Started to Implement the Parser

MathPad.xcodeproj/project.pbxproj

@@ -29,6 +29,10 @@
 		3BBBA3951905704200824E74 /* MPRangeTests.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BBBA3941905704200824E74 /* MPRangeTests.m */; };
 		3BC4660B19B2425A0033F13A /* MPDocument.xib in Resources */ = {isa = PBXBuildFile; fileRef = 3BF9978318DE623E009CF6C4 /* MPDocument.xib */; };
 		3BC4661419B245C60033F13A /* Fonts in Resources */ = {isa = PBXBuildFile; fileRef = 3BC4661319B245C60033F13A /* Fonts */; };
+		3BC46B4919B38C980033F13A /* MPExpressionEvaluator.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BC46B4819B38C980033F13A /* MPExpressionEvaluator.m */; };
+		3BC46B5E19B8BE760033F13A /* MPMath.lm in Sources */ = {isa = PBXBuildFile; fileRef = 3BC46B5D19B8BE760033F13A /* MPMath.lm */; };
+		3BD98B2519B8F0670035852A /* MPMath.ym in Sources */ = {isa = PBXBuildFile; fileRef = 3BD98B2419B8F0670035852A /* MPMath.ym */; };
+		3BE9C4B319B9CC70002CC508 /* MPParsedElement.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BE9C4B219B9CC70002CC508 /* MPParsedElement.m */; };
 		3BF9976F18DE623E009CF6C4 /* Cocoa.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = 3BF9976E18DE623E009CF6C4 /* Cocoa.framework */; };
 		3BF9977918DE623E009CF6C4 /* InfoPlist.strings in Resources */ = {isa = PBXBuildFile; fileRef = 3BF9977718DE623E009CF6C4 /* InfoPlist.strings */; };
 		3BF9977B18DE623E009CF6C4 /* main.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BF9977A18DE623E009CF6C4 /* main.m */; };
@@ -43,6 +47,33 @@
 		3BFAC39C1997BC7600B3EF67 /* NSString+MPExpressionElement.m in Sources */ = {isa = PBXBuildFile; fileRef = 3BFAC39B1997BC7600B3EF67 /* NSString+MPExpressionElement.m */; };
 /* End PBXBuildFile section */
 
