Related
Lets say I wanted to write a recursive anonymous function to calculate factorial values.
print(((int a) => a == 1? 1 : a * this(a - 1))(4));
I would expect this to print 24, which is 4! (this function is obviously prone to issues with negative numbers, but that's beside the point)
The problem is that this doesn't refer to the anonymous function in order to make a recursive call.
Is this something that's possible in dart? I've seen it in python before, where a function is assigned to a variable with the walrus operator ( := ) and is also recursive.
Here is an example that creates a list of the average value on each level of a binary tree:
return (get_levels := lambda l: ([mean(node.val for node in l)] + get_levels([child for node in l for child in [node.left, node.right] if child])) if l else [])([root])
As you can see, the lambda is called get_levels. It calculates the average of the current level, then makes a recursive call on the next level of the binary tree and appends it to the list of previous level averages.
The closest that I could come up with is this:
var getLevels;
List<double> averageOfLevels(TreeNode? root) {
return root == null ? [] : (getLevels = (List<TreeNode> level) => level.isNotEmpty ? <double>[level.map((node) => node.val).fold(0, (int l, int r) => l+r) / level.length] + getLevels([for(var node in level) ...[node.left, node.right]].whereType<TreeNode>().toList()) : <double>[])([root]);
}
But, as you can see, this required an additional line where the variable is defined ahead of time.
Is it possible to achieve something more similar to the python example using callable classes?
There's a classic Lisp/Scheme problem of how to create a recursive lambda. The same technique of creating one anonymous function that takes itself as an argument and then using another anonymous function to pass the first anonymous function to itself can be applied to Dart (albeit by sacrificing some type-safety; I can't think of a way to strongly type a Function that takes its own type as an argument). For example, a recursive factorial implementation:
void main() {
var factorial = (Function f, int x) {
return f(f, x);
}((Function self, int x) {
return (x <= 1) ? 1 : x * self(self, x - 1);
}, 4);
print('4! = $factorial'); // Prints: 4! = 24
}
All that said, this seems like a pretty contrived, academic problem. In practice, just create a named function. It can be a local function if you want to avoid polluting a global namespace. It would be far more readable and maintainable.
Is it possible to achieve something more similar to the python example using callable classes?
I'm not sure where you're going with that since Dart neither allows defining anonymous classes nor local classes, so even if you made a callable class, it would violate your request for being anonymous.
I have tried to implement Floor and Ceiling Function as defined in the following link
https://math.stackexchange.com/questions/3619044/floor-or-ceiling-function-encoding-in-first-order-logic/3619320#3619320
But Z3 query returning counterexample.
Floor Function
_X=Real('_X')
_Y=Int('_Y')
_W=Int('_W')
_n=Int('_n')
_Floor=Function('_Floor',RealSort(),IntSort())
..
_s.add(_X>=0)
_s.add(_Y>=0)
_s.add(Implies(_Floor(_X)==_Y,And(Or(_Y==_X,_Y<_X),ForAll(_W,Implies(And(_W>=0,_W<_X),And(_W ==_Y,_W<_Y))))))
_s.add(Implies(And(Or(_Y==_X,_Y<_X),ForAll(_W,Implies(And(_W>=0,_W<_X),And(_W==_Y,_W<_Y))),_Floor(_X)==_Y))
_s.add(Not(_Floor(0.5)==0))
Expected Result - Unsat
Actual Result - Sat
Ceiling Function
_X=Real('_X')
_Y=Int('_Y')
_W=Int('_W')
_Ceiling=Function('_Ceiling',RealSort(),IntSort())
..
..
_s.add(_X>=0)
_s.add(_Y>=0)
_s.add(Implies(_Ceiling(_X)==_Y,And(Or(_Y==_X,_Y<_X),ForAll(_W,Implies(And(_W>=0,_W<_X),And(_W ==_Y,_Y<_W))))))
_s.add(Implies(And(Or(_Y==_X,_Y<_X),ForAll(_W,Implies(And(_W>=0,_W<_X),And(_W==_Y,_Y<_W)))),_Ceiling(_X)==_Y))
_s.add(Not(_Ceilng(0.5)==1))
Expected Result - Unsat
Actual Result - Sat
[Your encoding doesn't load to z3, it gives a syntax error even after eliminating the '..', as your call to Implies needs an extra argument. But I'll ignore all that.]
