I have just started reading into propositional calculus/logic, and have realised that a lot of the foundational concepts in this area are similar to those encountered in programming. That is, propositions/sentences in logic (due to the fact that they have truth-values), are similar to Booleans in programming. Furthermore, most of the sentential connectives are reflected in the logical operators adopted in programming. For instance, in C++, !, &&, and || behave in the same way that ¬, ∧, and ∨ behave, respectively, in logic.
My question is whether there are (say, C++) "equivalents" for the logical operators of implication (->) and equivalence (<->)? If so, what are they? If not, what is the reason they have they not been adopted? So, although I cannot think of any reason why they would be adopted, I would like to know if there is a specific reason that they are omitted.
Implication can be replaced with <=, and equivalence is ==.
However, unlike && and ||, those don't convert their arguments to bool (since they're not inherently boolean operators).
Related
A question was posted about chained comparison operators and how they are interpreted in different languages.
Chaining comparison operators means that (x < y < z) would be interpreted as ((x < y) && (y < z)) instead of as ((x < y) < z).
The comments on that question show that Python, Perl 6, and Mathematica support chaining comparison operators, but what other languages support this feature and why is it not more common?
A quick look at the Python documentation shows that this feature has been since at least 1996. Is there a reason more languages have not added this syntax?
A statically typed language would have problems with type conversion, but are there other reasons this is not more common?
It should be more common, but I suspect it is not because it makes parsing languages more complex.
Benefits:
Upholds the principle of least surprise
Reads like math is taught
Reduces cognitive load (see previous 2 points)
Drawbacks:
Grammar is more complex for the language
Special case syntactic sugar
As to why not, my guesses are:
Language author(s) didn't think of it
Is on the 'nice to have' list
Was decided that it wasn't useful enough to justify implementing
The benefit is too small to justify complicating the language.
You don't need it that often, and it is easy to get the same effect cleanly with a few characters more.
Scheme (and probably most other Lisp family languages) supports multiple comparison efficiently within its grammar:
(< x y z)
This can be considered an ordinary function application of the < function with three arguments. See 6.2.5 Numerical Operations in the specification.
Clojure supports chained comparison too.
Chained comparison is a feature of BCPL, since the late 1960s.
I think ICON is the original language to have this, and in ICON it falls out of the way that booleans are handled as special 'fail' tags with all other values being treated as true.
Or are we all sticking to our taught "&&, ||, !" way?
Any thoughts in why we should use one or the other?
I'm just wondering because several answers state thate code should be as natural as possible, but I haven't seen a lot of code with "and, or, not" while this is more natural.
I like the idea of the not operator because it is more visible than the ! operator. For example:
if (!foo.bar()) { ... }
if (not foo.bar()) { ... }
I suggest that the second one is more visible and readable. I don't think the same argument necessarily applies to the and and or forms, though.
"What's in a name? That which we call &&, || or !
By any other name would smell as sweet."
In other words, natural depends on what you are used to.
Those were not supported in the old days. And even now you need to give a special switch to some compilers to enable these keywords. That's probably because old code base may have had some functions || variables named "and" "or" "not".
One problem with using them (for me anyway) is that in MSVC you have to include iso646.h or use the (mostly unusable) /Za switch.
The main problem I have with them is the Catch-22 that they're not commonly used, so they require my brain to actively process the meaning, where the old-fashioned operators are more or less ingrained (kind of like the difference between reading a learned language vs. your native language).
Though I'm sure I'd overcome that issue if their use became more universal. If that happened, then I'd have the problem that some boolean operators have keywords while others don't, so if alternate keywords were used, you might see expressions like:
if ((x not_eq y) and (y == z) or (z <= something)) {...}
when it seems to me they should have alternate tokens for all the (at least comparison) operators:
if ((x not_eq y) and (y eq z) or (z lt_eq something)) {...}
This is because the reason the alternate keywords (and digraphs and trigraphs) were provided was not to make the expressions more readable - it was because historically there have been (and maybe still are) keyboards and/or codepages in some localities that do not have certain punctuation characters. For example, the invariant part of the ISO 646 codepage (surprise) is missing the '|', '^' and '~' characters among others.
