The article Type classes: confluence, coherence and global uniqueness makes the following points -
[Coherence] states that every different valid typing derivation of a program leads to a resulting program that has the same dynamic semantics.
[..]
So, what is it that people often refer to when they compare Scala type classes to Haskell type classes? I am going to refer to this as global uniqueness of instances, defining to say: in a fully compiled program, for any type, there is at most one instance resolution for a given type class. Languages with local type class instances such as Scala generally do not have this property, but in Haskell, we find this property is a very convenient one when building abstractions like sets.
If you look at this paper on Modular implicits, it states -
[..] Scala’s coherence can rely on the weaker property of non-ambiguity
instead of canonicity. This means that you can define multiple implicit objects of type Showable[Int]
in your program without causing an error. Instead, Scala issues an error if the resolution of an implicit
parameter is ambiguous. For example, if two implicit objects of type Showable[Int] are in scope when
show is applied to an Int then the compiler will report an ambiguity error.
Both of these give the impression that Scala does ensure coherence but does not ensure global uniqueness of instances.
However, if you look at Martin Odersky's comments (1, 2), it seems that the term coherence is being used as shorthand for "uniqueness of instances", which would explain the terms "local coherence" and "global coherence".
Is this just an unfortunate case of the same term being used to mean two different things? They're certainly distinct -- OCaml's modular implicits ensure coherence (as per the first definition) but not global uniqueness of instances.
Does Scala guarantee coherence (as per the first definition) in the presence of implicits?
I think they mean the same thing in this case. Coherence is only put into question when you have more than one way of deriving the instance/implicit value; "every different valid typing derivation" is only interesting when there is more than once typing derivation. Both Scala and Haskell disallow at compile time instances which might lead to ambiguous derivations.
Scala
Odersky's comment says it for Scala: there is only ever one local way of resolving instances. In other words, there is only one valid local typing derivation. Trivially enough, it is coherent with itself. It isn't clear to me that it even makes sense to to talk about global coherence in Scala but, if it does, Scala definitely doesn't have it:
object Object1 {
implicit val i: Int = 9
println(implicitly[Int]) // valid typing derivation of `Int` => printing 9
}
object Object2 {
implicit val i: Int = 10
println(implicitly[Int]) // valid typing derivation of `Int` => printing 10
}
Haskell
Since Haskell instances are global, there is no point in distinguishing local/global coherence.
Haskell disallows at compile time having two instances where either instance head overlaps with the other. This turns finding type derivations into an unambiguous non-backtracking search problem. The non-ambiguity is again what gets us coherence.
Interestingly enough, GHC allows you to loosen this requirement with -XIncoherentInstances allowing you to write locally non-confluent instances, potentially breaking global coherence too.
Related
I'm new in Scala and don't understand some base things.
Scala does not contains primitives. Hence int, short and other "simple" number types are objects. So, according to JMM, they are not located at stack and subject to cleaning by GB. Cleaning by GB may be too expensive for some cases.
So I don't clearly understand, why Scala is considered faster than Java (in which primitives located in stack).
Scala does not contains primitives. Hence int, short and other "simple" number types are objects.
That is correct.
So, according to JMM,
The Java Memory Model is for Java. It is completely irrelevant to Scala.
they are not located at stack and subject to cleaning by GB. Cleaning by GB may be too expensive for some cases.
There is no such thing as a "stack" in Scala. The Scala Language Specification only mentions the term "stack" in very few places, and none of them have anything to do with Ints:
In section 1 Lexical Syntax, subsection 1.6 XML mode, it is said that because XML literals and Scala code can be arbitrarily nested, the parser has to use a stack data structure to keep track of the context.
In section 7 Implicits, subsection 7.2 Implicit parameters, it is said that to prevent an infinite recursion when searching for implicit, the compiler keeps a stack of "open types", which are types that it is currently searching an implicit for.
In section 6 Expressions, subsection 6.6 Function Applications, there is the following statement, specifying Proper Direct Tail Recursion:
A function application usually allocates a new frame on the program's run-time stack. However, if a local method or a final method calls itself as its last action, the call is executed using the stack-frame of the caller.