The short answer is, you can't really do this sort of thing in an SMT-Solver. If you could, then you can solve arbitrary Diophantine equations. Simply cast it in terms of Reals, solve it (there is a decision procedure for Reals), and then add the extra constraint that the result is an integer by saying Floor(solution) = solution. So, by this argument, you can see that modeling such functions will be beyond the capabilities of an SMT solver.
See this answer for details: Get fractional part of real in QF_UFNRA
Having said that, this does not mean you cannot code this up in Z3. It just means that it will be more or less useless. Here's how I would go about it:
from z3 import *
s = Solver()
Floor = Function('Floor',RealSort(),IntSort())
r = Real('R')
f = Int('f')
s.add(ForAll([r, f], Implies(And(f <= r, r < f+1), Floor(r) == f)))
Now, if I do this:
s.add(Not(Floor(0.5) == 0))
print(s.check())
you'll get unsat, which is correct. If you do this instead:
s.add(Not(Floor(0.5) == 1))
print(s.check())
you'll see that z3 simply loops forever. To make this usefull, you'd want the following to work as well:
test = Real('test')
s.add(test == 2.4)
result = Int('result')
s.add(Floor(test) == result)
print(s.check())
but again, you'll see that z3 simply loops forever.
So, bottom line: Yes, you can model such constructs, and z3 will correctly answer the simplest of queries. But with anything interesting, it'll simply loop forever. (Essentially whenever you'd expect sat and most of the unsat scenarios unless they can be constant-folded away, I'd expect z3 to simply loop.) And there's a very good reason for that, as I mentioned: Such theories are just not decidable and fall well out of the range of what an SMT solver can do.
If you are interested in modeling such functions, your best bet is to use a more traditional theorem prover, like Isabelle, Coq, ACL2, HOL, HOL-Light, amongst others. They are much more suited for working on these sorts of problems. And also, give a read to Get fractional part of real in QF_UFNRA as it goes into some of the other details of how you can go about modeling such functions using non-linear real arithmetic.
What are the benefits and drawbacks of the ?: operator as opposed to the standard if-else statement. The obvious ones being:
Conditional ?: Operator
Shorter and more concise when dealing with direct value comparisons and assignments
Doesn't seem to be as flexible as the if/else construct
Standard If/Else
Can be applied to more situations (such as function calls)
Often are unnecessarily long
Readability seems to vary for each depending on the statement. For a little while after first being exposed to the ?: operator, it took me some time to digest exactly how it worked. Would you recommend using it wherever possible, or sticking to if/else given that I work with many non-programmers?
I would basically recommend using it only when the resulting statement is extremely short and represents a significant increase in conciseness over the if/else equivalent without sacrificing readability.
Good example:
int result = Check() ? 1 : 0;
Bad example:
int result = FirstCheck() ? 1 : SecondCheck() ? 1 : ThirdCheck() ? 1 : 0;
This is pretty much covered by the other answers, but "it's an expression" doesn't really explain why that is so useful...
In languages like C++ and C#, you can define local readonly fields (within a method body) using them. This is not possible with a conventional if/then statement because the value of a readonly field has to be assigned within that single statement:
readonly int speed = (shiftKeyDown) ? 10 : 1;
is not the same as:
readonly int speed;
if (shifKeyDown)
speed = 10; // error - can't assign to a readonly
else
speed = 1; // error
In a similar way you can embed a tertiary expression in other code. As well as making the source code more compact (and in some cases more readable as a result) it can also make the generated machine code more compact and efficient:
MoveCar((shiftKeyDown) ? 10 : 1);
...may generate less code than having to call the same method twice:
if (shiftKeyDown)
MoveCar(10);
else
MoveCar(1);
Of course, it's also a more convenient and concise form (less typing, less repetition, and can reduce the chance of errors if you have to duplicate chunks of code in an if/else). In clean "common pattern" cases like this:
object thing = (reference == null) ? null : reference.Thing;
... it is simply faster to read/parse/understand (once you're used to it) than the long-winded if/else equivalent, so it can help you to 'grok' code faster.
Of course, just because it is useful does not mean it is the best thing to use in every case. I'd advise only using it for short bits of code where the meaning is clear (or made more clear) by using ?: - if you use it in more complex code, or nest ternary operators within each other it can make code horribly difficult to read.
