Why does Idris require that functions appear in the order of their definitions and mutual recursion declared with mutual?
I would expect Idris to perform a first pass of dependency analysis between functions, and reorder them automatically. I have always believed that Haskell does this. Why is this not possible in Idris?
In the tutorial it says (emphasis mine):
In general, functions and data types must be defined before use, since dependent types allow functions
to appear as part of types, and their reduction behaviour to affect type checking. However, this
restriction can be relaxed by using a mutual block, which allows data types and functions to be
defined simultaneously.
(Agda has this restriction as well, but has now removed the mutual keyword in favour of giving types then definitions.)
To expand on this: when you have dependant types, the automatic dependency analysis à la Haskell would be difficult or impossible, because the dependancy order at the type level may very well be different than the dependancy order at the value level. Haskell doesn't have this problem because values can not appear in types, so it can just do the dependancy analysis and then typecheck in that order. This is what the Idris tutorial is getting at about the reduction behaviour of values being required for the type checking.
I do not know whether the problem is even solvable in general with dependant types (you lose Hindley-Milner, for one thing), but I bet it wouldn't be efficient even if it were.
Related
I have a very CPU intensive F# program that depends on persistent data-structures - about 40% of the total CPU time is spent in the Map module. So I thought I'd try out the PersistentHashMap in FSharpX collections. (BTW, this is already a big improvement over the previous version of F# in VS2013 where the same program spent 70% of its time in Map. I also notice that running programs with the debugger attached doesn't have the huge penalty it did before - good work guys...) There is also a hot-spot where I'm re-sorting all the time, where instead I should be adding to a Heap, so I thought I'd give that a go as well.
Two issue became immediately apparent:
(1) Swapping out one for the other from an interface perspective proved harder than it seems it should - I.e., making a shim that let me switch from a Map to a PersistentMap, preserving both the needed module-based let-bound functions and Types necessary to use the each map. I know that having full HM type-inference (and no type-classes) is orthogonal to LSP-style referential transparency for the most part - but maybe I was missing some way to do this better with a minimal amount of code.
(2) The biggest problem (which I'd like to focus on here) is the reliance of the F# functional data-structs on oo-style dispatched equality and comparison via the IComparison (when 't : comparison), etc., family of interfaces.
Even for OO programs ISTM that the idea of dispatching equality and comparison is a bad idea -- an object "knows" how to perform its own domain-specific tasks, but it doesn't "know" for the most part what notion of equality is going to be necessary at various points in the program for various purposes -- so equality/comparison should not be part of the object's interface, but when these concepts are needed, they should always be mentioned explicitly. For example, there should never be a .Sort(), only a .SortWith(...). One could argue that even something as basic as structural equality in F# could be explicit a.StructEq(b) or a ~= b - otherwise you always get object.Equals -- but even stipulating that doing things this way is the best for a multi-paradigm language that's a first-class .Net citizen, it seems like there should at least be the option of using passed-in comparison and equality functions, but this is not the case.
This means that: (a) type constraints are enforced even if you don't want them, causing ripples of broken inferred typing (and hundreds of wavy red lines with it being unclear where the actual "problem" is) and (b), that by implementing a notion of equality or comparison that makes one container type happy in one part of your program (and in my case I want to use the same container and item type with two different notions of ordering in two different places), it is likely to silently break (or cause inefficiency, if one subsumes the other) in other parts of the code that depended on the default/previous implementation.
The only way around this that I could think of is wrapping each item a adapter object using new...with object expression - but I really don't want to create so much garbage just to get the code to work.
So, ISTM that we could have a "pure" version of each persistent data struct that could be loaded if desired (even basics like List, etc.) that do not depend on dispatched equality/comparison/hashing and do not impose type constraints - all such needs should be via a passed in fn's at the time of the call. (Dispatched eq/cmp would be only for used for interop with BCL collections that don't accept delegates.) Then we could have a [EqCmpHashThrowNotImplemented] attribute, and I could be sure that there were no default operations happening at all, and I would feel better about the efficiency and predictability of my code. (And this also let's one change from a Record to a Class or visa-versa w/o worrying about any changes in behavior due to default implementations.) Again, this would be optional, but done by with a simple import. (Which does mean that each base core collection type would have to be broken out into its own module, which isn't really a bad idea anyway.)
If I've overlooked a better way to do things or there are some patterns people are using here, I'd be interested.
