I never understood why recursion causes anyone any problems, because recursion is the absence of a special case limitation.
If I tell you that a function may call any function, then you already know everything you need to know for recursion. If we didn't have recursion, only then would I need to qualify what I just told you with the restriction that a function can only be active once.
When I show students recursion I can't understand their confusion. I think to myself 'but I already showed you functions can call any other function, why do you see this case differently?'
(Obviously I try to be more patient, understanding and anticipatory in person.)
I'll share why I struggled with recursion (as best as I remember):
Most programming I learned was imperative. As I wrote the code, I imagined the execution in my head. This led to a problem where when I was halfway through a function, and it referred to itself, my brain would segfault. How could something I was not yet done writing refer to itself? I hadn't finished yet, so my brain could not comprehend what such a reference would mean.
It was also difficult because I wanted to think of functions as nice neat pieces of code that would take some data, do it's thing, and return a value. I could mentally inline a function call without much effort.
But when recursion is introduced, the floor drops out of my mental inlining. Suddenly my mental effort for such things becomes huge. For me anyway. My brain doesn't like to float around in abstraction land for long, it needs to periodically be anchored in the concrete. Otherwise I quickly lose my sense of direction and orientation... I lose my context.
Declarative languages actually make these easier, for me, because I'm not mentally executing a recipe as I write. I am giving a piece-wise description of what something is. So there is no mental tracing.
I expect the a-ha moment for recursion is different for everyone. But just showing recursion in many different forms would probably help. For example, show fib sequence generation where instead of the function calling itself, each function calls a uniquely named function... such that you concretely demonstrate building the first 5 or so numbers in the sequence...
Then show the similarity of the functions, show what the computer has to keep track of with the nested function calls, and step by step work your way to straight recursion.
Show it in BASIC with GOTO statements.
Finding as many different ways to concretely demonstrate an abstract concept will help reach more people.
As someone who enjoys teaching programming[1], your comment was my favorite of the day[2]. My learning experience was similar to yours, starting with imperative languages, so you got me to think about how I think about recursion today, given our shared baggage:
1. I do still inline recursive functions, but I've learned to selectively inline just the base case when I first implement recursion. Paradoxically, experience with lisp helped me with recursion in C, particularly Common Lisp's trace facility which taught me to visualize stacks of multiple function calls (whether recursive or not) rather than a single one at a time.
2. I've learned to think declaratively even when I program in C. When writing a C function I might start out with a crisp definition in my head ("this function saves the reverse of the list seen so far in its second argument") so that I can rely on that definition even when the implementation isn't yet complete.
That should happen naturally, if you implement a compiler to native code. A "call" instruction is just a "goto/branch/jump" with some extra stack fiddling.
Also, I don't think pure functions are so easy mentally either. Try to understand "call with current continuation". ;)
I did, and I think my comment still makes sense in that context.
If I give you a list of requirements for a programming language that I want you to implement and it includes 'a function must be able to call any function' then you have recursion. You don't need additional separate requirement for 'and that function may be itself', as long as you've fully implemented the first requirement. In fact you'd need an extra requirement to prevent recursion, not to allow it.
That's what I mean by you shouldn't need to consider recursion as a special case.
The fact is, its easier to implement a language without recursion. See early programming languages that didn't. In such a case, you can simply treat the local variables as if they are global variables in the implementation. You've got to do something more complicated if you are going to handle local variables in a recursive case.
The fact it is not an additional requirement to allow recursion is irrealevent, what matter is that its extra complexity to handle that case correctly.
That's a great point. I think there is fundamental flaw in my virtual machine because recursion does not work, but calling other functions from within a function do work.
It may interest you to know that some older programming languages didn't originally support recursion, although they did support function calls (early FORTRAN being one example). The return address for a function call was typically stored in a fixed location associated with the target. So if you called that function once, you wouldn't be able to call it a second time until the first call had returned, otherwise you'd end up overwriting the first return address.
Not that I think that is the OP's problem - just a bit of interesting history. Support for recursion may seem obvious in hindsight, but there was a time where that wasn't the case.
Yes, but I generate the arguments from converting the AST into the internal byte code, so arguments are just a LOAD_NAME, etc. There seems to be a problem when the arguments are coming from the currently executing function's stack (instead of the AST) As I restore the context from current executing function execute data to the previous execute data, and pop the stack once, and push it into the old context's stack as the return value.
Also, just to be clear, I understand how recursion works as a user of a programming language, though implementing it is different than using it.
Recursion call should be exactly the same as an ordinate function call. The following is an example of asm code gen for function definition and recursive function call. Code gen to VM code should be similar. Hope it help.