I usually choose a ternary operator when I'd have a lot of duplicate code otherwise.
if (a > 0)
answer = compute(a, b, c, d, e);
else
answer = compute(-a, b, c, d, e);
With a ternary operator, this could be accomplished with the following.
answer = compute(a > 0 ? a : -a, b, c, d, e);
I find it particularly helpful when doing web development if I want to set a variable to a value sent in the request if it is defined or to some default value if it is not.
A really cool usage is:
x = foo ? 1 :
bar ? 2 :
baz ? 3 :
4;
Sometimes it can make the assignment of a bool value easier to read at first glance:
// With
button.IsEnabled = someControl.HasError ? false : true;
// Without
button.IsEnabled = !someControl.HasError;
I'd recommend limiting the use of the ternary(?:) operator to simple single line assignment if/else logic. Something resembling this pattern:
if(<boolCondition>) {
<variable> = <value>;
}
else {
<variable> = <anotherValue>;
}
Could be easily converted to:
<variable> = <boolCondition> ? <value> : <anotherValue>;
I would avoid using the ternary operator in situations that require if/else if/else, nested if/else, or if/else branch logic that results in the evaluation of multiple lines. Applying the ternary operator in these situations would likely result in unreadable, confusing, and unmanageable code. Hope this helps.
The conditional operator is great for short conditions, like this:
varA = boolB ? valC : valD;
I use it occasionally because it takes less time to write something that way... unfortunately, this branching can sometimes be missed by another developer browsing over your code. Plus, code isn't usually that short, so I usually help readability by putting the ? and : on separate lines, like this:
doSomeStuffToSomething(shouldSomethingBeDone()
? getTheThingThatNeedsStuffDone()
: getTheOtherThingThatNeedsStuffDone());
However, the big advantage to using if/else blocks (and why I prefer them) is that it's easier to come in later and add some additional logic to the branch,
if (shouldSomethingBeDone()) {
doSomeStuffToSomething(getTheThingThatNeedsStuffDone());
doSomeAdditionalStuff();
} else {
doSomeStuffToSomething(getTheOtherThingThatNeedsStuffDone());
}
or add another condition:
if (shouldSomethingBeDone()) {
doSomeStuffToSomething(getTheThingThatNeedsStuffDone());
doSomeAdditionalStuff();
} else if (shouldThisOtherThingBeDone()){
doSomeStuffToSomething(getTheOtherThingThatNeedsStuffDone());
}
So, in the end, it's about convenience for you now (shorter to use :?) vs. convenience for you (and others) later. It's a judgment call... but like all other code-formatting issues, the only real rule is to be consistent, and be visually courteous to those who have to maintain (or grade!) your code.
(all code eye-compiled)
One thing to recognize when using the ternary operator that it is an expression not a statement.
In functional languages like scheme the distinction doesn't exists:
(if (> a b) a b)
Conditional ?: Operator
"Doesn't seem to be as flexible as the if/else construct"
In functional languages it is.
When programming in imperative languages I apply the ternary operator in situations where I typically would use expressions (assignment, conditional statements, etc).
While the above answers are valid, and I agree with readability being important, there are 2 further points to consider:
In C#6, you can have expression-bodied methods.
This makes it particularly concise to use the ternary:
string GetDrink(DayOfWeek day)
=> day == DayOfWeek.Friday
? "Beer" : "Tea";
Behaviour differs when it comes to implicit type conversion.
If you have types T1 and T2 that can both be implicitly converted to T, then the below does not work:
T GetT() => true ? new T1() : new T2();
(because the compiler tries to determine the type of the ternary expression, and there is no conversion between T1 and T2.)
On the other hand, the if/else version below does work:
T GetT()
{
if (true) return new T1();
return new T2();
}
because T1 is converted to T and so is T2
If I'm setting a value and I know it will always be one line of code to do so, I typically use the ternary (conditional) operator. If there's a chance my code and logic will change in the future, I use an if/else as it's more clear to other programmers.
Of further interest to you may be the ?? operator.
The advantage of the conditional operator is that it is an operator. In other words, it returns a value. Since if is a statement, it cannot return a value.
