Algebraic boolean equation; final step to proving !((!A.B)+(B.!C)) = !B+(A.C) - boolean

note: sorry for the poor title, it's extremely difficult making one that "Accurately describes your question" that is not similar to other titles.
I'm fairly new to this and my teacher left us with this tough question to try do at home:
> !((!A.B)+(B.!C))
I already did most of the work:
(A.B)+(A.C)+(B.C)
What i want to know is, what are the next steps to simplifying this algebraic Boolean expression into
!B+(A.C)
Why does B become !B? And which is the redundant part of the expression?
edit: forgot to mention, i'm using De Morgan's Theorem to work this out.

Related

Boolean expression with a redundant overlapping term

I have simplified a Boolean expression using 14 Boolean Algebra law steps and now have a working resultant function which according to a KV map still has a redundant term.
In an attempt to remove this term I have tried various distribution, complement and identity applications followed by a deMorgans law, as well a Consensus Theorem approach. Of the text books I've consulted they all say there is no theory or set rules to resolving such an issue, just experience!
After much simplification (page and half) my resultant expression is,
z = ~a~cd + b~a + b~d + bc [1]
Using a KV map I get a slightly simpler expression of,
z = ~a~cd + b~d + bc [2]
The truth table of each expression is equivalent therefore the b~a of my first expression [1] appears to be redundant.
I expected to be able to cancel the redundant **b~a** function by applying the laws of Boolean algebra but after much experimenting I'm unable to find an entry point.
This is an assignment question so I do not expect anybody to do my homework but advise on how to approach this challenge would be appreciated.

Why do immutable objects enable functional programming?

I'm trying to learn scala and I'm unable to grasp this concept. Why does making an object immutable help prevent side-effects in functions. Can anyone explain like I'm five?
Interesting question, a bit difficult to answer.
Functional programming is very much about using mathematics to reason about programs. To do so, one needs a formalism that describe the programs and how one can make proofs about properties they might have.
There are many models of computation that provide such formalisms, such as lambda calculus and turing machines. And there's a certain degree of equivalency between them (see this question, for a discussion).
In a very real sense, programs with mutability and some other side effects have a direct mapping to functional program. Consider this example:
a = 0
b = 1
a = a + b
Here are two ways of mapping it to functional program. First one, a and b are part of a "state", and each line is a function from a state into a new state:
state1 = (a = 0, b = ?)
state2 = (a = state1.a, b = 1)
state3 = (a = state2.a + state2.b, b = state2.b)
Here's another, where each variable is associated with a time:
(a, t0) = 0
(b, t1) = 1
(a, t2) = (a, t0) + (b, t1)
So, given the above, why not use mutability?
Well, here's the interesting thing about math: the less powerful the formalism is, the easier it is to make proofs with it. Or, to put it in other words, it's too hard to reason about programs that have mutability.
As a consequence, there's very little advance regarding concepts in programming with mutability. The famous Design Patterns were not arrived at through study, nor do they have any mathematical backing. Instead, they are the result of years and years of trial and error, and some of them have since proved to be misguided. Who knows about the other dozens "design patterns" seen everywhere?
Meanwhile, Haskell programmers came up with Functors, Monads, Co-monads, Zippers, Applicatives, Lenses... dozens of concepts with mathematical backing and, most importantly, actual patterns of how code is composed to make up programs. Things you can use to reason about your program, increase reusability and improve correctness. Take a look at the Typeclassopedia for examples.
It's no wonder people not familiar with functional programming get a bit scared with this stuff... by comparison, the rest of the programming world is still working with a few decades-old concepts. The very idea of new concepts is alien.
Unfortunately, all these patterns, all these concepts, only apply with the code they are working with does not contain mutability (or other side effects). If it does, then their properties cease to be valid, and you can't rely on them. You are back to guessing, testing and debugging.
In short, if a function mutates an object then it has side effects. Mutation is a side effect. This is just true by definition.
In truth, in a purely functional language it should not matter if an object is technically mutable or immutable, because the language will never "try" to mutate an object anyway. A pure functional language doesn't give you any way to perform side effects.
Scala is not a pure functional language, though, and it runs in the Java environment in which side effects are very popular. In this environment, using objects that are incapable of mutation encourages you to use a pure functional style because it makes a side-effect oriented style impossible. You are using data types to enforce purity because the language does not do it for you.
Now I will say a bunch of other stuff in the hope that it helps this make sense to you.
Fundamental to the concept of a variable in functional languages is referential transparency.
Referential transparency means that there is no difference between a value, and a reference to that value. In a language where this is true, it makes it much simpler to think about a program works, since you never have to stop and ask, is this a value, or a reference to a value? Anyone who's ever programmed in C recognizes that a great part of the challenge of learning that paradigm is knowing which is which at all times.
In order to have referential transparency, the value that a reference refers to can never change.
(Warning, I'm about to make an analogy.)
Think of it this way: in your cell phone, you have saved some phone numbers of other people's cell phones. You assume that whenever you call that phone number, you will reach the person you intend to talk to. If someone else wants to talk to your friend, you give them the phone number and they reach that same person.
If someone changes their cell phone number, this system breaks down. Suddenly, you need to get their new phone number if you want to reach them. Maybe you call the same number six months later and reach a different person. Calling the same number and reaching a different person is what happens when functions perform side effects: you have what seems to be the same thing, but you try to use it, it turns out it's different now. Even if you expected this, what about all the people you gave that number to, are you going to call them all up and tell them that the old number doesn't reach the same person anymore?
You counted on the phone number corresponding to that person, but it didn't really. The phone number system lacks referential transparency: the number isn't really ALWAYS the same as the person.
Functional languages avoid this problem. You can give out your phone number and people will always be able to reach you, for the rest of your life, and will never reach anybody else at that number.
However, in the Java platform, things can change. What you thought was one thing, might turn into another thing a minute later. If this is the case, how can you stop it?
Scala uses the power of types to prevent this, by making classes that have referential transparency. So, even though the language as a whole isn't referentially transparent, your code will be referentially transparent as long as you use immutable types.
Practically speaking, the advantages of coding with immutable types are:
Your code is simpler to read when the reader doesn't have to look out for surprising side effects.
If you use multiple threads, you don't have to worry about locking because shared objects can never change. When you have side effects, you have to really think through the code and figure out all the places where two threads might try to change the same object at the same time, and protect against the problems that this might cause.