The generated code would be (all numbers are 10-based instead of hex for simplicity):
fn_foo:
push ebp ; save the caller's old frame pointer
mov ebp, esp ; the new frame pointer to current stack ptr
sub esp, 20 ; make new space in stack for params and locals
; EBP points to the base of the current frame
; the frame has 20 bytes in the stack
; var1 at [ebp-4]
; var2 at [ebp-8]
; var3 at [ebp-12]
; param1 at [ebp-16]
; param2 at [ebp-20]
...
mov [ebp-4], 1 ; assign 0x1 to var1
mov [ebp-8], 2 ; assign 0x2 to var2
add [ebp-8], [ebp-16] ; add param1 to var2
...
push [ebp-4] ; push var1 for the function call
push [ebp-8] ; push var2 for the function call
call fn_foo ; call function foo at address fn_foo
; the current EIP is saved in stack
; the return value will be in EAX
mov [ebp-12], eax ; save function return value to var3
...
mov eax, [ebp-12] ; set function return value from var3
mov esp, ebp ; pop frame
pop ebp ; restore old EBP to previous frame
ret ; return to the caller by popping the
; caller's address from stack into EIP.
; Execution will continue at the restored EIP address.
I definitely struggled to find a satisfying approach to recursion in my own current language project. What I'm doing right now is passing the closure value of the callee as a hidden first argument to every call. Nonrecursive functions just ignore that argument but recursive functions can always call themselves via that hidden argument.
It doesn't allow you to support syntactic mutual recursion but it's easy to do and can be implemented without data modification at any level.
Do you not have any kind of registry of functions in your language where you can look up a function from a name and then call it? Then you don't need to pass in the current function to itself as it can look itself up in the registry, like any other function could (again, no special cases needed).
There shouldn't be any need for recursive calls to be a special kind of call. They caller shouldn't need to know that it is calling itself (again, lack of special casing).
This is how recursion works in languages like Java, Python, Ruby, C.
In my language, there is no special global scope for variables; every program is basically one giant (extended and sugared) lambda calculus expression.
I do use lambda-lifting so that in the C code I generate, there is a C function in the global C namespace that is called to execute an object-language function but object-language functions also have closure environments so any kind of self-reference needs to include both the global C function and the closure environment for that particular closure.
Note that my language does support modularity (breaking programs into multiple files, basically). However, the mechanism for referring to "packages" (stuff in other files) uses a separate name system.
I agree that languages that bind all functions in a global scope can easily use that global scope to resolve recursive references. It's also easier when your language supports variable assignment and destructive updates of data structures. But my language doesn't support those things either. :)
Addendum: By the way, you mentioned Java, Python, and Ruby, which are all object-oriented. Of course, the recursion among methods in those languages arises in a way that's very similar to passing a callee as a hidden argument. In OO languages, the hidden argument is "self" or "this"!
What about using scope environments and variable binding? For lambda calculus, variable binding (of the single variable x) in an environment (the current application of lambda) is a fundamental part of it anyway.
A scope environment gives you a place to name "things". "Things" can be functions. It's just a name-value map. You create a local scope environment for every function invocation. You can bind things (value or functions) to names in the local environment. Then you can refer to "things" by their names, like calling a function using its name.
Parent scope environments can be nested in the local scope when the function is called. A search on a name not found on the current scope can be delegated to the parent scope, so that functions defined and named in outer scope can be referenced in inner scope.
Recursive call is not a problem for named function since you can look up the function by name. It becomes a problem for anonymous function (lambda) since it can't be looked by name. For that you can introduce a special name like "_lamb" for it. Upon entry of a function, you bind the current function to the name in the current environment. A reference to it would call the current function again. e.g. _lamb(). You can even have a special name "_parent" to bind to the parent environment. In that case you can call the anonymous parent function. E.g. _parent._lamb()
Function calling and recursive function have nothing to do with OO or Java/Python/Ruby. It has everything to do with name, binding, scope, and environment.
> Of course, the recursion among methods in those languages arises in a way that's very similar to passing a callee as a hidden argument. In OO languages, the hidden argument is "self" or "this"!
Self or this allows you to refer to the same object. You don't need to refer to the same object to wind up calling the same method. You could have two different objects that just have the same method. Maybe they share a class, or a mixin, or whatever. So I'm not sure self is relevant here.
Yes, I think I see your point. If I may put it in my own words, I think you are talking about "dynamic recursive activation" throughout this thread.
I don't mean to disagree with the point you are making! It's a valid point.
However, I would like to emphasize that some languages have syntactic properties that complicate things a bit and I feel that a comment about how things "should" be really ought to be qualified by something like, "in a mainstream Java-like language".
Consider the simply-typed lambda calculus, or Martin-Löf type theory. These languages don't allow general recursion but it's not because they are always poorly implemented!
My language has first class functions, as names are tied to values, and a value can be a function. With the opcode CALL_FUNCTION (in my VM), it does a searching of the hash table for the value.
For a program without recursive calls the students can get away with believing that local variables are statically allocated, but for a program with recursive calls the students must understand that local variables are allocated on the stack; that what appears (lexically) to be one variable in the source may be many variables at runtime!
I think the issue is it forces people to think about preconditions, postconditions and invariants in a very different way if they've come from imperative programming.
If I tell you that a function may call any function, then you already know everything you need to know for recursion. If we didn't have recursion, only then would I need to qualify what I just told you with the restriction that a function can only be active once.
When I show students recursion I can't understand their confusion. I think to myself 'but I already showed you functions can call any other function, why do you see this case differently?'
(Obviously I try to be more patient, understanding and anticipatory in person.)