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Re: infinite types
by blaat blaat 17 Jul '03

17 Jul '03

Oh yeah, and the person who _guesses_ what ex6 does in the supplied code wins a chocolate bar supplied by me ;-) Cheers, l4t3r _________________________________________________________________ Add photos to your messages with MSN 8. Get 2 months FREE*. http://join.msn.com/?page=features/featuredemail

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Re: infinite types
by blaat blaat 17 Jul '03

17 Jul '03

Uhm, of to my holliday in France. But, ah, oh, the joy of programming ;-). I thought I would humor this list by showing where the infinite types (is it?) discussion ended. I found it quite nice and the code is short so here goes ;-) To test: save the mail after the marker and run it in Hugs. There are some examples at the end of the file. ------- cut from here, save as "Reactive.hs" --------------------------------- -- A reactive system is modelled by the type -- -- R m = m -> (Nottaken | Taken (R m) [m]) -- -- It is _not_ a coalgebraic definition, it is _not_ an arrow, it is -- a recursive type in this case used to model asynchronous message -- passing systems. -- -- A system may be thought of as collection of (UML) -- transitions: s0 - event[guard]/action* -> s1 where states are -- hidden in the transitions, and a next-state is a transition, -- or something, I guess. Uhm, huh? ;-) -- -- Note that no explicit distinction between in- and output messages -- is made. This allows liberal, although slightly odd ;-), structural -- composition operators a la Broy, Bird-Meertens, Arrows, Fudgets, -- whatever. In a nutshell: stream processing functions. -- -- After reading the following oddball operators, you, uhm, might -- really want to define your own. Really ;-) -- -- This formalization has weak algebraic rules on the composition -- operators. -- -- Load this code in hugs and test the examples by typing ex0 to -- ex6. module Reactive where type R m = m -> Response m data Response m = Nottaken | Taken (R m) [m] ---------------------------------------------------------------------- -- -- onTaken: helper function onTaken::Response m -> (R m -> [m] -> a) -> a -> a onTaken Nottaken f g = g onTaken (Taken s oo) f g = f s oo ---------------------------------------------------------------------- -- -- The behavior of a system is, of course, a mapping from an input -- stream of messages to an output stream of messages. behavior::R m->[m]->[m] behavior s [] = [] behavior s (i:ii) = onTaken (s i) (\s0 oo-> oo ++ behavior s0 ii) (i:behavior s ii) ---------------------------------------------------------------------- -- Copy is a simple system which copies all input to its output. -- -- +++++ -- + + -- +++++ ---------------------------------------------------------------------- copy::R m copy m = Taken copy [m] ---------------------------------------------------------------------- -- Lift is a simple system which is the lifting of a function from -- messages to messages to a reactive system. -- -- +++++++++ -- + ^ + -- + f + -- + + -- +++++++++ ---------------------------------------------------------------------- lift::(m->m) -> R m lift f m = Taken (lift f) [f m] ---------------------------------------------------------------------- -- -- If we have a system on messages of type b, and translator functions -- between another type a, we can change the interface to a system -- on messages of type a. (This is a solution for not -- making an explicit distinction between input and output messages; -- now we can partition the messages of subsystems) -- -- +++++++++ -- + + -- + s:R a +:R b -- + + -- +++++++++ interface::(a->b)->(b->a)->R b->R a interface t f s i = onTaken (s (t i)) (\s1 oo->Taken (interface t f s1) (map f oo)) (Nottaken) ---------------------------------------------------------------------- -- -- The parallel composition of two systems s and r is the system which -- if s takes an input then makes s process it, otherwise if r takes an -- input then makes r process it, otherwise does not process it. -- -- Supposed to model the parallel composition of a collection of -- event handlers (like: sound subsystem, graphics subsystem, etc). -- -- +++++ -- + s + -- + + + -- + r + -- +++++ -- -- ( (a <+> b) <+> c = a <+> (b <+> c) ) parallel::R m->R m->R m parallel s0 s1 i = onTaken (s0 i) (\s2 oo->Taken (parallel s2 s1) oo) (onTaken (s1 i) (\s2 oo->Taken (parallel s0 s2) oo) (Nottaken)) infixr 5 <+> (<+>) = parallel ---------------------------------------------------------------------- -- -- The sequential composition of systems s and r takes an input if -- s accepts the input and then makes r process all output of s. -- All output by s which is not taken by r _passes through_ r. -- -- Supposed to model pipes (where exceptions or messages to the -- outside world leak through). -- -- -- +++++++ -- + s.r + -- +++++++ -- -- ( (a <.