        _expression = expression;
+    }
+    return self;
+}
+
+- (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors
+{
+    return [self parseExpectingVariableDefinition:NO
+                                           errors:errors];
+}
+
+- (MPParsedExpression *)parseExpectingVariableDefinition:(BOOL)flag
+                                                  errors:(NSArray *__autoreleasing *)errors
+{
+    MPParsedExpression *result = [[MPParsedExpression alloc] init];
+    self.currentTokenIndex = 0;
+    
+    BOOL hasVariableDefinition = NO;
+    NSString *variableName = nil;
+    [self skipWhitespaces];
+    if (self.currentToken.tokenType == MPVariableToken) {
+        variableName = self.currentToken.stringValue;
+        [self nextToken];
+        [self skipWhitespaces];
+        if (self.currentToken.tokenType == MPEqualsToken) {
+            [self nextToken];
+            hasVariableDefinition = YES;
+        }
+    }
+    if (flag && hasVariableDefinition) {
+        result.definedVariable = variableName;
+    } else if (flag) {
+        [self addErrorWithCode:3 localizedDescription:NSLocalizedString(@"Expected Variable Definition.", nil)];
+        if (errors) {
+            *errors = self.errors;
+        }
+        return nil;
+    } else if (hasVariableDefinition) {
+        [self addErrorWithCode:4 localizedDescription:NSLocalizedString(@"Unexpected Variable Definition.", nil)];
+        if (errors) {
+            *errors = self.errors;
+        }
+        return nil;
+    } else {
+        self.currentTokenIndex = 0;
+    }
+    
+    [self skipWhitespaces];
+    if (self.currentTokenIndex >= self.tokens.count) {
+        [self addErrorWithCode:5 localizedDescription:NSLocalizedString(@"Empty Expression.", nil)];
+        if (errors) {
+            *errors = self.errors;
+        }
+        return nil;
+    }
+    
+    [self runParserMachine];
+    if ([self errorOccured]) {
+        if (errors) {
+            *errors = self.errors;
+        }
+        return nil;
+    }
+    result.term = [[MPSumTerm alloc] initWithSummands:self.summands];
+    return result;
+}
+
+- (void)runParserMachine
+{
+    NSInteger state = 1;
+    NSInteger backtraceState = 0;
+    NSUInteger backtraceTokenIndex = self.currentTokenIndex;
+    BOOL alternateRoute = NO;
+    while (state != 0) {
+        switch (state) {
+            case -1:
+                state = backtraceState;
+                self.currentTokenIndex = backtraceTokenIndex;
+                alternateRoute = YES;
+                break;
+                
+            case 1:
+                [self skipWhitespaces];
+                if (self.currentToken.tokenType == MPOperatorListToken) {
+                    self.factorNegative = [self parseOperatorList:self.currentToken];
+                    [self nextToken];
+                    state = 2;
+                } else {
+                    self.factorNegative = NO;
+                    state = 2;
+                }
+                break;
+                
+            case 2:
+                [self skipWhitespaces];
+                if (self.currentToken.tokenType == MPElementaryFunctionToken) {
+                    [self.functionStack addObject:self.currentToken.stringValue];
+                    [self nextToken];
+                    state = 2;
+                } else {
+                    state = 3;
+                }
+                break;
+                
+            case 3:
+                [self skipWhitespaces];
+                if (self.currentToken.tokenType == MPGenericFunctionToken) {
+                    NSArray *errors;
+                    self.value = [[MPFunctionTerm alloc] initWithFunction:(MPFunction *)self.currentToken
+                                                                   errors:&errors];
+                    if (!self.value) {
+                        [self.errors addObjectsFromArray:errors];
+                    }
+                    [self nextToken];
+                    [self runSuffixMachine];
+                    if (self.value) {
+                        [self.valueGroup addObject:self.value];
+                    }
+                    state = 6;
+                } else {
+                    state = 4;
+                }
+                break;
+                
+            case 4:
+                if (self.currentToken.tokenType == MPNumberToken) {
+                    self.value = [[MPNumber alloc] initWithNumber:[self parseNumber:self.currentToken]];
+                    [self nextToken];
+                    [self runSuffixMachine];
+                    [self.valueGroup addObject:self.value];
+                    state = 5;
+                } else if (self.currentToken.tokenType == MPVariableToken) {
+                    self.value = [[MPVariable alloc] initWithVariableName:[self parseVariable:self.currentToken]];
+                    [self nextToken];
+                    [self runSuffixMachine];
+                    [self.valueGroup addObject:self.value];
+                    state = 5;
+                } else {
+                    self.errorTokenIndex = self.currentTokenIndex;
+                    fail();
+                }
+                break;
+                
+            case 5:
+                if (alternateRoute) {
+                    alternateRoute = NO;
+                    state = 6;
+                } else {
+                    backtraceState = 5;
+                    backtraceTokenIndex = self.currentTokenIndex;
+                    state = 4;
+                }
+                break;
+                
+            case 6:
+                [self collapseFactor];
+                [self skipWhitespaces];
+                backtraceState = 6;
+                backtraceTokenIndex = self.currentTokenIndex;
+                if (!alternateRoute && self.currentToken.tokenType == MPOperatorListToken) {
+                    [self collapseSummand];
+                    self.summandNegative = [self parseOperatorList:self.currentToken];
+                    [self nextToken];
+                    state = 1;
+                } else {
+                    state = 7;
+                }
+                break;
+                
+            case 7:
+                if (alternateRoute) {
+                    [self collapseSummand];
+                    alternateRoute = NO;
+                    success();
+                } else {
+                    backtraceState = 7;
+                    backtraceTokenIndex = self.currentTokenIndex;
+                    state = 8;
+                }
+                break;
+                
+            case 8:
+                [self skipWhitespaces];
+                if (self.currentToken.tokenType == MPMultiplicationSymbolToken) {
+                    [self nextToken];
+                    state = 1;
+                } else {
+                    state = 1;
+                }
+                break;
+                
+            default:
+                // Should never get here
+                break;
+        }
+    }
+}
+
+- (void)skipWhitespaces
+{
+    while ([self currentToken] != nil && [self currentToken].tokenType == MPWhitespaceToken) {
+        [self nextToken];
+    }
+}
+
+- (id<MPToken>)currentToken
+{
+    if (self.currentTokenIndex >= self.tokens.count) {
+        return nil;
+    }
+    return self.tokens[self.currentTokenIndex];
+}
+
+- (void)nextToken
+{
+    self.currentTokenIndex++;
+}
+
+- (NSMutableArray *)errors
+{
+    if (!_errors) {
+        _errors = [[NSMutableArray alloc] init];
+    }
+    return _errors;
+}
+
+- (NSMutableArray *)summands
+{
+    if (!_summands) {
+        _summands = [[NSMutableArray alloc] init];
+    }
+    return _summands;
+}
+
+- (NSMutableArray *)factors
+{
+    if (!_factors) {
+        _factors = [[NSMutableArray alloc] init];
+    }
+    return _factors;
+}
+
+- (NSMutableArray *)functionStack
+{
+    if (!_functionStack) {
+        _functionStack = [[NSMutableArray alloc] init];
+    }
+    return _functionStack;
+}
+
+- (NSMutableArray *)valueGroup
+{
+    if (!_valueGroup) {
+        _valueGroup = [[NSMutableArray alloc] init];
+    }
+    return _valueGroup;
+}
+
+- (BOOL)parseOperatorList:(id<MPToken>)token // Returns YES if list is overall negative
+{
+    NSString *operatorString = [[token.stringValue stringByReplacingOccurrencesOfString:@" " withString:@""]
+                                                   stringByReplacingOccurrencesOfString:@"+" withString:@""];
+    return (operatorString.length & 1) == 1;
+}
+
+- (NSDecimalNumber *)parseNumber:(id<MPToken>)token
+{
+    return [NSDecimalNumber decimalNumberWithString:token.stringValue
+                                             locale:[NSLocale currentLocale]];
+}
+
+- (NSString *)parseVariable:(id<MPToken>)token
+{
+    return token.stringValue;
+}
+
+- (void)collapseSummand
+{
+    if (self.factors.count > 0) {
+        MPTerm *summand = [[MPProductTerm alloc] initWithFactors:self.factors];
+        if (self.summandNegative) {
+            summand = [[MPNegatedTerm alloc] initWithTerm:summand];
+        }
+        [self.summands addObject:summand];
+    }
+    self.factors = nil;
+    self.summandNegative = NO;
+}
+
+- (void)collapseFactor
+{
+    if (self.valueGroup.count > 0) {
+        MPTerm *factor = [[MPProductTerm alloc] initWithFactors:self.valueGroup];
+        for (NSInteger index = self.functionStack.count - 1; index >= 0; index--) {
+            factor = [[MPElementaryFunctionTerm alloc] initWithFunctionIdentifier:self.functionStack[index]
+                                                                             term:factor];
+        }
+        if (self.factorNegative) {
+            factor = [[MPNegatedTerm alloc] initWithTerm:factor];
+        }
+        [self.factors addObject:factor];
+    }
+    self.valueGroup = nil;
+    self.functionStack = nil;
+    self.factorNegative = NO;
+}
+
+- (void)runSuffixMachine
+{
+    BOOL checkMore = YES;
+    while (checkMore) {
+        if (self.currentToken.tokenType == MPFactorialToken) {
+            [self nextToken];
+            if (self.value) {
+                MPFactorialTerm *term = [[MPFactorialTerm alloc] initWithTerm:self.value];
+                self.value = term;
+            }
+        } else if (self.currentToken.tokenType == MPPowerToken) {
+            [self nextToken];
+            if (self.value) {
+                NSArray *errors;
+                MPPowerTerm *term = [[MPPowerTerm alloc] initWithFunction:(MPFunction *)self.currentToken errors:&errors];
+                if (!term) {
+                    [self.errors addObjectsFromArray:errors];
+                }
+                term.baseTerm = self.value;
+                self.value = term;
+            }
+        } else {
+            checkMore = NO;
+        }
+    }
+}
+
+- (void)addErrorWithCode:(NSInteger)code
+    localizedDescription:(NSString *)description
+{
+    NSInteger errorIndex = [self.expression convertIndex:self.errorTokenIndex
+                                      fromReferenceFrame:MPTokenReferenceFrame
+                                        toReferenceFrame:MPSymbolReferenceFrame];
+    [self.errors addObject:[NSError errorWithDomain:MPMathKitErrorDomain
+                                               code:code
+                                           userInfo:@{NSLocalizedDescriptionKey: description,
+                                                      MPPathToExpressionKey: self.expression.indexPath,
+                                                      MPErrorIndexKey: @(errorIndex)}]];
+}
+
+- (BOOL)errorOccured
+{
+    [self skipWhitespaces];
+    if (self.currentTokenIndex < self.tokens.count) {
+        if (self.errorTokenIndex >= self.tokens.count) {
+            [self addErrorWithCode:0 localizedDescription:NSLocalizedString(@"Unexpected end. Expected Value.", nil)];
+        } else {
+            [self addErrorWithCode:1 localizedDescription:NSLocalizedString(@"Unexpected Symbol. Expected Value", nil)];
+        }
+    }
+    return self.errors.count > 0;
+}
+
+@end

