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MathKit/MPExpression.h

@@ -0,0 +1,910 @@
+//
+//  MPExpression.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 10.08.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+
+/*!
+ @header
+ The <code>MPExpression</code> class is used to represent a mathematical
+ expression. It is used in the storage layer of the MathKit Expression System. An
+ instance of the <code>MPExpression</code> class stores all contents related to
+ an expression and can manipulate them. However it is not able to evaluate the
+ represented expression by itself.
+ 
+ <h2>Structure of an Expression</h2>
+ 
+ Expressions consist of two types of elements: string elements and function
+ elements. String elements are represented by the <code>NSString</code> class.
+ In a valid expression string elements can only contain ASCII valid characters.
+ (and some other special characters) that make sense in a mathematical context.
+ Functions are represented by the <code>MPFunction</code> class. Functions
+ represent everything beyond simple text (such as powers, parenthesis and roots).
+ 
+ An expression should be pictured as a sequence of symbols that can either be
+ characters or functions. For the purposes of easier processing of expressions
+ it is possible to access complete string or function elements. Also there is a
+ third way of accessing an expression's contents: You can query individual tokens
+ of an expression. Tokens represent logical units inside an expression. For more
+ information on tokens see the <code>MPToken</code> class.
+ 
+ <h2>The Expression Tree</h2>
+ Like expressions functions can likewise have expressions as elements (also
+ called <i>children</i> in this context). Both expressions and functions are
+ mutable. Through this organization expression are organized in a tree-like
+ structure called the <i>expression tree</i>. See <code>MPFunction</code> for
+ details.
+ 
+ <h2>Terminology</h2>
+ 
+ When working with expressions note that there is a special terminology for an
+ expression's contents:
+ 
+ <b>Element:</b><br />
+ An element is either an instance of the <code>NSString</code> or <code>
+ MPFunction</code> class. String elements can be multiple characters long. For
+ example the expression <code>4+2²</code> consists of one string element
+ (<code>"4+2"</code>) and one function element (the square function). All
+ elements conform to the <code>MPExpressionElement</code> protocol.
+ 
+ <b>Token:</b><br />
+ Tokens are logical units within an expression. For example the expression
+ <code>4+2²</code> consists of 4 tokens: A number token (<code>4</code>), a plus
+ sign token (<code>+</code>), another number (<code>2</code>) and a power token
+ (the square function). All tokens conform to the <code>MPToken</code> protocol.
+ 
+ <b>Symbol:</b><br />
+ Symbols are the smallest possible part of an expression. A symbol is either a
+ single character or a single function. For example the expression
+ <code>4+2²</code> consists of 4 symbols: The characters <code>"4"</code>,
+ <code>"+"</code> and <code>"2"</code> and the square function.
+ 
+ <b>Item:</b></br />
+ The term <i>item</i> is used to describe any of the previous. When the term
+ <i>item</i> is used in the name of a function or method it necessary to specify
+ what exactly an item is supposed to be. Usually this is done through reference
+ frames.
+ 
+ <b>Reference Frame:</b><br />
+ A reference frame is a way to specify what an <i>item</i> is supposed to mean in
+ a specific context. It can either be an <i>element</i>, a <i>symbol</i> or a
+ <i>token</i>. For more information about reference frames see
+ <code>MPReferenceFrame</code>.
+ 
+ <b>Children:</b><br />
+ Children are sub-elements of functions. The term <i>children</i> normally refers
+ to any kind of elements in the context of the expression tree.
+ 
+ This terminology is consistent within the MathKit Expression System. Because
+ symbols are the smalles possible unit of measurement elements and tokens both
+ consist of one or more symbols. Similarly elements consist of one or more
+ tokens. You can convert between different reference frames using one the
+ following methods:
+ <pre>
+ @textblock
+- convertIndexFromReferenceFrame:toReferenceFrame:
+- convertIndexFromReferenceFrame:toReferenceFrame:offset:
+ @/textblock
+ </pre>
+ 
+ <h2>Evaluating Expressions</h2>
+ A <code>MPExpression</code> instance can not evaluate itself. There are however
+ the <code>-parse:</code> and
+ <code>-parseExpectingVariableDefinition:errors:</code> methods. These parse and
+ thereby convert a <code>MPExpression</code> instance into a
+ <code>MPParsedExpression</code> instance that can be evaluated. For more
+ information on evaluation see the <code>MPParsedExpression</code> and
+ <code>MPTerm</code> class as well as the previously mentioned methods.
+*/
+
+
+/*!
+    @const      MPIllegalElementException
+    @brief      Name for an exception that is raised if an invalid element is
+                added to an expression.
+ 
+    @discussion This exception may be raised during initialization of an
+                expression or when the expression is mutated. This exception
+                contains the invalid element in its <code>userInfo</code>
+                dictionary. You can query it using the
+                <code>MPIllegalElementExceptionElementKey</code> key.
+ */
+FOUNDATION_EXPORT NSString *const MPIllegalElementException;
+
+
+/*!
+    @const      MPIllegalElementExceptionElementKey
+    @brief      Predefined key for an invalid element that caused a
+                <code>MPIllegalElementException</code> to be raised.
+ 
+    @discussion The invalid element can be of any type. Numbers and structs are
+                wrapped in an <code>NSNumber</code> or <code>NSValue</code>
+                instance respectively.
+ */
+FOUNDATION_EXPORT NSString *const MPIllegalElementExceptionElementKey;
+
+
+/*!
+    @typedef    MPReferenceFrame
+    @brief      A reference frame specifies the way an <i>item</i> is to be
+                interpreted.
+ 
+    @constant   MPElementReferenceFrame
+                Specifies that items should be interpreted as elements.
+ 
+    @constant   MPSymbolReferenceFrame
+                Specifies that items should be interpreted as symbols.
+ 
+    @constant   MPTokenReferenceFrame
+                Specifies that items should be interpreted as tokens.
+  */
+typedef enum {
+    MPElementReferenceFrame,
+    MPSymbolReferenceFrame,
+    MPTokenReferenceFrame
+} MPReferenceFrame;
+
+
+
+@class MPExpression, MPFunction, MPRangePath, MPParsedExpression;
+@protocol MPExpressionElement, MPToken;
+
+
+/*!
+    @class      MPExpression
+    @brief      A <code>MPExpression</code> instance represents a mathematical
+                expression.
+ 
+    @discussion Every expression consists of string elements (represented by the
+                <code>NSString</code> class) and function elements (represented
+                by the <code>MPFunction</code> class). Functions and expressions
+                make up the expression tree.
+  */
+@interface MPExpression : NSObject <NSCopying, NSCoding>
+
+
+#pragma mark Creation Methods
+/*!
+ @methodgroup Creation Methods
+ */
+
+
+/*!
+    @method     init
+    @brief      Initlializes a new expression.
+ 
+    @discussion This method is a convenience initializer to initialize an
+                expression with <code>0</code> elements.
+ 
+    @return     An empty expression.
+ */
+- (instancetype)init;
+
+
+/*!
+    @method     initWithElement:
+    @brief      Initializes a new expression with the specified
+                <code>element</code>.
+
+    @discussion This method is a convenience initializer to initialize an
+                expression with a single element.
+ 
+    @param      element
+                The element to be added to the expression. The
+                <code>element</code> will be copied.
+ 
+    @return     An expression initialized with <code>element</code>.
+ */
+- (instancetype)initWithElement:(id<MPExpressionElement>)element;
+
+
+/*!
+    @method     initWithElements:
+    @brief      Initializes a new expression with the specified
+                <code>elements</code>.
+ 
+    @discussion All elements must conform to the <code>MPExpressionElement</code>
+                protocol. If one or more objects do not conform to that protocol
+                a <code>MPIllegalElementException</code> is raised.
+ 
+                This method is the designated initializer for the
+                <code>MPExpression</code> class.
+ 
+    @param      elements
+                The elements that should be added to the expression. Every
+                element must conform to the <code>MPExpressionElement</code>
+                protocol. Each element is copied and the copy is then added to
+                the expression. The object in the <code>elements</code> array is
+                not modified.
+ 
+    @return     An expression containing <code>elements</code>.
+ */
+- (instancetype)initWithElements:(NSArray *)elements; /* designated initializer */
+
+
+#pragma mark Querying Expressions
+/*!
+ @methodgroup Querying Expressions
+ */
+
+
+/*!
+    @property   parent
+    @brief      The receiver's parent.
+ 
+    @discussion The receiver's parent is the function in the expression tree that
+                contains the receiver.
+       @warning You should never set this property manually. If you are
+                implementing a custom subclass of <code>MPFunction</code> use the
+                <code>MPFunctionAccessorImplementation</code> macro.
+ 
+    @return     The parent of the receiver or <code>nil</code> if the receiver is
+                the root expression.
+ */
+@property (nonatomic, weak) MPFunction *parent;
+
+
+/*!
+    @method     rootExpression
+    @brief      Returns the root expression from the receiver's expression tree.
+ 
+    @discussion The root expression is the ultimate parent of all expressions and
+                functions in the expression tree. A root expression does not have
+                a parent.
+ 
+    @return     The root expression from the receiver's expression tree.
+ */
+- (MPExpression *)rootExpression;
+
+
+/*!
+    @method     indexPath
+    @brief      Returns the index path of the receiver in the expression tree.
+ 
+    @discussion The index path contains the indexes (starting from the root
+                expression of the receiver's expression tree) that lead to the
+                receiver. The indexes are expressed in the element reference
+                frame.
+ 
+    @return     The index path of the receiver in the expression tree.
+ */
+- (NSIndexPath *)indexPath;
+
+
+/*!
+    @method     countItemsInReferenceFrame:
+    @brief      Returns the number of items in the receiver in the specified
+                <code>referenceFrame</code>.
+ 
+    @param      referenceFrame
+                The reference frame that should be used to count the items.
+ 
+    @return     The current number of items in the receiver counted in the
+                specified <code>referenceFrame</code>.
+ */
+- (NSUInteger)countItemsInReferenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     itemAtIndex:referenceFrame:
+    @brief      Returns the item at <code>anIndex</code>.
+ 
+    @discussion The item is not copied before it is returned. So be aware that
+                if you mutate a <code>MPFunction</code> instance returned from
+                this function the receiver's expression tree will be updated to
+                reflect the change.
+ 
+    @param      anIndex
+                The index of the item. If the index is greater than the number of
+                items for the respective reference frame a
+                <code>NSRangeException</code> is raised.
+ 
+    @param      referenceFrame
+                The reference frame that should be used to identify the item at
+                <code>anIndex</code>.
+ 
+    @return     The item at <code>anIndex</code>.
+ */
+- (id)itemAtIndex:(NSUInteger)anIndex
+   referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     elementAtIndex:referenceFrame:
+    @brief      Returns the element at the specified index.
+ 
+    @discussion An element is either a string or a function. If
+                <code>anIndex</code> identifies a position inside a string
+                element the complete element is returned.
+ 
+                This method always returns elements. To query items in the
+                specified reference frame use
+                <code>-itemAtIndex:referenceFrame:</code>.
+ 
+    @param      anIndex
+                The index of the element.
+ 
+    @param      referenceFrame
+                The reference frame <code>anIndex</code> is specified in.
+ 
+    @return     The element at <code>anIndex</code>.
+ */
+- (id<MPExpressionElement>)elementAtIndex:(NSUInteger)anIndex
+                           referenceFrame:(MPReferenceFrame)referenceFrame;
+
+/*!
+    @method     indexOfElement:
+    @brief      Returns the index of <code>element</code> or
+                <code>NSNotFound</code> if it was not found.
+ 
+    @param      element
+                The element to find.
+ 
+    @return     The index of <code>element</code> expressed in the element
+                reference frame.
+ */
+- (NSUInteger)indexOfElement:(id<MPExpressionElement>)element;
+
+
+/*!
+    @method     itemsInRange:referenceFrame:
+    @brief      Returns an array of the items that are located in the specified
+                range.
+ 
+    @discussion The objects in the returned array are copied before they are
+                returned.
+ 
+                If the <code>range</code> exceeds the receiver's bounds a
+                <code>NSRangeException</code> is raised.
+ 
+    @param      aRange
+                The requested range within the receiver's bounds.
+ 
+    @param      referenceFrame
+                The referenceFrame <code>aRange</code> is expressed in.
+ 
+    @return     An array containing all elements in the specified range. The type
+                of the objects depends on the specified
+                <code>referenceFrame</code>.
+ */
+- (NSArray *)itemsInRange:(NSRange)aRange
+           referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     allItemsInReferenceFrame:
+    @brief      Returns an array of all items in the receiver for the specified
+                reference frame.
+ 
+    @discussion The elements in the returned array are not copied before they are
+                returned so be aware that mutations to any of the returned
+                objects will update the receiver's expression tree to reflect the
+                change.
+ 
+    @return     An array of all items in the receiver.
+ */
+- (NSArray *)allItemsInReferenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     elementAtIndexPath:
+    @brief      Returns the element at the specified index path.
+ 
+    @discussion This method finds the elements at the respective indexes starting
+                at the root expression from the receiver's expression tree.
+                The returned object can be a <code>NSString</code>, a
+                <code>MPFunction</code> or an <code>MPExpression</code> instance
+                depending on the specified <code>indexPath</code>. If any of the
+                indexes exceed the bounds of the respective receiver a
+                <code>NSRangeException</code> is raised.
+ 
+                If the index path does not contain any indexes the receiver
+                itself is returned.
+ 
+    @param      indexPath
+                The index path the required object is located at. The indexes are
+                expressed in the element reference frame.
+ 
+    @return     The element located at <code>indexPath</code>. The element is not
+                copied before it is returned. Be aware of the fact that any
+                mutations made to the returned object will update the receiver's
+                expression tree to reflect the change.
+ */
+- (id)elementAtIndexPath:(NSIndexPath *)indexPath;
+
+
+/*!
+    @method     convertIndex:fromReferenceFrame:toReferenceFrame:
+    @brief      Converts an index from one reference frame to another.
+ 
+    @discussion This method ignores any offsets into items the conversion between
+                reference frames can cause. If you are interested in the offset
+                use <code>-convertIndex:fromReferenceFrame:toReferenceFrame:offset:</code>
+                instead.
+ 
+    @param      anIndex
+                The index to be converted.
+ 
+    @param      fromReferenceFrame
+                The reference frame <code>anIndex</code> is specified in.
+ 
+    @param      toReferenceFrame
+                The reference frame <code>anIndex</code> should be converted to.
+ 
+    @return     An index specified in the <code>toReferenceFrame</code>. If
+                <code>anIndex</code> identifies a location inside an item in the
+                <code>toReferenceFrame</code> the index of the corresponding item
+                is returned.
+ */
+- (NSUInteger)convertIndex:(NSUInteger)anIndex
+        fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
+          toReferenceFrame:(MPReferenceFrame)toReferenceFrame;