Theoretically, at least, the compiler can optimize some code better if it uses only immutable types. I don't know if Java can do this effectively, though, since it allows side effects. This is a toss-up at best, anyway, because there are some problems that can be solved much more efficiently by using side effects.
I'm running with this 5 year old explanation:
class Account(var myMoney:List[Int] = List(10, 10, 1, 1, 1, 5)) {
def getBalance = println(myMoney.sum + " dollars available")
def myMoneyWithInterest = {
myMoney = myMoney.map(_ * 2)
println(myMoney.sum + " dollars will accru in 1 year")
}
}
Assume we are at an ATM and it is using this code to give us account information.
You do the following:
scala> val myAccount = new Account()
myAccount: Account = Account#7f4a6c40
scala> myAccount.getBalance
28 dollars available
scala> myAccount.myMoneyWithInterest
56 dollars will accru in 1 year
scala> myAccount.getBalance
56 dollars available
We mutated the account balance when we wanted to check our current balance plus a years worth of interest. Now we have an incorrect account balance. Bad news for the bank!
If we were using val instead of var to keep track of myMoney in the class definition, we would not have been able to mutate the dollars and raise our balance.
When defining the class (in the REPL) with val:
error: reassignment to val
myMoney = myMoney.map(_ * 2
Scala is telling us that we wanted an immutable value but are trying to change it!
Thanks to Scala, we can switch to val, re-write our myMoneyWithInterest method and rest assured that our Account class will never alter the balance.
One important property of functional programming is: If I call the same function twice with the same arguments I'll get the same result. This makes reasoning about code much easier in many cases.
Now imagine a function returning the attribute content of some object. If that content can change the function might return different results on different calls with the same argument. => no more functional programming.
First a few definitions:
A side effect is a change in state -- also called a mutation.
An immutable object is an object which does not support mutation, (side effects).
A function which is passed mutable objects (either as parameters or in the global environment) may or may not produce side effects. This is up to the implementation.
However, it is impossible for a function which is passed only immutable objects (either as parameters or in the global environment) to produce side effects. Therefore, exclusive use of immutable objects will preclude the possibility of side effects.
Nate's answer is great, and here is some example.
In functional programming, there is an important feature that when you call a function with same argument, you always get same return value.
This is always true for immutable objects, because you can't modify them after create it:
class MyValue(val value: Int)
def plus(x: MyValue) = x.value + 10
val x = new MyValue(10)
val y = plus(x) // y is 20
val z = plus(x) // z is still 20, plus(x) will always yield 20
But if you have mutable objects, you can't guarantee that plus(x) will always return same value for same instance of MyValue.
class MyValue(var value: Int)
def plus(x: MyValue) = x.value + 10
val x = new MyValue(10)
val y = plus(x) // y is 20
x.value = 30
val z = plus(x) // z is 40, you can't for sure what value will plus(x) return because MyValue.value may be changed at any point.
Why do immutable objects enable functional programming?
They don't.
Take one definition of "function," or "prodecure," "routine" or "method," which I believe applies to many programming languages: "A section of code, typically named, accepting arguments and/or returning a value."
Take one definition of "functional programming:" "Programming using functions." The ability to program with functions is indepedent of whether state is modified.
For instance, Scheme is considered a functional programming language. It features tail calls, higher-order functions and aggregate operations using functions. It also has mutable objects. While mutability destroys some nice mathematical qualities, it does not necessarily prevent "functional programming."
I've read all the answers and they don't satisfy me, because they mostly talk about "immutability", and not about its relation to FP.
The main question is:
Why do immutable objects enable functional programming?
So I've searched a bit more and I have another answer, I believe the easy answer to this question is: "Because Functional Programming is basically defined on the basis of functions that are easy to reason about". Here's the definition of Functional Programming:
The process of building software by composing pure functions.
If a function is not pure -- which means receiving the same input, it's not guaranteed to always produce the same output (e.g., if the function relies on a global object, or date and time, or a random number to compute the output) -- then that function is unpredictable, that's it! Now exactly the same story goes about "immutability" as well, if objects are not immutable, a function with the same object as its input may have different results (aka side effects) each time used, and this will make it hard to reason about the program.
I first tried to put this in a comment, but it got longer than the limit, I'm by no means a pro so please take this answer with a grain of salt.

Documenting Scala functional chains [closed]

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Scala (and functional programming, in general), advocates a style of programming where you produce functional "chains" of the form
collection.operation1(...).operation2(...)...
where the operations are various combinations of map, filter, etc.
Where the equivalent Java code might require 50 lines, the Scala code can be done in 1 or 2 lines. The functional chain can change an input collection to something completely different.
The disadvantage of the Scala code is that 10 minutes later (never mind 6 months later), I can't figure out what I was thinking, because the notation is so compact, and lacks type information (because of implied types).
How do you document this? Do you put a large block comment before the chain, changing an elegant 1 line solution into a bulky 40 line solution consisting of 39 lines of comment? Do you intersperse your comments like this?
collection.
// Select the items that meet condition X
filter(predicate_function).
// Change these items from A's to B's
map(transformation_function).
// etc.
Something else? No documentation? (Leave them guessing. They'll never "downsize" you then, because no one else can maintain the code. :-))
If you find yourself writing comments at that detail level, you're just repeating what the code says.
For long functional chains, define new functions to replace parts of the chain. Give these meaningful names. Then you might be able to avoid comments. The names of these functions themselves should explain what they do.
The best comments are the ones that explain why the code does something. Well-written code should make the "how" obvious from the code itself.
I don't write that code to begin with (unless it's a script for one-time use or playing around in the REPL).
If I can explain what the code does in one comment and the reads okay, then I keep it as a one liner:
// Find all real-valued square roots and group them in integer bins
ds.filter(_ >= 0).map(math.sqrt).groupBy(_.toInt).map(_._2)
If I can't understand this by reading carefully through the chain of commands, then I should break it up more into functionally distinct units. For example, if I expected someone to not realize that the square root of a negative number is not real-valued, I would say:
// Only non-negative numbers have a real-valued square root
val nonneg = ds.filter(_ >= 0)
// Find square roots and group them in integer bins
nonneg.map(math.sqrt).groupBy(_.toInt).map(_._2)
In particular, if someone doesn't know the Scala collections library well, and doesn't have the patience to spend five to ten minutes understanding one line of code, then either they shouldn't be working on my code (nor on anything else that accomplishes something nontrivial that they don't understand and don't have the patience to understand), or I should know in advance that I'm providing an e.g. language and mathematics tutorial in addition to writing working code, either by writing a paragraph explaining how the following line works, or breaking it out command by command, or including comments at the start of each anonymous function explaining what is going on (as appropriate).