In section 6 Expressions, subsection 6.20 Return Expressions, there is the following statement about one possible implementation strategy for non-local returns from nested functions:
Returning from the method from within a nested function may be implemented by throwing and catching a scala.runtime.NonLocalReturnControl. Any exception catches between the point of return and the enclosing methods might see and catch that exception. A key comparison makes sure that this exception is only caught by the method instance which is terminated by the return.
If the return expression is itself part of an anonymous function, it is possible that the enclosing method m has already returned before the return expression is executed. In that case, the thrown scala.runtime.NonLocalReturnControl will not be caught, and will propagate up the call stack.
Of these 4 instances, the first 2 clearly do not refer to the concept of a call stack but rather to the generic computer science data structure. The 4th one is only an example of a possible implementation strategy ("Returning from the method from within a nested function may be implemented by […]"). Only the 3rd one is actually relevant, as it indeed talks about a call stack. However, it does not say anything about allocating Ints, and it explicitly leaves the door open to alternative implementations as well, by stating that "usually" function application leads to allocation of a stack frame, but doesn't have to.
So I don't clearly understand, why Scala is considered faster than Java (in which primitives located in stack).
Actually, there is nothing in the Java Language Specification either that says that primitives are located on the stack. In fact, the Java Language Specification does not mandate the existence of a stack at all. It would be perfectly legal to implement Java without a stack.
There are exactly zero occurrences of the term "stack" in the JLS. There are a couple of mentions of the term "heap", but only in the compound term "heap pollution", which is simply a word describing a certain flaw in the type system, but does not necessarily require a heap, and does not mandate a heap.
And none of these mentions of "heap pollution" have anything to do with primitives.
Note that, when I say that the Scala Language Specification says nothing about stacks or heaps or how Ints are allocated, that is actually really important. Because the SLS doesn't say anything, implementors are allowed to do whatever they want, including making Ints primitive and allocating them on the stack.
And that is exactly what most Scala implementations do. The (now-defunct) Scala.NET implemented scala.Int as a .NET System.Int32. Scala-native implements scala.Int as a C int32_t. Scala.js implements scala.Int as an ECMAScript number. And Scala-JVM implements scala.Int as a JVM int.
If you check out the source code of scala.Int in the Scala-JVM repository (src/library/scala/Int.scala), you will find that it is actually empty! More precisely, it only contains documentation and declarations, but no definitions or implementations. Also, the class is marked final (meaning it can't be inherited from) and abstract (meaning it must be inherited from in order to provide overrides for the missing implementations), which is a contradiction.
How does this work? Well, the compiler knows what an Int is and how it works, and it simply generates the correct code for dealing with a JVM int. So, when it sees a call to scala.Int.+, it knows that instead it must generate an iadd bytecode instruction. Likewise, Scala-native will just generate the native integer addition instructions, and so on.
In other words, Ints are semantically defined as objects, but they are actually pragmatically implemented as primitives.
This is a general rule of how language specifications work: typically, they only describe what the result is that the programmer sees, but they leave it open to the implementor how to actually achieve that result. So, the SLS specifies that an Int must look as if it actually were an object, but there is nothing that says it actually has to be one.
They are handled the same way that Java handles those types, they're only boxed when strictly necessary. The details on how and when they are boxed may differ, but the compiler uses a primitive representation if it can do so. Here's what the docs say (this is just for Int, but it applies to other "primitive" types too):
Int, a 32-bit signed integer (equivalent to Java's int primitive type) is a subtype of scala.AnyVal. Instances of Int are not represented by an object in the underlying runtime system.
There is an implicit conversion from scala.Int => scala.runtime.RichInt which provides useful non-primitive operations.
https://www.scala-lang.org/api/2.13.6/scala/Int.html
The main difference, really, is that there aren't two separate types, like in Java, to represent the boxed and unboxed representations — both get the same Int type, whereas Java has int and Integer.
Here’s my thoughts on the question. Can anyone confirm, deny, or elaborate?
I wrote:
Scala doesn’t unify covariant List[A] with a GLB ⊤ assigned to List[Int], bcz afaics in subtyping “biunification” the direction of assignment matters. Thus None must have type Option[⊥] (i.e. Option[Nothing]), ditto Nil type List[Nothing] which can’t accept assignment from an Option[Int] or List[Int] respectively. So the value restriction problem originates from directionless unification and global biunification was thought to be undecidable until the recent research linked above.