+
+
+/*!
+    @method     convertIndex:fromReferenceFrame:toReferenceFrame:offset:
+    @brief      Converts an index from one reference frame to another.
+ 
+    @discussion If <code>anIndex</code> identifies a location inside an item in
+                the <code>toReferenceFrame</code> the index of the corresponding
+                item is returned. In that case the <code>offset</code> parameter
+                will be set to the number of symbols the offset goes into the
+                item at the returned index.
+ 
+    @param      anIndex
+                The index to be converted.
+ 
+    @param      fromReferenceFrame
+                The reference frame <code>anIndex</code> is specified in.
+ 
+    @param      toReferenceFrame
+                The reference frame <code>anIndex</code> should be converted to.
+ 
+    @param      offset
+                This output parameter will be set to the number of symbols that
+                are between the location identified by <code>anIndex</code> and
+                the index that is actually returned. The offset is specified in
+                the symbol reference frame. If you are not interested in the
+                offset pass <code>NULL</code>.
+ 
+    @return     An index specified in the <code>toReferenceFrame</code>
+                corresponding to <code>anIndex</code>.
+ */
+- (NSUInteger)convertIndex:(NSUInteger)anIndex
+        fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
+          toReferenceFrame:(MPReferenceFrame)toReferenceFrame
+                    offset:(NSUInteger *)offset;
+
+
+/*!
+    @method     convertRange:fromReferenceFrame:toReferenceFrame:
+    @brief      Converts a range from one reference frame to another.
+ 
+    @discussion This method just converts the location and target of the range
+                separately using
+                <code>-convertIndex:fromReferenceFrame:toReferenceFrame:</code>.
+                It ensures that the returned range definitely includes all items
+                that were specified by <code>aRange</code>.
+ 
+                The possibility that the returned range may
+                include more symbols than <code>aRange</code> is ignored. If you
+                need that information use
+                <code>-convertRange:fromReferenceFrame:toReferenceFrame:leadingOffset:trailingOffset:</code>.
+ 
+    @param      aRange
+                The range to be converted.
+ 
+    @param      fromReferenceFrame
+                The reference frame <code>aRange</code> is specified in.
+ 
+    @param      toReferenceFrame
+                The reference frame <code>aRange</code> is to be converted to.
+ 
+    @return     A range in the <code>toReferenceFrame</code> that includes the
+                the items identified by <code>aRange</code>.
+ */
+- (NSRange)convertRange:(NSRange)aRange
+     fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
+       toReferenceFrame:(MPReferenceFrame)toReferenceFrame;
+
+
+/*!
+    @method     convertRange:fromReferenceFrame:toReferenceFrame:leadingOffset:trailingOffset:
+    @brief      Converts a range from one reference frame to another.
+ 
+    @discussion This method just converts the location and target of the range
+                separately using
+                <code>-convertIndex:fromReferenceFrame:toReferenceFrame:</code>.
+                It ensures that the returned range definitely includes all items
+                that were specified by <code>aRange</code>.
+ 
+    @param      aRange
+                The range to be converted.
+ 
+    @param      fromReferenceFrame
+                The reference frame <code>aRange</code> is specified in.
+ 
+    @param      toReferenceFrame
+                The reference frame <code>aRange</code> is to be converted to.
+ 
+    @param      leadingOffset
+                The offset of the location of the returned range in respect to
+                the location of <code>aRange</code>.
+ 
+    @param      trailingOffset
+                The offset of the last index in the range in respect to the last
+                index of <code>aRange</code>.
+ 
+    @return     A range in the <code>toReferenceFrame</code> that includes the the items
+                specified by <code>aRange</code>.
+ */
+- (NSRange)convertRange:(NSRange)aRange
+     fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
+       toReferenceFrame:(MPReferenceFrame)toReferenceFrame
+          leadingOffset:(NSUInteger *)leadingOffset
+         trailingOffset:(NSUInteger *)trailingOffset;
+
+
+#pragma mark Mutating Expressions
+/*!
+ @methodgroup Mutating Expressions
+ */
+
+
+/*!
+    @method     replaceItemsInRange:referenceFrame:withElements:
+    @brief      Replaces the elements in the specified range with the contents of
+                the <code>elements</code> array.
+ 
+    @discussion This is the most primitive mutation method of
+                <code>MPExpression</code>. Every other mutating method must
+                ultimately call this method.
+ 
+                After the receiver has been mutated the integrety of the receiver
+                is restored. That basically means that subsequent strings are
+                joined and empty strings removed. After restoring integrity the
+                receiver sends a
+                <code>-changedElementsInIndexedRangePath:replacementLength:</code>
+                to itself. For more information see the documentation on that
+                method.
+ 
+    @param      aRange
+                The range of symbols (including functions) to replace.
+ 
+    @param      referenceFrame
+                The reference frame <code>aRange</code> is specified in.
+ 
+    @param      elements
+                The elements that should replace the symbols specified by
+                <code>range</code>.
+ */
+- (void)replaceItemsInRange:(NSRange)aRange
+             referenceFrame:(MPReferenceFrame)referenceFrame
+               withElements:(NSArray *)elements;
+
+
+/*!
+    @method     changedElementsInRangePath:replacementLength:
+    @brief      This is a notification message that is sent from the receiver to
+                itself after it has been mutated.
+ 
+    @discussion This method does nothing more than notify it's parent that it has
+                been mutated at the respective range path. If you want to get
+                notified about changes in an expression you should override this
+                method instead of
+                <code>-replaceSymbolsInRange:withElements:</code> because this
+                method gives you information about the elements that changed
+                during the mutation.
+ 
+    @param      rangePath
+                The range path at which the receiver was changed starting at the
+                receiver. The range addressed by <code>rangePath</code> is
+                expressed in the element reference frame.
+ 
+    @param      replacementLength
+                The number of elements replacing the elements specified by
+                <code>rangePath</code> (also specified in the element reference
+                frame).
+ */
+- (void)changedElementsInRangePath:(MPRangePath *)rangePath
+                 replacementLength:(NSUInteger)replacementLength;
+
+
+/*!
+    @method     subexpressionFromIndex:referenceFrame:
+    @brief      Creates an expression from the items in the receiver from the
+                specified index to the end.
+ 
+    @discussion The items from the receiver are copied. Mutations to the returned
+                expression will not change the receiver's expression tree.
+ 
+    @param      from
+                The index from which to start constructing the subexpression.
+ 
+    @param      referenceFrame
+                The reference frame <code>from</code> is specified in.
+ 
+    @return     An expression containing the items from the specified index to
+                the end of the receiver.
+ */
+- (MPExpression *)subexpressionFromIndex:(NSUInteger)from
+                          referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     subexpressionToIndex:referenceFrame:
+    @brief      Creates an expression from the items in the receiver from the
+                first to the specified item.
+ 
+    @discussion The items from the receiver are copied. Mutations to the returned
+                expression will not change the receiver's expression tree.
+ 
+    @param      to
+                The index of the first element not to include in the newly
+                constructed subexpression.
+ 
+    @param      referenceFrame
+                The reference frame <code>to</code> is specified in.
+ 
+    @return     An expression containing the items from the first item to the one
+                at the specified index.
+ */
+- (MPExpression *)subexpressionToIndex:(NSUInteger)to
+                        referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     subexpressionWithRange:referenceFrame:
+    @brief      Creates an expression from the items in the receiver within the
+                specified range.
+ 
+    @discussion The items from the receiver are copied. Mutations to the returned
+                expression will not change the receiver's expression tree.
+ 
+    @param      aRange
+                Specifies the items to be included in the newly created
+                subexpression.
+ 
+    @param      referenceFrame
+                The reference frame <code>aRange</code> is specified in.
+ 
+    @return     An expression containing the items in <code>aRange</code>.
+ */
+- (MPExpression *)subexpressionWithRange:(NSRange)aRange
+                          referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+#pragma mark Evaluating Expressions
+/*!
+ @methodgroup Evaluating Expressions
+ */
+
+
+/*!
+    @method     parse:
+    @brief      Parses the receiver.
+ 
+    @discussion This is a convenience method that calls
+                <code>-parseExpectingVariable:errors:</code> with <code>NO</code>
+                as the first argument.
+                
+    @param      errors
+                If the receiver (or any of its elements) contain syntax errors
+                this parameter is set to an appropriate value. All items in the
+                array are <code>NSError</code> instances. This parameter is never
+                set to an empty array. Pass <code>NULL</code> if you are not
+                interested in any errors that might occur.
+ 
+    @return     A <code>MPParsedExpression</code> instance that represents the
+                receiver and can be evaluated or <code>nil</code> if an error
+                occurs. In that case the <code>errors</code> parameter is set to
+                an array containing at least one <code>NSError</code> instance.
+ */
+- (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors;
+
+
+/*!
+    @method     parseExpectingVariable:errors:
+    @brief      Parses the receiver.
+ 
+    @param      flag
+                If <code>YES</code> the receiver must (exept for whitespaces)
+                begin with a single letter followed by an equals sign. If it
+                doesn't the expression is considered invalid. Specify
+                <code>NO</code> If the expression should be evaluatable by itself.
+ 
+    @param      errors
+                If the receiver (or any of its elements) contain syntax errors
+                this parameter is set to an appropriate value. All items in the
+                array are <code>NSError</code> instances. This parameter is never
+                set to an empty array. Pass <code>NULL</code> if you are not
+                interested in any errors that might occur.
+ 
+    @return     A <code>MPParsedExpression</code> instance that represents the
+                receiver and can be evaluated or <code>nil</code> if an error
+                occurs. In that case the <code>errors</code> parameter is set to
+                an array containing at least one <code>NSError</code> instance.
+ */
+- (MPParsedExpression *)parseExpectingVariable:(BOOL)flag
+                                        errors:(NSArray *__autoreleasing *)errors;
+
+@end
+
+
+
+/*!
+    @category   MPExpression (MPExpressionConvenience)
+    @brief      This category defines convenience methods for the
+                <code>MPExpression</code> class.
+ 
+    @discussion All convenience methods are completely defined in terms of other
+                methods of the <code>MPExpression</code> class.
+ */
+@interface MPExpression (MPExpressionConvenience)
+
+#pragma mark Querying Expressions
+/*!
+ @methodgroup Querying Expressions
+ */
+
+
+/*!
+    @method     countElements
+    @brief      Returns the number of elements in the receiver.
+ 
+    @return     The number of elements in the receiver expressed in the element
+                reference frame.
+ */
+- (NSUInteger)countElements;
+
+
+/*!
+    @method     countSymbols
+    @brief      Returns the number of symbols in the receiver.
+ 
+    @return     The number of symbols in the receiver expressed in the symbol
+                reference frame.
+ */
+- (NSUInteger)countSymbols;
+
+
+/*!
+    @method     countTokens
+    @brief      Returns the number of tokens in the receiver.
+ 
+    @return     The number of tokens in the receiver expressed in the token
+                reference frame.
+ */
+- (NSUInteger)countTokens;
+
+
+/*!
+    @method     elementAtIndex:
+    @brief      Returns the element at the specified index.
+ 
+    @param      anIndex
+                The index of the element specified in the element reference
+                frame.
+ 
+    @return     The element at <code>anIndex</code>.
+ */
+- (id<MPExpressionElement>)elementAtIndex:(NSUInteger)anIndex;
+
+
+/*!
+    @method     symbolAtIndex:
+    @brief      Returns the symbol at the specified index.
+ 
+    @param      anIndex
+                The index of the symbol specified in the symbol reference frame.
+ 
+    @return     The symbol at <code>anIndex</code>.
+ */
+- (id<MPExpressionElement>)symbolAtIndex:(NSUInteger)anIndex;
+
+
+/*!
+    @method     tokenAtIndex:
+    @brief      Returns the token at the specified index.
+ 
+    @param      anIndex
+                The index of the token specified in the token reference frame.
+ 
+    @return     The token at <code>anIndex</code>.
+ */
+- (id<MPToken>)tokenAtIndex:(NSUInteger)anIndex;
+
+
+#pragma mark Mutating Expressions
+/*!
+ @methodgroup Mutating Expressions
+ */
+
+
+/*!
+    @method     appendElement:
+    @brief      Appends <code>anElement</code> to the receiver.
+ 
+    @param      anElement
+                The element to append to the receiver.
+ */
+- (void)appendElement:(id<MPExpressionElement>)anElement;
+
+
+/*!
+    @method     appendElements:
+    @brief      Appends the objects from <code>elements</code> to the receiver.
+
+    @discussion All objects in the <code>elements</code> array must conform to
+                the <code>MPExpressionElement</code> protocol. If at least one
+                element does not conform to that protocol a
+                <code>MPIllegalElementException</code> is raised.
+ 
+    @param      elements
+                The elements to append to the receiver.
+ */
+- (void)appendElements:(NSArray *)elements;
+
+
+/*!
+    @method     insertElement:atIndex:referenceFrame:
+    @brief      Inserts <code>anElement</code> at the specified index.
+ 
+    @param      anElement
+                The element to be inserted.
+ 
+    @param      index
+                The index where to insert <code>anElement</code>.
+ 
+    @param      referenceFrame
+                The reference frame <code>index</code> is specified in.
+ */
+- (void)insertElement:(id<MPExpressionElement>)anElement
+              atIndex:(NSUInteger)index
+       referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     insertElements:atIndex:referenceFrame:
+    @brief      Inserts <code>elements</code> at the specified index.
+ 
+    @discussion All objects in the <code>elements</code> array must conform to
+                the <code>MPExpressionElement</code> protocol. If at least one
+                element does not conform to that protocol a
+                <code>MPIllegalElementException</code> is raised.
+ 
+    @param      elements
+                The elements to be inserted.
+ 
+    @param      index
+                The index where to insert <code>elements</code>.
+ 
+    @param      referenceFrame
+                The reference frame <code>index</code> is specified in.
+ */
+- (void)insertElements:(NSArray *)elements
+               atIndex:(NSUInteger)index
+        referenceFrame:(MPReferenceFrame)referenceFrame;
+
+
+/*!
+    @method     deleteElementsInRange:
+    @brief      Removes the elements identified by <code>range</code> from the
+                receiver.
+ 
+    @discussion If <code>range</code> exceeds the receiver's bounds a
+                <code>NSRangeException</code> is raised.
+ 
+    @param      range
+                The range of items to remove from the receiver.
+ 
+    @param      referenceFrame
+                The reference frame <code>range</code> is specified in.
+ */
+- (void)deleteElementsInRange:(NSRange)range
+               referenceFrame:(MPReferenceFrame)referenceFrame;
+
+@end