What are the practical differences between using modules with the use statement or isolated files with the include statement? I mean, if I have a subroutine that is used a lot throughout a program: when or why should I put it inside a module or just write it in a separate file and include it in every other part of the program where it needs to be used?
Also, would it be good practice to write all subroutines intended to go in a module in separate files and use include inside the module? Specially if the code in the subroutines is long, so as to keep the code better organized (that way all subroutines are packed in the mod, but if I have to edit one I don't need to go though a maze of code).
The conceptual differences between the two map through to very significant practical differences.
An INCLUDE line operates at the source level - it accomplishes simple ("dumb") text inclusion. In the absence of any special processor interpretation of the "filename" (no requirement for that actually to be a file) in the include line the complete source could quite easily be manually spliced together by the programmer and fed to the compiler with no difference what-so-ever in the semantics of the source. Included source has no real interpretation in isolation - its meaning is completely dependent on the context in which the include line that references the included source appears.
Modules operate at the much higher entity level of the program, i.e. at the level where the compiler is considering the things that the source actually describes. A module can be compiled in isolation of its downstream users and once it has been compiled the compiler knows exactly what things the module can provide to the program.
Typically what someone using include lines is hoping to do is what modules were actually designed to do.
Example issues:
Because entity declarations can be spread over multiple statements the entities described by included source might not be what you expect. Consider the following source to be included:
INTEGER :: i
In isolation it looks like this declares the name i as an integer scalar (or perhaps a function? Who knows!). Now consider the following scope that includes the above:
INCLUDE "source from above"
DIMENSION :: i(10,10)
i is now a rank two array! Perhaps you want to make it a POINTER? An ALLOCATABLE? A dummy argument? Perhaps that results in an error, or perhaps it is valid source! Throw implicit typing into the mix to really compound the potential fun.
An entity defined in a module is "completely" defined by the module. Attributes that are specific to the scope of use can be changed (VOLATILE, accessibility, etc), but the fundamental entity remains the same. Name clashes are explicitly called out and can be easily worked around with a rename clause on the USE statement.
Fortran has restrictions on statement ordering (specification statements must go before executable statements, etc.). Included source is also subject to those restrictions, again in the context of the point of inclusion, not the point of source definition.
Mix well with source ambiguity between statement function definitions (specification part) and assignment statements (executable part) for some completely obtuse error messages or, worse, silent acceptance by the compiler of erroneous code.
There are requirements on where the USE statement that references a module appears, but the source for the actual module program unit is completely independent of its point of use.
Fancy having some global state to be shared across related procedures and you want to use include? Let me introduce you to common blocks and the associated underlying concept of sequence association...
Sequence association is a unfortunate bleed-through of early underlying Fortran processor implementation that is an error prone, inflexible, anti-optimisation anachronism.
Module variables make common blocks and their associated evils completely unnecessary.
If you were using include lines, then note that you don't actually include the source of a commonly used procedure (the suggestion in your first paragraph is just going to result in a morass of syntax errors from the compiler). What you would typically do is include source that describes the interface of the procedure. For any non-trivial procedure the source that describes the interface is different from the complete source of the procedure - implying that you now need to maintain two source representations of the same thing. This is an error prone maintenance burden.
As mentioned - the compilers automatically gains knowledge of the interface of a module procedure (the compiler knowledge is "explicit" because it actually saw the procedure's code - hence the term "explicit interface"). No need for the programmer to do anything more.
A consequence of the above is that external subprograms should not be used at all unless there are very good reasons to the contrary (perhaps the existence of circular or excessively extensive dependencies) - the basic starting point should be to put everything in a module or main program.
Other posters have mentioned the source code organisation benefits of modules - including the ability to group related procedures and other "stuff" into the one package, with control over accessibility of internal implementation details.
I accept there is a valid use of INCLUDE lines as per the second paragraph of the question - where large modules become unwieldy in size. F2008 has addressed this with submodules, which also bring a number of other benefits. Once they become widely supported the include line work-around should be abandoned.
A second valid use is to overcome a lack of support by the language for generic programming techniques (what templates provide in C++) - i.e. where the types of objects involved in an operation may vary, but the token sequence that describes what to do on those objects is essentially the same. It might be another decade or so before the language sorts that out.