You may wish to view the context of the above comment.
ML’s value restriction will disallow parametric polymorphism in (formerly thought to be rare but maybe more prevalent) cases where it would otherwise be sound (i.e. type safe) to do so such as especially for partial application of curried functions (which is important in functional programming), because the alternative typing solutions create a stratification between functional and imperative programming as well as break encapsulation of modular abstract types. Haskell has an analogous dual monomorphisation restriction. OCaml has a relaxation of the restriction in some cases. I elaborated about some of these details.
EDIT: my original intuition as expressed in the above quote (that the value restriction may be obviated by subtyping) is incorrect. The answers IMO elucidate the issue(s) well and I’m unable to decide which in the set containing Alexey’s, Andreas’, or mine, should be the selected best answer. IMO they’re all worthy.
As I explained before, the need for the value restriction -- or something similar -- arises when you combine parametric polymorphism with mutable references (or certain other effects). That is completely independent from whether the language has type inference or not or whether the language also allows subtyping or not. A canonical counter example like
let r : ∀A.Ref(List(A)) = ref [] in
r := ["boo"];
head(!r) + 1
is not affected by the ability to elide the type annotation nor by the ability to add a bound to the quantified type.
Consequently, when you add references to F<: then you need to impose a value restriction to not lose soundness. Similarly, MLsub cannot get rid of the value restriction. Scala enforces a value restriction through its syntax already, since there is no way to even write the definition of a value that would have polymorphic type.
It's much simpler than that. In Scala values can't have polymorphic types, only methods can. E.g. if you write
val id = x => x
its type isn't [A] A => A.
And if you take a polymorphic method e.g.
def id[A](x: A): A = x
and try to assign it to a value
val id1 = id
again the compiler will try (and in this case fail) to infer a specific A instead of creating a polymorphic value.
So the issue doesn't arise.
EDIT:
If you try to reproduce the http://mlton.org/ValueRestriction#_alternatives_to_the_value_restriction example in Scala, the problem you run into isn't the lack of let: val corresponds to it perfectly well. But you'd need something like
val f[A]: A => A = {
var r: Option[A] = None
{ x => ... }
}
which is illegal. If you write def f[A]: A => A = ... it's legal but creates a new r on each call. In ML terms it would be like
val f: unit -> ('a -> 'a) =
fn () =>
let
val r: 'a option ref = ref NONE
in
fn x =>
let
val y = !r
val () = r := SOME x
in
case y of
NONE => x
| SOME y => y
end
end
val _ = f () 13
val _ = f () "foo"
which is allowed by the value restriction.
That is, Scala's rules are equivalent to only allowing lambdas as polymorphic values in ML instead of everything value restriction allows.
EDIT: this answer was incorrect before. I have completely rewritten the explanation below to gather my new understanding from the comments under the answers by Andreas and Alexey.
The edit history and the history of archives of this page at archive.is provides a recording of my prior misunderstanding and discussion. Another reason I chose to edit rather than delete and write a new answer, is to retain the comments on this answer. IMO, this answer is still needed because although Alexey answers the thread title correctly and most succinctly—also Andreas’ elaboration was the most helpful for me to gain understanding—yet I think the layman reader may require a different, more holistic (yet hopefully still generative essence) explanation in order to quickly gain some depth of understanding of the issue. Also I think the other answers obscure how convoluted a holistic explanation is, and I want naive readers to have the option to taste it. The prior elucidations I’ve found don’t state all the details in English language and instead (as mathematicians tend to do for efficiency) rely on the reader to discern the details from the nuances of the symbolic programming language examples and prerequisite domain knowledge (e.g. background facts about programming language design).
The value restriction arises where we have mutation of referenced1 type parametrised objects2. The type unsafety that would result without the value restriction is demonstrated in the following MLton code example:
val r: 'a option ref = ref NONE
val r1: string option ref = r
val r2: int option ref = r
val () = r1 := SOME "foo"
val v: int = valOf (!r2)
The NONE value (which is akin to null) contained in the object referenced by r can be assigned to a reference with any concrete type for the type parameter 'a because r has a polymorphic type a'. That would allow type unsafety because as shown in the example above, the same object referenced by r which has been assigned to both string option ref and int option ref can be written (i.e. mutated) with a string value via the r1 reference and then read as an int value via the r2 reference. The value restriction generates a compiler error for the above example.