+/* Begin PBXBuildRule section */
+		3B225D2F19B9105E00520A4D /* PBXBuildRule */ = {
+			isa = PBXBuildRule;
+			compilerSpec = com.apple.compilers.proxy.script;
+			filePatterns = "*.lm";
+			fileType = pattern.proxy;
+			isEditable = 1;
+			outputFiles = (
+				"$(DERIVED_FILE_DIR)/$(INPUT_FILE_BASE).yy.h",
+				"$(DERIVED_FILE_DIR)/$(INPUT_FILE_BASE).yy.m",
+			);
+			script = "cd \"$INPUT_FILE_DIR\"\nflex -o \"$DERIVED_SOURCES_DIR/$INPUT_FILE_BASE.yy.m\" --header-file=\"$DERIVED_SOURCES_DIR/$INPUT_FILE_BASE.yy.h\" \"$INPUT_FILE_NAME\"";
+		};
+		3B225D3019B9154A00520A4D /* PBXBuildRule */ = {
+			isa = PBXBuildRule;
+			compilerSpec = com.apple.compilers.proxy.script;
+			filePatterns = "*.ym";
+			fileType = pattern.proxy;
+			isEditable = 1;
+			outputFiles = (
+				"$(DERIVED_FILE_DIR)/$(INPUT_FILE_BASE).tab.h",
+				"$(DERIVED_FILE_DIR)/$(INPUT_FILE_BASE).tab.m",
+			);
+			script = "cd \"$INPUT_FILE_DIR\"\nbison -o \"$DERIVED_SOURCES_DIR/$INPUT_FILE_BASE.tab.m\" --defines=\"$DERIVED_SOURCES_DIR/$INPUT_FILE_BASE.tab.h\" \"$INPUT_FILE_NAME\"";
+		};
+/* End PBXBuildRule section */
+
 /* Begin PBXContainerItemProxy section */
 		3BF9979318DE623E009CF6C4 /* PBXContainerItemProxy */ = {
 			isa = PBXContainerItemProxy;
@@ -57,6 +88,10 @@
 		3B0F69A719028BC600817707 /* MPException.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = MPException.h; sourceTree = "<group>"; };
 		3B0F69A819028C6000817707 /* MPException.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPException.m; sourceTree = "<group>"; };
 		3B0F69AB1902A82C00817707 /* MPExpressionTests.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPExpressionTests.m; sourceTree = "<group>"; };
+		3B225D2C19B90F6A00520A4D /* MPMath.yy.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; name = MPMath.yy.m; path = "../../../../Library/Developer/Xcode/DerivedData/MathPad-egifwdrtxebksadhtzugiovuvzcy/Build/Intermediates/MathPad.build/Debug/MathPad.build/DerivedSources/MPMath.yy.m"; sourceTree = "<group>"; };
+		3B225D3119B9162E00520A4D /* MPMath.yy.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; name = MPMath.yy.h; path = "../../../../Library/Developer/Xcode/DerivedData/MathPad-egifwdrtxebksadhtzugiovuvzcy/Build/Intermediates/MathPad.build/Debug/MathPad.build/DerivedSources/MPMath.yy.h"; sourceTree = "<group>"; };
+		3B225D3219B9168600520A4D /* MPMath.tab.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; name = MPMath.tab.m; path = "../../../../Library/Developer/Xcode/DerivedData/MathPad-egifwdrtxebksadhtzugiovuvzcy/Build/Intermediates/MathPad.build/Debug/MathPad.build/DerivedSources/MPMath.tab.m"; sourceTree = "<group>"; };
+		3B225D3419B916D000520A4D /* MPMath.tab.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; name = MPMath.tab.h; path = "../../../../Library/Developer/Xcode/DerivedData/MathPad-egifwdrtxebksadhtzugiovuvzcy/Build/Intermediates/MathPad.build/Debug/MathPad.build/DerivedSources/MPMath.tab.h"; sourceTree = "<group>"; };
 		3B528D0D199417740054DB5F /* MPLayout.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPLayout.h; sourceTree = "<group>"; };
 		3B528D0E199417E10054DB5F /* MPExpressionLayout.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPExpressionLayout.h; sourceTree = "<group>"; };
 		3B528D0F199417E10054DB5F /* MPExpressionLayout.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPExpressionLayout.m; sourceTree = "<group>"; };
@@ -78,10 +113,19 @@
 		3BB09EDD190728220080A5ED /* NSIndexPath+MPAdditions.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = "NSIndexPath+MPAdditions.m"; sourceTree = "<group>"; };
 		3BB09EDF190736160080A5ED /* MPSumFunctionLayout.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPSumFunctionLayout.h; sourceTree = "<group>"; };
 		3BB09EE0190736160080A5ED /* MPSumFunctionLayout.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPSumFunctionLayout.m; sourceTree = "<group>"; };
-		3BBBA3591903EA9B00824E74 /* MPModel.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = MPModel.h; sourceTree = "<group>"; };
