// // 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, MPExpressionEvaluator, MPParseError; @protocol MPExpressionElement; /*! @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 functions (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. To query the contents of an expressions there are two options: You can query on a per-element basis (that is string elements and function elements as described before). This is called the @em index reference frame (or @em indexed reference frame). You also can query an expression on a per-symbol basis. This is called the @em location reference frame (or @c located reference frame). Using the located reference frame is useful if you are dealing with user actions since the user does not necessarily see a visual separation between different elements but only sees the symbols that are drawn on the screen. You can convert between the two reference frames using the following methods: @code - (NSUInteger)indexOfElementAtSymbolLocation:offset: // Converts from the located to the indexed reference frame - (NSUInteger)locationOfElementAtIndex: // Converts from the indexed to the located reference frame @endcode In the indexed reference frame both functions and strings have a dimension of 1. In the located reference frame the length of a string is determined by sending it a @c -length message. In that frame functions still have a length of 1. 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 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)element; /*! @method initWithElements: @brief Initializes a newly created expression with the given 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 the elements from @c elements. */ - (instancetype)initWithElements:(NSArray *)elements; /* designated initializer */ #pragma mark 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 not set this property manually unless you are implementing a subclass of @c MPFunction. @return The parent of the receiver or @c nil if the receiver is the root expression. */ @property (nonatomic, weak) MPFunction *parent; /*! @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 one of the several mutation methods). The number of elements is expressed in the indexed reference frame. (The respective method for the located reference frame is @c -length). @return The current number of elements in the receiver. */ - (NSUInteger)numberOfElements; /*! @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. @note This method can also be called using indexed subscript getter syntax. @param anIndex The index of the element expressed in the indexed reference frame. If the index is greater than or equal to the number of elements in the receiver an @c NSRangeException is raised. @return The element at @c anIndex. */ - (id)elementAtIndex:(NSUInteger)anIndex; /*! @method elementsInIndexedRange: @brief Returns an array of the elements that are located in the specified range. The range is specified in the indexed reference frame. @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 expressed in the indexed reference frame. @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 *)elementsInIndexedRange:(NSRange)range; /*! @method elements @brief Returns an array of all elements in the receiver. @discussion The elements in the returned array are not copied before they are returned. @return An array of all elements from the receiver. */ - (NSArray *)elements; #pragma mark Mutating Expressions /*! @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 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 -didChangeElementsInIndexedRangePath:replacementLength: to itself. For more information see the documentation on that method. @param range The @c range of symbols (including functions) to replace specified in the located reference frame. @param elements The elements that should replace the symbols specified by @c range. */ - (void)replaceSymbolsInRange:(NSRange)range withElements:(NSArray *)elements; #pragma mark Evaluating Expressions /*! @method evaluateWitError: @brief Evaluates the receiving expression. @discussion This is a convenience method for evaluating an expression. If you want more control over the evaluation process use the @c evaluator property of the receiver. @param error If the receiver (or any of its elements) contains a syntax error or can not be evaluated this parameter is set to an appropriate value. Pass @c NULL if you are not interested in any errors that 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 *)evaluateWithError:(MPParseError *__autoreleasing *)error; /*! @property evaluator @brief Returns an object that can evaluate the receiver. @discussion To just evaluate an expression it is recommended to send it an @c evaluateWithError: message. You can however use this property instead if you need more control over the evaluation process. */ @property (readonly, nonatomic, strong) MPExpressionEvaluator *evaluator; #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 /*! @method didChangeElementsInIndexedRangePath: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 indexed reference frame. @param replacementLength The number of elements replacing the elements specified by @c rangePath. */ - (void)didChangeElementsInIndexedRangePath:(MPRangePath *)rangePath replacementLength:(NSUInteger)replacementLength; #pragma mark Basic NSObject Methods // TODO: Check this // - (BOOL)isEqualToExpression:(MPExpression *)anExpression; @end /* --------------------------------------------------------------------------- */ /* Extension Methods */ /* --------------------------------------------------------------------------- */ @interface MPExpression (MPExpressionExtension) #pragma mark Querying Expressions /*! @method length @brief Returns the length of the receiver. @discussion The length of an expression is calculated by going 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. The result of this method is expressed in the located reference frame. The respective method for the indexed reference frame is @c -numberOfSymbols. @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 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 indexed 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; // Subscripting is supported in the indexed reference frame - (id)objectAtIndexedSubscript:(NSUInteger)idx; #pragma mark Working With Expressions /*! @method elementAtLocation: @brief Returns the element that is located at @c location. @discussion This method finds an element in the located reference frame. If @c location is greater or equal to the @c length of the receiver a @c NSRangeException is