There is some performance benefit of using the the ? operator in eg. MS Visual C++, but this is a really a compiler specific thing. The compiler can actually optimize out the conditional branch in some cases.
The scenario I most find myself using it is for defaulting values and especially in returns
return someIndex < maxIndex ? someIndex : maxIndex;
Those are really the only places I find it nice, but for them I do.
Though if you're looking for a boolean this might sometimes look like an appropriate thing to do:
bool hey = whatever < whatever_else ? true : false;
Because it's so easy to read and understand, but that idea should always be tossed for the more obvious:
bool hey = (whatever < whatever_else);
If you need multiple branches on the same condition, use an if:
if (A == 6)
f(1, 2, 3);
else
f(4, 5, 6);
If you need multiple branches with different conditions, then if statement count would snowball, you'll want to use the ternary:
f( (A == 6)? 1: 4, (B == 6)? 2: 5, (C == 6)? 3: 6 );
Also, you can use the ternary operator in initialization.
const int i = (A == 6)? 1 : 4;
Doing that with if is very messy:
int i_temp;
if (A == 6)
i_temp = 1;
else
i_temp = 4;
const int i = i_temp;
You can't put the initialization inside the if/else, because it changes the scope. But references and const variables can only be bound at initialization.
The ternary operator can be included within an rvalue, whereas an if-then-else cannot; on the other hand, an if-then-else can execute loops and other statements, whereas the ternary operator can only execute (possibly void) rvalues.
On a related note, the && and || operators allow some execution patterns which are harder to implement with if-then-else. For example, if one has several functions to call and wishes to execute a piece of code if any of them fail, it can be done nicely using the && operator. Doing it without that operator will either require redundant code, a goto, or an extra flag variable.
With C# 7, you can use the new ref locals feature to simplify the conditional assignment of ref-compatible variables. So now, not only can you do:
int i = 0;
T b = default(T), c = default(T);
// initialization of C#7 'ref-local' variable using a conditional r-value⁽¹⁾
ref T a = ref (i == 0 ? ref b : ref c);
...but also the extremely wonderful:
// assignment of l-value⁽²⁾ conditioned by C#7 'ref-locals'
(i == 0 ? ref b : ref c) = a;
That line of code assigns the value of a to either b or c, depending on the value of i.
Notes
1. r-value is the right-hand side of an assignment, the value that gets assigned.
2. l-value is the left-hand side of an assignment, the variable that receives the assigned value.
I have been learning about metatables in Lua and I wanted to implement range operators as in Ruby, so I used this model
debug.setmetatable(1, {
__concat = function(a, b)
if a > b then
error(table.concat({
"attempt to create a range of values with a",
"minimum larger than the maximum"
}, " "))
elseif a == b then
return a
else
return unpack((function(nStart,nEnd)
local nTable = {}
for it = nStart,nEnd do
table.insert(nTable, it)
end
return nTable
end)(a, b))
end
end
})
print(6 .. 6)
But it seems that that it continues to use the default behavior. Is there any way to get this to work? I am aware that I could make a function to emulate the behavior and call it with range(n,n2) or similar but that defeats the purpose. Thanks.
Please see section 3.4.5 of the Lua 5.2 manual.
The string concatenation operator in Lua is denoted by two dots ('..'). If both operands are strings or numbers, then they are converted to strings according to the rules mentioned in §3.4.2. Otherwise, the __concat metamethod is called (see §2.4).
If you want to change this behavior, look into lvm.c, specifically the luaV_concat function.
I'm writing a LSL to Lua translator, and I'm having all sorts of trouble implementing incrementing and decrementing operators. LSL has such things using the usual C like syntax (x++, x--, ++x, --x), but Lua does not. Just to avoid massive amounts of typing, I refer to these sorts of operators as "crements". In the below code, I'll use "..." to represent other parts of the expression.
... x += 1 ...
Wont work, coz Lua only has simple assignment.
... x = x + 1 ...
Wont work coz that's a statement, and Lua can't use statements in expressions. LSL can use crements in expressions.
function preIncrement(x) x = x + 1; return x; end
... preIncrement(x) ...
While it does provide the correct value in the expression, Lua is pass by value for numbers, so the original variable is not changed. If I could get this to actually change the variable, then all is good. Messing with the environment might not be such a good idea, dunno what scope x is. I think I'll investigate that next. The translator could output scope details.