Although I've been programming C++ from quite some time, I did not know that the keywords "and" "or" and "not" were allowed, and I've never seen it used.
I searched through my C++ book, and I found a small section mentioning alternative representation for the normal operators "&&", "||" and "!", where it explains those are available for people with non-standard keyboards that do not have the "&!|" symbols.
A bit like trigraphs in C.
Basically, I would be confused by their use, and I think I would not be the only one.
Using a representation which is non-standard, should really have a good reason to be used.
And if used, it should be used consistently in the code, and described in the coding standard.
The digraph and trigraph operators were actually designed more for systems that didn't carry the standard ASCII character set - such as IBM mainframes (which use EBCDIC). In the olden days of mechanical printers, there was this thing called a "48-character print chain" which, as its name implied, only carried 48 characters. A-Z (uppercase), 0-9 and a handful of symbols. Since one of the missing symbols was an underscore (which rendered as a space), this could make working with languages like C and PL/1 a real fun activity (is this 2 words or one word with an underscore???).
Conventional C/C++ is coded with the symbols and not the digraphs. Although I have been known to #define "NOT", since it makes the meaning of a boolean expression more obvious, and it's visually harder to miss than a skinny little "!".
I wish I could use || and && in normal speech. People try very hard to misunderstand when I say "and" or "or"...
I personally like operators to look like operators. It's all maths, and unless you start using "add" and "subtract" operators too it starts to look a little inconsistent.
I think some languages suit the word-style and some suit the symbols if only because it's what people are used to and it works. If it ain't broke, don't fix it.
There is also the question of precedence, which seems to be one of the reasons for introducing the new operators, but who can be bothered to learn more rules than they need to?
In cases where I program with names directly mapped to the real world, I tend to use 'and' and 'or', for example:
if(isMale or isBoy and age < 40){}
It's nice to use 'em in Eclipse+gcc, as they are highlighted. But then, the code doesn't compile with some compilers :-(
Using these operators is harmful. Notice that and and or are logical operators whereas the similar-looking xor is a bitwise operator. Thus, arguments to and and or are normalized to 0 and 1, whereas those to xor aren't.
Imagine something like
char *p, *q; // Set somehow
if(p and q) { ... } // Both non-NULL
if(p or q) { ... } // At least one non-NULL
if(p xor q) { ... } // Exactly one non-NULL
Bzzzt, you have a bug. In the last case you're testing whether at least one of the bits in the pointers is different, which probably isn't what you thought you were doing because then you would have written p != q.
This example is not hypothetical. I was working together with a student one time and he was fond of these literate operators. His code failed every now and then for reasons that he couldn't explain. When he asked me, I could zero in on the problem because I knew that C++ doesn't have a logical xor operator, and that line struck me as very odd.
BTW the way to write a logical xor in C++ is
!a != !b
I like the idea, but don't use them. I'm so used to the old way that it provides no advantage to me doing it either way. Same holds true for the rest of our group, however, I do have concerns that we might want to switch to help avoid future programmers from stumbling over the old symbols.
So to summarize: it's not used a lot because of following combination
old code where it was not used
habit (more standard)
taste (more math-like)
Thanks for your thoughts
This came up in a conversation with a friend of my nephew who is home from uni. Personally beside the most frequently used ones I never found it all that important and just use parenthesis. But I don't have to take his exam. Anything clever out there?
Edit Well, a rare moment of near unanimity on SO! If only professors listened.
I know this probably doesn't help you in the context of your exam, but I'll answer the question for anyone else who might stumble upon this:
Don't try to memorize operator precedence, beyond the "common cases" e.g. arithmetic. If your statement is unclear, either split it into multiple statements or toss in parenthesis.
Given that there are 16 levels of precedence, I don't think there's an easy trick to memorizing them (no "Roy G Biv" or other mnemonic that I know of).
IMO, the important ones to remember are postfix > unary (i.e., *p++ == *(p++)), unary > arithmetic (~a+b == (~a)+b), bitwise > logical (a|b&&c == (a|b)&&c)), and that conditional, assignment, and comma operators make up the bottom 3 in that order (a=b,c == (a=b),c).
This is why reference manuals were invented. That doesn't help during an exam, of course.