raised. @param location The location of the element to find expressed in the located reference frame. @return The element located at @c location. */ - (id)elementAtLocation:(NSUInteger)location; /*! @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 indexed 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 elementsInIndexedRangePath: @brief Returns the elements in the specified range path. @discussion This method works similar to @c elementAtIndexPath: except that it queries multiple elements at once. @param rangePath The range path the requested objects are located at. The complete range path is expressed in the indexed reference frame. @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 *)elementsInIndexedRangePath:(MPRangePath *)rangePath; /*! @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 indexed reference frame. */ - (NSUInteger)indexOfElement:(id)element; #pragma mark Converting Between Indexes and Locations /*! @method indexOfElementAtLocation:offset: @brief Calculates the index of the element the specified location points to. @discussion The @c location is in the located reference frame whereas the returned value is an index. This method converts from the former to the latter. This method prefers higher indexes. This means that if the returned @c offset would be equal to the length of the element at the calculated index, insead index+1 is returned and the @c offset is set to @c 0. If the @c location exceeds the receiver's bounds a @c NSRangeException will be raised. @param location The location of which you want the corresponding element index. @param offset An output parameter that gets set to the offst into the symbol whose index is returned. If location for example points to the symbol @c '2' in the string element @c '123' the offset @c would be set to @c 1. @return The index of the element the location points to. */ - (NSUInteger)indexOfElementAtLocation:(NSUInteger)location offset:(out NSUInteger *)offset; /*! @method locationOfElementAtIndex: @brief Calculates the location of the element at @c index. @discussion @c index is expressed in the indexed reference frame. Use this method to convert an index into the located reference frame. If the index exceeds the receiver's number of elements a @c NSRangeException will be raised. @param index The index of the element that is to be converted into the length reference frame. @return The number of symbols (in the length reference frame) before the element at @c index. */ - (NSUInteger)locationOfElementAtIndex:(NSUInteger)index; /*! @method indexedRangeForRange: @brief Converts @c aRange from the located reference frame into the indexed reference frame. @discussion If the range exceeds the receiver's bounds a @c NSRangeException is raised. @param aRange The range to be converted. Expressed in the located reference frame. @return @c aRange converted into the indexed reference frame. */ - (NSRange)indexedRangeForRange:(NSRange)aRange; /*! @method rangeForIndexedRange: @brief Converts @c aRange from the indexed reference frame into the located reference frame. @discussion In the range exceeds the receiver's bounds a @c NSRangeException is raised. @param aRange The range to be converted. Expressed in the indexed reference frame. @return @c aRange converted into the located reference frame. */ - (NSRange)rangeForIndexedRange:(NSRange)aRange; #pragma mark Mutating Expressions - (MPExpression *)subexpressionFromIndex:(NSUInteger)from; - (MPExpression *)subexpressionToIndex:(NSUInteger)to; - (MPExpression *)subexpressionWithIndexedRange:(NSRange)range; /*! @method subexpressionFromLocation: @brief Creates a new expression from the specified location (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 located 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 from the given location to the end of the receiver. */ - (MPExpression *)subexpressionFromLocation:(NSUInteger)from; /*! @method subexpressionToLocation: @brief Creates a new expression from the beginning to the specified location (exclusive). @discussion The elements in the newly created expression are copied to the new expression. The location is specified in the located 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 with the first @c to symbols of the receiver. */ - (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 located 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 with the symbols in the specified range. */ - (MPExpression *)subexpressionWithRange:(NSRange)range; - (void)replaceElementsInIndexedRange:(NSRange)range withElements:(NSArray *)elements; /*! @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 atIndex:(NSUInteger)index; - (void)insertElements:(NSArray *)elements atIndex:(NSUInteger)index; /*! @method insertElement:atLocation: @brief Inserts @c anElement at @c location. @discussion The location is specified in the length reference frame. If the given location exceeds the receiver's bounds a @c NSRangeException is raised. @param anElement The element to be inserted into the receiver. @param location The location @c anElement should be inserted at. */ - (void)insertElement:(id)anElement atLocation:(NSUInteger)location; /*! @method insertElements:atLocation: @brief Inserts the elements from @c elements at @c location. @discussion The location is specified in the length reference frame. If the given location exceeds the receiver's bounds a @c NSRangeException is raised. @param elements The elements to be inserted into the receiver. @param location The location the elements in @c elements should be inserted into the receiver. */ - (void)insertElements:(NSArray *)elements atLocation:(NSUInteger)location; - (void)deleteElementsInIndexedRange:(NSRange)range; /*! @method deleteElementsInRange: @brief Removes the elements specified by @c range from the receiver. @discussion The range is specified in the length reference frame. If @c range exceeds the receiver's bounds a @c NSRangeException is raised. @param range The range to remove from the receiver. */ - (void)deleteElementsInRange:(NSRange)range; /*! @method mutableElements @brief Returns a proxy mutable array object that responds to all methods defined by @c NSMutableArray. @discussion Mutations on the proxy object also change the receiver. The proxy object does not respond to coding methods. Copying the proxy object will not duplicate it. @return A proxy object that responds to all methods defined by @c NSMutableArray. */ // - (NSMutableArray *)mutableElements; /* Subscripting is supported for elements in the indexed reference frame */ - (void)setObject:(id)obj atIndexedSubscript:(NSUInteger)idx; @end