Assuming the above function exists -
... x = preIncrement(x) ...
Wont work for the "it's a statement" reason.
Other solutions start to get really messy.
x = preIncrement(x)
... x ...
Works fine, except when the original LSL code is something like this -
while (doOneThing(x++))
{
doOtherThing(x);
}
Which becomes a whole can of worms. Using tables in the function -
function preIncrement(x) x[1] = x[1] + 1; return x[1]; end
temp = {x}
... preincrement(temp) ...
x = temp[1]
Is even messier, and has the same problems.
Starting to look like I might have to actually analyse the surrounding code instead of just doing simple translations to sort out what the correct way to implement any given crement will be. Anybody got any simple ideas?
I think to really do this properly you're going to have to do some more detailed analysis, and splitting of some expressions into multiple statements, although many can probably be translated pretty straight-forwardly.
Note that at least in C, you can delay post-increments/decrements to the next "sequence point", and put pre-increments/decrements before the previous sequence point; sequence points are only located in a few places: between statements, at "short-circuit operators" (&& and ||), etc. (more info here)
So it's fine to replace x = *y++ + z * f (); with { x = *y + z * f(); y = y + 1; }—the user isn't allowed to assume that y will be incremented before anything else in the statement, only that the value used in *y will be y before it's incremented. Similarly, x = *--y + z * f(); can be replaced with { y = y - 1; x = *y + z * f (); }
Lua is designed to be pretty much impervious to implementations of this sort of thing. It may be done as kind of a compiler/interpreter issue, since the interpreter can know that variables only change when a statement is executed.
There's no way to implement this kind of thing in Lua. Not in the general case. You could do it for global variables by passing a string to the increment function. But obviously it wouldn't work for locals, or for variables that are in a table that is itself global.
Lua doesn't want you to do it; it's best to find a way to work within the restriction. And that means code analysis.
Your proposed solution only will work when your Lua variables are all global. Unless this is something LSL also does, you will get trouble translating LSL programs that use variables called the same way in different places.
Lua is only able of modifying one lvalue per statement - tables being passed to functions are the only exception to this rule. You could use a local table to store all locals, and that would help you out with the pre-...-crements; they can be evaluated before the expression they are contained in is evauated. But the post-...-crements have to be evaluated later on, which is simply not possible in lua - at least not without some ugly code involving anonymous functions.
So you have one options: you must accept that some LSL statements will get translated to several Lua statements.
Say you have a LSL statement with increments like this:
f(integer x) {
integer y = x + x++;
return (y + ++y)
}
You can translate this to a Lua statement like this:
function f(x) {
local post_incremented_x = x + 1 -- extra statement 1 for post increment
local y = x + post_incremented_x
x = post_incremented_x -- extra statement 2 for post increment
local pre_incremented_y = y + 1
return y + pre_incremented_y
y = pre_incremented_y -- this line will never be executed
}
So you basically will have to add two statements per ..-crement used in your statements. For complex structures, that will mean calculating the order in which the expressions are evaluated.
For what is worth, I like with having post decrements and predecrements as individual statements in languages. But I consider it a flaw of the language when they can also be used as expressions. The syntactic sugar quickly becomes semantic diabetes.
After some research and thinking I've come up with an idea that might work.
For globals -
function preIncrement(x)
_G[x] = _G[x] + 1
return _G[x]
end
... preIncrement("x") ...
For locals and function parameters (which are locals to) I know at the time I'm parsing the crement that it is local, I can store four flags to tell me which of the four crements is being used in the variables AST structure. Then when it comes time to output the variables definition, I can output something like this -
local x;
function preIncrement_x() x = x + 1; return x; end
function postDecrement_x() local y = x; x = x - 1; return y; end
... preIncrement_x() ...
In most of your assessment of configurability to the code. You are trying to hard pass data types from one into another. And call it a 'translator'. And in all of this you miss regex and other pattern match capacities. Which are far more present in LUA than LSL. And since the LSL code is being passed into LUA. Try using them, along with other functions. Which would define the work more as a translator, than a hard pass.
Yes I know this was asked a while ago. Though, for other viewers of this topic. Never forget the environments you are working in. EVER. Use what they give you to the best ability you can.