Anyway, if you can't understand what it does, you probably need some intermediate values. They are very helpful for mental-resetting ("I can't see how to get from A to C!...but...okay, I can understand A to B. And I can understand B to C.")
If your chained operations are all monadic transforms: map, flatMap, filter, then it's often much, much clearer to rewrite the logic as a for-comprehension.
coll.filter(predicate).map(transform)
could become
for(elem <- coll if predicate) yield transform(elem)
it's even easier to show off the power of the technique if you have a longer sequence of operations, such as with Kassen's example:
def eligibleCustomers(products: Seq[Product]) = for {
product <- products
customer <- product.customers
paying <- customer if customer.isPremium
eligible <- paying if paying.age < 20
} yield eligible
If you don't want to split it in multiple methods as hammar suggested you can split the line and give the intermediate values names (and optionally types).
def eligibleCustomers: List[Customer] = {
val customers = products.flatMap(_.customers)
val paying = customers.filter(_.isPremium)
val eligible = paying.filter(_.age < 20)
eligible
}
The linelength is a somehow natural indicator, when your chain is getting too long. :)
Of course, it will depend upon how trivial the chain is:
customerdata.filter (_.age < 40).filter (_.city == "Rio").
filter (_.income > 3000).filter (_.joined < 2005)
filter (_.sex == 'f'). ...
I recently had your impression, where an application of 3 files, one of them a bit lengthy, consisting of 4 classes, one of them not trivial, and of about 10 to 20 methods. Each method was about 5 to 10 lines, and each 2 of them could have been easily combined to a lager one, but I had to convince myself, that although measuring the elegance in spared lines of codes isn't completely wrong, sparing lines isn't the goal itself.
But splitting a method into two often makes complexity per line lower, but not the overall complexity, to understand the whole program.
If the problem domain is complex - filter data at different levels, rowwise, columnwise, map it, group it, build averages, build graphs, paginate them ... - the complicated job has to be done somewhere.
The program isn't more easy to understand, you just have to hit page down less often. It is a readjustment, that you have to read a line of code more slowly.
It doesn't bother me that much now I'm used to Scala. If you want to be more explicit with types, you can always, for example, replace things like map(_.foo) with map { a:A => a.foo } to make the code more readable in lengthy/complex operations. Not that I usually find the need to do that.

Methods of simplifying ugly nested if-else trees in C#

Sometimes I'm writing ugly if-else statements in C# 3.5; I'm aware of some different approaches to simplifying that with table-driven development, class hierarchy, anonimous methods and some more.
The problem is that alternatives are still less wide-spread than writing traditional ugly if-else statements because there is no convention for that.
What depth of nested if-else is normal for C# 3.5? What methods do you expect to see instead of nested if-else the first? the second?
if i have ten input parameters with 3 states in each, i should map functions to combination of each state of each parameter (really less, because not all the states are valid, but sometimes still a lot). I can express these states as a hashtable key and a handler (lambda) which will be called if key matches.
It is still mix of table-driven, data-driven dev. ideas and pattern matching.
what i'm looking for is extending for C# such approaches as this for scripting (C# 3.5 is rather like scripting)
http://blogs.msdn.com/ericlippert/archive/2004/02/24/79292.aspx
Good question. "Conditional Complexity" is a code smell. Polymorphism is your friend.
Conditional logic is innocent in its infancy, when it’s simple to understand and contained within a
few lines of code. Unfortunately, it rarely ages well. You implement several new features and
suddenly your conditional logic becomes complicated and expansive. [Joshua Kerevsky: Refactoring to Patterns]
One of the simplest things you can do to avoid nested if blocks is to learn to use Guard Clauses.
double getPayAmount() {
if (_isDead) return deadAmount();
if (_isSeparated) return separatedAmount();
if (_isRetired) return retiredAmount();
return normalPayAmount();
};
The other thing I have found simplifies things pretty well, and which makes your code self-documenting, is Consolidating conditionals.
double disabilityAmount() {
if (isNotEligableForDisability()) return 0;
// compute the disability amount
Other valuable refactoring techniques associated with conditional expressions include Decompose Conditional, Replace Conditional with Visitor, Specification Pattern, and Reverse Conditional.
There are very old "formalisms" for trying to encapsulate extremely complex expressions that evaluate many possibly independent variables, for example, "decision tables" :
http://en.wikipedia.org/wiki/Decision_table
But, I'll join in the choir here to second the ideas mentioned of judicious use of the ternary operator if possible, identifying the most unlikely conditions which if met allow you to terminate the rest of the evaluation by excluding them first, and add ... the reverse of that ... trying to factor out the most probable conditions and states that can allow you to proceed without testing of the "fringe" cases.
The suggestion by Miriam (above) is fascinating, even elegant, as "conceptual art;" and I am actually going to try it out, trying to "bracket" my suspicion that it will lead to code that is harder to maintain.
My pragmatic side says there is no "one size fits all" answer here in the absence of a pretty specific code example, and complete description of the conditions and their interactions.
I'm a fan of "flag setting" : meaning anytime my application goes into some less common "mode" or "state" I set a boolean flag (which might even be static for the class) : for me that simplifies writing complex if/then else evaluations later on.
best, Bill
Simple. Take the body of the if and make a method out of it.
This works because most if statements are of the form:
if (condition):
action()
In other cases, more specifically :
if (condition1):
if (condition2):
action()
simplify to:
if (condition1 && condition2):
action()
I'm a big fan of the ternary operator which get's overlooked by a lot of people. It's great for assigning values to variables based on conditions. like this
foobarString = (foo == bar) ? "foo equals bar" : "foo does not equal bar";
Try this article for more info.
It wont solve all your problems, but it is very economical.
I know that this is not the answer you are looking for, but without context your questions is very hard to answer. The problem is that the way to refactor such a thing really depends on your code, what it is doing, and what you are trying to accomplish. If you had said that you were checking the type of an object in these conditionals we could throw out an answer like 'use polymorphism', but sometimes you actually do just need some if statements, and sometimes those statements can be refactored into something more simple. Without a code sample it is hard to say which category you are in.