MathKit/MPExpression.m

@@ -35,7 +35,7 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
     @brief      Private method. Returns an array containing all tokens from the
                 receiver.
  
-    @return     All items in the @c MPTokenReferenceFrame.
+    @return     All items in the <code>MPTokenReferenceFrame</code>.
  */
 - (NSArray *)tokens;
 
@@ -45,8 +45,8 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
     @brief      Private method. Checks whether all objects in the specified array
                 are valid expression elements.
 
-    @discussion If an object is not valid a @c MPIllegalElementException is
+    @discussion If an object is not valid a
-                raised.
+                <code>MPIllegalElementException</code> is raised.
  
     @param      elements
                 The array of objects to be validated.
@@ -65,7 +65,7 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
 /*!
     @method     _replaceSymbolsInRange:withElements:
     @brief      Private method. Replaces the symbols in the specified range with
-                the elements from the @c elements array.
+                the elements from the <code>elements</code> array.
 
     @discussion This is the most primitive mutation method of the @c MPExpression
                 class.
@@ -73,7 +73,7 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
     @param      range
                 The range of symbols to be replaced. The range is specified in 
                 the symbol reference frame. If the range exceeds the receiver's
-                bounds a @c NSRangeException is raised.
+                bounds a <code>NSRangeException</code> is raised.
  
     @param      elements
                 The elements that should replace the symbols in the specified
@@ -85,14 +85,15 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
 
 /*!
     @method     _splitElementsAtLocation:insertionIndex:
-    @brief      Splits the receiver's elements at the specified @c location.
+    @brief      Splits the receiver's elements at the specified
+                <code>location</code>.
 
     @discussion The split location can be inside a string element. In that case
                 the string is replaced with two other smaller strings.
  
                 Splitting the elements destroys the receiver's integrity. The
-                receiver of this message must also receive a @c -fixElements
+                receiver of this message must also receive a
-                message soon afterwards.
+                <code>-fixElements</code> message soon afterwards.
  
     @param      location
                 The index where to split the elements. Specified in the symbol
@@ -105,9 +106,9 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
                 element at the location where the elements were previously
                 splitted.
  
-    @return     @c YES if a string element was split into two smaller strings, @c
+    @return     @c YES if a string element was split into two smaller strings,
-                NO if the split @c location corresponds to a location between two
+                <code>NO</code> if the split <code>location</code> corresponds to
-                elements.
+                a location between two elements.
  */
 - (BOOL)_splitElementsAtLocation:(NSUInteger)location
                   insertionIndex:(NSUInteger *)insertionIndex;
@@ -635,26 +636,6 @@ NSString *const MPIllegalElementExceptionElementKey = @"MPIllegalElementExceptio
 #pragma mark Evaluating Expressions
 
 
-- (NSDecimalNumber *)evaluateWithErrors:(NSArray *__autoreleasing *)errors
-{
-    NSArray *parsingErrors;
-    MPParsedExpression *parsedExpression = [self parse:&parsingErrors];
-    NSError *evaluationError;
-    NSDecimalNumber *result = parsedExpression ? [parsedExpression evaluate:&evaluationError] : nil;
-    if (errors && (parsedExpression || evaluationError)) {
-        NSMutableArray *localErrors = [[NSMutableArray alloc] initWithCapacity:parsingErrors.count+1];
-        if (parsingErrors) {
-            [localErrors addObjectsFromArray:parsingErrors];
-        }
-        if (evaluationError) {
-            [localErrors addObject:evaluationError];
-        }
-        *errors = localErrors;
-    }
-    return result;
-}
-
-
 - (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors
 {
     return [self parseExpectingVariable:NO

MathKit/MPPowerFunctionLayout.m

@@ -33,9 +33,11 @@
     return [NSIndexSet indexSetWithIndex:0];
 }
 
+#warning Broken Power Layout
 - (NSPoint)offsetOfChildLayoutAtIndex:(NSUInteger)index
 {
-    CGFloat y = (self.baseBounds.size.height + self.baseBounds.origin.y) / 2;
+    NSRect exponentBounds = [self childLayoutAtIndex:0].bounds;
+    CGFloat y = (self.baseBounds.size.height + self.baseBounds.origin.y) - ((exponentBounds.size.height + exponentBounds.origin.y) / 2);
     return NSMakePoint(kPowerFunctionExponentXOffset, y);
 }
 
@@ -52,13 +54,14 @@
 - (NSRect)generateBounds
 {
     NSRect exponentBounds = [self childLayoutAtIndex:0].bounds;
-    CGFloat y = self.baseBounds.origin.y;
+    CGFloat height = [self offsetOfChildLayoutAtIndex:0].y + exponentBounds.size.height + exponentBounds.origin.y;
-    CGFloat height = -y + [self offsetOfChildLayoutAtIndex:0].y + exponentBounds.size.height + exponentBounds.origin.y;
     CGFloat width = kPowerFunctionExponentXOffset + exponentBounds.size.width + kPowerFunctionTrailingOffset;
-    return NSMakeRect(0, y, width, height);
+    return NSMakeRect(0, 0, width, height);
 }
 
 - (void)draw
-{}
+{
+    [[NSBezierPath bezierPathWithRect:self.bounds] stroke];
+}
 