MathPad/MPExpressionTokenizer.m

@@ -51,12 +51,7 @@
                             @"([\\*∙⋅])|"
                             @"([+-](?:\\s*[+-])*)|"
                             @"((?:\\d+(?:%@\\d+)?)|(?:%@\\d+))|"
-                            @"(sin)|"
-                            @"(cos)|"
-                            @"(tan)|"
-                            @"(asin)|"
-                            @"(acos)|"
-                            @"(atan)|"
+                            @"(sin|cos|tan|asin|acos|atan)|"
                             @"([A-Za-z])|"
                             @"(!)|"
                             @"(=)|"
@@ -76,16 +71,11 @@
             NSRange multiplicationSymbolRange = [match rangeAtIndex:1];
             NSRange operatorRange = [match rangeAtIndex:2];
             NSRange numberRange = [match rangeAtIndex:3];
-            NSRange sinRange = [match rangeAtIndex:4];
-            NSRange cosRange = [match rangeAtIndex:5];
-            NSRange tanRange = [match rangeAtIndex:6];
-            NSRange asinRange = [match rangeAtIndex:7];
-            NSRange acosRange = [match rangeAtIndex:8];
-            NSRange atanRange = [match rangeAtIndex:9];
-            NSRange variableRange = [match rangeAtIndex:10];
-            NSRange factorialRange = [match rangeAtIndex:11];
-            NSRange equalsRange = [match rangeAtIndex:12];
-            NSRange whitespaceRange = [match rangeAtIndex:13];
+            NSRange elementaryFunctionRange = [match rangeAtIndex:4];
+            NSRange variableRange = [match rangeAtIndex:5];
+            NSRange factorialRange = [match rangeAtIndex:6];
+            NSRange equalsRange = [match rangeAtIndex:7];
+            NSRange whitespaceRange = [match rangeAtIndex:8];
         