 		3BBBA38419047FC900824E74 /* MPView.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = MPView.h; sourceTree = "<group>"; };
 		3BBBA3941905704200824E74 /* MPRangeTests.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPRangeTests.m; sourceTree = "<group>"; };
 		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>"; };
+		3BC46B4719B38C980033F13A /* MPExpressionEvaluator.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPExpressionEvaluator.h; sourceTree = "<group>"; };
+		3BC46B4819B38C980033F13A /* MPExpressionEvaluator.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPExpressionEvaluator.m; sourceTree = "<group>"; };
+		3BC46B5D19B8BE760033F13A /* MPMath.lm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.lex; path = MPMath.lm; sourceTree = "<group>"; };
+		3BD98B1E19B8CE490035852A /* libl.a */ = {isa = PBXFileReference; lastKnownFileType = archive.ar; name = libl.a; path = ../../../../../usr/lib/libl.a; sourceTree = "<group>"; };
+		3BD98B2419B8F0670035852A /* MPMath.ym */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.yacc; path = MPMath.ym; sourceTree = "<group>"; };
+		3BE9C4B019B91978002CC508 /* MPMath.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = MPMath.h; sourceTree = "<group>"; };
+		3BE9C4B119B9CC70002CC508 /* MPParsedElement.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = MPParsedElement.h; sourceTree = "<group>"; };
+		3BE9C4B219B9CC70002CC508 /* MPParsedElement.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = MPParsedElement.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; };
@@ -113,8 +157,8 @@
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				3B74BFB319A4C51800E5B5DE /* CoreText.framework in Frameworks */,
 				3BF9976F18DE623E009CF6C4 /* Cocoa.framework in Frameworks */,
+				3B74BFB319A4C51800E5B5DE /* CoreText.framework in Frameworks */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -133,21 +177,10 @@
 		3B87E350190082B300259938 /* Model */ = {
 			isa = PBXGroup;
 			children = (
-				3BBBA3591903EA9B00824E74 /* MPModel.h */,
+				3BC46B4B19B38CB60033F13A /* Base Expression Classes */,
-				3BFAC38D1997B61300B3EF67 /* MPExpression.h */,
+				3BC46B4C19B38CD20033F13A /* Independant Classes */,
-				3BFAC38E1997B61300B3EF67 /* MPExpression.m */,
-				3BFAC3961997B67400B3EF67 /* MPExpressionElement.h */,
-				3B87E35E19009D5F00259938 /* MPFunction.h */,
-				3B87E35F19009D5F00259938 /* MPFunction.m */,
-				3BFAC39A1997BC7600B3EF67 /* NSString+MPExpressionElement.h */,
-				3BFAC39B1997BC7600B3EF67 /* NSString+MPExpressionElement.m */,
-				3B87E35B1900933200259938 /* MPRangePath.h */,
-				3B87E35C1900933200259938 /* MPRangePath.m */,
-				3BB09EDC190728220080A5ED /* NSIndexPath+MPAdditions.h */,
-				3BB09EDD190728220080A5ED /* NSIndexPath+MPAdditions.m */,
-				3B0F69A719028BC600817707 /* MPException.h */,
-				3B0F69A819028C6000817707 /* MPException.m */,
 				3BB09EBC1905EF210080A5ED /* Functions */,
+				3BC46B4D19B38CFB0033F13A /* Helpers */,
 			);
 			name = Model;
 			sourceTree = "<group>";
@@ -225,6 +258,76 @@
 			name = "Function Layouts";
 			sourceTree = "<group>";
 		};
+		3BC4661819B3692A0033F13A /* Temp */ = {
+			isa = PBXGroup;
+			children = (
+				3BC4661519B365070033F13A /* MPArrayCache.h */,
+				3BC4661619B365070033F13A /* MPArrayCache.m */,
+			);
+			name = Temp;
+			sourceTree = "<group>";
+		};
+		3BC46B4B19B38CB60033F13A /* Base Expression Classes */ = {
+			isa = PBXGroup;
+			children = (
+				3BFAC38D1997B61300B3EF67 /* MPExpression.h */,
+				3BFAC38E1997B61300B3EF67 /* MPExpression.m */,
+				3BFAC3961997B67400B3EF67 /* MPExpressionElement.h */,
+				3B87E35E19009D5F00259938 /* MPFunction.h */,
+				3B87E35F19009D5F00259938 /* MPFunction.m */,
+				3BC46B4F19B506F20033F13A /* Evaluation */,
+			);
+			name = "Base Expression Classes";
+			sourceTree = "<group>";
+		};
+		3BC46B4C19B38CD20033F13A /* Independant Classes */ = {
+			isa = PBXGroup;
+			children = (