Placing procedures into modules and using those modules makes the interface of the procedure explicit. It allows a Fortran compiler to check for consistency between the actual arguments in a call and the dummy arguments of the procedure. This guards against a variety of programmer mistakes. An explicit interface is also necessary for certain "advanced" features of Fortran >=90; for example, optional or keyword arguments. Without the explicit interface, the compiler won't generate the correct call. Merely including a file doesn't provide these advantages.
M.S.B.'s answer is great and is probably the most important reason to prefer modules over include. I'd like to add a few more thoughts.
Using modules reduces your compiled binary size if that is something that is important to you. A module is compiled once, and when you use it you are symbolically loading that module to use the code. When you include a file, you are actually inserting the new code into your routine. If you use include a lot it can cause your binary to be large and also increase your compile time.
You can also use modules to fake OOP style coding in Fortran 90 through clever use of public and private functions and user defined types in a module. Even if you didn't want to do that, it provides a nice way to group functions that logically belong together.
I see that Sorm already supports org.joda.time.DateTime. Is there a possibility to add support for other types?
For example, my case class has a java.nio.charset.Charset or Locale field, which I would like to convert to a string. Suppose I have functions to accomplish the conversion from the custom type to/from a SQL type, how can I tell Sorm to use it?
SORM's support for a certain datatype is quite more complex than just ability to convert to and from an SQL type. Values of some types may span several columns (e.g. Tuple, Range), others may require intermediate tables (Seq, Set, Map) and all of them require an individual approach to translating query clauses. All that would have resulted in a quite complex ad-hoc type-mapping API if one was to be exposed.
But the thing is the above is really not the reason why such an API is not exposed and most probably not to ever be. You see, SORM's philosophy is essentially all about pure immutable data model and the cleanest way to design such one is to use standard Scala's immutable datatypes and case classes.
So the clean way for you to design your application with SORM would be to convert those stateful Java's classes to immutable values in your application. For instance you could implement a custom case class Charset (...) in your model, register it with SORM's Instance and have your conversion functions work between this type and the Java's one in your application. Besides that, you could implement this Charset as an Enumeration, which seems to be the most appropriate.
Concerning your argument about the Joda Time types support, it's there mostly because some data types were needed to represent the SQL's timestamps. See this logic as reverse to what you were thinking of.
I have seen many people in the Scala community advise on avoiding subtyping "like a plague". What are the various reasons against the use of subtyping? What are the alternatives?
Types determine the granularity of composition, i.e. of extensibility.
For example, an interface, e.g. Comparable, that combines (thus conflates) equality and relational operators. Thus it is impossible to compose on just one of the equality or relational interface.
In general, the substitution principle of inheritance is undecidable. Russell's paradox implies that any set that is extensible (i.e. does not enumerate the type of every possible member or subtype), can include itself, i.e. is a subtype of itself. But in order to identify (decide) what is a subtype and not itself, the invariants of itself must be completely enumerated, thus it is no longer extensible. This is the paradox that subtyped extensibility makes inheritance undecidable. This paradox must exist, else knowledge would be static and thus knowledge formation wouldn't exist.
Function composition is the surjective substitution of subtyping, because the input of a function can be substituted for its output, i.e. any where the output type is expected, the input type can be substituted, by wrapping it in the function call. But composition does not make the bijective contract of subtyping-- accessing the interface of the output of a function, does not access the input instance of the function.
Thus composition does not have to maintain the future (i.e. unbounded) invariants and thus can be both extensible and decidable. Subtyping can be MUCH more powerful where it is provably decidable, because it maintains this bijective contract, e.g. a function that sorts a immutable list of the supertype, can operate on the immutable list of the subtype.
So the conclusion is to enumerate all the invariants of each type (i.e. of its interfaces), make these types orthogonal (maximize granularity of composition), and then use function composition to accomplish extension where those invariants would not be orthogonal. Thus a subtype is appropriate only where it provably models the invariants of the supertype interface, and the additional interface(s) of the subtype are provably orthogonal to the invariants of the supertype interface. Thus the invariants of interfaces should be orthogonal.
Category theory provides rules for the model of the invariants of each subtype, i.e. of Functor, Applicative, and Monad, which preserve function composition on lifted types, i.e. see the aforementioned example of the power of subtyping for lists.
One reason is that equals() is very hard to get right when sub-typing is involved. See How to Write an Equality Method in Java. Specifically "Pitfall #4: Failing to define equals as an equivalence relation". In essence: to get equality right under sub-typing, you need a double dispatch.