             if (MPRangeExists(multiplicationSymbolRange)) {
                 range = multiplicationSymbolRange;
@@ -96,24 +86,9 @@
             } else if (MPRangeExists(numberRange)) {
                 range = numberRange;
                 tokenType = MPNumberToken;
-            } else if (MPRangeExists(sinRange)) {
-                range = sinRange;
-                tokenType = MPSinToken;
-            } else if (MPRangeExists(cosRange)) {
-                range = cosRange;
-                tokenType = MPCosToken;
-            } else if (MPRangeExists(tanRange)) {
-                range = tanRange;
-                tokenType = MPTanToken;
-            } else if (MPRangeExists(asinRange)) {
-                range = asinRange;
-                tokenType = MPASinToken;
-            } else if (MPRangeExists(acosRange)) {
-                range = acosRange;
-                tokenType = MPACosToken;
-            } else if (MPRangeExists(atanRange)) {
-                range = atanRange;
-                tokenType = MPATanToken;
+            } else if (MPRangeExists(elementaryFunctionRange)) {
+                range = elementaryFunctionRange;
+                tokenType = MPElementaryFunctionToken;
             } else if (MPRangeExists(variableRange)) {
                 range = variableRange;
                 tokenType = MPVariableToken;

MathPad/MPFactorialTerm.h

@@ -0,0 +1,17 @@
+//
+//  MPFactorialTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+@interface MPFactorialTerm : MPTerm
+
+- (instancetype)initWithTerm:(MPTerm *)term; /* designated initializer */
+
+@property (readonly, nonatomic, strong) MPTerm *term;
+
+@end

MathPad/MPFactorialTerm.m

@@ -0,0 +1,32 @@
+//
+//  MPFactorialTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFactorialTerm.h"
+
+@implementation MPFactorialTerm
+
+- (instancetype)initWithTerm:(MPTerm *)term
+{
+    self = [super init];
+    if (self) {
+        NSAssert(term != nil, @"term must not be nil.");
+        _term = term;
+    }
+    return self;
+}
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *value = [self.value evaluate:error];
+    if (!value) {
+        return nil;
+    }
+    return [[NSDecimalNumber alloc] initWithDouble:tgamma(value.doubleValue + 1)];
+}
+
+@end

MathPad/MPFractionFunction.m

@@ -8,8 +8,8 @@
 
 #import "MPFractionFunction.h"
 
+#import "MPFractionTerm.h"
 #import "MPExpression.h"
-#import "MPExpressionTree.h"
 
 @implementation MPFractionFunction
 
@@ -21,14 +21,9 @@ MPFunctionAccessorImplementation(DenominatorExpression, _denominatorExpression)
     return @[@"nominatorExpression", @"denominatorExpression"];
 }
 
-- (BOOL)validate:(NSError *__autoreleasing *)error
+- (Class)functionTermClass
 {
-    return [[self.nominatorExpression parse] validate:error] && [[self.denominatorExpression parse] validate:error];
-}
-
-- (NSDecimalNumber *)evaluate
-{
-    return [[[self.nominatorExpression parse] evaluate] decimalNumberByDividingBy:[[self.denominatorExpression parse] evaluate]];
+    return [MPFractionTerm class];
 }
 
 - (NSString *)description

MathPad/MPFractionTerm.h

@@ -0,0 +1,13 @@
+//
+//  MPFractionTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFunctionTerm.h"
+
+@interface MPFractionTerm : MPFunctionTerm
+
+@end

MathPad/MPFractionTerm.m

@@ -0,0 +1,27 @@
+//
+//  MPFractionTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFractionTerm.h"
+
+@implementation MPFractionTerm
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *nominator = [[self expressionAtIndex:0] evaluate:error];
+    if (!nominator) {
+        return nil;
+    }
+    NSDecimalNumber *denominator = [[self expressionAtIndex:1] evaluate:error];
+    if (!denominator) {
+        return nil;
+    }
+#warning Division by zero ahead
+    return [nominator decimalNumberByDividingBy:denominator];
+}
+
+@end

MathPad/MPFunction+MPToken.m

@@ -9,31 +9,25 @@
 #import "MPFunction+MPToken.h"
 
 #import "MPExpression.h"
+#import "MPPowerFunction.h"
 
 @implementation MPFunction (MPToken)
 
 - (MPTokenType)tokenType
 {
-    return MPGenericFunctionToken;
+    return [self isMemberOfClass:[MPPowerFunction class]] ? MPPowerToken : MPGenericFunctionToken;
 }
 
 
 - (NSRange)range
 {
-    NSUInteger selfIndex = [self.parent indexOfElement:self];
-    return NSMakeRange([self.parent convertIndex:selfIndex
+    return NSMakeRange([self.parent convertIndex:[self.parent indexOfElement:self]
                               fromReferenceFrame:MPElementReferenceFrame
                                 toReferenceFrame:MPSymbolReferenceFrame],
                        1);
 }
 
 
-- (BOOL)exists
-{
-    return YES;
-}
-
-
 - (NSString *)stringValue
 {
     return [self description];

MathPad/MPFunction.h

@@ -26,7 +26,7 @@
 
 
 
-@class MPFunction, MPExpression, MPRangePath;
+@class MPFunction, MPExpression, MPRangePath, MPFunctionTerm;
 @protocol MPExpressionElement;
 
 
@@ -241,6 +241,12 @@
  */
 - (void)didChangeChildAtIndex:(NSUInteger)index;
 
+
+#pragma mark Evaluating Functions
+
+
+- (BOOL)expectsVariableDefinitionInChildAtIndex:(NSUInteger)index;
+
 @end
 
 
@@ -256,6 +262,10 @@
  */
 @interface MPFunction (MPSubclassOverride)
 
+/* In Addition to the methods listed below MPFunction subclasses should also
+ * override the NSObject methods -description and -hash.
+ */
+
 #pragma mark Working With the Expression Tree
 /*!
  @methodgroup Working With the Expression Tree
@@ -281,40 +291,6 @@
  @methodgroup Evaluating Functions
  */
 