+				3B87E35B1900933200259938 /* MPRangePath.h */,
+				3B87E35C1900933200259938 /* MPRangePath.m */,
+				3B0F69A719028BC600817707 /* MPException.h */,
+				3B0F69A819028C6000817707 /* MPException.m */,
+			);
+			name = "Independant Classes";
+			sourceTree = "<group>";
+		};
+		3BC46B4D19B38CFB0033F13A /* Helpers */ = {
+			isa = PBXGroup;
+			children = (
+				3BFAC39A1997BC7600B3EF67 /* NSString+MPExpressionElement.h */,
+				3BFAC39B1997BC7600B3EF67 /* NSString+MPExpressionElement.m */,
+				3BB09EDC190728220080A5ED /* NSIndexPath+MPAdditions.h */,
+				3BB09EDD190728220080A5ED /* NSIndexPath+MPAdditions.m */,
+			);
+			name = Helpers;
+			sourceTree = "<group>";
+		};
+		3BC46B4F19B506F20033F13A /* Evaluation */ = {
+			isa = PBXGroup;
+			children = (
+				3BC46B5D19B8BE760033F13A /* MPMath.lm */,
+				3BD98B2419B8F0670035852A /* MPMath.ym */,
+				3BE9C4B019B91978002CC508 /* MPMath.h */,
+				3BD98B2619B8F3F10035852A /* Generated */,
+				3BC46B4719B38C980033F13A /* MPExpressionEvaluator.h */,
+				3BC46B4819B38C980033F13A /* MPExpressionEvaluator.m */,
+				3BE9C4B119B9CC70002CC508 /* MPParsedElement.h */,
+				3BE9C4B219B9CC70002CC508 /* MPParsedElement.m */,
+			);
+			name = Evaluation;
+			sourceTree = "<group>";
+		};
+		3BD98B2619B8F3F10035852A /* Generated */ = {
+			isa = PBXGroup;
+			children = (
+				3B225D3119B9162E00520A4D /* MPMath.yy.h */,
+				3B225D2C19B90F6A00520A4D /* MPMath.yy.m */,
+				3B225D3419B916D000520A4D /* MPMath.tab.h */,
+				3B225D3219B9168600520A4D /* MPMath.tab.m */,
+			);
+			name = Generated;
+			sourceTree = "<group>";
+		};
 		3BF9976218DE623E009CF6C4 = {
 			isa = PBXGroup;
 			children = (
@@ -247,6 +350,7 @@
 		3BF9976D18DE623E009CF6C4 /* Frameworks */ = {
 			isa = PBXGroup;
 			children = (
+				3BD98B1E19B8CE490035852A /* libl.a */,
 				3B74BFB219A4C51800E5B5DE /* CoreText.framework */,
 				3BF9976E18DE623E009CF6C4 /* Cocoa.framework */,
 				3BF9979018DE623E009CF6C4 /* XCTest.framework */,
@@ -268,6 +372,7 @@
 		3BF9977418DE623E009CF6C4 /* MathPad */ = {
 			isa = PBXGroup;
 			children = (
+				3BC4661819B3692A0033F13A /* Temp */,
 				3B87E350190082B300259938 /* Model */,
 				3B87E351190082BB00259938 /* View */,
 				3B87E352190082C000259938 /* Controller */,
@@ -320,6 +425,8 @@
 				3BF9976918DE623E009CF6C4 /* Resources */,
 			);
 			buildRules = (
+				3B225D3019B9154A00520A4D /* PBXBuildRule */,
+				3B225D2F19B9105E00520A4D /* PBXBuildRule */,
 			);
 			dependencies = (
 			);
@@ -368,6 +475,7 @@
 			knownRegions = (
 				en,
 				Base,
+				English,
 			);
 			mainGroup = 3BF9976218DE623E009CF6C4;
 			productRefGroup = 3BF9976C18DE623E009CF6C4 /* Products */;
@@ -409,8 +517,12 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				3BE9C4B319B9CC70002CC508 /* MPParsedElement.m in Sources */,
 				3B688D9919982DF50006B4AB /* MPLayout.m in Sources */,
+				3BD98B2519B8F0670035852A /* MPMath.ym in Sources */,
+				3BC46B5E19B8BE760033F13A /* MPMath.lm in Sources */,
 				3BB09EE1190736160080A5ED /* MPSumFunctionLayout.m in Sources */,
+				3BC46B4919B38C980033F13A /* MPExpressionEvaluator.m in Sources */,
 				3B87E3561900856F00259938 /* MPExpressionView.m in Sources */,
 				3BB09EC91906FD830080A5ED /* MPSumFunction.m in Sources */,
 				3BB09EB21905DE500080A5ED /* MPExpressionStorage.m in Sources */,
@@ -571,6 +683,7 @@
 			buildSettings = {
 				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
 				COMBINE_HIDPI_IMAGES = YES;
+				FRAMEWORK_SEARCH_PATHS = "$(inherited)";
 				GCC_PRECOMPILE_PREFIX_HEADER = YES;
 				GCC_PREFIX_HEADER = "MathPad/MathPad-Prefix.pch";
 				INFOPLIST_FILE = "MathPad/MathPad-Info.plist";
@@ -584,6 +697,7 @@
 			buildSettings = {
 				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
 				COMBINE_HIDPI_IMAGES = YES;
+				FRAMEWORK_SEARCH_PATHS = "$(inherited)";
 				GCC_PRECOMPILE_PREFIX_HEADER = YES;
 				GCC_PREFIX_HEADER = "MathPad/MathPad-Prefix.pch";
 				INFOPLIST_FILE = "MathPad/MathPad-Info.plist";