I was told years ago by an instructor that 3 is a magic number. And as he applied it it-else statements he suggested that if I needed more that 3 if's then I should probably use a case statement instead.
switch (testValue)
{
case = 1:
// do something
break;
case = 2:
// do something else
break;
case = 3:
// do something more
break;
case = 4
// do what?
break;
default:
throw new Exception("I didn't do anything");
}
If you're nesting if statements more than 3 deep then you should probably take that as a sign that there is a better way. Probably like Avirdlg suggested, separating the nested if statements into 1 or more methods. If you feel you are absolutely stuck with multiple if-else statements then I would wrap all the if-else statements into a single method so it didn't ugly up other code.
If the entire purpose is to assign a different value to some variable based upon the state of various conditionals, I use a ternery operator.
If the If Else clauses are performing separate chunks of functionality. and the conditions are complex, simplify by creating temporary boolean variables to hold the true/false value of the complex boolean expressions. These variables should be suitably named to represent the business sense of what the complex expression is calculating. Then use the boolean variables in the If else synatx instead of the complex boolean expressions.
One thing I find myself doing at times is inverting the condition followed by return; several such tests in a row can help reduce nesting of if and else.
Not a C# answer, but you probably would like pattern matching. With pattern matching, you can take several inputs, and do simultaneous matches on all of them. For example (F#):
let x=
match cond1, cond2, name with
| _, _, "Bob" -> 9000 // Bob gets 9000, regardless of cond1 or 2
| false, false, _ -> 0
| true, false, _ -> 1
| false, true, _ -> 2
| true, true, "" -> 0 // Both conds but no name gets 0
| true, true, _ -> 3 // Cond1&2 give 3
You can express any combination to create a match (this just scratches the surface). However, C# doesn't support this, and I doubt it will any time soon. Meanwhile, there are some attempts to try this in C#, such as here: http://codebetter.com/blogs/matthew.podwysocki/archive/2008/09/16/functional-c-pattern-matching.aspx. Google can turn up many more; perhaps one will suit you.
try to use patterns like strategy or command
In simple cases you should be able to get around with basic functional decomposition. For more complex scenarios I used Specification Pattern with great success.

Is the Scala 2.8 collections library a case of "the longest suicide note in history"? [closed]

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I have just started to look at the Scala collections library re-implementation which is coming in the imminent 2.8 release. Those familiar with the library from 2.7 will notice that the library, from a usage perspective, has changed little. For example...
> List("Paris", "London").map(_.length)
res0: List[Int] List(5, 6)
...would work in either versions. The library is eminently useable: in fact it's fantastic. However, those previously unfamiliar with Scala and poking around to get a feel for the language now have to make sense of method signatures like:
def map[B, That](f: A => B)(implicit bf: CanBuildFrom[Repr, B, That]): That
For such simple functionality, this is a daunting signature and one which I find myself struggling to understand. Not that I think Scala was ever likely to be the next Java (or /C/C++/C#) - I don't believe its creators were aiming it at that market - but I think it is/was certainly feasible for Scala to become the next Ruby or Python (i.e. to gain a significant commercial user-base)
Is this going to put people off coming to Scala?
Is this going to give Scala a bad name in the commercial world as an academic plaything that only dedicated PhD students can understand? Are CTOs and heads of software going to get scared off?
Was the library re-design a sensible idea?
If you're using Scala commercially, are you worried about this? Are you planning to adopt 2.8 immediately or wait to see what happens?
Steve Yegge once attacked Scala (mistakenly in my opinion) for what he saw as its overcomplicated type-system. I worry that someone is going to have a field day spreading FUD with this API (similarly to how Josh Bloch scared the JCP out of adding closures to Java).
Note - I should be clear that, whilst I believe that Joshua Bloch was influential in the rejection of the BGGA closures proposal, I don't ascribe this to anything other than his honestly-held beliefs that the proposal represented a mistake.
Despite whatever my wife and coworkers keep telling me, I don't think I'm an idiot: I have a good degree in mathematics from the University of Oxford, and I've been programming commercially for almost 12 years and in Scala for about a year (also commercially).
Note the inflammatory subject title is a quotation made about the manifesto of a UK political party in the early 1980s. This question is subjective but it is a genuine question, I've made it CW and I'd like some opinions on the matter.
I hope it's not a "suicide note", but I can see your point. You hit on what is at the same time both a strength and a problem of Scala: its extensibility. This lets us implement most major functionality in libraries. In some other languages, sequences with something like map or collect would be built in, and nobody has to see all the hoops the compiler has to go through to make them work smoothly. In Scala, it's all in a library, and therefore out in the open.
In fact the functionality of map that's supported by its complicated type is pretty advanced. Consider this:
scala> import collection.immutable.BitSet
import collection.immutable.BitSet
scala> val bits = BitSet(1, 2, 3)
bits: scala.collection.immutable.BitSet = BitSet(1, 2, 3)
scala> val shifted = bits map { _ + 1 }
shifted: scala.collection.immutable.BitSet = BitSet(2, 3, 4)
scala> val displayed = bits map { _.toString + "!" }
displayed: scala.collection.immutable.Set[java.lang.String] = Set(1!, 2!, 3!)
See how you always get the best possible type? If you map Ints to Ints you get again a BitSet, but if you map Ints to Strings, you get a general Set. Both the static type and the runtime representation of map's result depend on the result type of the function that's passed to it. And this works even if the set is empty, so the function is never applied! As far as I know there is no other collection framework with an equivalent functionality. Yet from a user perspective this is how things are supposed to work.
The problem we have is that all the clever technology that makes this happen leaks into the type signatures which become large and scary. But maybe a user should not be shown by default the full type signature of map? How about if she looked up map in BitSet she got:
map(f: Int => Int): BitSet (click here for more general type)
The docs would not lie in that case, because from a user perspective indeed map has the type (Int => Int) => BitSet. But map also has a more general type which can be inspected by clicking on another link.
We have not yet implemented functionality like this in our tools. But I believe we need to do this, to avoid scaring people off and to give more useful info. With tools like that, hopefully smart frameworks and libraries will not become suicide notes.
I do not have a PhD, nor any other kind of degree neither in CS nor math nor indeed any other field. I have no prior experience with Scala nor any other similar language. I have no experience with even remotely comparable type systems. In fact, the only language that I have more than just a superficial knowledge of which even has a type system is Pascal, not exactly known for its sophisticated type system. (Although it does have range types, which AFAIK pretty much no other language has, but that isn't really relevant here.) The other three languages I know are BASIC, Smalltalk and Ruby, none of which even have a type system.