-
-/*!
-    @method     validate:
-    @brief      Validates the function and all its children for syntax errors.
- 
-    @param      error
-                If the validation fails this parameter should be set to an
-                appropriate value.
- 
-    @return     @c YES if the validation was successful, @c NO otherwise.
- */
-- (BOOL)validate:(NSError *__autoreleasing *)error;
-
-
-/*!
-    @method     evaluate:
-    @brief      Evaluates the function.
- 
-    @discussion Function evaluation should actually perform math. Also the
-                implementation of this method assumes that the function and all
-                children are valid (as determined by the @c -validate: method).
- 
-    @param      error
-                If a mathematical error occurs it is reflected in this parameter.
-                Depending on the error this method then either returns @c nil or
-                @c NaN.
- 
-    @return     The result of the evaluation or @c nil or @c NaN if an evaluation
-                error occured (such as a division by @c 0).
- */
-- (NSDecimalNumber *)evaluate:(NSError *__autoreleasing *)error;
-
-/* In Addition to the above methods MPFunction subclasses should also override
- * the NSObject methods -description and -hash.
- */
+- (Class)functionTermClass;
 
 @end

MathPad/MPFunction.m

@@ -12,6 +12,8 @@
 #import "MPRangePath.h"
 #import "NSIndexPath+MPAdditions.h"
 
+#import "MPFunctionTerm.h"
+
 
 
 @implementation MPFunction
@@ -131,6 +133,15 @@
 }
 
 
+#pragma mark Evaluating Functions
+
+
+- (BOOL)expectsVariableDefinitionInChildAtIndex:(NSUInteger)index
+{
+    return NO;
+}
+
+
 #pragma mark Working With Functions
 
 

MathPad/MPFunctionTerm.h

@@ -0,0 +1,23 @@
+//
+//  MPFunctionTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 12.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+#import "MPParsedExpression.h"
+#import "MPFunction.h"
+
+
+
+@interface MPFunctionTerm : MPTerm
+
+- (instancetype)initWithFunction:(MPFunction *)function
+                          errors:(NSArray *__autoreleasing *)errors; /* designated initializer */
+
+- (MPParsedExpression *)expressionAtIndex:(NSUInteger)anIndex;
+
+@end

MathPad/MPFunctionTerm.m

@@ -0,0 +1,72 @@
+//
+//  MPFunctionTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 12.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFunctionTerm.h"
+
+#import "MPParsedExpression.h"
+
+#import "MPToken.h"
+#import "MPTokenStream.h"
+#import "MPExpression.h"
+
+
+
+@interface MPFunctionTerm ()
+
+@property (nonatomic, strong) NSArray *parsedExpressions;
+
+@end
+
+
+
+@implementation MPFunctionTerm
+
+- (instancetype)initWithFunction:(MPFunction *)function
+                          errors:(NSArray *__autoreleasing *)errors
+{
+    NSAssert(function != nil, @"function must not be nil.");
+    if ([self isMemberOfClass:[MPFunctionTerm class]]) {
+        return [[function.functionTermClass alloc] initWithFunction:function
+                                                             errors:errors];
+    }
+    self = [super init];
+    if (self) {
+        NSMutableArray *parsedExpressions = [[NSMutableArray alloc] initWithCapacity:function.childrenAccessors.count];
+        NSUInteger childIndex = 0;
+        BOOL errorOccured = NO;
+        NSMutableArray *mutableErrors = [[NSMutableArray alloc] init];
+        for (NSString *accessor in function.childrenAccessors) {
+            MPExpression *expression = [function valueForKey:accessor];
+            NSArray *localErrors;
+            MPParsedExpression *parsedExpression = [expression parseExpectingVariable:[function expectsVariableDefinitionInChildAtIndex:childIndex]
+                                                                               errors:&localErrors];
+            if (parsedExpression) {
+                [parsedExpressions addObject:parsedExpression];
+            } else {
+                [mutableErrors addObjectsFromArray:localErrors];
+                errorOccured = YES;
+            }
+            childIndex++;
+        }
+        if (errorOccured) {
+            if (errors) {
+                *errors = mutableErrors;
+            }
+            return nil;
+        }
+        self.parsedExpressions = parsedExpressions;
+    }
+    return self;
+}
+
+- (MPParsedExpression *)expressionAtIndex:(NSUInteger)anIndex
+{
+    return [self.parsedExpressions objectAtIndex:anIndex];
+}
+
+@end

MathPad/MPNegatedTerm.h

@@ -0,0 +1,17 @@
+//
+//  MPNegatedTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 22.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+@interface MPNegatedTerm : MPTerm
+
+- (instancetype)initWithTerm:(MPTerm *)term; /* designated initializer */
+
+@property (readonly, nonatomic, strong) MPTerm *term;
+
+@end

MathPad/MPNegatedTerm.m

@@ -0,0 +1,32 @@
+//
+//  MPNegatedTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 22.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPNegatedTerm.h"
+
+@implementation MPNegatedTerm
+
+- (instancetype)initWithTerm:(MPTerm *)term
+{
+    self = [super init];
+    if (self) {
+        NSAssert(term != nil, @"term must not be nil.");
+        _term = term;
+    }
+    return self;
+}
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *value = [self.term evaluate:error];
+    if (value) {
+        value = [value decimalNumberByMultiplyingBy:[[NSDecimalNumber alloc] initWithInteger:-1]];
+    }
+    return value;
+}
+
+@end

MathPad/MPNumber.h

@@ -6,11 +6,13 @@
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
-#import "MPValueGroup.h"
+#import "MPTerm.h"
 
 @class MPNumber;
 
-@interface MPNumber : NSObject <MPValue>
+@interface MPNumber : MPTerm
+
+- (instancetype)initWithNumber:(NSDecimalNumber *)number; /* designated initializer */
 
 @property (readonly, nonatomic, strong) NSDecimalNumber *number;
 

MathPad/MPNumber.m

@@ -8,44 +8,24 @@
 
 #import "MPNumber.h"
 
+#import "MPParsedExpression.h"
+
 #import "MPTokenStream.h"
 #import "MPToken.h"
 
 @implementation MPNumber
 
-- (instancetype)init
+- (instancetype)initWithNumber:(NSDecimalNumber *)number
 {
     self = [super init];
     if (self) {
+        NSAssert(number != nil, @"number must not be nil.");
+        _number = number;
     }
     return self;
 }
 
