05:10 <pyro-> now i am writing a cpsTransform function :D
05:10 <pyro-> it already works, but the current version introduces superflous continuations
05:10 <pyro-> so i am trying to fix :D
05:10 <ReinH> pyro-: Here's a CPS transform function: flip ($)
05:11 <pyro-> i will find out about flip
05:11 <ReinH>@src flip
05:11 <lambdabot> flip f x y = f y x
05:11 <ReinH> pyro-: the essence of CPS can be described as follows:
05:11 <ReinH> :t flip ($)
05:11 <lambdabot> b -> (b -> c) -> c
05:12 <ReinH> is the type of a function which takes a value and produces a suspended computation that takes a continuation and runs it against the value
05:12 <ReinH> for example:
05:12 <ReinH> > let c = flip ($) 3 in c show
05:12 <lambdabot> "3"
05:12 <ReinH> > let c = flip ($) 3 in c succ
05:12 <lambdabot> 4
05:13 <mm_freak_> direct style: f x = 3*x + 1
05:13 <mm_freak_> CPS: f x k = k (3*x + 1)
05:13 <mm_freak_> the rules are: take a continuation argument and be fully polymorphic on the result type
05:13 <mm_freak_> f :: Integer -> (Integer -> r) -> r
05:14 <mm_freak_> as long as your result type is fully polymorphic and doesn't unify with anything else in the type signature you can't do anything wrong other than to descend
05:38 <ReinH> So for example, if you have an incredibly simple expression language like data Expr a = Val a | Neg a | Add a a
05:38 <ReinH> a (more) initial encoding of an expression would be Add (Val 1) (Neg (Val 1))
05:38 <ReinH> A (more) final encoding might be (1 - 1) or even 0
05:39 <ReinH> The initial encoding generally is more flexible (you can still write a double-negation elimination rule, for instance
05:39 <ReinH> the final encoding is less flexible, but also does more work up-front
05:40 <ReinH> More initial encodings tend to force you to use quantification and type-level tricks, CPS and pre-applied functions tend to appear more in final encodings
05:40 <ReinH> An even smaller example:
05:40 <ReinH> \f z -> foldr f z [1,2,3] is a final encoding of the list [1,2,3]
05:41 <ReinH> pyro-: I'm not really a lisper, but I'm always looking for good reading material
05:41 <ReinH> for bonus points, the foldr encoding is *invertible* as well :)
05:44 <ReinH> pyro-: the relevance is that you seem to be using the cps transform in a more initial encoding than I usually see it
05:44 <ReinH> not that this is at all bad
05:46 <bitemyapp> ReinH: where does the invertibility in the final encoding come from?
05:46 <ReinH> foldr (:) [] :)
05:46 <ReinH> it's not generally so
05:46 <bitemyapp> > foldr (:) [] [1, 2, 3]
05:46 <lambdabot> [1,2,3]
05:47 <bitemyapp> I may not understand the proper meaning of invertibility in this case.
05:47 <bitemyapp> Do you mean invertibility from final to initial encoding?
05:47 <ReinH> Just that, yes
05:47 <bitemyapp> how would it get you back to final from initial?
05:47 <ReinH> I'm not sure if that's the correct term
05:47 <bitemyapp> I don't think it is, but the intent is understood and appreciated.
05:48 <bitemyapp> invertibility implies isomorphism, implies ability to go final -> initial -> final
05:48 <ReinH> well, there is an isomorphism
05:48 <bitemyapp> well, we've established final -> initial, where's initial -> final for this example?
05:49 <bitemyapp> I figured it was a morphism of some sort, but with only a final -> initial and not a way to get back, I wasn't sure which.
05:49 <ReinH> toInitial k = k (:) []; toFinal xs = \f z -> foldr f z xs
Jake It would be great if you give some examples when find your
notebook :) And link to the book about pure functional data structures
which you are talking about.
Also If some "haskell.org" maintainers are here I'd like to recommend
them to pay more attention to optimality/performance questions.
Because almost first question which is apeared in head of standart
C/C++ programmer is "Do I get same perfomance?" (even if he do not
need it).
Maybe some simple and cool PDF tutorial which describes why haskell
could be as fast as others will be great to have.
```
```
Richard A. O'Keefe:
> I am teaching myself haskell. The first impression is very good...
> Anyway I am trying to backport my algorithm written in C. The key to
> performance is to have ability to remove element from the end of a
> list in O(1).
You can't. Not in *any* programming language. That's because
lists are one of many possible implementations of the "sequence"
concept, and they are optimised to support some operations at
the expense of others. At the beginning level, you should think
of all Haskell data structures as immutable; fixed; frozen;
forever unchanged. You can't even remove an element from the
front of a Haskell list, at all. All you can do is to forget
about the original list and concentrate on its tail.
> But the original haskell functions last and init are O(n).
Haskell lists are singly linked lists. Even by going to
assembly code, you could not make these operations O(1)
without *using a different data structure*.
> My questions are:
> 1) Is last function is something like "black box" written in C++ which
> perform O(1)?
No.
> 2) Or will optimizer (llvm?) reduce init&last complexity to 1?
No.
> 3) Some people suggest to use sequences package, but still how do they
> implement O(1) init&last sequences equivalent in haskell?
Well, you could try reading Chris Okasaki's functional data
structures book.
There is a classic queue representation devised for Lisp
last century which represents
<a,b,c,d,e>
by ([a,b],[e,d,c])
so that you can push and pop at either end.
When the end you are working on runs out, you
reverse the other end, e.g.,
([],[e,d,c]) -> ([c,d,e],[]).
That can give you a queue with *amortised* constant time.
(There is a technical issue which I'll avoid for now.)
But let's start at the beginning.
You have an interesting problem, P.
You have an algorithm for it, A, written in C.
You want an algorithm for it, H, written in Haskell.
Your idea is to make small local syntactic changes
to A to turn in into H.
That's probably going to fail, because C just
loves to smash things, and Haskell hates to.
Maybe you should be using quite a different approach,
one that would be literally unthinkable in C.
After all, being able to do things that are unthinkable
in C is one of the reasons for learning Haskell.
Why not tell us what problem P is?
```
```
Tony Morris:
data SnocList a = SnocList ([a] -> [a])
Inserts to the front and end in O(1).
```
### I consider the follow dispositve on the subject.
```
Edward Kmett:
Note: all of the options for playing with lists and queues and fingertrees come with trade-offs.
Finger trees give you O(log n) appends and random access, O(1) cons/uncons/snoc/unsnoc etc. but _cost you_ infinite lists.
Realtime queues give you the O(1) uncons/snoc. There are catenable output restricted deques that can preserve those and can upgrade you to O(1) append, but we've lost unsnoc and random access along the way.
Skew binary random access lists give you O(log n) drop and random access and O(1) cons/uncons, but lose the infinite lists, etc.
Tarjan and Mihaescu's deque may get you back worst-case bounds on more of the, but we still lose O(log n) random access and infinite lists.
Difference lists give you an O(1) append, but alternating between inspection and construction can hit your asymptotics.
Lists are used by default because they cleanly extend to the infinite cases, anything more clever necessarily loses some of that power.