And yet, I have no trouble at all understanding the signature of the map function you posted. It looks to me like pretty much the same signature that map has in every other language I have ever seen. The difference is that this version is more generic. It looks more like a C++ STL thing than, say, Haskell. In particular, it abstracts away from the concrete collection type by only requiring that the argument is IterableLike, and also abstracts away from the concrete return type by only requiring that an implicit conversion function exists which can build something out of that collection of result values. Yes, that is quite complex, but it really is only an expression of the general paradigm of generic programming: do not assume anything that you don't actually have to.
In this case, map does not actually need the collection to be a list, or being ordered or being sortable or anything like that. The only thing that map cares about is that it can get access to all elements of the collection, one after the other, but in no particular order. And it does not need to know what the resulting collection is, it only needs to know how to build it. So, that is what its type signature requires.
So, instead of
map :: (a → b) → [a] → [b]
which is the traditional type signature for map, it is generalized to not require a concrete List but rather just an IterableLike data structure
map :: (IterableLike i, IterableLike j) ⇒ (a → b) → i → j
which is then further generalized by only requiring that a function exists that can convert the result to whatever data structure the user wants:
map :: IterableLike i ⇒ (a → b) → i → ([b] → c) → c
I admit that the syntax is a bit clunkier, but the semantics are the same. Basically, it starts from
def map[B](f: (A) ⇒ B): List[B]
which is the traditional signature for map. (Note how due to the object-oriented nature of Scala, the input list parameter vanishes, because it is now the implicit receiver parameter that every method in a single-dispatch OO system has.) Then it generalized from a concrete List to a more general IterableLike
def map[B](f: (A) ⇒ B): IterableLike[B]
Now, it replaces the IterableLike result collection with a function that produces, well, really just about anything.
def map[B, That](f: A ⇒ B)(implicit bf: CanBuildFrom[Repr, B, That]): That
Which I really believe is not that hard to understand. There's really only a couple of intellectual tools you need:
You need to know (roughly) what map is. If you gave only the type signature without the name of the method, I admit, it would be a lot harder to figure out what is going on. But since you already know what map is supposed to do, and you know what its type signature is supposed to be, you can quickly scan the signature and focus on the anomalies, like "why does this map take two functions as arguments, not one?"
You need to be able to actually read the type signature. But even if you have never seen Scala before, this should be quite easy, since it really is just a mixture of type syntaxes you already know from other languages: VB.NET uses square brackets for parametric polymorphism, and using an arrow to denote the return type and a colon to separate name and type, is actually the norm.
You need to know roughly what generic programming is about. (Which isn't that hard to figure out, since it's basically all spelled out in the name: it's literally just programming in a generic fashion).
None of these three should give any professional or even hobbyist programmer a serious headache. map has been a standard function in pretty much every language designed in the last 50 years, the fact that different languages have different syntax should be obvious to anyone who has designed a website with HTML and CSS and you can't subscribe to an even remotely programming related mailinglist without some annoying C++ fanboy from the church of St. Stepanov explaining the virtues of generic programming.
Yes, Scala is complex. Yes, Scala has one of the most sophisticated type systems known to man, rivaling and even surpassing languages like Haskell, Miranda, Clean or Cyclone. But if complexity were an argument against success of a programming language, C++ would have died long ago and we would all be writing Scheme. There are lots of reasons why Scala will very likely not be successful, but the fact that programmers can't be bothered to turn on their brains before sitting down in front of the keyboard is probably not going to be the main one.
Same thing in C++:
template <template <class, class> class C,
class T,
class A,
class T_return,
class T_arg
>
C<T_return, typename A::rebind<T_return>::other>
map(C<T, A> &c,T_return(*func)(T_arg) )
{
C<T_return, typename A::rebind<T_return>::other> res;
for ( C<T,A>::iterator it=c.begin() ; it != c.end(); it++ ){
res.push_back(func(*it));
}
return res;
}
Well, I can understand your pain, but, quite frankly, people like you and I -- or pretty much any regular Stack Overflow user -- are not the rule.
What I mean by that is that... most programmers won't care about that type signature, because they'll never see them! They don't read documentation.
As long as they saw some example of how the code works, and the code doesn't fail them in producing the result they expect, they won't ever look at the documentation. When that fails, they'll look at the documentation and expect to see usage examples at the top.
With these things in mind, I think that:
Anyone (as in, most people) who ever comes across that type signature will mock Scala to no end if they are pre-disposed against it, and will consider it a symbol of Scala's power if they like Scala.
If the documentation isn't enhanced to provide usage examples and explain clearly what a method is for and how to use it, it can detract from Scala adoption a bit.
In the long run, it won't matter. That Scala can do stuff like that will make libraries written for Scala much more powerful and safer to use. These libraries and frameworks will attract programmers atracted to powerful tools.
Programmers who like simplicity and directness will continue to use PHP, or similar languages.
Alas, Java programmers are much into power tools, so, in answering that, I have just revised my expectation of mainstream Scala adoption. I have no doubt at all that Scala will become a mainstream language. Not C-mainstream, but perhaps Perl-mainstream or PHP-mainstream.
Speaking of Java, did you ever replace the class loader? Have you ever looked into what that involves? Java can be scary, if you look at the places framework writers do. It's just that most people don't. The same thing applies to Scala, IMHO, but early adopters have a tendency to look under each rock they encounter, to see if there's something hiding there.
Is this going to put people off coming to Scala?
Yes, but it will also prevent people from being put off. I've considered the lack of collections that use higher-kinded types to be a major weakness ever since Scala gained support for higher-kinded types. It make the API docs more complicated, but it really makes usage more natural.
Is this going to give scala a bad name in the commercial world as an academic plaything that only dedicated PhD students can understand? Are CTOs and heads of software going to get scared off?
Some probably will. I don't think Scala is accessible to many "professional" developers, partially due to the complexity of Scala and partly due to the unwillingness of many developers to learn. The CTOs who employ such developers will rightly be scared off.
Was the library re-design a sensible idea?
Absolutely. It makes collections fit much better with the rest of the language and the type system, even if it still has some rough edges.
If you're using scala commercially, are you worried about this? Are you planning to adopt 2.8 immediately or wait to see what happens?
I'm not using it commercially. I'll probably wait until at least a couple revs into the 2.8.x series before even trying to introduce it so that the bugs can be flushed out. I'll also wait to see how much success EPFL has in improving its development a release processes. What I'm seeing looks hopeful, but I work for a conservative company.
One the more general topic of "is Scala too complicated for mainstream developers?"...
Most developers, mainstream or otherwise, are maintaining or extending existing systems. This means that most of what they use is dictated by decisions made long ago. There are still plenty of people writing COBOL.