-- (instancetype)initWithTokenStream:(MPTokenStream *)tokenStream
-{
-    self = [self init];
-    if (self) {
-        [tokenStream beginIgnoringWhitespaceTokens];
-        MPToken *token = tokenStream.currentToken;
-        if (token.tokenType == MPNumberToken) {
-            _number = [NSDecimalNumber decimalNumberWithString:token.stringValue locale:[NSLocale currentLocale]];
-        } else {
-            @throw [NSException exceptionWithName:NSInternalInconsistencyException
-                                           reason:@"Expected Number"
-                                         userInfo:nil];
-        }
-        [tokenStream currentTokenConsumed];
-        [tokenStream endIgnoringOrAcceptingWhitespaceTokens];
-    }
-    return self;
-}
-
-- (BOOL)validate:(NSError *__autoreleasing *)error
-{
-    return YES;
-}
-
-- (NSDecimalNumber *)evaluate
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
 {
     return self.number;
 }

MathPad/MPParenthesisFunction.m

@@ -10,7 +10,7 @@
 #import "MPParenthesisFunction.h"
 
 #import "MPExpression.h"
-#import "MPExpressionTree.h"
+#import "MPParenthesisTerm.h"
 
 @implementation MPParenthesisFunction
 
@@ -21,14 +21,9 @@ MPFunctionAccessorImplementation(Expression, _expression)
     return @[@"expression"];
 }
 
-- (BOOL)validate:(NSError *__autoreleasing *)error
+- (Class)functionTermClass
 {
-    return [[self.expression parse] validate:error];
-}
-
-- (NSDecimalNumber *)evaluate
-{
-    return [[self.expression parse] evaluate];
+    return [MPParenthesisTerm class];
 }
 
 - (NSString *)description

MathPad/MPParenthesisTerm.h

@@ -0,0 +1,13 @@
+//
+//  MPParenthesisTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFunctionTerm.h"
+
+@interface MPParenthesisTerm : MPFunctionTerm
+
+@end

MathPad/MPParenthesisTerm.m

@@ -0,0 +1,18 @@
+//
+//  MPParenthesisTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPParenthesisTerm.h"
+
+@implementation MPParenthesisTerm
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    return [[self expressionAtIndex:0] evaluate:error];
+}
+
+@end

MathPad/MPParsedExpression.h

@@ -0,0 +1,34 @@
+//
+//  MPParsedExpression.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 14.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+@class MPParsedExpression, MPTokenStream, MPTerm;
+@protocol MPToken;
+
+/*!
+ @const      MPMathKitErrorDomain
+ @brief      Predefined error domain for errors from the MathKit framework.
+ 
+ @discussion Errors in MathKit can occur during parsing of expressions or
+ during evaluation of expressions. These two can be distinguished
+ by the error code. Parsing errors have lower error codes.
+ Evaluation errors (math errors) have error codes from @c 100 upwards.
+ */
+FOUNDATION_EXPORT NSString *const MPMathKitErrorDomain;
+
+FOUNDATION_EXPORT NSString *const MPPathToExpressionKey;
+FOUNDATION_EXPORT NSString *const MPErrorIndexKey;
+
+
+@interface MPParsedExpression : NSObject
+
+@property (nonatomic, strong) NSString *definedVariable;
+@property (nonatomic, strong) MPTerm *term;
+
+- (NSDecimalNumber *)evaluate:(NSError *__autoreleasing *)error;
+
+@end

MathPad/MPParsedExpression.m

@@ -0,0 +1,27 @@
+//
+//  MPParsedExpression.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 14.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPParsedExpression.h"
+
+#import "MPTokenStream.h"
+#import "MPToken.h"
+
+#import "MPTerm.h"
+
+NSString *const MPMathKitErrorDomain = @"MPMathKitErrorDomain";
+NSString *const MPPathToExpressionKey = @"MPPathToExpressionKey";
+NSString *const MPErrorIndexKey = @"MPErrorIndexKey";
+
+@implementation MPParsedExpression
+
+- (NSDecimalNumber *)evaluate:(NSError *__autoreleasing *)error
+{
+    return [self.term evaluate:error];
+}
+
+@end

MathPad/MPPowerFunction.h

@@ -6,12 +6,19 @@
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
-#import "MPSuffixFunction.h"
+#import "MPFunction.h"
 
 @class MPPowerFunction, MPExpression;
 
-@interface MPPowerFunction : MPSuffixFunction
+@interface MPPowerFunction : MPFunction
 
+/*!
+ @property   baseValue
+ @brief      The receiver's base value.
+ 
+ @discussion The base value is the thing a suffix function applies to (e.g.
+ a power's base).
+ */
 @property (nonatomic, strong) MPExpression *exponentExpression;
 
 @end

MathPad/MPPowerFunction.m

@@ -9,9 +9,6 @@
 #import "MPPowerFunction.h"
 
 #import "MPExpression.h"
-#import "MPExpressionTree.h"
-
-#import "MPValueGroup.h"
 
 @implementation MPPowerFunction
 
@@ -22,30 +19,6 @@ MPFunctionAccessorImplementation(ExponentExpression, _exponentExpression)
     return @[@"exponentExpression"];
 }
 
-- (BOOL)validate:(NSError *__autoreleasing *)error
-{
-    if (!self.baseValue) {
-        if (error) {
-            *error = MPParseError(11,
-                                  NSLocalizedString(@"No Base For Power.", @"Error message. This is displayed when a power does not have a base value."),
-                                  nil);
-        }
-        return NO;
-    }
-    return [self.baseValue validate:error] && [[self.exponentExpression parse] validate:error];
-}
-
-- (NSDecimalNumber *)evaluate
-{
-    NSDecimalNumber *base = [self.baseValue evaluate];
-    NSDecimalNumber *exponent = [[self.exponentExpression parse] evaluate];
-    if ([base isEqualToNumber:@(0)] && [exponent isEqualToNumber:@(0)]) {
-        // The C pow function returns 1 for pow(0, 0). Mathematically this should be undefined.
-        return [NSDecimalNumber notANumber];
-    }
-    return [[NSDecimalNumber alloc] initWithDouble:pow(base.doubleValue, exponent.doubleValue)];
-}
-
 - (NSString *)description
 {
     return [NSString stringWithFormat:@"^%@", self.exponentExpression.description];