A typing complication arises to prevent3 the (re-)quantification (i.e. binding or determination) of the type parameter (aka type variable) of a said reference (and the object it points to) to a type which differs when reusing an instance of said reference that was previously quantified with a different type.
Such (arguably bewildering and convoluted) cases arise for example where successive function applications (aka calls) reuse the same instance of such a reference. IOW, cases where the type parameters (pertaining to the object) for a reference are (re-)quantified each time the function is applied, yet the same instance of the reference (and the object it points to) being reused for each subsequent application (and quantification) of the function.
Tangentially, the occurrence of these is sometimes non-intuitive due to lack of explicit universal quantifier ∀ (since the implicit rank-1 prenex lexical scope quantification can be dislodged from lexical evaluation order by constructions such as let or coroutines) and the arguably greater irregularity (as compared to Scala) of when unsafe cases may arise in ML’s value restriction:
Andreas wrote:
Unfortunately, ML does not usually make the quantifiers explicit in its syntax, only in its typing rules.
Reusing a referenced object is for example desired for let expressions which analogous to math notation, should only create and evaluate the instantiation of the substitutions once even though they may be lexically substituted more than once within the in clause. So for example, if the function application is evaluated as (regardless of whether also lexically or not) within the in clause whilst the type parameters of substitutions are re-quantified for each application (because the instantiation of the substitutions are only lexically within the function application), then type safety can be lost if the applications aren’t all forced to quantify the offending type parameters only once (i.e. disallow the offending type parameter to be polymorphic).
The value restriction is ML’s compromise to prevent all unsafe cases while also preventing some (formerly thought to be rare) safe cases, so as to simplify the type system. The value restriction is considered a better compromise, because the early (antiquated?) experience with more complicated typing approaches that didn’t restrict any or as many safe cases, caused a bifurcation between imperative and pure functional (aka applicative) programming and leaked some of the encapsulation of abstract types in ML functor modules. I cited some sources and elaborated here. Tangentially though, I’m pondering whether the early argument against bifurcation really stands up against the fact that value restriction isn’t required at all for call-by-name (e.g. Haskell-esque lazy evaluation when also memoized by need) because conceptually partial applications don’t form closures on already evaluated state; and call-by-name is required for modular compositional reasoning and when combined with purity then modular (category theory and equational reasoning) control and composition of effects. The monomorphisation restriction argument against call-by-name is really about forcing type annotations, yet being explicit when optimal memoization (aka sharing) is required is arguably less onerous given said annotation is needed for modularity and readability any way. Call-by-value is a fine tooth comb level of control, so where we need that low-level control then perhaps we should accept the value restriction, because the rare cases that more complex typing would allow would be less useful in the imperative versus applicative setting. However, I don’t know if the two can be stratified/segregated in the same programming language in smooth/elegant manner. Algebraic effects can be implemented in a CBV language such as ML and they may obviate the value restriction. IOW, if the value restriction is impinging on your code, possibly it’s because your programming language and libraries lack a suitable metamodel for handling effects.
Scala makes a syntactical restriction against all such references, which is a compromise that restricts for example the same and even more cases (that would be safe if not restricted) than ML’s value restriction, but is more regular in the sense that we’ll not be scratching our head about an error message pertaining to the value restriction. In Scala, we’re never allowed to create such a reference. Thus in Scala, we can only express cases where a new instance of a reference is created when it’s type parameters are quantified. Note OCaml relaxes the value restriction in some cases.
Note afaik both Scala and ML don’t enable declaring that a reference is immutable1, although the object they point to can be declared immutable with val. Note there’s no need for the restriction for references that can’t be mutated.
The reason that mutability of the reference type1 is required in order to make the complicated typing cases arise, is because if we instantiate the reference (e.g. in for example the substitutions clause of let) with a non-parametrised object (i.e. not None or Nil4 but instead for example a Option[String] or List[Int]), then the reference won’t have a polymorphic type (pertaining to the object it points to) and thus the re-quantification issue never arises. So the problematic cases are due to instantiation with a polymorphic object then subsequently assigning a newly quantified object (i.e. mutating the reference type) in a re-quantified context followed by dereferencing (reading) from the (object pointed to by) reference in a subsequent re-quantified context. As aforementioned, when the re-quantified type parameters conflict, the typing complication arises and unsafe cases must be prevented/restricted.