MathPad/MPArrayCache.h

@@ -0,0 +1,34 @@
+//
+//  MPArrayCache.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 31.08.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import <Foundation/Foundation.h>
+
+// A wrapper around NSCache to support index-based caches. Indexes are
+// automatically adjusted to represent array-like behaviours.
+@interface MPArrayCache : NSObject {
+    @private
+    NSCache *_cache;
+}
+
+- (id)init; /* designated initializer */
+
+- (void)cacheObject:(id)object
+           forIndex:(NSUInteger)index;
+- (id)cachedObjectForIndex:(NSUInteger)index;
+
+- (void)clearCacheAtIndex:(NSUInteger)index
+        replacementLength:(NSUInteger)replacementLength;
+- (void)clearCacheInRange:(NSRange)range
+        replacementLength:(NSUInteger)replacementLength;
+
+- (void)replaceCachedObjectAtIndex:(NSUInteger)index
+                       withObjects:(NSArray *)objects;
+- (void)replaceCachedObjectsInRange:(NSRange)range
+                        withObjects:(NSArray *)objects;
+
+@end

MathPad/MPArrayCache.m

@@ -0,0 +1,59 @@
+//
+//  MPArrayCache.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 31.08.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPArrayCache.h"
+
+@implementation MPArrayCache {
+    NSUInteger lastIndex;
+}
+
+- (instancetype)init
+{
+    self = [super init];
+    if (self) {
+        lastIndex = 0;
+        _cache = [[NSCache alloc] init];
+    }
+    return self;
+}
+
+- (void)cacheObject:(id)object
+           forIndex:(NSUInteger)index
+{
+    [_cache setObject:object
+               forKey:@(index)];
+    if (index > lastIndex) {
+        lastIndex = index;
+    }
+}
+
+- (id)cachedObjectForIndex:(NSUInteger)index
+{
+    return [_cache objectForKey:@(index)];
+}
+
+- (void)clearCacheAtIndex:(NSUInteger)index replacementLength:(NSUInteger)replacementLength
+{
+    [_cache removeObjectForKey:@(index)];
+    for (NSUInteger i = index+1; i < lastIndex; i++) {
+        id object = [_cache objectForKey:@(i)];
+        if (object) {
+            [_cache removeObjectForKey:@(i)];
+        }
+    }
+    lastIndex += replacementLength - 1;
+}
+
+- (void)clearCacheInRange:(NSRange)range replacementLength:(NSUInteger)replacementLength;
+
+- (void)replaceCachedObjectAtIndex:(NSUInteger)index
+                       withObjects:(NSArray *)objects;
+- (void)replaceCachedObjectsInRange:(NSRange)range
+                        withObjects:(NSArray *)objects;
+
+@end

MathPad/MPExpressionEvaluator.h

@@ -0,0 +1,30 @@
+//
+//  MPExpressionEvaluator.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 31.08.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import <Foundation/Foundation.h>
+#import "MPExpression.h"
+
+@class MPExpressionEvaluator, MPExpression, MPParsedElement;
+
+@interface MPExpressionEvaluator : NSObject
+
+- (instancetype)initWithExpression:(MPExpression *)expression;
+
+@property (readonly, nonatomic, strong) MPExpression *expression;
+
+#pragma mark Lexing
+- (MPParsedElement *)structuredRepresentationOfElementAtIndex:(NSUInteger)index;
+
+#pragma mark Evaluating Expressions
+@property (readonly, nonatomic, strong) NSDictionary *variableBindings;
+
+- (void)bindValue:(double)value toVariableName:(NSString *)name;
+
+- (double)evaluateWithError:(NSError *__autoreleasing *)error;
+
+@end