MathPad/MPPowerTerm.h

@@ -0,0 +1,15 @@
+//
+//  MPPowerTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFunctionTerm.h"
+
+@interface MPPowerTerm : MPFunctionTerm
+
+@property (nonatomic, strong) MPTerm *baseTerm;
+
+@end

MathPad/MPPowerTerm.m

@@ -0,0 +1,36 @@
+//
+//  MPPowerTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPPowerTerm.h"
+#import "MPParsedExpression.h"
+
+@implementation MPPowerTerm
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *exponent = [[self expressionAtIndex:0] evaluate:error];
+    if (!exponent) {
+        return nil;
+    }
+    NSDecimalNumber *base = [self.baseTerm evaluate:error];
+    if (!base) {
+        return nil;
+    }
+    if ([base isEqualToNumber:@(0)] && [exponent isEqualToNumber:@(0)]) {
+        // The C pow function returns 1 for pow(0, 0). Mathematically this should be undefined.
+        if (error) {
+            *error = [NSError errorWithDomain:MPMathKitErrorDomain
+                                         code:101
+                                     userInfo:@{NSLocalizedDescriptionKey: NSLocalizedString(@"0 to the power of 0 is undefined.", nil)}];
+        }
+        return nil;
+    }
+    return [[NSDecimalNumber alloc] initWithDouble:pow(base.doubleValue, exponent.doubleValue)];
+}
+
+@end

MathPad/MPProductTerm.h

@@ -0,0 +1,17 @@
+//
+//  MPProductTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+@interface MPProductTerm : MPTerm
+
+- (instancetype)initWithFactors:(NSArray *)factors; /* designated initializer */
+
+@property (readonly, nonatomic, strong) NSArray *factors;
+
+@end

MathPad/MPProductTerm.m

@@ -0,0 +1,50 @@
+//
+//  MPProductTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPProductTerm.h"
+
+#import "MPParsedExpression.h"
+#import "MPPowerFunction.h"
+
+#import "MPFunctionTerm.h"
+#import "MPElementaryFunctionTerm.h"
+#import "MPNumber.h"
+#import "MPFactorialTerm.h"
+#import "MPPowerTerm.h"
+#import "MPVariable.h"
+
+#import "MPTokenStream.h"
+#import "MPToken.h"
+
+@implementation MPProductTerm
+
+- (instancetype)initWithFactors:(NSArray *)factors
+{
+    self = [super init];
+    if (self) {
+        NSAssert(factors != nil, @"factors must not be nil.");
+        NSAssert(factors.count > 0, @"factors must not be empty.");
+        _factors = factors;
+    }
+    return self;
+}
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *value = [NSDecimalNumber one];
+    for (MPTerm *factor in self.factors) {
+        NSDecimalNumber *currentValue = [factor evaluate:error];
+        if (!currentValue) {
+            return nil;
+        }
+        value = [value decimalNumberByMultiplyingBy:currentValue];
+    }
+    return value;
+}
+
+@end

MathPad/MPSumFunction.m

@@ -8,8 +8,8 @@
 
 #import "MPSumFunction.h"
 
+#import "MPSumFunctionTerm.h"
 #import "MPExpression.h"
-#import "MPExpressionTree.h"
 #import "MPEvaluationContext.h"
 
 
@@ -27,54 +27,16 @@ MPFunctionAccessorImplementation(SumExpression, _sumExpression)
     return @[@"startExpression", @"targetExpression", @"sumExpression"];
 }
 
-
-#pragma mark Evaluating Functions
-
-
-- (BOOL)validate:(NSError *__autoreleasing *)error
+- (BOOL)expectsVariableDefinitionInChildAtIndex:(NSUInteger)index
 {
-    MPExpressionTree *startTree = [self.startExpression parse];
-    if (![startTree validateExpectingVariableDefinition:YES error:error]) {
-        return NO;
-    }
-    
-    MPExpressionTree *targetTree = [self.targetExpression parse];
-    if (![targetTree validate:error]) {
-        return NO;
-    }
-    
-    [[MPEvaluationContext sharedContext] push];
-    [[MPEvaluationContext sharedContext] defineVariable:startTree.definedVariable withValue:[NSDecimalNumber notANumber]];
-    MPExpressionTree *sumTree = [self.sumExpression parse];
-    if (![sumTree validate:error]) {
-        return NO;
-    }
-    [[MPEvaluationContext sharedContext] pop];
-    return YES;
+    return index == 0;
 }
 
-
-- (NSDecimalNumber *)evaluate
+- (Class)functionTermClass
 {
-    MPExpressionTree *startTree = [self.startExpression parse];
-    NSDecimalNumber *start = [startTree evaluate];
-    NSDecimalNumber *target = [[self.targetExpression parse] evaluate];
-    MPExpressionTree *sumTree = [self.sumExpression parse];
-    
-    NSDecimalNumber *value = [NSDecimalNumber zero];
-    
-    [[MPEvaluationContext sharedContext] push];
-    for (NSDecimalNumber *current = start;
-         [current compare:target] <= 0;
-         current = [current decimalNumberByAdding:[[NSDecimalNumber alloc] initWithInteger:1]]) {
-        [[MPEvaluationContext sharedContext] defineVariable:startTree.definedVariable withValue:current];
-        value = [value decimalNumberByAdding:[sumTree evaluate]];
-    }
-    [[MPEvaluationContext sharedContext] pop];
-    return value;
+    return [MPSumFunctionTerm class];
 }
 
-
 #pragma mark Working With Functions
 
 

MathPad/MPSumFunctionTerm.h

@@ -0,0 +1,13 @@
+//
+//  MPSumFunctionTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPFunctionTerm.h"
+
+@interface MPSumFunctionTerm : MPFunctionTerm
+
+@end