I think the general context is for the lanaguage to be as "pure" as possible (ie using as much as possible pure functions), and comes from the comparison with Haskell.
From "Ruminations of a Programmer"
Scala, being a hybrid OO-FP language has to take care of issues like subtyping (which Haskell does not have).
As mentioned in this PSE answer:
no way to restrict a subtype so that it can't do more than the type it inherits from.
For example, if the base class is immutable and defines a pure method foo(...), derived classes must not be mutable or override foo() with a function that is not pure
But the actual recommendation would be to use the best solution adapted to the program you are currently developing.
Focusing on subtyping, ignoring the issues related to classes, inheritance, OOP, etc.. We have the idea subtyping represents a isa relation between types. For example, types A and B have different operations but if A isa B we then can use any of B's operations on an A.
OTOH, using another traditional relation, if C hasa B then we can reuse any of B's operations on a C. Usually languages let you write one with a nicer syntax, a.opOnB instead of a.super.opOnB as it would be in the case of composition, c.b.opOnB
The problem is that in many cases there's more than one way to relate two types. For example Real can be embedded in Complex assuming 0 on the imaginary part, but Complex can be embedded in Real by ignoring the imaginary part, so both can be seen as subtypes of the other and subtyping forces one relation to be viewed as preferred. Also, there are more possible relations (e.g. view Complex as a Real using theta component of polar representation).
In formal terminology we usually say morphism to such relations between types and there are special kinds of morphisms for relations with different properties (e.g. isomorphism, homomorphism).
In a language with subtyping usually there's much more sugar on isa relations and given many possible embeddings we tend to see unnecessary friction whenever we're using the unpreferred relation. If we bring inheritance, classes and OOP to the mix the problem becomes much more visible and messy.
My answer does not answer why it is avoided but tries to give another hint at why it can be avoided.
Using "type classes" you can add an abstraction over existing types/classes without modifying them. Inheritance is used to express that some classes are specializations of a more abstract class. But with type classes you can take any existing classes and express that they all share a common property, for example they are Comparable. And as long as you are not concerned with them being Comparable you don't even notice it. The classes don't inherit any methods from some abstract Comparable type as long as you don't use them. It's a bit like programming in dynamic languages.
Further reads:
http://blog.tmorris.net/the-power-of-type-classes-with-scala-implicit-defs/
http://debasishg.blogspot.com/2010/07/refactoring-into-scala-type-classes.html
I don't know Scala, but I think the mantra 'prefer composition over inheritance' applies for Scala exactly the way it does for every other OO programming language (and subtyping is often used with the same meaning as 'inheritance'). Here
Prefer composition over inheritance?
you will find some more information.
I think lots of Scala programmers are former Java programmers. They are used to think in term of Object Oriented subtyping and they should be able to easily find OO-like solution for most problems. But Functional Programing is a new paradigm to discover, so people ask for a different kind of solutions.
This is the best paper I have found on the subject. A motivating quote from the paper –
We argue that while some of the simpler aspects of object-oriented languages are
compatible with ML, adding a full-fledged class-based object system to ML leads to an excessively complex
type system and relatively little expressive gain
What is open recursion? Is it specific to OOP?
(I came across this term in this tweet by Daniel Spiewak.)
just copying http://www.comlab.ox.ac.uk/people/ralf.hinze/talks/Open.pdf:
"Open recursion Another handy feature offered by most languages with objects and classes is the ability for one method body to invoke another method of the same object via a special variable called self or, in some langauges, this. The special behavior of self is that it is late-bound, allowing a method defined in one class to invoke another method that is defined later, in some subclass of the first. "
This paper analyzes the possibility of adding OO to ML, with regards to expressivity and complexity. It has the following excerpt on objects, which seems to make this term relatively clear –
3.3. Objects
The simplest form of object is just a record of functions that share a common closure environment that
carries the object state (we can call these simple objects). The function members of the record may or may not
be defined as mutually recursive. However, if one wants to support inheritance with overriding, the structure
of objects becomes more complicated. To enable open recursion, the call-graph of the method functions
cannot be hard-wired, but needs to be implemented indirectly, via object self-reference. Object self-reference
can be achieved either by construction, making each object a recursive, self-referential value (the fixed-point
model), or dynamically, by passing the object as an extra argument on each method call (the self-application
or self-passing model).5 In either case, we will call these self-referential objects.