 @end

MathPad.xcodeproj/project.pbxproj

@@ -8,105 +8,105 @@
 
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-		3B7B3A1719CC44E4005849E5 /* MPExpressionTokenizer.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPExpressionTokenizer.m; sourceTree = "<group>"; };
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-		3B7B3A2B19CC467E005849E5 /* MPToken.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPToken.m; sourceTree = "<group>"; };
-		3B7B3A5219CC50B1005849E5 /* MPFunction+MPToken.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = "MPFunction+MPToken.h"; sourceTree = "<group>"; };
-		3B7B3A5319CC50B1005849E5 /* MPFunction+MPToken.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = "MPFunction+MPToken.m"; sourceTree = "<group>"; };
 		3B85830D19BB5E5500D76A8D /* MathKit.framework */ = {isa = PBXFileReference; explicitFileType = wrapper.framework; includeInIndex = 0; path = MathKit.framework; sourceTree = BUILT_PRODUCTS_DIR; };
 		3B85831119BB5E5500D76A8D /* MathKit-Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = "MathKit-Info.plist"; sourceTree = "<group>"; };
 		3B85831319BB5E5500D76A8D /* en */ = {isa = PBXFileReference; lastKnownFileType = text.plist.strings; name = en; path = en.lproj/InfoPlist.strings; sourceTree = "<group>"; };
@@ -205,53 +254,9 @@
 		3B85832519BB5E5500D76A8D /* MathKitTests-Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = "MathKitTests-Info.plist"; sourceTree = "<group>"; };
 		3B85832719BB5E5500D76A8D /* en */ = {isa = PBXFileReference; lastKnownFileType = text.plist.strings; name = en; path = en.lproj/InfoPlist.strings; sourceTree = "<group>"; };
 		3B85833219BB5F2D00D76A8D /* MathKit.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = MathKit.h; sourceTree = "<group>"; };
-		3B87E3541900856F00259938 /* MPExpressionView.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; name = MPExpressionView.h; path = ../MathPad/MPExpressionView.h; sourceTree = "<group>"; };
-		3B87E3551900856F00259938 /* MPExpressionView.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; name = MPExpressionView.m; path = ../MathPad/MPExpressionView.m; sourceTree = "<group>"; };
-		3B87E35B1900933200259938 /* MPRangePath.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPRangePath.h; sourceTree = "<group>"; };
-		3B87E35C1900933200259938 /* MPRangePath.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPRangePath.m; sourceTree = "<group>"; };
-		3B87E35E19009D5F00259938 /* MPFunction.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPFunction.h; sourceTree = "<group>"; };
-		3B87E35F19009D5F00259938 /* MPFunction.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPFunction.m; sourceTree = "<group>"; };
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-		3B9265C61A2147DF00AD2809 /* MPNegatedTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPNegatedTerm.m; sourceTree = "<group>"; };
-		3BB09EB01905DE500080A5ED /* MPExpressionStorage.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; name = MPExpressionStorage.h; path = ../MathPad/MPExpressionStorage.h; sourceTree = "<group>"; };
-		3BB09EB11905DE500080A5ED /* MPExpressionStorage.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; name = MPExpressionStorage.m; path = ../MathPad/MPExpressionStorage.m; sourceTree = "<group>"; };
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-		3BB09EDD190728220080A5ED /* NSIndexPath+MPAdditions.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = "NSIndexPath+MPAdditions.m"; sourceTree = "<group>"; };
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-		3BC4661319B245C60033F13A /* Fonts */ = {isa = PBXFileReference; lastKnownFileType = folder; path = Fonts; sourceTree = "<group>"; };
 		3BC4661519B365070033F13A /* MPArrayCache.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPArrayCache.h; sourceTree = "<group>"; };
 		3BC4661619B365070033F13A /* MPArrayCache.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPArrayCache.m; sourceTree = "<group>"; };
-		3BCA0C7E1A12619500C9E3E0 /* MPTerm.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPTerm.h; sourceTree = "<group>"; };
-		3BCA0C7F1A12619500C9E3E0 /* MPTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPTerm.m; sourceTree = "<group>"; };
-		3BCA0C831A1405C000C9E3E0 /* MPFunctionTerm.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPFunctionTerm.h; sourceTree = "<group>"; };
-		3BCA0C841A1405C000C9E3E0 /* MPFunctionTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPFunctionTerm.m; sourceTree = "<group>"; };
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-		3BEFF7501A16B06600301C0C /* MPParsedExpression.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPParsedExpression.m; sourceTree = "<group>"; };
-		3BEFF7531A17AA3200301C0C /* MPProductTerm.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPProductTerm.h; sourceTree = "<group>"; };
-		3BEFF7541A17AA3200301C0C /* MPProductTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPProductTerm.m; sourceTree = "<group>"; };
-		3BEFF7601A1804AF00301C0C /* MPFactorialTerm.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPFactorialTerm.h; sourceTree = "<group>"; };
-		3BEFF7611A1804AF00301C0C /* MPFactorialTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPFactorialTerm.m; sourceTree = "<group>"; };
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-		3BEFF7691A1807B000301C0C /* MPParenthesisTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPParenthesisTerm.m; sourceTree = "<group>"; };
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-		3BEFF76D1A18083C00301C0C /* MPPowerTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPPowerTerm.m; sourceTree = "<group>"; };
-		3BEFF7701A180C8800301C0C /* MPFractionTerm.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPFractionTerm.h; sourceTree = "<group>"; };
-		3BEFF7711A180C8800301C0C /* MPFractionTerm.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPFractionTerm.m; sourceTree = "<group>"; };
-		3BF54BB71A18D08400883BFA /* MPExpressionParser.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPExpressionParser.h; sourceTree = "<group>"; };
-		3BF54BB81A18D08400883BFA /* MPExpressionParser.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPExpressionParser.m; sourceTree = "<group>"; };
-		3BF59AFB19D80ECC00E54292 /* MPFunctionsViewController.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPFunctionsViewController.h; sourceTree = "<group>"; };
-		3BF59AFC19D80ECC00E54292 /* MPFunctionsViewController.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPFunctionsViewController.m; sourceTree = "<group>"; };
-		3BF59AFD19D80ECC00E54292 /* MPFunctionsViewController.xib */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = file.xib; path = MPFunctionsViewController.xib; sourceTree = "<group>"; };
-		3BF59B0119D81EE600E54292 /* MPWhiteView.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPWhiteView.h; sourceTree = "<group>"; };
-		3BF59B0219D81EE600E54292 /* MPWhiteView.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPWhiteView.m; sourceTree = "<group>"; };
 		3BF9976B18DE623E009CF6C4 /* MathPad.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = MathPad.app; sourceTree = BUILT_PRODUCTS_DIR; };
 		3BF9976E18DE623E009CF6C4 /* Cocoa.framework */ = {isa = PBXFileReference; lastKnownFileType = wrapper.framework; name = Cocoa.framework; path = System/Library/Frameworks/Cocoa.framework; sourceTree = SDKROOT; };
 		3BF9977118DE623E009CF6C4 /* AppKit.framework */ = {isa = PBXFileReference; lastKnownFileType = wrapper.framework; name = AppKit.framework; path = System/Library/Frameworks/AppKit.framework; sourceTree = SDKROOT; };
@@ -271,11 +276,6 @@
 		3BF9979018DE623E009CF6C4 /* XCTest.framework */ = {isa = PBXFileReference; lastKnownFileType = wrapper.framework; name = XCTest.framework; path = Library/Frameworks/XCTest.framework; sourceTree = DEVELOPER_DIR; };
 		3BF9979718DE623E009CF6C4 /* MathPadTests-Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = "MathPadTests-Info.plist"; sourceTree = "<group>"; };
 		3BF9979918DE623E009CF6C4 /* en */ = {isa = PBXFileReference; lastKnownFileType = text.plist.strings; name = en; path = en.lproj/InfoPlist.strings; sourceTree = "<group>"; };
-		3BFAC38D1997B61300B3EF67 /* MPExpression.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPExpression.h; sourceTree = "<group>"; };
-		3BFAC38E1997B61300B3EF67 /* MPExpression.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPExpression.m; sourceTree = "<group>"; };
-		3BFAC3961997B67400B3EF67 /* MPExpressionElement.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = MPExpressionElement.h; sourceTree = "<group>"; };
-		3BFAC39A1997BC7600B3EF67 /* NSString+MPExpressionElement.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = "NSString+MPExpressionElement.h"; sourceTree = "<group>"; };
-		3BFAC39B1997BC7600B3EF67 /* NSString+MPExpressionElement.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = "NSString+MPExpressionElement.m"; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -322,6 +322,7 @@
 		3B7172E519C7112C00FEAA5B /* Resources */ = {
 			isa = PBXGroup;
 			children = (
+				3B6338A41A3A4D1200698BFB /* Fonts */,
 				3B7172E819C7147000FEAA5B /* FunctionsButtonDisclosure@2x.png */,
 				3B7172E919C7147000FEAA5B /* FunctionsButtonDisclosure.png */,
 			);
@@ -372,10 +373,10 @@
 		3B85833119BB5EC800D76A8D /* View */ = {
 			isa = PBXGroup;
 			children = (
-				3B87E3541900856F00259938 /* MPExpressionView.h */,
+				3B6338AE1A3A4D6A00698BFB /* MPExpressionView.h */,
-				3B87E3551900856F00259938 /* MPExpressionView.m */,
+				3B6338AF1A3A4D6A00698BFB /* MPExpressionView.m */,
-				3BB09EB01905DE500080A5ED /* MPExpressionStorage.h */,
+				3B6338B21A3A4D7900698BFB /* MPExpressionStorage.h */,
-				3BB09EB11905DE500080A5ED /* MPExpressionStorage.m */,
+				3B6338B31A3A4D7900698BFB /* MPExpressionStorage.m */,
 				3BB09ED819071C270080A5ED /* Private */,
 			);
 			name = View;
@@ -385,8 +386,8 @@
 			isa = PBXGroup;
 			children = (
 				3BC46B4B19B38CB60033F13A /* Base Expression Classes */,
-				3B87E35B1900933200259938 /* MPRangePath.h */,
+				3B6338A01A3A4CFC00698BFB /* MPRangePath.h */,
-				3B87E35C1900933200259938 /* MPRangePath.m */,
+				3B6338A11A3A4CFC00698BFB /* MPRangePath.m */,
 				3BC46B4D19B38CFB0033F13A /* Helpers */,
 			);
 			name = Model;
@@ -399,7 +400,6 @@
 				3BF9978318DE623E009CF6C4 /* MPDocument.xib */,
 				3BF9978618DE623E009CF6C4 /* MainMenu.xib */,
 				3BF9978918DE623E009CF6C4 /* Images.xcassets */,