MathPad/MPSumFunctionTerm.m

@@ -0,0 +1,38 @@
+//
+//  MPSumFunctionTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 15.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPSumFunctionTerm.h"
+
+@implementation MPSumFunctionTerm
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    MPParsedExpression *startExpression = [self expressionAtIndex:0];
+    MPParsedExpression *targetExpression = [self expressionAtIndex:1];
+    MPParsedExpression *sumExpression = [self expressionAtIndex:2];
+    
+    NSDecimalNumber *start = [startExpression evaluate:error];
+    NSDecimalNumber *target = [targetExpression evaluate:error];
+    NSDecimalNumber *value = [NSDecimalNumber zero];
+    
+    for (NSDecimalNumber *current = start;
+         [current compare:target] <= 0;
+         current = [current decimalNumberByAdding:[[NSDecimalNumber alloc] initWithInteger:1]]) {
+        if (![self redefineVariable:startExpression.definedVariable value:current error:error]) {
+            return nil;
+        }
+        NSDecimalNumber *currentValue = [sumExpression evaluate:error];
+        if (!currentValue) {
+            return nil;
+        }
+        value = [value decimalNumberByAdding:currentValue];
+    }
+    return value;
+}
+
+@end

MathPad/MPSumTerm.h

@@ -0,0 +1,18 @@
+//
+//  MPSumTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 14.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+@interface MPSumTerm : MPTerm
+
+- (instancetype)initWithSummands:(NSArray *)summands; /* designated initializer */
+
+@property (readonly, nonatomic, strong) NSArray *summands;
+
+@end
+

MathPad/MPSumTerm.m

@@ -0,0 +1,43 @@
+//
+//  MPSumTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 14.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPSumTerm.h"
+
+#import "MPParsedExpression.h"
+#import "MPProductTerm.h"
+
+#import "MPTokenStream.h"
+#import "MPToken.h"
+
+@implementation MPSumTerm
+
+- (instancetype)initWithSummands:(NSArray *)summands
+{
+    self = [super init];
+    if (self) {
+        NSAssert(summands != nil, @"summands must not be nil.");
+        NSAssert(summands.count > 0, @"summands must not be empty.");
+        _summands = summands;
+    }
+    return self;
+}
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *value = [NSDecimalNumber zero];
+    for (MPTerm *summand in self.summands) {
+        NSDecimalNumber *currentValue = [summand evaluate:error];
+        if (!currentValue) {
+            return nil;
+        }
+        value = [value decimalNumberByAdding:currentValue];
+    }
+    return value;
+}
+
+@end

MathPad/MPTerm.h

@@ -0,0 +1,28 @@
+//
+//  MPTerm.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 11.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+
+@class MPTerm, MPTokenStream;
+@protocol MPToken;
+
+@interface MPTerm : NSObject
+
+- (NSDecimalNumber *)evaluate:(NSError *__autoreleasing *)error;
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error;
+
+- (BOOL)defineVariable:(NSString *)variableName
+                 value:(NSDecimalNumber *)value
+                 error:(NSError *__autoreleasing *)error;
+- (BOOL)redefineVariable:(NSString *)variableName
+                   value:(NSDecimalNumber *)value
+                   error:(NSError *__autoreleasing *)error;
+- (NSDecimalNumber *)valueForVariable:(NSString *)variableName
+                                error:(NSError *__autoreleasing *)error;
+- (void)undefineVariable:(NSString *)variableName; // Should rarely be needed, defined variables are automatically undefined at the end of evaluation.
+
+@end

MathPad/MPTerm.m

@@ -0,0 +1,85 @@
+//
+//  MPTerm.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 11.11.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPTerm.h"
+
+#import "MPParsedExpression.h"
+#import "MPSumTerm.h"
+#import "MPEvaluationContext.h"
+
+@implementation MPTerm
+
+- (NSDecimalNumber *)evaluate:(NSError *__autoreleasing *)error
+{
+    [[MPEvaluationContext sharedContext] push];
+    NSDecimalNumber *result = [self doEvaluation:error];
+    [[MPEvaluationContext sharedContext] pop];
+    return result;
+}
+
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
+{
+    NSLog(@"%@", self.class);
+    return nil;
+}
+
+- (BOOL)defineVariable:(NSString *)variableName
+                 value:(NSDecimalNumber *)value
+                 error:(NSError *__autoreleasing *)error
+{
+    BOOL couldDefineVariable = [[MPEvaluationContext sharedContext] defineVariable:variableName
+                                                                             value:value];
+    if (!couldDefineVariable) {
+        if (error) {
+            NSString *localizedDescription = [NSString stringWithFormat:NSLocalizedString(@"Redifinition of variable \"%@\".", nil), variableName];
+            *error = [NSError errorWithDomain:MPMathKitErrorDomain
+                                         code:100
+                                     userInfo:@{NSLocalizedDescriptionKey: localizedDescription}];
+        }
+    }
+    return couldDefineVariable;
+}
+
+- (BOOL)redefineVariable:(NSString *)variableName
+                   value:(NSDecimalNumber *)value
+                   error:(NSError *__autoreleasing *)error
+{
+    BOOL couldDefineVariable = [[MPEvaluationContext sharedContext] redefineVariable:variableName
+                                                                               value:value];
+    if (!couldDefineVariable) {
+        if (error) {
+            NSString *localizedDescription = [NSString stringWithFormat:NSLocalizedString(@"Redifinition of variable \"%@\".", nil), variableName];
+            *error = [NSError errorWithDomain:MPMathKitErrorDomain
+                                         code:100
+                                     userInfo:@{NSLocalizedDescriptionKey: localizedDescription}];
+        }
+    }
+    return couldDefineVariable;
+}
+
+- (NSDecimalNumber *)valueForVariable:(NSString *)variableName
+                                error:(NSError *__autoreleasing *)error
+{
+    NSDecimalNumber *value = [[MPEvaluationContext sharedContext] valueForVariable:variableName];
+    if (!value) {
+        if (error) {
+            NSString *localizedDescription = [NSString stringWithFormat:NSLocalizedString(@"Undefined variable \"%@\".", nil), variableName];
+            *error = [NSError errorWithDomain:MPMathKitErrorDomain
+                                         code:101
+                                     userInfo:@{NSLocalizedDescriptionKey: localizedDescription}];
+        }
+    }
+    return value;
+}
+
+- (void)undefineVariable:(NSString *)variableName
+{
+    [[MPEvaluationContext sharedContext] undefineVariable:variableName];
+}
+
+@end

MathPad/MPToken.h

@@ -23,24 +23,11 @@
     @constant   MPOperatorListToken
                 A list of operators (+ and - symbols). The token may be longer
                 than the number of operators if there are spaces between them.
- 
-    @constant   MPSinToken
-                The sin function.
- 
-    @constant   MPCosToken
-                The cos function.
- 
-    @constant   MPTanToken
-                The tan function.
- 
-    @constant   MPASinToken
-                The asin function.
- 
-    @constant   MPACosToken
-                The acos function.
- 
-    @constant   MPATanToken
-                The atan function.
+
+    @constant   MPElementaryFunction
+                @em Most elementary functions are represented by this token type.
+                Elementary functions not categorized as such are those that can
+                not be represented as text (e.g. roots and powers).
  