Phew! If you understood that without reviewing linked examples, I’m impressed.
1 IMO to instead employ the phrase “mutable references” instead of “mutability of the referenced object” and “mutability of the reference type” would be more potentially confusing, because our intention is to mutate the object’s value (and its type) which is referenced by the pointer— not referring to mutability of the pointer of what the reference points to. Some programming languages don’t even explicitly distinguish when they’re disallowing in the case of primitive types a choice of mutating the reference or the object they point to.
2 Wherein an object may even be a function, in a programming language that allows first-class functions.
3 To prevent a segmentation fault at runtime due to accessing (read or write of) the referenced object with a presumption about its statically (i.e. at compile-time) determined type which is not the type that the object actually has.
4 Which are NONE and [] respectively in ML.
I am reading Foundations of path dependent types. On the first page, on the right column it is written:
Our motivation is twofold. First, we believe objects with type members
are not fully understood. It is not clear what causes the complexity,
which pieces of complexity are essential to the concept or accidental
to a language implementation or calculus that tries to achieve
something else. Second, we believe objects with type members are
really useful. They can encode a variety of other, usually separate
type system features. Most importantly, they unify concepts from
object and module systems, by adding a notion of nominality to otherwise structural systems.
Could someone clarify/explain what does "object vs module" system mean?
Or in general, what does
"they (objects with type members) unify concepts from
object and module systems, by adding a notion of nominality to otherwise structural systems."
mean ?
What concepts? From where ?
Nominality in the object names / values ?
Structure in the types ? Or the other way around?
Where do type members here belong to ? To module system ? Object system ? How? Why?
EDIT:
How does this unification relate to path dependent types ? It seems to me that they allow this unification to happen (objects with type members). Is that so ?
If yes, how ?
Could you give a simple example what that means ? (I.e. path dependent types allowing the unification of module and object systems vs. why would the unification not be possible happen if we would not have path dependent types?)
EDIT 2:
From the paper:
To make any use of type members, programmers need a way to refer to
them. This means that types must be able to refer to objects, i.e.
contain terms that serve as static approximation of a set of dynamic
objects. In other words, some level of dependent types is required;
the usual notion is that of path-dependent types.
So my understanding so far (with the help of Jesper's answer) :
This paragraph above partially answers some of the questions above. The main seems to be to have objects with type members and to have that path dependent types are needed because objects are dynamic/runtime dependent but types are static (defined at compile time) so just by having objects that lead to type members would not work because then those type members would not be defined clearly at compile time.
Path dependent types help here by pinning down the path leading to a type member at compile time (by requiring that the objects are already known/defined at compile time), so even if the path goes via objects (that can change during compile time) but if those objects are fixed already at compile time then their type members can have a clear meaning at compile time too.
I'm not sure I fully understand what your question is, but I'll take a stab at it. :) I think the authors mainly are referring to ML style modules where a signature corresponds to a Scala trait and a structure corresponds to a Scala object. Scala unifies the concepts of record values, objects and modules which in most other languages (like ML, Rust etc.) are separate concepts. The main benefit is that in Scala modules/objects can be passed around as normal function arguments (while in ML you have to use special functors for this).
In ML a module is checked for compatibility with a signature (trait in Scala) based on its structure (similar to structural typing in Scala), but in Scala the module must implement the trait by name (nominal typing). So even if two modules/objects have the same structure in Scala they might not be compatible with each other depending on their super type hierarchy.
A really powerful feature regarding type members in Scala is that you can use a trait even if you don't know the exact type of its type members as long as you do it in a type safe way (I think this is also possible in ML modules), for example:
trait A {
type X
def getX: X
def setX(x: X): Unit
}
def foo(a: A) = a.setX(a.getX)
In foo the Scala compiler doesn't know the exact type of a.X but a value of the type can still be used in a way the compiler knows is safe. This is not possible in Rust for example.
The next version of the Scala compiler, Dotty, will be based on the theory described in the paper you reference. This unification of modules and objects combined with subtyping, traits and type members is one reason that Scala is unique and very powerful.
