// // MPExpression.h // MathPad // // Created by Kim Wittenburg on 10.08.14. // Copyright (c) 2014 Kim Wittenburg. All rights reserved. // @import Foundation; #import "NSString+MPExpressionElement.h" @class MPExpression, MPFunction, MPRangePath; @protocol MPExpressionElement; /*! @class MPExpression @brief An expression is the base object for any mathematical expression. @discussion Every expression consists of string elements (represented by the @c NSString class) and function (represented by the @c MPFunction class) elements which both can be contained within an expression. Functions in turn can have expressions as elements (also called 'children' in this context). Both expressions and functions are mutable. Through this organization expression are organized in a tree-like structure (called the 'expression tree') allowing easy and logical access to each element. An expression can evaluate itself giving you either a result or possibly an error if the expression was not constructed correctly. */ @interface MPExpression : NSObject #pragma mark Creation Methods /*! @method init @brief Initlializes a newly created expression. @discussion This method is a convenience initializer to initialize an empty expression. @return An expression. */ - (instancetype)init; /*! @method initWithElement: @brief Initializes a newly created expression with one 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)element; /*! @method initWithElements: @brief Initializes a newly created expression with the given elements. @discussion This method is the designated initializer for the @c MPExpression class. @param elements The elements that should be added to the expression. Each element is copied and the copy is then added to the expression. @return An expression containing the elements from @c elements. */ - (instancetype)initWithElements:(NSArray *)elements; /* designated initializer */ #pragma mark Working With the Expression Tree /*! @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. You should not set this property manually because that can cause inconsistencies in the expression tree. @return The parent of the receiver or @c nil if the receiver is the root expression. */ @property (nonatomic, weak) MPFunction *parent; /*! @method fixElements @brief Repairs any inconsistencies in the receiver. @discussion This method goes over all elements in the receiver and tries to repair inconsistencies that occured when mutating the receiver. Since this method is called automatically everytime the receiver is mutated there should be little need for you to call it yourself. */ - (void)fixElements; #pragma mark Primitive Methods /*! @method length @brief Returns the length of the receiver. @discussion The length of an expression is calculated by walking over each element in the receiver and sending it a @c length message. This method should be used to determine the number of digits or symbols in an expression. To address a symbol in the expression counted in the @c length reference frame of an expression the word 'location' is used. @return The length of the receiver. This is the number of symbols in all elements in the receiver where a function element is counted as a single symbol. */ - (NSUInteger)length; /*! @method numberOfElements @brief Returns the number of elements in the receiver. @discussion The number of elements may vary from the number of elements that were added to the receiver (using either @c -initWithElements: or @ -replaceElementsInRange:withElements:) To address a specific symbol in an expression the word 'index' is used. The index of elements is used when you access an expression's elements using subscript syntax. @return The current number of elements in the receiver. */ - (NSUInteger)numberOfElements; /* Subscripting is supported for indexes and elements */ - (void)setObject:(id)obj atIndexedSubscript:(NSUInteger)idx; - (id)objectAtIndexedSubscript:(NSUInteger)idx; /*! @method elementAtIndex: @brief Returns the element at @c anIndex. @discussion The element 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. This method can also be called using indexed subscript getter syntax. @param anIndex The index of the element. If the index is greater than or equal to the number of elements in the receiver an @c NSRangeException is raised. @return The element located at @c anIndex. */ - (id)elementAtIndex:(NSUInteger)anIndex; /*! @method elementsInRange: @brief Returns an array of the elements that are located in the specified range. The range is specified in indexes. @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 element will be reflected in the receiver. If the @c range exceeds the receiver's bounds an @c NSRangeException is raised. @param range The requested range within the receiver's bounds. @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 *)elementsInRange:(NSRange)range; /*! @method indexOfElement: @brief Returns the index of @c element or @c NSNotFound if it was not found. @discussion @param @return */ #warning Implementation may be faulty - (NSUInteger)indexOfElement:(id)element; /*! @method replaceSymbolsInRange:withElements: @brief Replaces the elements in the given 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 @c -fixElements is called to restore integrity of the receiver. After the receiver has been mutated (and integrity has been restored) the receiver sends a @c -didChangeElementsInRangePath:replacementLength: to itself. For more information see the documentation on that method. @param range The @c range is specified in the length reference frame. Because of this this method can be directly used for user interaction. @param elements The elements that should replace the symbols specified by @c range. */ - (void)replaceSymbolsInRange:(NSRange)range withElements:(NSArray *)elements; // TODO: - (NSUInteger)indexOfElementAtSymbolLocation:(NSUInteger)location; #warning Evaluating must possibly return error - (double)doubleValue; // Evaluates Expression #pragma mark Notifications // All notification methods should create a new rangePath with the receiver's index added to the beginning of the path and then ascend the message to it's parent // TODO: More notifications /*! @method didChangeElementsInRangePath: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. @param replacementLength The number of elements replacing the elements specified by @c rangePath. */ - (void)didChangeElementsInRangePath:(MPRangePath *)rangePath replacementLength:(NSUInteger)replacementLength; #pragma mark Basic NSObject Methods /*! @method isEqualToExpression: @brief Returns wether the receiver is equal to @c anExpression. @param anExpression The expression the receiver should be compared to. @return @c YES if @c anExpression is equal to the receiver, @c NO otherwise. */ - (BOOL)isEqualToExpression:(MPExpression *)anExpression; - (NSString *)description; - (NSUInteger)hash; @end /* --------------------------------------------------------------------------- */ /* Extension Methods */ /* --------------------------------------------------------------------------- */ @interface MPExpression (MPExpressionExtension) #pragma mark Working With the Expression Tree /*! @method elementAtIndexPath: @brief Returns the element at the specified index path. @discussion 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. @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 elementsInRangePath: @brief Returns the elements in the specified range path. @discussion If any of the indexes or the range exceed the bounds of the respective receiver an @c NSRangeException is raised. @param rangePath The range path the requested objects are located at. @return An array of objects specified by the range path. The returned elements are not copied before they are returned. Be aware that any mutations made to the returned objects are reflected in the receiver. */ - (NSArray *)elementsInRangePath:(MPRangePath *)rangePath; /*! @method indexPath @brief Returns the index path of the receiver in the expression tree. @discussion The index path is calculated by walking up the expression tree collecting the respective index of the receiver. @return The index path of the receiver in the expression tree. */ - (NSIndexPath *)indexPath; #pragma mark Working With Expressions /*! @method subexpressionFromLocation: @brief Creates a new expression from the specified index (inclusive) to the end of the receiver. @discussion The elements in the newly created expression are copied to the new expression. The location is specified in the length reference frame. If the given location exceeds the receiver's bounds a @c NSRangeException is raised. @param from The first location to be included in the new expression. @return A new expression. */ - (MPExpression *)subexpressionFromLocation:(NSUInteger)from; /*! @method subexpressionToLocation: @brief Creates a new expression from the beginning to the specified index (exclusive). @discussion The elements in the newly created expression are copied to the new expression. The location is specified in the length reference frame. If the given location exceeds the receiver's bounds a @c NSRangeException is raised. @param to The first location not to be included in the new expression or the length of the new expression. @return A new expression. */ - (MPExpression *)subexpressionToLocation:(NSUInteger)to; /*! @method subexpressionWithRange: @brief Creates a new expression with the symbols in the specified range. @discussion The elements in the newly created expression are copied to the new exoression. The range is specified in the length reference frame. If the given range exceeds the receiver's bounds a @c NSRangeException is raised. @param range The range from which to create the new expression. @return A new expression. */ - (MPExpression *)subexpressionWithRange:(NSRange)range; #pragma mark Mutating Expressions /*! @method appendElement: @brief Appends @c anElement to the receiver. @param anElement The element to append to the receiver. */ - (void)appendElement:(id)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; - (void)insertElement:(id)anElement atLocation:(NSUInteger)index; - (void)insertElements:(NSArray *)elements atLocation:(NSUInteger)index; - (void)deleteElementsInRange:(NSRange)range; #pragma mark Evaluating Expressions - (float)floatValue; - (int)intValue; - (NSInteger)integerValue; - (long long)longLongValue; #pragma mark Querying Expressions - (NSArray *)elements; @end