     @constant   MPNumberToken
                 A number. This may be an integer or a floating point number.
@@ -66,18 +53,15 @@
                 Any symbol that does not match any other token.
  */
 typedef NS_ENUM(NSUInteger, MPTokenType) {
+    MPEOFToken = 0,
     MPMultiplicationSymbolToken,
     MPOperatorListToken,
-    MPSinToken,
-    MPCosToken,
-    MPTanToken,
-    MPASinToken,
-    MPACosToken,
-    MPATanToken,
+    MPElementaryFunctionToken,
     MPNumberToken,
     MPVariableToken,
-    MPFactorialToken,
     MPEqualsToken,
+    MPFactorialToken,
+    MPPowerToken,
     MPGenericFunctionToken,
     
     MPWhitespaceToken,

MathPad/MPTokenStream.m

@@ -18,7 +18,7 @@
 @property (nonatomic) NSUInteger currentTokenIndex;
 @property (nonatomic) NSUInteger eofLocation;
 
-@property (nonatomic) BOOL *whitespaceIgnores;
+@property (nonatomic) BOOL *whitespaceStates;
 @property (nonatomic) NSUInteger maxWhitespaceIgnores;
 @property (nonatomic) NSUInteger currentWhitespaceIgnoreState;
 
@@ -34,7 +34,7 @@
     self = [super init];
     if (self) {
         self.tokens = tokens;
-        self.whitespaceIgnores = malloc(10 * sizeof(BOOL));
+        self.whitespaceStates = malloc(10 * sizeof(BOOL));
         self.maxWhitespaceIgnores = 10;
         self.currentWhitespaceIgnoreState = 0;
         [self beginAcceptingWhitespaceTokens];
@@ -66,14 +66,14 @@
     self.currentWhitespaceIgnoreState++;
     if (self.currentWhitespaceIgnoreState >= self.maxWhitespaceIgnores) {
         self.maxWhitespaceIgnores += 10;
-        BOOL *reallocatedWhitespaceIgnores = realloc(self.whitespaceIgnores, self.maxWhitespaceIgnores);
+        BOOL *reallocatedWhitespaceIgnores = realloc(self.whitespaceStates, self.maxWhitespaceIgnores);
         if (reallocatedWhitespaceIgnores) {
-            self.whitespaceIgnores = reallocatedWhitespaceIgnores;
+            self.whitespaceStates = reallocatedWhitespaceIgnores;
         } else {
             @throw [NSException exceptionWithName:NSInternalInconsistencyException reason:@"Realloc Failed" userInfo:nil];
         }
     }
-    self.whitespaceIgnores[self.currentWhitespaceIgnoreState] = state;
+    self.whitespaceStates[self.currentWhitespaceIgnoreState] = state;
 }
 
 
@@ -85,7 +85,7 @@
 
 - (void)skipWhitespaces
 {
-    if (self.whitespaceIgnores[self.currentWhitespaceIgnoreState]) {
+    if (self.whitespaceStates[self.currentWhitespaceIgnoreState]) {
         return;
     }
     while (_currentTokenIndex < self.tokens.count) {
@@ -93,7 +93,7 @@
         if (token.tokenType != MPWhitespaceToken) {
             return;
         }
-        [self currentTokenConsumed];
+        _currentTokenIndex++;
     }
 }
 
@@ -134,7 +134,7 @@
 
 - (void)dealloc
 {
-    free(self.whitespaceIgnores);
+    free(self.whitespaceStates);
 }
 
 @end

MathPad/MPVariable.h

@@ -6,11 +6,13 @@
 //  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
 //
 
-#import "MPValueGroup.h"
+#import "MPTerm.h"
 
 @class MPVariable;
 
-@interface MPVariable : NSObject <MPValue>
+@interface MPVariable : MPTerm
+
+- (instancetype)initWithVariableName:(NSString *)variableName; /* designated initializer */
 
 @property (readonly, nonatomic, strong) NSString *variableName;
 

MathPad/MPVariable.m

@@ -8,63 +8,30 @@
 
 #import "MPVariable.h"
 
+#import "MPParsedExpression.h"
+
 #import "MPTokenStream.h"
 #import "MPToken.h"
 
 #import "MPExpression.h"
 #import "MPEvaluationContext.h"
 
-@implementation MPVariable {
-    NSRange _range;
-}
+@implementation MPVariable
 
-- (instancetype)init
+- (instancetype)initWithVariableName:(NSString *)variableName
 {
     self = [super init];
     if (self) {
+        NSAssert(variableName != nil, @"variableName must not be nil.");
+        _variableName = variableName;
     }
     return self;
 }
 
-- (instancetype)initWithTokenStream:(MPTokenStream *)tokenStream
+- (NSDecimalNumber *)doEvaluation:(NSError *__autoreleasing *)error
 {
-    self = [self init];
-    if (self) {
-        [tokenStream beginIgnoringWhitespaceTokens];
-        MPToken *token = tokenStream.currentToken;
-        if (token.tokenType == MPVariableToken) {
-            _variableName = token.stringValue;
-            _range = token.range;
-        } else {
-            @throw [NSException exceptionWithName:NSInternalInconsistencyException reason:@"Expected Variable" userInfo:nil];
-        }
-        [tokenStream currentTokenConsumed];
-        [tokenStream endIgnoringOrAcceptingWhitespaceTokens];
-    }
-    return self;
-}
-
-- (NSRange)range
-{
-    return _range;
-}
-
-- (BOOL)validate:(NSError *__autoreleasing *)error
-{
-    if (![[MPEvaluationContext sharedContext] isVariableDefined:self.variableName]) {
-        if (error) {
-            *error = MPParseError(9,
-                                  NSLocalizedString(@"Undefined Variable.", @"Error message. This is displayed when an expression contains an undefined variable."),
-                                  nil);
-        }
-        return NO;
-    }
-    return YES;
-}
-
-- (NSDecimalNumber *)evaluate
-{
-    return [[MPEvaluationContext sharedContext] valueForVariable:self.variableName];
+    return [self valueForVariable:self.variableName
+                            error:error];
 }
 
 @end