Tomorrow's mainstream developer will work maintaining and extending the applications that are being built today. Many of these applications are not being built by mainstream developers. Tomorrow's mainstream developers will use the language that is being used by today's most successful developers of new applications.
One way that the Scala community can help ease the fear of programmers new to Scala is to focus on practice and to teach by example--a lot of examples that start small and grow gradually larger. Here are a few sites that take this approach:
Daily Scala
Learning Scala in small bites
Simply Scala
After spending some time on these sites, one quickly realizes that Scala and its libraries, though perhaps difficult to design and implement, are not so difficult to use, especially in the common cases.
I have an undergraduate degree from a cheap "mass market" US university, so I'd say I fall into the middle of the user intelligence (or at least education) scale :) I've been dabbling with Scala for just a few months and have worked on two or three non-trivial apps.
Especially now that IntelliJ has released their fine IDE with what IMHO is currently the best Scala plugin, Scala development is relatively painless:
I find I can use Scala as a "Java without semicolons," i.e. I write similar-looking code to what I'd do in Java, and benefit a little from syntactic brevity such as that gained by type inference. Exception handling, when I do it at all, is more convenient. Class definition is much less verbose without the getter/setter boilerplate.
Once in a while I manage to write a single line to accomplish the equivalent of multiple lines of Java. Where applicable, chains of functional methods like map, fold, collect, filter etc. are fun to compose and elegant to behold.
Only rarely do I find myself benefitting from Scala's more high-powered features: Closures and partial (or curried) functions, pattern matching... that kinda thing.
As a newbie, I continue to struggle with the terse and idiomatic syntax. Method calls without parameters don't need parentheses except where they do; cases in the match statement need a fat arrow ( => ), but there are also places where you need a thin arrow ( -> ). Many methods have short but rather cryptic names like /: or \: - I can get my stuff done if I flip enough manual pages, but some of my code ends up looking like Perl or line noise. Ironically, one of the most popular bits of syntactic shorthand is missing in action: I keep getting bitten by the fact that Int doesn't define a ++ method.
This is just my opinion: I feel like Scala has the power of C++ combined with the complexity and readability of C++. The syntactic complexity of the language also makes the API documentation hard to read.
Scala is very well thought out and brilliant in many respects. I suspect many an academic would love to program in it. However, it's also full of cleverness and gotchas, it has a much higher learning curve than Java and is harder to read. If I scan the fora and see how many developers are still struggling with the finer points of Java, I cannot conceive of Scala ever becoming a mainstream language. No company will be able to justify sending its developers on a 3 week Scala course when formerly they only needed a 1 week Java course.
I think primary problem with that method is that the (implicit bf : CanBuildFrom[Repr, B, That]) goes without any explanation. Even though I know what implicit arguments are there's nothing indicating how this affects the call. Chasing through the scaladoc only leaves me more confused (few of the classes related to CanBuildFrom even have documentation).
I think a simple "there must be an implicit object in scope for bf that provides a builder for objects of type B into the return type That" would help somewhat, but it's kind of a heady concept when all you really want to do is map A's to B's. In fact, I'm not sure that's right, because I don't know what the type Repr means, and the documentation for Traversable certainly gives no clue at all.
So, I'm left with two options, neither of them pleasant:
Assume it will just work how the old map works and how map works in most other languages
Dig into the source code some more
I get that Scala is essentially exposing the guts of how these things work and that ultimately this is provide a way to do what oxbow_lakes is describing. But it's a distraction in the signature.
I'm a Scala beginner and I honestly don't see a problem with that type signature. The parameter is the function to map and the implicit parameter the builder to return the correct collection. Clear and readable.
The whole thing's quite elegant, actually. The builder type parameters let the compiler choose the correct return type while the implicit parameter mechanism hides this extra parameter from the class user. I tried this:
Map(1 -> "a", 2 -> "b").map((t) => (t._2) -> (t._1)) // returns Map("a" -> 1, "b" -> 2)
Map(1 -> "a", 2 -> "b").map((t) => t._2) // returns List("a", "b")
That's polymorphism done right.
Now, granted, it's not a mainstream paradigm and it will scare away many. But, it will also attract many who value its expressiveness and elegance.
Unfortunately the signature for map that you gave is an incorrect one for map and there is indeed legitimate criticism.
The first criticism is that by subverting the signature for map, we have something that is more general. It is a common error to believe that this is a virtue by default. It isn't. The map function is very well defined as a covariant functor Fx -> (x -> y) -> Fy with adherence to the two laws of composition and identity. Anything else attributed to "map" is a travesty.
The given signature is something else, but it is not map. What I suspect it is trying to be is a specialised and slightly altered version of the "traverse" signature from the paper, The Essence of the Iterator Pattern. Here is its signature:
traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)
I shall convert it to Scala:
def traverse[A, B](f: A => F[B], a: T[A])(implicit t: Traversable[T], ap: Applicative[F]): F[T[B]
Of course it fails -- it is not general enough! Also, it is slightly different (note that you can get map by running traverse through the Identity functor). However, I suspect that if the library writers were more aware of library generalisations that are well documented (Applicative Programming with Effects precedes the aforementioned), then we wouldn't see this error.
Second, the map function is a special-case in Scala because of its use in for-comprehensions. This unfortunately means that a library designer who is better equipped cannot ignore this error without also sacrificing the syntactic sugar of comprehensions. In other words, if the Scala library designers were to destroy a method, then this is easily ignored, but please not map!
I hope someone speaks up about it, because as it is, it will become harder to workaround the errors that Scala insists on making, apparently for reasons that I have strong objections to. That is, the solution to "the irresponsible objections from the average programmer (i.e. too hard!)" is not "appease them to make it easier for them" but instead, provide pointers and assistance to become better programmers. Myself and Scala's objectives are in contention on this issue, but back to your point.
You were probably making your point, predicting specific responses from "the average programmer." That is, the people who will claim "but it is too complicated!" or some such. These are the Yegges or Blochs that you refer to. My response to these people of the anti-intellectualism/pragmatism movement is quite harsh and I'm already anticipating a barrage of responses, so I will omit it.
I truly hope the Scala libraries improve, or at least, the errors can be safely tucked away in a corner. Java is a language where "trying to do anything useful" is so incredibly costly, that it is often not worth it because the overwhelming amount of errors simply cannot be avoided. I implore Scala to not go down the same path.
I totally agree with both the question and Martin's answer :). Even in Java, reading javadoc with generics is much harder than it should be due to the extra noise. This is compounded in Scala where implicit parameters are used as in the questions's example code (while the implicits do very useful collection-morphing stuff).