-				3BC4661319B245C60033F13A /* Fonts */,
 			);
 			name = Resources;
 			sourceTree = "<group>";
@@ -407,14 +407,14 @@
 		3BB09EBC1905EF210080A5ED /* Functions */ = {
 			isa = PBXGroup;
 			children = (
-				3BB09EC71906FD830080A5ED /* MPSumFunction.h */,
+				3B6338541A3A4BE800698BFB /* MPFractionFunction.h */,
-				3BB09EC81906FD830080A5ED /* MPSumFunction.m */,
+				3B6338551A3A4BE800698BFB /* MPFractionFunction.m */,
-				3B7172EC19C9FA8E00FEAA5B /* MPParenthesisFunction.h */,
+				3B63384C1A3A4BD100698BFB /* MPParenthesisFunction.h */,
-				3B7172ED19C9FA8E00FEAA5B /* MPParenthesisFunction.m */,
+				3B63384D1A3A4BD100698BFB /* MPParenthesisFunction.m */,
-				3B5FF73919DB2FF500C8348A /* MPPowerFunction.h */,
+				3B6338561A3A4BE800698BFB /* MPPowerFunction.h */,
-				3B5FF73A19DB2FF500C8348A /* MPPowerFunction.m */,
+				3B6338571A3A4BE800698BFB /* MPPowerFunction.m */,
-				3B69B67A19E4915E0028E608 /* MPFractionFunction.h */,
+				3B63384E1A3A4BD100698BFB /* MPSumFunction.h */,
-				3B69B67B19E4915E0028E608 /* MPFractionFunction.m */,
+				3B63384F1A3A4BD100698BFB /* MPSumFunction.m */,
 			);
 			name = Functions;
 			sourceTree = "<group>";
@@ -422,17 +422,17 @@
 		3BB09ED819071C270080A5ED /* Private */ = {
 			isa = PBXGroup;
 			children = (
-				3BF59AFB19D80ECC00E54292 /* MPFunctionsViewController.h */,
+				3B6338B61A3A4D9400698BFB /* MPFunctionsViewController.h */,
-				3BF59AFC19D80ECC00E54292 /* MPFunctionsViewController.m */,
+				3B6338B71A3A4D9400698BFB /* MPFunctionsViewController.m */,
-				3BF59AFD19D80ECC00E54292 /* MPFunctionsViewController.xib */,
+				3B6338B81A3A4D9400698BFB /* MPFunctionsViewController.xib */,
-				3BF59B0119D81EE600E54292 /* MPWhiteView.h */,
+				3B6338B91A3A4D9400698BFB /* MPWhiteView.h */,
-				3BF59B0219D81EE600E54292 /* MPWhiteView.m */,
+				3B6338BA1A3A4D9400698BFB /* MPWhiteView.m */,
-				3B528D0D199417740054DB5F /* MPLayout.h */,
+				3B6338C01A3A4DA500698BFB /* MPLayout.h */,
-				3B688D9819982DF50006B4AB /* MPLayout.m */,
+				3B6338C11A3A4DA500698BFB /* MPLayout.m */,
-				3B528D0E199417E10054DB5F /* MPExpressionLayout.h */,
+				3B6338C41A3A4DB600698BFB /* MPExpressionLayout.h */,
-				3B528D0F199417E10054DB5F /* MPExpressionLayout.m */,
+				3B6338C51A3A4DB600698BFB /* MPExpressionLayout.m */,
-				3B528D11199417E90054DB5F /* MPFunctionLayout.h */,
+				3B6338C81A3A4DC400698BFB /* MPFunctionLayout.h */,
-				3B528D12199417E90054DB5F /* MPFunctionLayout.m */,
+				3B6338C91A3A4DC400698BFB /* MPFunctionLayout.m */,
 				3BB09EE21907361C0080A5ED /* Function Layouts */,
 			);
 			name = Private;
@@ -442,14 +442,14 @@
 		3BB09EE21907361C0080A5ED /* Function Layouts */ = {
 			isa = PBXGroup;
 			children = (
-				3BB09EDF190736160080A5ED /* MPSumFunctionLayout.h */,
+				3B6338CC1A3A4DE100698BFB /* MPFractionFunctionLayout.h */,
-				3BB09EE0190736160080A5ED /* MPSumFunctionLayout.m */,
+				3B6338CD1A3A4DE100698BFB /* MPFractionFunctionLayout.m */,
-				3B7172F019C9FC6700FEAA5B /* MPParenthesisFunctionLayout.h */,
+				3B6338CE1A3A4DE100698BFB /* MPParenthesisFunctionLayout.h */,
-				3B7172F119C9FC6700FEAA5B /* MPParenthesisFunctionLayout.m */,
+				3B6338CF1A3A4DE100698BFB /* MPParenthesisFunctionLayout.m */,
-				3B69B66A19DB41B90028E608 /* MPPowerFunctionLayout.h */,
+				3B6338D01A3A4DE100698BFB /* MPPowerFunctionLayout.h */,
-				3B69B66B19DB41B90028E608 /* MPPowerFunctionLayout.m */,
+				3B6338D11A3A4DE100698BFB /* MPPowerFunctionLayout.m */,
-				3B69B67E19E493630028E608 /* MPFractionFunctionLayout.h */,
+				3B6338D21A3A4DE100698BFB /* MPSumFunctionLayout.h */,
-				3B69B67F19E493630028E608 /* MPFractionFunctionLayout.m */,
+				3B6338D31A3A4DE100698BFB /* MPSumFunctionLayout.m */,
 			);
 			name = "Function Layouts";
 			sourceTree = "<group>";
@@ -466,19 +466,19 @@
 		3BC46B4B19B38CB60033F13A /* Base Expression Classes */ = {
 			isa = PBXGroup;
 			children = (
-				3BFAC38D1997B61300B3EF67 /* MPExpression.h */,
+				3B6338321A3A4B5800698BFB /* MPExpression.h */,
-				3BFAC38E1997B61300B3EF67 /* MPExpression.m */,
+				3B6338331A3A4B5800698BFB /* MPExpression.m */,
-				3BFAC3961997B67400B3EF67 /* MPExpressionElement.h */,
+				3B6338341A3A4B5800698BFB /* MPExpressionElement.h */,
-				3BFAC39A1997BC7600B3EF67 /* NSString+MPExpressionElement.h */,
+				3B6338381A3A4B7600698BFB /* NSString+MPExpressionElement.h */,
-				3BFAC39B1997BC7600B3EF67 /* NSString+MPExpressionElement.m */,
+				3B6338391A3A4B7600698BFB /* NSString+MPExpressionElement.m */,
-				3B87E35E19009D5F00259938 /* MPFunction.h */,
+				3B6338401A3A4B9500698BFB /* MPFunction.h */,
-				3B87E35F19009D5F00259938 /* MPFunction.m */,
+				3B6338411A3A4B9500698BFB /* MPFunction.m */,
-				3B7B3A1619CC44E4005849E5 /* MPExpressionTokenizer.h */,
+				3B6338441A3A4BA500698BFB /* MPExpressionTokenizer.h */,
-				3B7B3A1719CC44E4005849E5 /* MPExpressionTokenizer.m */,
+				3B6338451A3A4BA500698BFB /* MPExpressionTokenizer.m */,
-				3B7B3A2A19CC467E005849E5 /* MPToken.h */,
+				3B63383C1A3A4B8500698BFB /* MPToken.h */,
-				3B7B3A2B19CC467E005849E5 /* MPToken.m */,
+				3B63383D1A3A4B8500698BFB /* MPToken.m */,
-				3B7B3A5219CC50B1005849E5 /* MPFunction+MPToken.h */,
+				3B6338481A3A4BB300698BFB /* MPFunction+MPToken.h */,
-				3B7B3A5319CC50B1005849E5 /* MPFunction+MPToken.m */,
+				3B6338491A3A4BB300698BFB /* MPFunction+MPToken.m */,
 				3BB09EBC1905EF210080A5ED /* Functions */,
 				3BC46B4F19B506F20033F13A /* Evaluation */,
 			);
@@ -488,10 +488,10 @@
 		3BC46B4D19B38CFB0033F13A /* Helpers */ = {
 			isa = PBXGroup;
 			children = (
-				3BB09EDC190728220080A5ED /* NSIndexPath+MPAdditions.h */,
+				3B6338A61A3A4D2600698BFB /* NSIndexPath+MPAdditions.h */,
-				3BB09EDD190728220080A5ED /* NSIndexPath+MPAdditions.m */,
+				3B6338A71A3A4D2600698BFB /* NSIndexPath+MPAdditions.m */,
-				3B52CEDA19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.h */,
+				3B6338AA1A3A4D3000698BFB /* NSRegularExpression+MPParsingAdditions.h */,
-				3B52CEDB19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.m */,
+				3B6338AB1A3A4D3000698BFB /* NSRegularExpression+MPParsingAdditions.m */,
 			);
 			name = Helpers;
 			sourceTree = "<group>";
@@ -499,32 +499,32 @@
 		3BC46B4F19B506F20033F13A /* Evaluation */ = {
 			isa = PBXGroup;
 			children = (
-				3BF54BB71A18D08400883BFA /* MPExpressionParser.h */,
+				3B63385C1A3A4C0700698BFB /* MPExpressionParser.h */,
-				3BF54BB81A18D08400883BFA /* MPExpressionParser.m */,
+				3B63385D1A3A4C0700698BFB /* MPExpressionParser.m */,
-				3BEFF74F1A16B06600301C0C /* MPParsedExpression.h */,
+				3B6338661A3A4C2B00698BFB /* MPParsedExpression.h */,
-				3BEFF7501A16B06600301C0C /* MPParsedExpression.m */,
+				3B6338671A3A4C2B00698BFB /* MPParsedExpression.m */,
-				3BCA0C7E1A12619500C9E3E0 /* MPTerm.h */,
+				3B63387A1A3A4C7E00698BFB /* MPTerm.h */,
-				3BCA0C7F1A12619500C9E3E0 /* MPTerm.m */,
+				3B63387B1A3A4C7E00698BFB /* MPTerm.m */,
-				3B9265C51A2147DF00AD2809 /* MPNegatedTerm.h */,
+				3B6338601A3A4C2B00698BFB /* MPNegatedTerm.h */,
-				3B9265C61A2147DF00AD2809 /* MPNegatedTerm.m */,
+				3B6338611A3A4C2B00698BFB /* MPNegatedTerm.m */,
-				3BEFF74B1A16A4DA00301C0C /* MPSumTerm.h */,
+				3B6338781A3A4C7E00698BFB /* MPSumTerm.h */,
-				3BEFF74C1A16A4DA00301C0C /* MPSumTerm.m */,
+				3B6338791A3A4C7E00698BFB /* MPSumTerm.m */,
-				3BEFF7531A17AA3200301C0C /* MPProductTerm.h */,
+				3B63386A1A3A4C2B00698BFB /* MPProductTerm.h */,
-				3BEFF7541A17AA3200301C0C /* MPProductTerm.m */,
+				3B63386B1A3A4C2B00698BFB /* MPProductTerm.m */,
-				3BEFF7601A1804AF00301C0C /* MPFactorialTerm.h */,
+				3B6338841A3A4CA500698BFB /* MPFactorialTerm.h */,
-				3BEFF7611A1804AF00301C0C /* MPFactorialTerm.m */,
+				3B6338851A3A4CA500698BFB /* MPFactorialTerm.m */,
-				3B69B6BB19E948740028E608 /* MPElementaryFunctionTerm.h */,
+				3B6338881A3A4CAF00698BFB /* MPElementaryFunctionTerm.h */,
-				3B69B6BC19E948740028E608 /* MPElementaryFunctionTerm.m */,
+				3B6338891A3A4CAF00698BFB /* MPElementaryFunctionTerm.m */,
-				3B69B69B19E6F2110028E608 /* MPNumber.h */,
+				3B6338621A3A4C2B00698BFB /* MPNumber.h */,
-				3B69B69C19E6F2110028E608 /* MPNumber.m */,
+				3B6338631A3A4C2B00698BFB /* MPNumber.m */,
-				3B69B69F19E6F2420028E608 /* MPVariable.h */,
+				3B63387C1A3A4C7E00698BFB /* MPVariable.h */,
-				3B69B6A019E6F2420028E608 /* MPVariable.m */,
+				3B63387D1A3A4C7E00698BFB /* MPVariable.m */,
-				3BCA0C831A1405C000C9E3E0 /* MPFunctionTerm.h */,
+				3B63388C1A3A4CBE00698BFB /* MPFunctionTerm.h */,
-				3BCA0C841A1405C000C9E3E0 /* MPFunctionTerm.m */,
+				3B63388D1A3A4CBE00698BFB /* MPFunctionTerm.m */,
-				3B78C85219C2DA5300516335 /* MPEvaluationContext.h */,
+				3B6338901A3A4CCA00698BFB /* MPEvaluationContext.h */,
-				3B78C85319C2DA5300516335 /* MPEvaluationContext.m */,
+				3B6338911A3A4CCA00698BFB /* MPEvaluationContext.m */,
-				3B591BB919C58D000061D86B /* MPMathRules.h */,
+				3B6338941A3A4CD100698BFB /* MPMathRules.h */,
-				3B591BBA19C58D000061D86B /* MPMathRules.m */,
+				3B6338951A3A4CD100698BFB /* MPMathRules.m */,
 				3BEFF75F1A17FF5C00301C0C /* Functions */,
 			);
 			name = Evaluation;
@@ -533,14 +533,14 @@
 		3BEFF75F1A17FF5C00301C0C /* Functions */ = {
 			isa = PBXGroup;
 			children = (
-				3BEFF7641A18066300301C0C /* MPSumFunctionTerm.h */,
+				3B6338981A3A4CE100698BFB /* MPSumFunctionTerm.h */,
-				3BEFF7651A18066300301C0C /* MPSumFunctionTerm.m */,
+				3B6338991A3A4CE100698BFB /* MPSumFunctionTerm.m */,
-				3BEFF7681A1807B000301C0C /* MPParenthesisTerm.h */,
+				3B6338641A3A4C2B00698BFB /* MPParenthesisTerm.h */,
-				3BEFF7691A1807B000301C0C /* MPParenthesisTerm.m */,
+				3B6338651A3A4C2B00698BFB /* MPParenthesisTerm.m */,
-				3BEFF76C1A18083C00301C0C /* MPPowerTerm.h */,
+				3B6338681A3A4C2B00698BFB /* MPPowerTerm.h */,
-				3BEFF76D1A18083C00301C0C /* MPPowerTerm.m */,
+				3B6338691A3A4C2B00698BFB /* MPPowerTerm.m */,
-				3BEFF7701A180C8800301C0C /* MPFractionTerm.h */,
+				3B63389C1A3A4CEF00698BFB /* MPFractionTerm.h */,
-				3BEFF7711A180C8800301C0C /* MPFractionTerm.m */,
+				3B63389D1A3A4CEF00698BFB /* MPFractionTerm.m */,
 			);
 			name = Functions;
 			sourceTree = "<group>";
@@ -638,49 +638,49 @@
 			isa = PBXHeadersBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
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 				3B85834C19BB661100D76A8D /* MathKit.h in Headers */,
-				3BEFF76E1A18083C00301C0C /* MPPowerTerm.h in Headers */,
+				3B63383A1A3A4B7600698BFB /* NSString+MPExpressionElement.h in Headers */,