EDIT: To expand a bit why path dependent types increases the flexibility of Scala's module/object system, let's expand the example above with:
def bar(a: A, b: A) = a.setX(b.getX)
This will result in a compilation error:
error: type mismatch;
found : b.T
required: a.T
def foo(a: A, b: A) = a.setX(b.getX)
^
and correctly so because a.T and b.T could resolve to different types. You can fix it by using a path dependent type:
def bar(a: A)(b: A { type X = a.X }) = a.setX(b.getX)
Or add a type parameter:
def bar[T](a: A { type X = T }, b: A { type X = T }) = a.setX(b.getX)
So, path dependent types eliminates some need of type parameters, and also allows us to express existential types efficiently (corresponding to A[_] or A[T] forSome { type T } if A had a type parameter instead of a type member).
Structural types are one of those "wow, cool!" features of Scala. However, For every example I can think of where they might help, implicit conversions and dynamic mixin composition often seem like better matches. What are some common uses for them and/or advice on when they are appropriate?
Aside from the rare case of classes which provide the same method but aren't related nor do implement a common interface (for example, the close() method -- Source, for one, does not extend Closeable), I find no use for structural types with their present restriction. If they were more flexible, however, I could well write something like this:
def add[T: { def +(x: T): T }](a: T, b: T) = a + b
which would neatly handle numeric types. Every time I think structural types might help me with something, I hit that particular wall.
EDIT
However unuseful I find structural types myself, the compiler, however, uses it to handle anonymous classes. For example:
implicit def toTimes(count: Int) = new {
def times(block: => Unit) = 1 to count foreach { _ => block }
}
5 times { println("This uses structural types!") }
The object resulting from (the implicit) toTimes(5) is of type { def times(block: => Unit) }, ie, a structural type.
I don't know if Scala does that for every anonymous class -- perhaps it does. Alas, that is one reason why doing pimp my library that way is slow, as structural types use reflection to invoke the methods. Instead of an anonymous class, one should use a real class to avoid performance issues in pimp my library.
Structural types are very cool constructs in Scala. I've used them to represent multiple unrelated types that share an attribute upon which I want to perform a common operation without a new level of abstraction.
I have heard one argument against structural types from people who are strict about an application's architecture. They feel it is dangerous to apply a common operation across types without an associative trait or parent type, because you then leave the rule of what type the method should apply to open-ended. Daniel's close() example is spot on, but what if you have another type that requires different behavior? Someone who doesn't understand the architecture might use it and cause problems in the system.
I think structural types are one of these features that you don't need that often, but when you need it, it helps you a lot. One area where structural types really shine is "retrofitting", e.g. when you need to glue together several pieces of software you have no source code for and which were not intended for reuse. But if you find yourself using structural types a lot, you're probably doing it wrong.
[Edit]
Of course implicits are often the way to go, but there are cases when you can't: Imagine you have a mutable object you can modify with methods, but which hides important parts of it's state, a kind of "black box". Then you have to work somehow with this object.
Another use case for structural types is when code relies on naming conventions without a common interface, e.g. in machine generated code. In the JDK we can find such things as well, like the StringBuffer / StringBuilder pair (where the common interfaces Appendable and CharSequence are way to general).
Structural types gives some benefits of dynamic languages to a statically linked language, specifically loose coupling. If you want a method foo() to call instance methods of class Bar, you don't need an interface or base-class that is common to both foo() and Bar. You can define a structural type that foo() accepts and whose Bar has no clue of existence. As long as Bar contains methods that match the structural type signatures, foo() will be able to call.
It's great because you can put foo() and Bar on distinct, completely unrelated libraries, that is, with no common referenced contract. This reduces linkage requirements and thus further contributes for loose coupling.
In some situations, a structural type can be used as an alternative to the Adapter pattern, because it offers the following advantages:
Object identity is preserved (there is no separate object for the adapter instance, at least in the semantic level).
You don't need to instantiate an adapter - just pass a Bar instance to foo().
You don't need to implement wrapper methods - just declare the required signatures in the structural type.
The structural type doesn't need to know the actual instance class or interface, while the adapter must know Bar so it can call its methods. This way, a single structural type can be used for many actual types, whereas with adapter it's necessary to code multiple classes - one for each actual type.
