Application has higher precedence than abstraction.
In this sense, what is lambda calculus abstraction? I'm confused at what there is to have precedence over?
Lambda abstraction is λx.M, for some variable x and arbitrary term M.
Application is (MN), for some arbitrary terms M and N.
Precedence is the question which of several operation is to be performed first if more than one reading is possible because the term is ambiguous due to omission of brackets. For example in arithmetic, multiplication by convention has precedence over addition, which means that 5+2×3 is read as 5+(2×3) and not as (5+2)×3. The multiplication operator is evaluated first and binds the terms closest to it, and addition comes secondary, embedding the multiplication term.
W.r.t. to lambda calculus, the convention that application has higher precedence than abstraction means that in case of doubt because brackets have been ommitted, you will first try to form an application and only afterwards perform abstraction, so application "binds" stronger, and an abstraction term will be formed later and subsume the application term.
E.g., λx.M N could in principle be read as either λx.(MN) or (λx.M)M, but since application has precedence over abstraction, you first form the possible application (MN) and then the abstraction λx.(MN). If it were the other way round, i.e. if abstraction had precedence over application, then you would first try to form an abstraction term (λx.M), then application with the term you already got ((λx.M)M).
So by defining that application has precedence over abstraction, λx.M N = λx.(MN), and not ((λx.M)M).
Related
Let's have two lines of code:
&car->speed
&(car->speed)
Are these two lines equivalent? Will I get in both cases address to the speed?
If they are equivalents, what is better to choose as coding convention?
Are these two lines equivalent? Will I get in both cases address to the speed?
Yes. -> has higher precedence than that of unary &, therefore &car->speed and &(car->speed) are equivalent.
If they are equivalents, what is better to choose as coding convention?
Go with second as it shows the intended behaviour that you are interested in the address of speed.
This question already asked here several times. Postfix expression operators have higher priority than unary operators. So these two expressions
&car->speed
&(car->speed)
are equivalent.
Or another similar example with other unary operator !
!car->speed
!(car->speed)
As for coding convention I would prefer
&car->speed
and if you want to ampersandify car alone, use this:
( &car )->speed
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.
Lately, I have seen a lot of questions being asked about output for some crazy yet syntactically allowed code statements like like i = ++i + 1 and i=(i,i++,i)+1;.
Frankly realistically speaking hardly anyone writes any such code in actual programing.To be frank I have never encountered any such code in my professional experience. So I usually end up skipping such questions here on SO. But lately the sheer volume of such Q's being asked makes me think if I am missing out some important theory by skipping such Q's. I gather that the such Q's revolve around Sequence points. I hardly know anything about sequence points to be frank and I am just wondering if not knowing about it is a handicap in some way. So can someone please explain the theory /concept of Sequence points, or If possible point to a resource which explains about the concept. Also, is it worth to invest time in knowing about this concept/theory?
The simplest answer I can think of is:
C++ is defined in terms of an abstract machine. The output of a program executed on the abstract machine is defined ONLY in terms of the order that "side effects" are performed. And Side effects are defined as calls into IO library functions, and changes to variables marked volatile.
C++ compilers are allowed to do whatever they want internally to optimize code, but they cannot change the order of writes to volatile variables, and io calls.
Sequence points define the c/c++ program's heartbeat - side effects before the sequence point are "complete" and side effects after the sequence point have not yet taken place. But, side effects (or, code that can effect a side effect indirectly( within a sequence point can be re-ordered.
Which is why understanding them is important. Without that understanding, your fundamental understanding of what a c++ program is (And how it might be optimized by an agressive compiler) is flawed.
See http://en.wikipedia.org/wiki/Sequence_point.
It's a quite simple concept, so you don't need to invest much time :)
The exact technical details of sequence points can get hairy, yes. But following these guideline solves almost all the practical issues:
If an expression modifies a value, there must be a sequence point between the modification and any other use of that value.
If you're not sure whether two uses of a value are separated by a sequence point or not, break up your code into more statements.
Here "modification" includes assignment operations on the left-hand value in =, +=, etc., and also the ++x, x++, --x, and x-- syntaxes. (It's usually these increment/decrement expressions where some people try to be clever and end up getting into trouble.)
Luckily, there are sequence points in most of the "expected" places:
At the end of every statement or declaration.
At the beginning and end of every function call.
At the built-in && and || operators.
At the ? in a ternary expression.
At the built-in , comma operator. (Most commonly seen in for conditions, e.g. for (a=0, b=0; a<m && b<n; ++a, ++b).) A comma which separates function arguments is not the comma operator and is not a sequence point.
Overloaded operator&&, operator||, and operator, do not cause sequence points. Potential surprises from that fact is one reason overloading them is usually discouraged.
It is worth knowing that sequence points exist because if you don't know about them you can easily write code which seems to run fine in testing but actually is undefined and might fail when you run it on another computer or with different compile options. In particular if you write for example x++ as part of a larger expression that also includes x you can easily run into problems.
I don't think it is necessary to learn all the rules fully - but you need to know when you need to check the specification, or perhaps better - when to rewrite your code to make it so that you aren't relying on sequence points rules if a simpler design would work too.
int n,n_squared;
for(n=n_squared=0;n<100;n_squared+=n+ ++n)
printf("%i squared might or might not be %i\n",n,n_squared);
... doesn't always do what you think it will do. This can make debugging painful.
The reason is the ++n retrieves, modifies, and stores the value of n, which could be before or after n is retrieved. Therefore, the value of n_squared isn't clearly defined after the first iteration. Sequence points guarantee that the subexpressions are evaluated in order.
I read a book that uses infix, infixr, and infixl in the sample programs. I'm wondering what the differences are. I'm guessing that infixr performs operation from right to left, and vice versa.
Yes, the r/l indicates the associativity. Without testing I'd assume that infix has normal left associativity.
infix defines the operator to be left-associative, infixr defines it to be right-associative. infixl does not exist.
It depends on the implementation. The SML '97 standard is a little different from SML/NJ and Mlton. You get slightly different behaviour with each in terms of associativity rules and the way expressions are parenthesised depending on priority (the standard is a bit stricter than the implementations).
after this question, I don't know what to think.
In OCaml, if you do something like -1.0**2.0 (because of the typing you need to have float), you obtain 1.00. According to the standard order of operations, the result should be -1 (as in python).
I wasn't able to find the reason or a clear definition of the operator precedence in OCaml...
Is this because of the type system ? or the fact that there's a binding underneath with pow ?
As the very page you quote says, "The order in which the unary operator − (usually read "minus") acts is often problematical." -- it quotes Excel and bc as having the same priority for it as O'CAML, but also says "In written or printed mathematics" it works as in Python. So, essentially, there's no universal consensus on this specific issue.
Operator precedence is syntax-directed in OCaml, which means that the first character of the function identifier (and whether it's unary or binary) determines the operator precedence according to a fixed sequence. Contrast this with languages like Haskell, where the operator precedence can be specified at function definition regardless of which characters are used to form the function identifier.