The name "open recursion" is a bit misleading at first, because it has nothing to do with the recursion that normally is used (a function calling itself); and to that extent, there is no closed recursion.
It basically means, that a thing is referring to itself. I can only guess, but I do think that the term "open" comes from open as in "open for extension".
In that sense an object is open to extension, but still referring to itself.
Perhaps a small example can shed some light on the concept.
Imaging you write a Python class like this one:
class SuperClass:
def method1(self):
self.method2()
def method2(self):
print(self.__class__.__name__)
If you ran this by
s = SuperClass()
s.method1()
It will print "SuperClass".
Now we create a subclass from SuperClass and override method2:
class SubClass(SuperClass):
def method2(self):
print(self.__class__.__name__)
and run it:
sub = SubClass()
sub.method1()
Now "SubClass" will be printed.
Still, we only call method1() as before. Inside method1() the method2() is called, but both are bound to the same reference (self in Python, this in Java). During sub-classing SuperClass method2() is changed, which means that an object of SubClass refers to a different version of this method.
That is open recursion.
In most cases, you override methods and call the overridden methods directly.
This scheme here is using an indirection over self-reference.
P.S.: I don't think this has been invented but discovered and then explained.
Open recursion allows to call another methods of object from within, through special variable like this or self.
In short, open recursion is about something actually not related to OOP, but more general.
The relation with OOP comes from the fact that many typical "OOP" PLs have such properties, but it is essentially not tied to any distinguishing features about OOP.
So there are different meanings, even in same "OOP" language. I will illustrate it later.
Etymology
As mentioned here, the terminology is likely coined in the famous TAPL by BCP, which illustrates the meaning by concrete OOP languages.
TAPL does not define "open recursion" formally. Instead, it points out the "special behavior of self (or this) is that it is late-bound, allowing a method defined in one class to invoke another method that is defined later, in some subclass of the first".
Nevertheless, neither of "open" and "recursion" comes from the OOP basis of a language. (Actually, it is also nothing to do with static types.) So the interpretation (or the informal definition, if any) in that source is overspecified in nature.
Ambiguity
The mentioning in TAPL clearly shows "recursion" is about "method invocation". However, it is not that simple in real languages, which usually do not have primitive semantic rules on the recursive invocation itself. Real languages (including the ones considered as OOP languages) usually specify the semantics of such invocation for the notation of the method calls. As syntactic devices, such calls are subject to the evaluation of some kind of expressions relying on the evaluations of its subexpressions. These evaluations imply the resolution of method name, under some independent rules. Specifically, such rules are about name resolution, i.e. to determine the denotation of a name (typically, a symbol, an identifier, or some "qualified" name expressions) in the subexpression. Name resolution often respects to scoping rules.
OTOH, the "late-bound" property emphasizes how to find the target implementation of the named method. This is a shortcut of evaluation of specific call expressions, but it is not general enough, because entities other than methods can also have such "special" behavior, even make such behavior not special at all.
A notable ambiguity comes from such insufficient treatment. That is, what does a "binding" mean. Traditionally, a binding can be modeled as a pair of a (scoped) name and its bound value, i.e. a variable binding. In the special treatment of "late-bound" ones, the set of allowed entities are smaller: methods instead of all named entities. Besides the considerably undermining the abstraction power of the language rules at meta level (in the language specification), it does not cease the necessity of traditional meaning of a binding (because there are other non-method entities), hence confusing. The use of a "late-bound" is at least an instance of bad naming. Instead of "binding", a more proper name would be "dispatching".
Worse, the use in TAPL directly mix the two meanings when dealing with "recusion". The "recursion" behavior is all about finding the entity denoted by some name, not just specific to method invocation (even in those OOP language).
The title of the chapter (Case Study: Imperative Objects) also suggests some inconsistency. Obviously, the so-called late binding of method invocation has nothing to do with imperative states, because the resolution of the dispatching does not require mutable metadata of invocation. (In some popular sense of implementation, the virtual method table need not to be modifiable.)
Openness
The use of "open" here looks like mimic to open (lambda) terms. An open term has some names not bound yet, so the reduction of such a term must do some name resolution (to compute the value of the expression), or the term is not normalized (never terminate in evaluation). There is no difference between "late" or "early" for the original calculi because they are pure, and they have the Church-Rosser property, so whether "late" or not does not alter the result (if it is normalized).