The only drawback of structural types compared to adapters is that a structural type can't be used to translate method signatures. So, when signatures doesn't match, you must use adapters that will have some translation logic. I particularly don't like to code "intelligent" adapters because in many times they are more than just adapters and cause increased complexity. If a class client needs some additional method, I prefer to simply add such method, since it usually doesn't affect footprint.
I have read that Scala's type system is weakened by Java interoperability and therefore cannot perform some of the same powers as Haskell's type system. Is this true? Is the weakness because of type erasure, or am I wrong in every way? Is this difference the reason that Scala has no typeclasses?
The big difference is that Scala doesn't have Hindley-Milner global type inference and instead uses a form of local type inference, requiring you to specify types for method parameters and the return type for overloaded or recursive functions.
This isn't driven by type erasure or by other requirements of the JVM. All possible difficulties here can be overcome, and have been, just consider Jaskell - http://docs.codehaus.org/display/JASKELL/Home
H-M inference doesn't work in an object-oriented context. Specifically, when type-polymorphism is used (as opposed to the ad-hoc polymorphism of type classes). This is crucial for strong interop with other Java libraries, and (to a lesser extent) to get the best possible optimisation from the JVM.
It's not really valid to state that either Haskell or Scala has a stronger type system, just that they are different. Both languages are pushing the boundaries for type-based programming in different directions, and each language has unique strengths that are hard to duplicate in the other.
Scala's type system is different from Haskell's, although Scala's concepts are sometimes directly inspired by Haskell's strengths and its knowledgeable community of researchers and professionals.
Of course, running on a VM not primarily intended for functional programming in the first place creates some compatibility concerns with existing languages targeting this platform.
Because most of the reasoning about types happens at compile time, the limitations of Java (as a language and as a platform) at runtime are nothing to be concerned about (except Type Erasure, although exactly this bug seems to make the integration into the Java ecosystem more seamless).
As far as I know the only "compromise" on the type system level with Java is a special syntax to handle Raw Types. While Scala doesn't even allow Raw Types anymore, it accepts older Java class files with that bug.
Maybe you have seen code like List[_] (or the longer equivalent List[T] forSome { type T }). This is a compatibility feature with Java, but is treated as an existential type internally too and doesn't weaken the type system.
Scala's type system does support type classes, although in a more verbose way than Haskell. I suggest reading this paper, which might create a different impression on the relative strength of Scala's type system (the table on page 17 serves as a nice list of very powerful type system concepts).
Not necessarily related to the power of the type system is the approach Scala's and Haskell's compilers use to infer types, although it has some impact on the way people write code.
Having a powerful type inference algorithm can make it worthwhile to write more abstract code (you can decide yourself if that is a good thing in all cases).
In the end Scala's and Haskell's type system are driven by the desire to provide their users with the best tools to solve their problems, but have taken different paths to that goal.
another interesting point to consider is that Scala directly supports the classical OO-style. Which means, there are subtype relations (e.g. List is a subclass of Seq). And this makes type inference more tricky. Add to this the fact that you can mix in traits in Scala, which means that a given type can have multiple supertype relations (making it yet more tricky)
Scala does not have rank-n types, although it may be possible to work around this limitation in certain cases.
I only have little experenice with Haskell, but the most obvious thing I note that Scala type system different from Haskell is the type inference.
In Scala, there is no global type inference, you must explicit tell the type of function arguments.
For example, in Scala you need to write this:
def add (x: Int, y: Int) = x + y
instead of
add x y = x + y
This may cause problem when you need generic version of add function that work with all kinds of type has the "+" method. There is a workaround for this, but it will get more verbose.
But in real use, I found Scala's type system is powerful enough for daily usage, and I almost never use those workaround for generic, maybe this is because I come from Java world.
And the limitation of explicit declare the type of arguments is not necessary a bad thing, you need document it anyway.
Well are they Turing reducible?
See Oleg Kiselyov's page http://okmij.org/ftp/
...
One can implement the lambda calculus in Haskell's type system. If Scala can do that, then in a sense Haskell's type system and Scala's type system compute the same types. The questions are: How natural is one over the other? How elegant is one over the other?