I don't think its a problem with the language per se - I think its more a tooling issue. And while I agree with what Jörg W Mittag says, I think looking at scaladoc (or the documentation of a type in your IDE) - it should require as little brain power as possible to grok what a method is, what it takes and returns. There shouldn't be a need to hack up a bit of algebra on a bit of paper to get it :)
For sure IDEs need a nice way to show all the methods for any variable/expression/type (which as with Martin's example can have all the generics inlined so its nice and easy to grok). I like Martin's idea of hiding the implicits by default too.
To take the example in scaladoc...
def map[B, That](f: A => B)(implicit bf: CanBuildFrom[Repr, B, That]): That
When looking at this in scaladoc I'd like the generic block [B, That] to be hidden by default as well as the implicit parameter (maybe they show if you hover a little icon with the mouse) - as its extra stuff to grok reading it which usually isn't that relevant. e.g. imagine if this looked like...
def map(f: A => B): That
nice and clear and obvious what it does. You might wonder what 'That' is, if you mouse over or click it it could expand the [B, That] text highlighting the 'That' for example.
Maybe a little icon could be used for the [] declaration and (implicit...) block so its clear there are little bits of the statement collapsed? Its hard to use a token for it, but I'll use a . for now...
def map.(f: A => B).: That
So by default the 'noise' of the type system is hidden from the main 80% of what folks need to look at - the method name, its parameter types and its return type in nice simple concise way - with little expandable links to the detail if you really care that much.
Mostly folks are reading scaladoc to find out what methods they can call on a type and what parameters they can pass. We're kinda overloading users with way too much detail right how IMHO.
Here's another example...
def orElse[A1 <: A, B1 >: B](that: PartialFunction[A1, B1]): PartialFunction[A1, B1]
Now if we hid the generics declaration its easier to read
def orElse(that: PartialFunction[A1, B1]): PartialFunction[A1, B1]
Then if folks hover over, say, A1 we could show the declaration of A1 being A1 <: A. Covariant and contravariant types in generics add lots of noise too which can be rendered in a much easier to grok way to users I think.
I don't know how to break it to you, but I have a PhD from Cambridge, and I'm using 2.8 just fine.
More seriously, I hardly spent any time with 2.7 (it won't inter-op with a Java library I am using) and started using Scala just over a month ago. I have some experience with Haskell (not much), but just ignored the stuff you're worried about and looked for methods that matched my experience with Java (which I use for a living).
So: I am a "new user" and I wasn't put off - the fact that it works like Java gave me enough confidence to ignore the bits I didn't understand.
(However, the reason I was looking at Scala was partly to see whether to push it at work, and I am not going to do so yet. Making the documentation less intimidating would certainly help, but what surprised me is how much it is still changing and being developed (to be fair what surprised me most was how awesome it is, but the changes came a close second). So I guess what I am saying is that I'd rather prefer the limited resources were put into getting it into a final state - I don't think they were expecting to be this popular this soon.)
Don't know Scala at all, however a few weeks ago I could not read Clojure. Now I can read most of it, but can not write anything yet beyond the most simplistic examples. I suspect Scala is no different. You need a good book or course depending on how you learn. Just reading the map declaration above, I got maybe 1/3 of it.
I believe the bigger problems are not the syntax of these languages, but adopting and internalizing the paradigms that make them usable in everyday production code. For me Java was not a huge leap from C++, which was not a huge leap from C, which was not a leap at all from Pascal, nor Basic etc... But coding in a functional language like Clojure is a huge leap (for me anyway). I guess in Scala you can code in Java style or Scala style. But in Clojure you will create quite the mess trying to keep your imperative habits from Java.
Scala has a lot of crazy features (particularly where implicit parameters are concerned) that look very complicated and academic, but are designed to make things easy to use. The most useful ones get syntactic sugar (like [A <% B] which means that an object of type A has an implicit conversion to an object of type B) and a well-documented explanation of what they do. But most of the time, as a client of these libraries you can ignore the implicit parameters and trust them to do the right thing.
Is this going to put people off coming to Scala?
I don't think it is the main factor that will affect how popular Scala will become, because Scala has a lot of power and its syntax is not as foreign to a Java/C++/PHP programmer as Haskell, OCaml, SML, Lisps, etc..
But I do think Scala's popularity will plateau at less than where Java is today, because I also think the next mainstream language must be much simplified, and the only way I see to get there is pure immutability, i.e. declarative like HTML, but Turing complete. However, I am biased because I am developing such a language, but I only did so after ruling out over a several month study that Scala could not suffice for what I needed.
Is this going to give Scala a bad name in the commercial world as an academic plaything that only dedicated PhD students can understand? Are CTOs and heads of software going to get scared off?
I don't think Scala's reputation will suffer from the Haskell complex. But I think that some will put off learning it, because for most programmers, I don't yet see a use case that forces them to use Scala, and they will procrastinate learning about it. Perhaps the highly-scalable server side is the most compelling use case.
And, for the mainstream market, first learning Scala is not a "breath of fresh air", where one is writing programs immediately, such as first using HTML or Python. Scala tends to grow on you, after one learns all the details that one stumbles on from the start. However, maybe if I had read Programming in Scala from the start, my experience and opinion of the learning curve would have been different.
Was the library re-design a sensible idea?
Definitely.
If you're using Scala commercially, are you worried about this? Are you planning to adopt 2.8 immediately or wait to see what happens?
I am using Scala as the initial platform of my new language. I probably wouldn't be building code on Scala's collection library if I was using Scala commercially otherwise. I would create my own category theory based library, since the one time I looked, I found Scalaz's type signatures even more verbose and unwieldy than Scala's collection library. Part of that problem perhaps is Scala's way of implementing type classes, and that is a minor reason I am creating my own language.
I decided to write this answer, because I wanted to force myself to research and compare Scala's collection class design to the one I am doing for my language. Might as well share my thought process.
The 2.8 Scala collections use of a builder abstraction is a sound design principle. I want to explore two design tradeoffs below.
WRITE-ONLY CODE: After writing this section, I read Carl Smotricz's comment which agrees with what I expect to be the tradeoff. James Strachan and davetron5000's comments concur that the meaning of That (it is not even That[B]) and the mechanism of the implicit is not easy to grasp intuitively. See my use of monoid in issue #2 below, which I think is much more explicit. Derek Mahar's comment is about writing Scala, but what about reading the Scala of others that is not "in the common cases".