-				3B85833819BB63BD00D76A8D /* MPExpression.h in Headers */,
+				3B6338C21A3A4DA500698BFB /* MPLayout.h in Headers */,
-				3B85833919BB63C500D76A8D /* MPExpressionElement.h in Headers */,
+				3B6338721A3A4C2B00698BFB /* MPParsedExpression.h in Headers */,
-				3B69B67C19E4915E0028E608 /* MPFractionFunction.h in Headers */,
+				3B6338B01A3A4D6A00698BFB /* MPExpressionView.h in Headers */,
-				3BEFF7551A17AA3200301C0C /* MPProductTerm.h in Headers */,
+				3B6338DA1A3A4DE100698BFB /* MPSumFunctionLayout.h in Headers */,
-				3B78C85419C2DA5300516335 /* MPEvaluationContext.h in Headers */,
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-				3B85834419BB654D00D76A8D /* NSString+MPExpressionElement.h in Headers */,
+				3B6338501A3A4BD100698BFB /* MPParenthesisFunction.h in Headers */,
-				3BCA0C851A1405C000C9E3E0 /* MPFunctionTerm.h in Headers */,
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-				3B7172F219C9FC6700FEAA5B /* MPParenthesisFunctionLayout.h in Headers */,
+				3B6338D81A3A4DE100698BFB /* MPPowerFunctionLayout.h in Headers */,
-				3B52CEDC19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.h in Headers */,
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-				3BEFF76A1A1807B000301C0C /* MPParenthesisTerm.h in Headers */,
+				3B6338521A3A4BD100698BFB /* MPSumFunction.h in Headers */,
-				3B85833A19BB63D400D76A8D /* MPFunction.h in Headers */,
+				3B6338CA1A3A4DC400698BFB /* MPFunctionLayout.h in Headers */,
-				3B69B66C19DB41B90028E608 /* MPPowerFunctionLayout.h in Headers */,
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-				3B85834319BB653700D76A8D /* MPSumFunction.h in Headers */,
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-				3BCA0C801A12619500C9E3E0 /* MPTerm.h in Headers */,
+				3B6338961A3A4CD100698BFB /* MPMathRules.h in Headers */,
-				3B85834119BB651E00D76A8D /* MPRangePath.h in Headers */,
+				3B6338421A3A4B9500698BFB /* MPFunction.h in Headers */,
-				3B69B69D19E6F2110028E608 /* MPNumber.h in Headers */,
+				3B63388E1A3A4CBE00698BFB /* MPFunctionTerm.h in Headers */,
-				3B85834519BB655200D76A8D /* NSIndexPath+MPAdditions.h in Headers */,
+				3B6338D41A3A4DE100698BFB /* MPFractionFunctionLayout.h in Headers */,
-				3B5FF73B19DB2FF500C8348A /* MPPowerFunction.h in Headers */,
+				3B6338741A3A4C2B00698BFB /* MPPowerTerm.h in Headers */,
-				3B7172EE19C9FA8E00FEAA5B /* MPParenthesisFunction.h in Headers */,
+				3B6338371A3A4B5800698BFB /* MPExpressionElement.h in Headers */,
-				3BF54BB91A18D08400883BFA /* MPExpressionParser.h in Headers */,
+				3B6338BE1A3A4D9400698BFB /* MPWhiteView.h in Headers */,
-				3BEFF7511A16B06600301C0C /* MPParsedExpression.h in Headers */,
+				3B6338A21A3A4CFC00698BFB /* MPRangePath.h in Headers */,
-				3BEFF7721A180C8800301C0C /* MPFractionTerm.h in Headers */,
+				3B63386E1A3A4C2B00698BFB /* MPNumber.h in Headers */,
-				3B85834619BB655C00D76A8D /* MPExpressionView.h in Headers */,
+				3B6338C61A3A4DB600698BFB /* MPExpressionLayout.h in Headers */,
-				3B85834719BB655F00D76A8D /* MPExpressionStorage.h in Headers */,
+				3B63385A1A3A4BE800698BFB /* MPPowerFunction.h in Headers */,
-				3B9265C71A2147DF00AD2809 /* MPNegatedTerm.h in Headers */,
+				3B63389A1A3A4CE100698BFB /* MPSumFunctionTerm.h in Headers */,
-				3BF59AFE19D80ECC00E54292 /* MPFunctionsViewController.h in Headers */,
+				3B6338921A3A4CCA00698BFB /* MPEvaluationContext.h in Headers */,
-				3B7B3A2C19CC467E005849E5 /* MPToken.h in Headers */,
+				3B63386C1A3A4C2B00698BFB /* MPNegatedTerm.h in Headers */,
-				3B7B3A1819CC44E4005849E5 /* MPExpressionTokenizer.h in Headers */,
+				3B63385E1A3A4C0700698BFB /* MPExpressionParser.h in Headers */,
-				3BF59B0319D81EE600E54292 /* MPWhiteView.h in Headers */,
+				3B63384A1A3A4BB300698BFB /* MPFunction+MPToken.h in Headers */,
-				3B85834819BB65B600D76A8D /* MPLayout.h in Headers */,
+				3B63383E1A3A4B8500698BFB /* MPToken.h in Headers */,
-				3BEFF7661A18066300301C0C /* MPSumFunctionTerm.h in Headers */,
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-				3B85834919BB65B600D76A8D /* MPExpressionLayout.h in Headers */,
+				3B63388A1A3A4CAF00698BFB /* MPElementaryFunctionTerm.h in Headers */,
-				3BEFF7621A1804AF00301C0C /* MPFactorialTerm.h in Headers */,
+				3B6338861A3A4CA500698BFB /* MPFactorialTerm.h in Headers */,
-				3B7B3A5419CC50B1005849E5 /* MPFunction+MPToken.h in Headers */,
+				3B6338581A3A4BE800698BFB /* MPFractionFunction.h in Headers */,
-				3B69B6BD19E948740028E608 /* MPElementaryFunctionTerm.h in Headers */,
+				3B6338761A3A4C2B00698BFB /* MPProductTerm.h in Headers */,
-				3B591BBB19C58D000061D86B /* MPMathRules.h in Headers */,
+				3B6338351A3A4B5800698BFB /* MPExpression.h in Headers */,
-				3BEFF74D1A16A4DA00301C0C /* MPSumTerm.h in Headers */,
+				3B6338BB1A3A4D9400698BFB /* MPFunctionsViewController.h in Headers */,
-				3B69B68019E493630028E608 /* MPFractionFunctionLayout.h in Headers */,
+				3B6338D61A3A4DE100698BFB /* MPParenthesisFunctionLayout.h in Headers */,
-				3B69B6A119E6F2420028E608 /* MPVariable.h in Headers */,
+				3B6338821A3A4C7E00698BFB /* MPVariable.h in Headers */,
-				3B85834A19BB65B600D76A8D /* MPFunctionLayout.h in Headers */,
+				3B6338B41A3A4D7900698BFB /* MPExpressionStorage.h in Headers */,
-				3B85834B19BB65B600D76A8D /* MPSumFunctionLayout.h in Headers */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -805,10 +805,11 @@
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				3BF59B0019D80ECC00E54292 /* MPFunctionsViewController.xib in Resources */,
+				3B6338A51A3A4D1200698BFB /* Fonts in Resources */,
 				3B7172EA19C7147000FEAA5B /* FunctionsButtonDisclosure@2x.png in Resources */,
 				3B7172EB19C7147000FEAA5B /* FunctionsButtonDisclosure.png in Resources */,
 				3B85831419BB5E5500D76A8D /* InfoPlist.strings in Resources */,
+				3B6338BD1A3A4D9400698BFB /* MPFunctionsViewController.xib in Resources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -827,7 +828,6 @@
 				3BF9977918DE623E009CF6C4 /* InfoPlist.strings in Resources */,
 				3BF9978A18DE623E009CF6C4 /* Images.xcassets in Resources */,
 				3BC4660B19B2425A0033F13A /* MPDocument.xib in Resources */,
-				3BC4661419B245C60033F13A /* Fonts in Resources */,
 				3BF9977F18DE623E009CF6C4 /* Credits.rtf in Resources */,
 				3BF9978818DE623E009CF6C4 /* MainMenu.xib in Resources */,
 			);
@@ -848,47 +848,47 @@
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 			buildActionMask = 2147483647;
 			files = (
-				3BEFF76F1A18083C00301C0C /* MPPowerTerm.m in Sources */,
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-				3B5FF73C19DB2FF500C8348A /* MPPowerFunction.m in Sources */,
+				3B63385F1A3A4C0700698BFB /* MPExpressionParser.m in Sources */,
-				3BBEA94219BB79A700133766 /* MPExpressionLayout.m in Sources */,
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-				3BF54BBA1A18D08400883BFA /* MPExpressionParser.m in Sources */,
+				3B6338591A3A4BE800698BFB /* MPFractionFunction.m in Sources */,
-				3B7B3A1919CC44E4005849E5 /* MPExpressionTokenizer.m in Sources */,
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-				3B591BBC19C58D000061D86B /* MPMathRules.m in Sources */,
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-				3B69B6BE19E948740028E608 /* MPElementaryFunctionTerm.m in Sources */,
+				3B6338D51A3A4DE100698BFB /* MPFractionFunctionLayout.m in Sources */,
-				3B7172EF19C9FA8E00FEAA5B /* MPParenthesisFunction.m in Sources */,
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-				3B7B3A5519CC50B1005849E5 /* MPFunction+MPToken.m in Sources */,
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-				3BBEA93D19BB79A700133766 /* NSString+MPExpressionElement.m in Sources */,
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-				3BEFF7521A16B06600301C0C /* MPParsedExpression.m in Sources */,
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-				3B7172F319C9FC6700FEAA5B /* MPParenthesisFunctionLayout.m in Sources */,
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-				3BEFF76B1A1807B000301C0C /* MPParenthesisTerm.m in Sources */,
+				3B6338731A3A4C2B00698BFB /* MPParsedExpression.m in Sources */,
-				3BEFF7631A1804AF00301C0C /* MPFactorialTerm.m in Sources */,
+				3B6338771A3A4C2B00698BFB /* MPProductTerm.m in Sources */,
-				3BEFF7731A180C8800301C0C /* MPFractionTerm.m in Sources */,
+				3B6338B51A3A4D7900698BFB /* MPExpressionStorage.m in Sources */,
-				3BEFF7671A18066300301C0C /* MPSumFunctionTerm.m in Sources */,
+				3B63386F1A3A4C2B00698BFB /* MPNumber.m in Sources */,
-				3BBEA93A19BB79A700133766 /* MPSumFunction.m in Sources */,
+				3B6338CB1A3A4DC400698BFB /* MPFunctionLayout.m in Sources */,
-				3BBEA93E19BB79A700133766 /* NSIndexPath+MPAdditions.m in Sources */,
+				3B63384B1A3A4BB300698BFB /* MPFunction+MPToken.m in Sources */,
-				3B52CEDD19BEE63000CEDCFC /* NSRegularExpression+MPParsingAdditions.m in Sources */,
+				3B6338BF1A3A4D9400698BFB /* MPWhiteView.m in Sources */,
-				3BEFF7561A17AA3200301C0C /* MPProductTerm.m in Sources */,
+				3B6338931A3A4CCA00698BFB /* MPEvaluationContext.m in Sources */,
-				3B69B67D19E4915E0028E608 /* MPFractionFunction.m in Sources */,
+				3B6338C31A3A4DA500698BFB /* MPLayout.m in Sources */,
-				3BEFF74E1A16A4DA00301C0C /* MPSumTerm.m in Sources */,
+				3B63387F1A3A4C7E00698BFB /* MPSumTerm.m in Sources */,
-				3BF59AFF19D80ECC00E54292 /* MPFunctionsViewController.m in Sources */,
+				3B6338811A3A4C7E00698BFB /* MPTerm.m in Sources */,
-				3BCA0C861A1405C000C9E3E0 /* MPFunctionTerm.m in Sources */,
+				3B6338B11A3A4D6A00698BFB /* MPExpressionView.m in Sources */,
-				3BCA0C811A12619500C9E3E0 /* MPTerm.m in Sources */,
+				3B6338AD1A3A4D3000698BFB /* NSRegularExpression+MPParsingAdditions.m in Sources */,
-				3B69B66D19DB41B90028E608 /* MPPowerFunctionLayout.m in Sources */,
+				3B63388B1A3A4CAF00698BFB /* MPElementaryFunctionTerm.m in Sources */,
-				3BBEA93619BB79A700133766 /* MPFunction.m in Sources */,
+				3B6338511A3A4BD100698BFB /* MPParenthesisFunction.m in Sources */,
-				3BBEA93519BB79A700133766 /* MPExpression.m in Sources */,
+				3B6338871A3A4CA500698BFB /* MPFactorialTerm.m in Sources */,
-				3BBEA93B19BB79A700133766 /* MPRangePath.m in Sources */,
+				3B6338431A3A4B9500698BFB /* MPFunction.m in Sources */,
-				3BBEA94319BB79A700133766 /* MPFunctionLayout.m in Sources */,
+				3B6338751A3A4C2B00698BFB /* MPPowerTerm.m in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};