> b) <.> c = a <.> (b <.> c) ) -- sequential::R m->R m->R m sequential s0 s1 i = onTaken (s0 i) (\s2 oo-> onTaken (seqloop s1 oo) (\s3 oo1-> (Taken (sequential s2 s3) oo1)) (Nottaken)) (Nottaken) seqloop::R m->[m]->Response m seqloop s [] = Taken s [] seqloop s (i:ii) = onTaken (s i) (\s1 oo0-> onTaken (seqloop s1 ii) (\s2 oo1 -> Taken s2 (oo0++oo1)) (Nottaken)) (onTaken (seqloop s ii) (\s1 oo -> Taken s1 (i:oo)) (Nottaken)) infix 6 <.> (<.>) = sequential ---------------------------------------------------------------------- -- -- Feedback on a system s feeds _all_ output of s back to s. All -- output which is not accepted by s _passes through_ s (and the -- loop). -- -- Feedback folds all the transitions taken over fed back output -- into _one_ big transition... -- -- +++++ -- -+-++ s +-+-- -- | +++++ ^ -- +--------+ ---------------------------------------------------------------------- feedback::R m->R m feedback s i = onTaken (s i) (\s0 oo0-> onTaken (feedloop s0 oo0) (\s1 oo1-> Taken (feedback s1) (oo1)) (Nottaken)) (Nottaken) feedloop::R m->[m]->Response m feedloop s [] = Taken s [] feedloop s (i:ii) = onTaken (s i) (\s0 oo-> feedloop s0 (ii++oo)) (onTaken (feedloop s ii) (\s0 oo -> Taken s0 (i:oo)) (Nottaken)) feed = feedback ---------------------------------------------------------------------- -- small examples: ---------------------------------------------------------------------- test s = take 40 (behavior s (repeat 1)) ex0 = test copy ex1 = test (lift (*2) <.> lift ((-)1)) ex2 = test (lift (+1) <+> lift (*2)) ex3 = test (lift (+2) <+> copy <.> lift (+3)) ex4 = test (feed copy) -- infinite computation ex5 = test (interface (\i->'a') (\a->5) copy) ---------------------------------------------------------------------- -- bigger example: ---------------------------------------------------------------------- data Msg = Tick | Out Int | Add Int | AddResult Int | Write Int Int | Fetch Int | Read Int Int deriving (Show) add::Maybe Int -> R Msg add Nothing (Add j) = Taken (add (Just j)) [] add (Just i) (Add j) = Taken (add Nothing ) [AddResult (i+j)] add _ _ = Nottaken register::Int->Int->R Msg register i _ (Write j r) | i == j = Taken (register i r) [] register i r (Fetch j) | i == j = Taken (register i r) [Read i r] register _ _ _ = Nottaken controller::R Msg controller Tick = Taken controller [Fetch 0, Fetch 1] controller (Read i j) = Taken controller [Add j, Write (1-i) j] controller (AddResult i) = Taken controller [Out i, Write 1 i] controller _ = Nottaken ex6 = test (interface (\_->Tick) (\(Out i)-> i) (feed (register 0 0<+>register 1 1<+>add Nothing<+>controller))) ---------------------------------------------------------------------- -- This code is licensed under the Big-Kazooba-Ritual license: -- -- You may copy, modify or distribute this software provided that -- you first perform the ritual described in section a. -- -- If you ever meet one of the authors of this work you can be asked, -- and must comply, to perform the ritual as described in section a. -- -- You must add this license to any derivatives of this work. -- -- a. Lift your left leg, close your eyes and jump in the air. -- Now tap the point of your nose exactly two times with your -- right index finger. To complete: say the words -- "thank you Big Kazooba" -- -- You may open your eyes now. -- -- The disabled may opt not to perform this ritual but have a -- volunteer perform the ritual on their behalf. -- -- Anyone, of suited position, may opt to command any number of -- subordinates to perform the ritual instead. -- -- Thank you, -- l4t3r ---------------------------------------------------------------------- _________________________________________________________________ MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*. http://join.msn.com/?page=features/virus