MathPad/MPExpressionEvaluator.m

@@ -0,0 +1,56 @@
+//
+//  MPExpressionEvaluator.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 31.08.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPExpressionEvaluator.h"
+#import "MPExpression.h"
+
+#import "MPParsedElement.h"
+#import "MPMath.h"
+
+@implementation MPExpressionEvaluator {
+    NSMutableDictionary *_variableBindings;
+}
+- (id)initWithExpression:(MPExpression *)expression
+{
+    self = [super init];
+    if (self) {
+        _expression = expression;
+        _variableBindings = [[NSMutableDictionary alloc] init];
+    }
+    return self;
+}
+
+#pragma mark Lexing
+- (MPParsedElement *)structuredRepresentationOfElementAtIndex:(NSUInteger)index
+{
+    NSString *string = (NSString *)[self.expression elementAtIndex:index];
+    YY_BUFFER_STATE buffer = yy_scan_string(string.UTF8String);
+    yyparse();
+    yy_delete_buffer(buffer);
+    return [parseResult copy];
+}
+
+#pragma mark Evaluating Expressions
+- (NSDictionary *)variableBindings
+{
+    return [_variableBindings copy];
+}
+
+- (void)bindValue:(double)value toVariableName:(NSString *)name
+{
+    [_variableBindings setObject:@(value)
+                          forKey:name];
+}
+
+- (double)evaluateWithError:(NSError *__autoreleasing *)error
+{
+    MPParsedElement *element = [self structuredRepresentationOfElementAtIndex:0];
+    return element.standaloneValue;
+}
+
+@end

MathPad/MPMath.h

@@ -0,0 +1,20 @@
+//
+//  YYParse.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 05.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPMath.yy.h"
+#import "MPMath.tab.h"
+#import "MPParsedElement.h"
+
+#ifndef MathPad_YYParse_h
+#define MathPad_YYParse_h
+
+extern MPParsedElement *parseResult;
+
+int yyparse();
+
+#endif

MathPad/MPMath.lm

@@ -0,0 +1,16 @@
+%option noyywrap
+%{
+    @import Foundation;
+    #include "MPMath.tab.h"
+%}
+%%
+    /* Ignore Whitespaces */
+[ \t\n]         ;
+    /* Operators. Divisions are automatically transformed into fractions and dealt
+   with elsewhere. */
+\+   { return PLUS; }
+-    { return MINUS; }
+\*   { return DOT; }
+    /* Numbers */
+[0-9]+(\.[0-9]+)?  { yylval.number = atof(yytext); return NUMBER; }
+%%

MathPad/MPMath.ym

@@ -0,0 +1,126 @@
+%{
+    #import "MPMath.h"
+    #define AT @
+    
+    MPParsedElement *parseResult;
+    
+    int yylex();
+    int yyparse();
+    FILE *yyin;
+    
+    void yyerror(const char *s);
+%}
+
+%error-verbose
+
+%initial-action
+{
+    parseResult = [[MPParsedElement alloc] init];
+};
+
+%union {
+	double number;
+}
+    /* Terminals */
+%token PLUS
+%left MINUS
+%token DOT
+%token <number> NUMBER
+
+    /* Nonterminals */
+%type <number> summands
+%type <number> factor
+%type <number> product
+
+%%
+
+element:
+        factor                   { parseResult.isFactor = YES;
+                                   parseResult.factor = $1;
+                                 }
+        | operator
+        | prefix summands suffix
+        ;
+
+factor:
+        DOT product DOT { $$ = $2;
+                        }
+        | DOT product   { $$ = $2;
+                        }
+        | product DOT   { $$ = $1;
+                        }
+        | product       { $$ = $1;
+                        }
+        ;
+
+product:
+        product DOT product { $$ = $1 * $3;
+                            }
+        | product product   { $$ = $1 * $2;
+                            }
+        | NUMBER            { $$ = $1;
+                            }
+        ;
+
+operator:
+        PLUS    { parseResult.suffixMultiplicator = 1;
+                  parseResult.hasSuffixMultiplicator = YES;
+                }
+        | MINUS { parseResult.suffixMultiplicator = -1;
+                  parseResult.hasSuffixMultiplicator = YES;
+                  NSLog(AT"Op");
+                }
+        | DOT   { parseResult.isFactor = YES;
+                  parseResult.factor = 1;
+                }
+        |       { parseResult.isFactor = YES;
+                  parseResult.factor = 1;
+                }
+        ;
+
+prefix:
+        DOT product { parseResult.prefixMultiplicator = $2;
+                      parseResult.hasPrefixMultiplicator = YES;
+                      parseResult.prefixOperatorExplicit = YES;
+                    }
+        | product   { parseResult.prefixMultiplicator = $1;
+                      parseResult.hasPrefixMultiplicator = YES;
+                      parseResult.prefixOperatorExplicit = YES;
+                    }
+        |           { parseResult.hasPrefixMultiplicator = NO;
+                    }
+        ;
+
+summands:
+        summands summand
+        | summand
+        ;
+
+summand:
+        PLUS product    { [parseResult.summands addObject:AT($2)];
+                        }
+        | MINUS product { [parseResult.summands addObject:AT(-$2)];
+                        }
+        ;
+
+suffix:
+        PLUS    { parseResult.suffixMultiplicator = 1;
+                  parseResult.hasSuffixMultiplicator = YES;
+                }
+        | MINUS { parseResult.suffixMultiplicator = -1;
+                  parseResult.hasSuffixMultiplicator = YES;
+                }
+        | DOT   { parseResult.suffixMultiplicator = 0;
+                  parseResult.hasSuffixMultiplicator = YES;
+                }
+        |       { parseResult.hasSuffixMultiplicator = NO;
+                }
+        ;
+
+%%
+
+void yyerror(const char *s) {
+    NSLog(@"EEK, parse error!  Message: %s", s);
+	// might as well halt now:
+	exit(-1);
+}