MathPad/MPExpression.h

@@ -1,840 +0,0 @@
-//
-//  MPExpression.h
-//  MathPad
-//
-//  Created by Kim Wittenburg on 10.08.14.
-//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
-//
-
-
-
-/*!
-    @const      MPIllegalElementException
-    @brief      Name for an exception that is raised if an invalid element is
-                added to an expression.
- 
-    @discussion This exception may be raised during initialization of an
-                expression or when the expression is mutated. This exception
-                always contains the @c MPIllegalElementExceptionElementKey key in
-                its @c userInfo dictionary.
- */
-FOUNDATION_EXPORT NSString *const MPIllegalElementException;
-
-
-/*!
-    @const      MPIllegalElementExceptionElementKey
-    @brief      Predefined key for the invalid element that caused an exception
-                to be raised.
- 
-    @discussion The invalid element can be of any type.
- */
-FOUNDATION_EXPORT NSString *const MPIllegalElementExceptionElementKey;
-
-
-/*!
-    @typedef    MPReferenceFrame
-    @brief      A reference frame describes what an @em item in an expression is.
- 
-    @discussion Reference frames have to be passed in multiple methods of the @c
-                MPExpression class. You can convert between reference frames
-                using the following methods:
-                <pre>
- @textblock
-- convertIndexFromReferenceFrame:toReferenceFrame:
-  - convertIndexFromReferenceFrame:toReferenceFrame:offset:
- @/textblock
-                </pre>
-
-                There are three different types of items (reference frames):
-                symbols, tokens and elements. A symbol is the smalles possible
-                unit in an expression. Thus a token consists of one or more
-                symbols. Similarly an element consists of one or more tokens.
- 
-    @constant   MPElementReferenceFrame
-                Specifies that items should be interpreted as elements. An
-                element is either a @c NSString object or a @c MPFunction object.
- 
-    @constant   MPSymbolReferenceFrame
-                Specifies that items should be interpreted as symbols. A symbol
-                can be a single character (represented by the @c NSString class)
-                or a @c MPFunction object.
- 
-    @constant   MPTokenReferenceFrame
-                Specifies that items should be interpreted as tokens. A token is
-                a logical unit of content in an expression. This can be a single
-                character (e.g. '+'), an arbitrary number of characters (e.g. a
-                number) or a @c MPFunction object.
- 
-                All tokens conform to the @c MPToken protocol.
- */
-typedef NS_ENUM(NSUInteger, MPReferenceFrame) {
-    MPElementReferenceFrame,
-    MPSymbolReferenceFrame,
-    MPTokenReferenceFrame
-};
-
-
-
-@class MPExpression, MPFunction, MPRangePath, MPParsedExpression;
-@protocol MPExpressionElement, MPToken;
-
-
-/*!
-    @class      MPExpression
-    @brief      An @c MPExpression object is the base object for any mathematical
-                expression.
- 
-    @discussion Every expression consists of string elements (represented by the
-                @c NSString class) and function elements (represented by the @c
-                MPFunction class). Functions likewise can have expressions as
-                elements (also called <i>children</i> in this context). Both
-                expressions and functions are mutable. Through this organization
-                expression are organized in a tree-like structure called the
-                'expression tree'.
- 
-                An expression can evaluate itself giving you either a
-                result or possibly an error if the expression was not constructed
-                correctly or could not be evaluated.
-  */
-@interface MPExpression : NSObject <NSCopying, NSCoding>
-
-
-#pragma mark Creation Methods
-/*!
- @methodgroup Creation Methods
- */
-
-
-/*!
-    @method     init
-    @brief      Initlializes a newly created expression.
- 
-    @discussion This method is a convenience initializer to initialize an
-                expression with @c 0 elements.
- 
-    @return     An expression.
- */
-- (instancetype)init;
-
-
-/*!
-    @method     initWithElement:
-    @brief      Initializes a newly created expression with @c element.
-
-    @discussion This method is a convenience initializer to initialize an
-                expression with a single element.
- 
-    @param      element
-                The element to be added to the expression. The @c element will be
-                copied.
- 
-    @return     An expression initialized with @c element.
- */
-- (instancetype)initWithElement:(id<MPExpressionElement>)element;
-
-
-/*!
-    @method     initWithElements:
-    @brief      Initializes a newly created expression with the specified
-                elements.
- 
-    @discussion All elements must conform to the @c MPExpressionElement protocol.
-                If one or more objects do not conform to that protocol an @c
-                MPIllegalElementException is raised.
- 
-                This method is the designated initializer for the @c MPExpression
-                class.
- 
-    @param      elements
-                The elements that should be added to the expression. Every
-                element must conform to the @c MPExpressionElement protocol. Each
-                element is copied and the copy is then added to the expression.
-                The object in the @c elements array is not modified.
- 
-    @return     An expression containing @c elements.
- */
-- (instancetype)initWithElements:(NSArray *)elements; /* designated initializer */
-
-
-#pragma mark Querying Expressions
-/*!
- @methodgroup Querying Expressions
- */
-
-
-/*!
-    @property   parent
-    @brief      The receiver's parent.
- 
-    @discussion Expressions are organized in a tree-like structure. Through this
-                property an expression's containing function can be accessed.
-       @warning You should never set this property manually. If you are
-                implementing a custom subclass of @c MPFunction use the @c
-                MPFunctionAccessorImplementation macro.
- 
-    @return     The parent of the receiver or @c nil if the receiver is the root
-                expression.
- */
-@property (nonatomic, weak) MPFunction *parent;
-
-
-/*!
-    @method     rootExpression
-    @brief      Returns the root expression from the receiver's expression tree.
- 
-    @discussion The root expression is the ultimate parent of all expressions and
-                functions in the expression tree. A root expression does not have
-                a parent.
- 
-    @return     The root expression from the receiver's expression tree.
- */
-- (MPExpression *)rootExpression;
-
-
-/*!
-    @method     indexPath
-    @brief      Returns the index path of the receiver in the expression tree.
- 
-    @discussion The index path is calculated by going up the expression tree
-                collecting the respective index of the receiver. The indexes are
-                expressed in the element reference frame. If any of the indexes
-                exceed the respective receiver's bounds a @c NSRangeException is
-                raised.
- 
-    @return     The index path of the receiver in the expression tree.
- */
-- (NSIndexPath *)indexPath;
-
-
-/*!
-    @method     countItemsInReferenceFrame:
-    @brief      Returns the number of items in the receiver in the respective
-                reference frame.
- 
-    @param      referenceFrame
-                The reference frame that should be used to count the items.
- 
-    @return     The current number of items in the receiver counted in the
-                specified reference frame.
- */
-- (NSUInteger)countItemsInReferenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     itemAtIndex:referenceFrame:
-    @brief      Returns the item at @c anIndex.
- 
-    @discussion The item is not copied before it is returned. So be aware that
-                if you mutate a @c MPFunction object returned from this function
-                the changes will be reflected in the receiver.
- 
-    @param      anIndex
-                The index of the item. If the index is greater than the number of
-                items for the respective reference frame an @c NSRangeException
-                is raised.
- 
-    @param      referenceFrame
-                The reference frame that should be used to identify the item at
-                @c anIndex.
- 
-    @return     The item at @c anIndex.
- */
-- (id)itemAtIndex:(NSUInteger)anIndex
-   referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     elementAtIndex:referenceFrame:
-    @brief      Returns the element at the specified index.
- 
-    @discussion An element is either a string or a function. If @c anIndex
-                specifies a position inside a string the complete string element
-                is returned.
- 
-                This method does not return any item in any reference frame but
-                only complete elements. Use @c -itemAtIndex:referenceFrame: for
-                that purpose.
- 
-    @param      anIndex
-                The index of the element.
- 
-    @param      referenceFrame
-                The reference frame @c anIndex is specified in.
- 
-    @return     The item at @c anIndex.
- */
-- (id<MPExpressionElement>)elementAtIndex:(NSUInteger)anIndex
-                           referenceFrame:(MPReferenceFrame)referenceFrame;
-
-/*!
-    @method     indexOfElement:
-    @brief      Returns the index of @c element or @c NSNotFound if it was not
-                found.
- 
-    @param      element
-                The element to find.
- 
-    @return     The index of @c element expressed in the element reference frame.
- */
-- (NSUInteger)indexOfElement:(id<MPExpressionElement>)element;
-
-
-/*!
-    @method     itemsInRange:referenceFrame:
-    @brief      Returns an array of the items that are located in the specified
-                range.
- 
-    @discussion The objects in the returned array are not copied before they are
-                returned. You should be aware of the fact that mutations to any
-                returned objects will be reflected in the receiver.
- 
-                If the @c range exceeds the receiver's bounds an @c
-                NSRangeException is raised.
- 
-    @param      aRange
-                The requested range within the receiver's bounds.
- 
-    @param      referenceFrame
-                The referenceFrame @c aRange is expressed in.
- 
-    @return     An array of objects that conform to the @c MPExpressionElement
-                protocol (that is @c NSString objects and @c MPFunction objects).
-                The length of the returned array is equal to the length of the
-                specified range.
- */
-- (NSArray *)itemsInRange:(NSRange)aRange
-           referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     allItemsInReferenceFrame:
-    @brief      Returns an array of all items in the receiver for the specified
-                reference frame.
- 
-    @discussion The elements in the returned array are not copied before they are
-                returned so be aware that mutations to any of the returned
-                objects will be reflected in the receiver.
- 
-    @return     An array of all items in the receiver.
- */
-- (NSArray *)allItemsInReferenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     elementAtIndexPath:
-    @brief      Returns the element at the specified index path.
- 
-    @discussion This method @em walks down the expression tree (including
-                functions) using the specified index path and finds the
-                corresponding element. The returned object can be an @c NSString,
-                a @c MPFunction or an @c MPExpression depending on the element @c
-                indexPath points to. If any of the indexes exceed the bounds of
-                the respective receiver an @c NSRangeException is raised.
- 
-                If the index path does not contain any indexes the receiver
-                itself is returned.
- 
-    @param      indexPath
-                The index path the required object is located at. The indexes are
-                expressed in the element reference frame.
- 
-    @return     The element located at @c indexPath. The element is not copied
-                before it is returned. Be aware of the fact that any mutations
-                made to the returned object are reflected in the receiver.
- */
-- (id)elementAtIndexPath:(NSIndexPath *)indexPath;
-
-
-/*!
-    @method     convertIndex:fromReferenceFrame:toReferenceFrame:
-    @brief      Converts an index from one reference frame to another.
- 
-    @discussion This method ignores any offsets into items the conversion between
-                reference frames can cause. If you are interested in the offset
-                use @c -convertIndex:fromReferenceFrame:toReferenceFrame:offset:
-                instead.
- 
-    @param      anIndex
-                The index to be converted.
- 
-    @param      fromReferenceFrame
-                The reference frame @c anIndex is specified in.
- 
-    @param      toReferenceFrame
-                The reference frame @c anIndex should be converted to.
- 
-    @return     An index specified in the @c toReferenceFrame. If @c anIndex
-                specifies a location inside an item in the @c toReferenceFrame
-                the index of the corresponding item is returned.
- */
-- (NSUInteger)convertIndex:(NSUInteger)anIndex
-        fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
-          toReferenceFrame:(MPReferenceFrame)toReferenceFrame;
-
-
-/*!
-    @method     convertIndex:fromReferenceFrame:toReferenceFrame:offset:
-    @brief      Converts an index from one reference frame to another.
- 
-    @discussion If @c anIndex specifies a location inside an item in the @c
-                toReferenceFrame the index of the corresponding item is returned.
- 
-    @param      anIndex
-                The index to be converted.
- 
-    @param      fromReferenceFrame
-                The reference frame @c anIndex is specified in.
- 
-    @param      toReferenceFrame
-                The reference frame @c anIndex should be converted to.
- 
-    @param      offset
-                This output parameter will be set to the number of symbols that
-                are between the location specified by @c anIndex and the index
-                that is actually returned. The offset is specified in the symbol
-                reference frame. If you are not interested in the offset pass
-                @c NULL.
- 
-    @return     An index specified in the @c toReferenceFrame corresponding to
-                @c anIndex.
- */
-- (NSUInteger)convertIndex:(NSUInteger)anIndex
-        fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
-          toReferenceFrame:(MPReferenceFrame)toReferenceFrame
-                    offset:(out NSUInteger *)offset;
-
-
-/*!
-    @method     convertRange:fromReferenceFrame:toReferenceFrame:
-    @brief      Converts a range from one reference frame to another.
- 
-    @discussion This method just converts the location and target of the range
-                separately using @c
-                -convertIndex:fromReferenceFrame:toReferenceFrame:. This method
-                ensures that the returned range definitely includes all items
-                that were specified by @c aRange.
- 
-                This method ignores the possibility that the returned range may
-                include more than @a aRange. If you need that information use
-                @c -convertRange:fromReferenceFrame:toReferenceFrame:leadingOffset:trailingOffset:.
- 
-    @param      aRange
-                The range to be converted.
- 
-    @param      fromReferenceFrame
-                The reference frame @c aRange is specified in.
- 
-    @param      toReferenceFrame
-                The reference frame @c aRange is to be converted to.
- 
-    @return     A range in the @c toReferenceFrame that includes the the items
-                specified by @c aRange.
- */
-- (NSRange)convertRange:(NSRange)aRange
-     fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
-       toReferenceFrame:(MPReferenceFrame)toReferenceFrame;
-
-
-/*!
-    @method     convertRange:fromReferenceFrame:toReferenceFrame:leadingOffset:trailingOffset:
-    @brief      Converts a range from one reference frame to another.
- 
-    @discussion This method just converts the location and target of the range
-                separately using @c
-                -convertIndex:fromReferenceFrame:toReferenceFrame:. This method
-                ensures that the returned range definitely includes all items
-                that were specified by @c aRange.
- 
-    @param      aRange
-                The range to be converted.
- 
-    @param      fromReferenceFrame
-                The reference frame @c aRange is specified in.
- 
-    @param      toReferenceFrame
-                The reference frame @c aRange is to be converted to.
- 
-    @param      leadingOffset
-                The offset of the location of the returned range in respect to
-                the location of @c aRange.
- 
-    @param      trailingOffset
-                The offset of the last index in the range in respect to the last
-                index of @c aRange.
- 
-    @return     A range in the @c toReferenceFrame that includes the the items
-                specified by @c aRange.
- */
-- (NSRange)convertRange:(NSRange)aRange
-     fromReferenceFrame:(MPReferenceFrame)fromReferenceFrame
-       toReferenceFrame:(MPReferenceFrame)toReferenceFrame
-          leadingOffset:(NSUInteger *)leadingOffset
-         trailingOffset:(NSUInteger *)trailingOffset;
-
-
-#pragma mark Mutating Expressions
-/*!
- @methodgroup Mutating Expressions
- */
-
-
-/*!
-    @method     replaceItemsInRange:referenceFrame:withElements:
-    @brief      Replaces the elements in the specified range with the contents of
-                the @c elements array.
- 
-    @discussion This is the most primitive mutation method of @c MPExpression.
-                Every other mutating method utlimately must call this method.
- 
-                After the receiver has been mutated the integrety of the receiver
-                is restored. That basically means that subsequent strings are
-                joined and empty strings removed. After restoring integrity the
-                receiver sends a @c
-                -changedElementsInIndexedRangePath:replacementLength: to
-                itself. For more information see the documentation on that
-                method.
- 
-    @param      aRange
-                The @c range of symbols (including functions) to replace.
- 
-    @param      referenceFrame
-                The reference frame @c aRange is specified in.
- 
-    @param      elements
-                The elements that should replace the symbols specified by @c
-                range.
- */
-- (void)replaceItemsInRange:(NSRange)aRange
-             referenceFrame:(MPReferenceFrame)referenceFrame
-               withElements:(NSArray *)elements;
-
-
-/*!
-    @method     changedElementsInRangePath:replacementLength:
-    @brief      Called after the receiver has been mutated.
- 
-    @discussion This method does nothing more than notify it's parent that it has
-                been mutated at the receiver's index. If you need to know about
-                changes in an expression you should override this method instead
-                of @c -replaceSymbolsInRange:withElements: because this method
-                gives you information about the number of elements changed during
-                the mutation.
- 
-    @param      rangePath
-                The range path at which the receiver was changed starting at the
-                receiver. The range addressed by @c rangePath is expressed in the
-                element reference frame.
- 
-    @param      replacementLength
-                The number of elements replacing the elements specified by @c
-                rangePath (also specified in the element reference frame).
- */
-- (void)changedElementsInRangePath:(MPRangePath *)rangePath
-                 replacementLength:(NSUInteger)replacementLength;
-
-
-/*!
-    @method     subexpressionFromIndex:referenceFrame:
-    @brief      Creates an expression from the items in the receiver from the
-                specified index to the end.
- 
-    @discussion The items from the receiver are copied. Mutations to the returned
-                expression will not change the receiver.
- 
-    @param      from
-                The index from which to start constructing the subexpression.
- 
-    @param      referenceFrame
-                The reference frame @c from is specified in.
- 
-    @return     An expression containing the items from the specified index to
-                the end of the receiver.
- */
-- (MPExpression *)subexpressionFromIndex:(NSUInteger)from
-                          referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     subexpressionToIndex:referenceFrame:
-    @brief      Creates an expression from the items in the receiver from the
-                first item to the end.
- 
-    @discussion The items from the receiver are copied. Mutations to the returned
-                expression will not change the receiver.
- 
-    @param      to
-                The index of the first element not to include in the newly
-                constructed subexpression.
- 
-    @param      referenceFrame
-                The reference frame @c to is specified in.
- 
-    @return     An expression containing the items from the first item to the one
-                at the specified index.
- */
-- (MPExpression *)subexpressionToIndex:(NSUInteger)to
-                        referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     subexpressionWithRange:referenceFrame:
-    @brief      Creates an expression from the items in the receiver within the
-                specified range.
- 
-    @discussion The items from the receiver are copied. Mutations to the returned
-                expression will not change the receiver.
- 
-    @param      aRange
-                Specifies the items to be included in the newly created
-                subexpression.
- 
-    @param      referenceFrame
-                The reference frame @c aRange is specified in.
- 
-    @return     An expression containing the items in @c aRange.
- */
-- (MPExpression *)subexpressionWithRange:(NSRange)aRange
-                          referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-#pragma mark Evaluating Expressions
-/*!
- @methodgroup Evaluating Expressions
- */
-
-
-/*!
-    @method     evaluateWitErrors:
-    @brief      Evaluates the receiver.
- 
-    @discussion This is a convenience method for evaluating an expression. If you
-                want more control over the evaluation process use @c -parse
-                instead.
- 
-    @param      errors
-                If the receiver (or any of its elements) contain syntax errors or
-                can not be evaluated this parameter is set to an appropriate
-                value. All items in the array are @c NSError instances. This
-                parameter is never set to an empty array.
-                Pass @c NULL if you are not interested in any errors that might
-                occur.
- 
-    @return     The result of the evaluation or @c nil of the receiver could not
-                be evaluated. In that case the @c error parameter is set to an
-                appropriate value.
- */
-- (NSDecimalNumber *)evaluateWithErrors:(NSArray *__autoreleasing *)errors;
-
-
-/*!
-    @method     parse:
-    @brief      Parses the receiver.
- 
-    @discussion This is a convenience method that calls @c
-                -parseExpectingVariable:errors: with @c NO as the first argument.
-                
-    @param      errors
-                If the receiver (or any of its elements) contain syntax errors
-                this parameter is set to an appropriate value. All items in the
-                array are @c NSError instances. This parameter is never set to an
-                empty array.
-                Pass @c NULL if you are not interested in any errors that might
-                occur.
- 
-    @return     A @c MPParsedExpression object that represents the receiver and
-                can be evaluated or @c nil if an error occurs. In that case the
-                @c errors parameter is set to an array containing at least one
-                @c NSError instance.
- */
-- (MPParsedExpression *)parse:(NSArray *__autoreleasing *)errors;
-
-
-/*!
-    @method     parseExpectingVariable:errors:
-    @brief      Parses the receiver.
- 
-    @param      flag
-                If @c YES the receiver must (exept for whitespaces) begin with a
-                single letter followed by an equals sign. If it doesn't the
-                expression is considered invalid. Specify @c NO If the expression
-                should be evaluatable by itself.
- 
-    @param      errors
-                If the receiver (or any of its elements) contain syntax errors
-                this parameter is set to an appropriate value. All items in the
-                array are @c NSError instances. This parameter is never set to an
-                empty array.
-                Pass @c NULL if you are not interested in any errors that might
-                occur.
- 
-    @return     A @c MPParsedExpression object that represents the receiver and
-                can be evaluated or @c nil if an error occurs. In that case the
-                @c errors parameter is set to an array containing at least one
-                @c NSError instance.
- */
-- (MPParsedExpression *)parseExpectingVariable:(BOOL)flag
-                                        errors:(NSArray *__autoreleasing *)errors;
-
-@end
-
-
-
-/*!
-    @category   MPExpression (MPExpressionConvenience)
-    @brief      This category defines convenience methods for the @c MPExpression
-                class.
- 
-    @discussion All convenience methods are completely defined in terms of other
-                methods of the @c MPExpression class.
- */
-@interface MPExpression (MPExpressionConvenience)
-
-#pragma mark Querying Expressions
-/*!
- @methodgroup Querying Expressions
- */
-
-
-/*!
-    @method     countElements
-    @brief      Returns the number of elements in the receiver.
- 
-    @return     The number of elements in the receiver expressed in the element
-                reference frame.
- */
-- (NSUInteger)countElements;
-
-
-/*!
-    @method     countSymbols
-    @brief      Returns the number of symbols in the receiver.
- 
-    @return     The number of symbols in the receiver expressed in the symbol
-                reference frame.
- */
-- (NSUInteger)countSymbols;
-
-
-/*!
-    @method     countTokens
-    @brief      Returns the number of tokens in the receiver.
- 
-    @return     The number of tokens in the receiver expressed in the token
-                reference frame.
- */
-- (NSUInteger)countTokens;
-
-
-/*!
-    @method     elementAtIndex:
-    @brief      Returns the element at the specified index.
- 
-    @param      anIndex
-                The index of the element specified in the element reference
-                frame.
- 
-    @return     The element at @c anIndex.
- */
-- (id<MPExpressionElement>)elementAtIndex:(NSUInteger)anIndex;
-
-
-/*!
-    @method     symbolAtIndex:
-    @brief      Returns the symbol at the specified index.
- 
-    @param      anIndex
-                The index of the symbol specified in the symbol reference frame.
- 
-    @return     The symbol at @c anIndex.
- */
-- (id<MPExpressionElement>)symbolAtIndex:(NSUInteger)anIndex;
-
-
-/*!
-    @method     tokenAtIndex:
-    @brief      Returns the token at the specified index.
- 
-    @param      anIndex
-                The index of the token specified in the token reference frame.
- 
-    @return     The token at @c anIndex.
- */
-- (id<MPToken>)tokenAtIndex:(NSUInteger)anIndex;
-
-
-#pragma mark Mutating Expressions
-/*!
- @methodgroup Mutating Expressions
- */
-
-
-/*!
-    @method     appendElement:
-    @brief      Appends @c anElement to the receiver.
- 
-    @param      anElement
-                The element to append to the receiver.
- */
-- (void)appendElement:(id<MPExpressionElement>)anElement;
-
-
-/*!
-    @method     appendElements:
-    @brief      Appends the objects from @c elements to the receiver.
- 
-    @param      elements
-                The elements to append to the receiver.
- */
-- (void)appendElements:(NSArray *)elements;
-
-
-/*!
-    @method     insertElement:atIndex:referenceFrame:
-    @brief      Inserts @c anElement at the specified index.
- 
-    @param      anElement
-                The element to be inserted.
- 
-    @param      index
-                The index where to insert @c anElement.
- 
-    @param      referenceFrame
-                The reference frame @c index is specified in.
- */
-- (void)insertElement:(id<MPExpressionElement>)anElement
-              atIndex:(NSUInteger)index
-       referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     insertElements:atIndex:referenceFrame:
-    @brief      Inserts @c elements at the specified index.
- 
-    @param      elements
-                The elements to be inserted.
- 
-    @param      index
-                The index where to insert @c elements.
- 
-    @param      referenceFrame
-                The reference frame @c index is specified in.
- */
-- (void)insertElements:(NSArray *)elements
-               atIndex:(NSUInteger)index
-        referenceFrame:(MPReferenceFrame)referenceFrame;
-
-
-/*!
-    @method     deleteElementsInRange:
-    @brief      Removes the elements specified by @c range from the receiver.
- 
-    @param      range
-                The range of items to remove from the receiver.
- 
-    @param      referenceFrame
-                The reference frame @c range is specified in.
- */
-- (void)deleteElementsInRange:(NSRange)range
-               referenceFrame:(MPReferenceFrame)referenceFrame;
-
-@end