What I do to remember operator precedence (other than arithmetic, which works the same as arithmetic on paper) is that the unary operator always has precedence. Beyond that, I look it up and use parenthesis, as Steven suggests.
Defined this way, we can do neither ++x++ nor ++x--. But on the other hand, both (++x)++ and (++x)-- are useful expressions: (++x)++ increments x by two and returns the value "in the middle", while (++x)-- is essentially equivalent to x+1 but completely avoids having to call operator+, which can be quite useful sometimes.
So why is the precedence not defined to have ++x++ automatically expand to (++x)++ rather than ++(x++)? Is there some hidden meaning to the latter which I don't understand, or is it just to keep the precedence a simple list with all prefix operators making up one single level?
EDIT Ok, I didn't explicitly say it, but: of course I meant x to be user-defined type. For built-in types, (x+=2)-1 is of course better than (++x)++, and x+1 is a lot better than (++x)--. The situation that I have in mind is an iterator to a rather complicated type of semi-associative container, where operators += and + (being designed for random access) have to rebuild a cache in order to work efficiently for general requests, and are therefore an order of magnitude slower than ++. But of course I can modify them to always check first if the argument is a very small integer, and in that case just call operator++ repeatedly instead of doing the random-access procedure. That should work fine here, though I could imagine I might at some point have a situation in which I want operator+= to always go the random-access way, regardless of how small numbers I present it.
So... for me, I would conclude the answer to be:
the advantage of having a simple and well-memorizeable precedence list in which all postfix operators come before any of the prefix operators is sufficient to tolerate the minor drawback of always having to use parentheses to compose pre- and postfix operators ++/--, as this composition is used very seldom.
The simpler "C does it this way", while it seems likely to be the real reason, is far less satisfying in to me, because since ++x++ was not allowed at all in C it would have been possible to redefine this very composition without damaging any existing code.
Anyway, I will go on using (++x)--, as the parentheses really do not hurt so much.
(++x)++ increments x by two and returns the value "in the middle"
Why not (x += 2) - 1 or (++x, x++)? Both seem to be clearer. For scalars, both are well-defined also in C++03, as opposed to your proposed expression.
(++x)-- is essentially equivalent to x+1 but completely avoids having to call operator+, which can be quite useful sometimes.
That's an arbitrary statement without any explanation. So I'm going to throw into the pool:
x+1 is essentially equivalent to (++x)-- but completely avoids having to call operator++ and operator-- which can be useful sometimes.
So why is the precedence not defined to have ++x++ automatically expand to (++x)++ rather than ++(x++)
Just to make such arcane corner cases not error out? No way. Can you please recite man operator for me? If you cannot do that, better not try and write ++x++ in your code.
C++ standard just kept the C rules and obviously those weren't fixed considering operator overloading and idioms yet be invented in a yet to be invented language.
Looking at what is available in D.M. Ritchie Home Page, on see that this precedence is already present in B (Unary operators are bound right to left. Thus -!x++ is bound -(!(x++)) in Users' Reference to B) and I didn't see increment operators in BCPL.
Both (++x)++ and (++x)-- invoke undefined behaviour [assuming x to be a primitive type]. For user defined type the scenario would be different. However it is not generally recommended to use such confusing expressions in your code.
As far as the precendence is concerned this answer explains why post increment has higher precedence than pre increment.
Or are we all sticking to our taught "&&, ||, !" way?
Any thoughts in why we should use one or the other?
I'm just wondering because several answers state thate code should be as natural as possible, but I haven't seen a lot of code with "and, or, not" while this is more natural.
I like the idea of the not operator because it is more visible than the ! operator. For example:
if (!foo.bar()) { ... }
if (not foo.bar()) { ... }
I suggest that the second one is more visible and readable. I don't think the same argument necessarily applies to the and and or forms, though.
"What's in a name? That which we call &&, || or !
By any other name would smell as sweet."
In other words, natural depends on what you are used to.
Those were not supported in the old days. And even now you need to give a special switch to some compilers to enable these keywords. That's probably because old code base may have had some functions || variables named "and" "or" "not".