MathPad/MPParsedElement.h

@@ -0,0 +1,39 @@
+//
+//  MPParsedElement.h
+//  MathPad
+//
+//  Created by Kim Wittenburg on 05.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import <Foundation/Foundation.h>
+
+// DEBUG STUFF
+// Simple Operator:  +/-/*
+// Simple Factor:    * 5.4 * / * 5,4 / 5,4 * / 5,4
+// Independant Math: -1+2-3
+
+@interface MPParsedElement : NSObject <NSCopying>
+
+@property (nonatomic) BOOL isFactor;
+@property (nonatomic) double factor;
+
+@property (nonatomic, strong) NSMutableArray *summands;
+
+@property (nonatomic) double prefixMultiplicator;
+@property (nonatomic) BOOL hasPrefixMultiplicator;
+@property (nonatomic, getter = isPrefixOperatorExplicit) BOOL prefixOperatorExplicit;
+@property (nonatomic) double suffixMultiplicator;
+@property (nonatomic) BOOL hasSuffixMultiplicator;
+
+// No error checking done. The string parsed may for example end with an operator
+- (double)valueAtBeginning;
+- (double)valueAtEnd;
+- (double)standaloneValue;
+
+// For error checking
+- (BOOL)isValidElementAtBeginning;
+- (BOOL)isValidElementInBetween;
+- (BOOL)isValidElementAtEnd;
+
+@end

MathPad/MPParsedElement.m

@@ -0,0 +1,60 @@
+//
+//  MPParsedElement.m
+//  MathPad
+//
+//  Created by Kim Wittenburg on 05.09.14.
+//  Copyright (c) 2014 Kim Wittenburg. All rights reserved.
+//
+
+#import "MPParsedElement.h"
+
+@implementation MPParsedElement
+
+- (instancetype)init
+{
+    self = [super init];
+    if (self) {
+        _summands = [[NSMutableArray alloc] init];
+    }
+    return self;
+}
+
+- (double)standaloneValue
+{
+    if (self.isFactor) {
+        return self.factor;
+    }
+    return self.prefixMultiplicator + [[self.summands valueForKeyPath:@"@sum.self"] doubleValue];
+}
+
+- (BOOL)isValidElementAtBeginning
+{
+    return NO;
+}
+
+- (BOOL)isValidElementInBetween
+{
+    return YES;
+}
+
+- (BOOL)isValidElementAtEnd
+{
+    return NO;
+}
+
+#pragma mark NSCopying
+- (id)copyWithZone:(NSZone *)zone
+{
+    MPParsedElement *copy = [[MPParsedElement allocWithZone:zone] init];
+    copy.isFactor = self.isFactor;
+    copy.factor = self.factor;
+    copy.summands = self.summands.mutableCopy;
+    copy.prefixMultiplicator = self.prefixMultiplicator;
+    copy.hasPrefixMultiplicator = self.hasPrefixMultiplicator;
+    copy.prefixOperatorExplicit = self.prefixOperatorExplicit;
+    copy.suffixMultiplicator = self.suffixMultiplicator;
+    copy.hasSuffixMultiplicator = self.hasSuffixMultiplicator;
+    return copy;
+}
+
+@end