This is not the same in the language with potentially different paths of dispatching. Even that the implicit evaluation implied by the dispatching itself is pure, it is sensitive to the order among other evaluations with side effects which may have dependency on the concrete invocation target (for example, one overrider may mutate some global state while another can not). Of course in a strictly pure language there can be no observable differences even for any radically different invocation targets, a language rules all of them out is just useless.
Then there is another problem: why it is OOP-specific (as in TAPL)? Given that the openness is qualifying "binding" instead of "dispatching of method invocation", there are certainly other means to get the openness.
One notable instance is the evaluation of a procedure body in traditional Lisp dialects. There can be unbound symbols in the body and they are only resolved when the procedure being called (rather than being defined). Since Lisps are significant in PL history and the are close to lambda calculi, attributing "open" specifically to OOP languages (instead of Lisps) is more strange from the PL tradition. (This is also a case of "making them not special at all" mentioned above: every names in function bodies are just "open" by default.)
It is also arguable that the OOP style of self/this parameter is equivalent to the result of some closure conversion from the (implicit) environment in the procedure. It is questionable to treat such features primitive in the language semantics.
(It may be also worth noting, the special treatment of function calls from symbol resolution in other expressions is pioneered by Lisp-2 dialects, not any of typical OOP languages.)
More cases
As mentioned above, different meanings of "open recursion" may coexist in a same "OOP" language.
C++ is the first instance here, because there are sufficient reasons to make them coexist.
In C++, name resolution are all static, normatively name lookup. The rules of name lookup vary upon different scopes. Most of them are consistent with identifier lookup rules in C (except for the allowance of implicit declarations in C but not in C++): you must first declare the name, then the name can be lookup in the source code (lexically) later, otherwise the program is ill-formed (and it is required to issue an error in the implementation of the language). The strict requirement of such dependency of names are considerable "closed", because there are no later chance to recover from the error, so you cannot directly have names mutually referenced across different declarations.
To work around the limitation, there can be some additional declarations whose sole duty is to break the cyclic dependency. Such declarations are called "forward" declarations. Using of forward declarations still does not require "open" recursion, because every well-formed use must statically see the previous declaration of that name, so each name lookup does not require additional "late" binding.
However, C++ classes have special name lookup rules: some entities in the class scope can be referred in the context prior to their declaration. This makes mutual recursive use of name across different declarations possible without any additional "forward" declarations to break the cycle. This is exactly the "open recursion" in TAPL sense except that it is not about method invocation.
Moreover, C++ does have "open recursion" as per the descriptions in TAPL: this pointer and virtual functions. Rules to determine the target (overrider) of virtual functions are independent to the name lookup rules. A non-static member defined in a derived class generally just hide the entities with same name in the base classes. The dispatching rules kick in only on virtual function calls, after the name lookup (the order is guaranteed since evaulations of C++ function calls are strict, or applicative). It is also easy to introduce a base class name by using-declaration without worry about the type of the entity.
Such design can be seen as an instance of separate of concerns. The name lookup rules allows some generic static analysis in the language implementation without special treatment of function calls.
OTOH, Java have some more complex rules to mix up name lookup and other rules, including how to identify the overriders. Name shadowing in Java subclasses is specific to the kind of entities. It is more complicate to distinguish overriding with overloading/shadowing/hiding/obscuring for different kinds. There also cannot be techniques of C++'s using-declarations in the definition of subclasses. Such complexity does not make Java more or less "OOP" than C++, anyway.
Other consequences
Collapsing the bindings about name resolution and dispatching of method invocation leads to not only ambiguity, complexity and confusion, but also more difficulties on the meta level. Here meta means the fact that name binding can exposing properties not only available in the source language semantics, but also subject to the meta languages: either the formal semantic of the language or its implementation (say, the code to implement an interpreter or a compiler).
For example, as in traditional Lisps, binding-time can be distinguished from evaluation-time, because program properties revealed in binding-time (value binding in the immediate contexts) is more close to meta properties compared to evaluation-time properties (like the concrete value of arbitrary objects). An optimizing compiler can deploy the code generation immediately depending on the binding-time analysis either statically at the compile-time (when the body is to be evaluate more than once) or derferred at runtime (when the compilation is too expensive). There is no such option for languages blindly assume all resolutions in closed recursion faster than open ones (and even making them syntactically different at the very first). In such sense, OOP-specific open recursion is not just not handy as advertised in TAPL, but a premature optimization: giving up metacompilation too early, not in the language implementation, but in the language design.