One problem with using them (for me anyway) is that in MSVC you have to include iso646.h or use the (mostly unusable) /Za switch.
The main problem I have with them is the Catch-22 that they're not commonly used, so they require my brain to actively process the meaning, where the old-fashioned operators are more or less ingrained (kind of like the difference between reading a learned language vs. your native language).
Though I'm sure I'd overcome that issue if their use became more universal. If that happened, then I'd have the problem that some boolean operators have keywords while others don't, so if alternate keywords were used, you might see expressions like:
if ((x not_eq y) and (y == z) or (z <= something)) {...}
when it seems to me they should have alternate tokens for all the (at least comparison) operators:
if ((x not_eq y) and (y eq z) or (z lt_eq something)) {...}
This is because the reason the alternate keywords (and digraphs and trigraphs) were provided was not to make the expressions more readable - it was because historically there have been (and maybe still are) keyboards and/or codepages in some localities that do not have certain punctuation characters. For example, the invariant part of the ISO 646 codepage (surprise) is missing the '|', '^' and '~' characters among others.
Although I've been programming C++ from quite some time, I did not know that the keywords "and" "or" and "not" were allowed, and I've never seen it used.
I searched through my C++ book, and I found a small section mentioning alternative representation for the normal operators "&&", "||" and "!", where it explains those are available for people with non-standard keyboards that do not have the "&!|" symbols.
A bit like trigraphs in C.
Basically, I would be confused by their use, and I think I would not be the only one.
Using a representation which is non-standard, should really have a good reason to be used.
And if used, it should be used consistently in the code, and described in the coding standard.
The digraph and trigraph operators were actually designed more for systems that didn't carry the standard ASCII character set - such as IBM mainframes (which use EBCDIC). In the olden days of mechanical printers, there was this thing called a "48-character print chain" which, as its name implied, only carried 48 characters. A-Z (uppercase), 0-9 and a handful of symbols. Since one of the missing symbols was an underscore (which rendered as a space), this could make working with languages like C and PL/1 a real fun activity (is this 2 words or one word with an underscore???).
Conventional C/C++ is coded with the symbols and not the digraphs. Although I have been known to #define "NOT", since it makes the meaning of a boolean expression more obvious, and it's visually harder to miss than a skinny little "!".
I wish I could use || and && in normal speech. People try very hard to misunderstand when I say "and" or "or"...
I personally like operators to look like operators. It's all maths, and unless you start using "add" and "subtract" operators too it starts to look a little inconsistent.
I think some languages suit the word-style and some suit the symbols if only because it's what people are used to and it works. If it ain't broke, don't fix it.
There is also the question of precedence, which seems to be one of the reasons for introducing the new operators, but who can be bothered to learn more rules than they need to?
In cases where I program with names directly mapped to the real world, I tend to use 'and' and 'or', for example:
if(isMale or isBoy and age < 40){}
It's nice to use 'em in Eclipse+gcc, as they are highlighted. But then, the code doesn't compile with some compilers :-(
Using these operators is harmful. Notice that and and or are logical operators whereas the similar-looking xor is a bitwise operator. Thus, arguments to and and or are normalized to 0 and 1, whereas those to xor aren't.
Imagine something like
char *p, *q; // Set somehow
if(p and q) { ... } // Both non-NULL
if(p or q) { ... } // At least one non-NULL
if(p xor q) { ... } // Exactly one non-NULL
Bzzzt, you have a bug. In the last case you're testing whether at least one of the bits in the pointers is different, which probably isn't what you thought you were doing because then you would have written p != q.
This example is not hypothetical. I was working together with a student one time and he was fond of these literate operators. His code failed every now and then for reasons that he couldn't explain. When he asked me, I could zero in on the problem because I knew that C++ doesn't have a logical xor operator, and that line struck me as very odd.
BTW the way to write a logical xor in C++ is
!a != !b
I like the idea, but don't use them. I'm so used to the old way that it provides no advantage to me doing it either way. Same holds true for the rest of our group, however, I do have concerns that we might want to switch to help avoid future programmers from stumbling over the old symbols.
So to summarize: it's not used a lot because of following combination
old code where it was not used
habit (more standard)
taste (more math-like)
Thanks for your thoughts