One criticism I have read about Scala, is that it is easier to write it, than read the code that others have written. And I find this to be occasionally true for various reasons (e.g. many ways to write a function, automatic closures, Unit for DSLs, etc), but I am undecided if this is major factor. Here the use of implicit function parameters has pluses and minuses. On the plus side, it reduces verbosity and automates selection of the builder object. In Odersky's example the conversion from a BitSet, i.e. Set[Int], to a Set[String] is implicit. The unfamiliar reader of the code might not readily know what the type of collection is, unless they can reason well about the all the potential invisible implicit builder candidates which might exist in the current package scope. Of course, the experienced programmer and the writer of the code will know that BitSet is limited to Int, thus a map to String has to convert to a different collection type. But which collection type? It isn't specified explicitly.
AD-HOC COLLECTION DESIGN: After writing this section, I read Tony Morris's comment and realized I am making nearly the same point. Perhaps my more verbose exposition will make the point more clear.
In "Fighting Bit Rot with Types" Odersky & Moors, two use cases are presented. They are the restriction of BitSet to Int elements, and Map to pair tuple elements, and are provided as the reason that the general element mapping function, A => B, must be able to build alternative destination collection types. However, afaik this is flawed from a category theory perspective. To be consistent in category theory and thus avoid corner cases, these collection types are functors, in which each morphism, A => B, must map between objects in the same functor category, List[A] => List[B], BitSet[A] => BitSet[B]. For example, an Option is a functor that can be viewed as a collection of sets of one Some( object ) and the None. There is no general map from Option's None, or List's Nil, to other functors which don't have an "empty" state.
There is a tradeoff design choice made here. In the design for collections library of my new language, I chose to make everything a functor, which means if I implement a BitSet, it needs to support all element types, by using a non-bit field internal representation when presented with a non-integer type parameter, and that functionality is already in the Set which it inherits from in Scala. And Map in my design needs to map only its values, and it can provide a separate non-functor method for mapping its (key,value) pair tuples. One advantage is that each functor is then usually also an applicative and perhaps a monad too. Thus all functions between element types, e.g. A => B => C => D => ..., are automatically lifted to the functions between lifted applicative types, e.g. List[A] => List[B] => List[C] => List[D] => .... For mapping from a functor to another collection class, I offer a map overload which takes a monoid, e.g. Nil, None, 0, "", Array(), etc.. So the builder abstraction function is the append method of a monoid and is supplied explicitly as a necessary input parameter, thus with no invisible implicit conversions. (Tangent: this input parameter also enables appending to non-empty monoids, which Scala's map design can't do.) Such conversions are a map and a fold in the same iteration pass. Also I provide a traversable, in the category sense, "Applicative programming with effects" McBride & Patterson, which also enables map + fold in a single iteration pass from any traversable to any applicative, where most every collection class is both. Also the state monad is an applicative and thus is a fully generalized builder abstraction from any traversable.
So afaics the Scala collections is "ad-hoc" in the sense that it is not grounded in category theory, and category theory is the essense of higher-level denotational semantics. Although Scala's implicit builders are at first appearance "more generalized" than a functor model + monoid builder + traversable -> applicative, they are afaik not proven to be consistent with any category, and thus we don't know what rules they follow in the most general sense and what the corner cases will be given they may not obey any category model. It is simply not true that adding more variables makes something more general, and this was one of huge benefits of category theory is it provides rules by which to maintain generality while lifting to higher-level semantics. A collection is a category.
I read somewhere, I think it was Odersky, as another justification for the library design, is that programming in a pure functional style has the cost of limited recursion and speed where tail recursion isn't used. I haven't found it difficult to employ tail recursion in every case that I have encountered so far.
Additionally I am carrying in my mind an incomplete idea that some of Scala's tradeoffs are due to trying to be both an mutable and immutable language, unlike for example Haskell or the language I am developing. This concurs with Tony Morris's comment about for comprehensions. In my language, there are no loops and no mutable constructs. My language will sit on top of Scala (for now) and owes much to it, and this wouldn't be possible if Scala didn't have the general type system and mutability. That might not be true though, because I think Odersky & Moors ("Fighting Bit Rot with Types") are incorrect to state that Scala is the only OOP language with higher-kinds, because I verified (myself and via Bob Harper) that Standard ML has them. Also appears SML's type system may be equivalently flexible (since 1980s), which may not be readily appreciated because the syntax is not so much similar to Java (and C++/PHP) as Scala. In any case, this isn't a criticism of Scala, but rather an attempt to present an incomplete analysis of tradeoffs, which is I hope germane to the question. Scala and SML don't suffer from Haskell's inability to do diamond multiple inheritance, which is critical and I understand is why so many functions in the Haskell Prelude are repeated for different types.
It seems necessary to state ones degree here: B.A. in Political Science and B.ed in Computer Science.
To the point:
Is this going to put people off coming to Scala?
Scala is difficult, because its underlying programming paradigm is difficult. Functional programming scares a lot of people. It is possible to build closures in PHP but people rarely do. So no, not this signature but all the rest will put people off, if they do not have the specific education to make them value the power of the underlying paradigm.
If this education is available, everyone can do it. Last year I build a chess computer with a bunch of school kids in SCALA! They had their problems but they did fine in the end.
If you're using Scala commercially, are you worried about this? Are you planning to adopt 2.8 immediately or wait to see what happens?
I would not be worried.
I have a maths degree from Oxford too! It took me a while to 'get' the new collections stuff. But I like it a lot now that I do. In fact, the typing of 'map' was one of the first big things that bugged me in 2.7 (perhaps since the first thing I did was subclass one of the collection classes).
Reading Martin's paper on the new 2.8 collections really helped explain the use of implicits, but yes the documentation itself definitely needs to do a better job of explaining the role of different kind of implicits within method signatures of core APIs.
My main concern is more this: when is 2.8 going to be released? When will the bug reports stop coming in for it? have scala team bitten off more than they can chew with 2.8 / tried to change too much at once?
I'd really like to see 2.8 stabilised for release as a priority before adding anything else new at all, and wonder (while watching from the sidelines) if some improvements could be made to the way the development roadmap for the scala compiler is managed.
What about error messages in use site?
And what about when comes the use case one needs to integrate existing types with a custom one that fits a DSL. One have to be well educated on matters of association, precedence, implicit conversions, implicit parameters, higher kinds, and maybe existential types.
It's very good to know that mostly it's simple but it's not necessarily enough. At least there must be one guy who knows this stuff if widespread library is to be designed.