Is it recommended to define ivars for readonly synthesized properties?

I have come to find that many of the times in which I want to have a synthesized readonly property, I merely implement the getter method of that property in terms of other variables with no need for an ivar, for example (Note: I am defining ivars in the interface because I am using OmniGraffle UML software and it does not recognize ivars auto-generated by synthesized properties):

@interface Editor : UIView {
    BOOL _wordWrap;
    BOOL _showLineNumbers;
    NSDictionary *_options;
}

@property (nonatomic) BOOL wordWrap;
@property (nonatomic) BOOL showLineNumbers;
@property (nonatomic, copy, readonly) NSDictionary *options;

@end

@implementation Editor

@synthesize wordWrap = _wordWrap;
@synthesize showLineNumbers = _showLineNumbers;
@synthesize options = _options;

- (NSDictionary *)options {
    return @{   
                @"WordWrap"         : [NSNumber numberWithBool:self.wordWrap],
                @"ShowLineNumbers"  : [NSNumber numberWithBool:self.showLineNumbers],
            };
}

@end

In the above Editor class, is it necessary for me to define the _options ivar in the header definition and more importantly does the auto-generated ivar take up memory or space in the symbol table? Also, would it be more efficient to use copy, retain, or no value in this case? Just curious.

First: stop putting your ivar declarations in your @interface. They belong in your @implementation. See this answer for a detailed explanation.

Anyway, given what you've written, your @synthesize options = _options has no effect.

That @synthesize has two possible effects:

1. It adds an instance variable named _options, if your class doesn't have one.

2. It generates a getter method, options, that returns the value of _options, if your class doesn't have a method named options.

Since you manually defined the instance variable and the getter, the @synthesize does nothing. You can remove it entirely without changing the meaning of your program.

Specifying copy on a readonly property has no effect. The copy and retain (or, more properly under ARC, strong) attributes only affect the generated setter method, and the compiler doesn't generate a setter for a readonly property. (If you change the property to readwrite in a class extension, then copy matters.)

Yes, the _options ivar takes up both memory (for each instance of Editor) and space in the symbol table. Since you're not using the _options ivar, you should delete it entirely. You should also delete the @synthesize entirely, so the compiler doesn't generate the _options ivar for you.