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RE: Hugs Humor
by Simon Marlow 17 Jul '03

17 Jul '03

Jerzy Karczmarczuk writes: > I am abhorred by the fact that adding ... :: Rational > changes the lexical meaning of a literal. It doesn't. A literal with a decimal point always means (fromRational (X%Y)) for some appropriate X and Y. Adding a type signature changes the dynamic meaning of the literal, not the lexical meaning (something we're used to in Haskell, no?). Cheers, Simon

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Re: Case expressions, matching, and "constants"
by Graham Klyne 17 Jul '03

17 Jul '03

At 12:03 17/07/03 +0100, Bayley, Alistair wrote: >This is what I've turned it into to get it to work. It seems a bit clumsy; >is there a better way to write this? > > > test n = > > case True of > > _ | n == one -> "one" > > | n == two -> "two" > > | otherwise -> "three" The 'case' is somewhat redundant. How about: > test n | n == one = "one" > | n == two = "two" > | otherwise = "three" #g ------------------- Graham Klyne <GK(a)NineByNine.org> PGP: 0FAA 69FF C083 000B A2E9 A131 01B9 1C7A DBCA CB5E

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Worldwide Partners program
by The TechNews 17 Jul '03

17 Jul '03

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Old alternative syntax for list comprehensions?
by Peter Pudney 17 Jul '03

17 Jul '03

I recently wanted to generate an infinite list of pairs [(i,j) | i <- [1..], j <- [1..]] Of course, this list comprehension never gets around to generating pairs (2,_). The solution I was after is easily done: [(i,s-i) | s <- [2..], i <- [1..s-1]] But I have a vague recollection of an alternative syntax, something like [(i,j) \ i <- [..], j <- [1..]] that generated a list something like [(1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...]. Did I dream this, or was it a feature of Miranda*, Gopher or Hugs many years ago? Peter

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Re: infinite types
by blaat blaat 16 Jul '03

16 Jul '03

> > > type R m = m -> Maybe (R m, [m]) > > > > I don't think there's an extension of Haskell with regular type > > unification. It's certainly possible, but there's an equivalent in > > standard Haskell: > > > > newtype R m = MkR (m -> Maybe (R m, [m])) > >It will possibly be more convenient to break the cycle in another place, >where >we will wrap and pattern match anyway: > >type R m = m -> Response m >data Response m > | NotTaken > | Taken (R m) [m] Thanks everyone for responding so swiftly. The trick by Marcin really cleaned up my code, thanks! Cheers, l4t3r _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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Haskell book recommendation?
by bjkwak 16 Jul '03

16 Jul '03

Hi! Searching for a new programming language for my work, I got interested in functional languages. After several weeks of googling and searching, I decided to learn Haskell. I have downloaded and read some tutorials from the Haskell home page, but most of them are incomplete and I decided to buy a book or two. I have found a list of books on Haskell in the Haskell home page, but I cannot decide from the information given in the page. Could any body give me some advice? I have some experience in C, but never programmed in functional language before. I have read about 1/4 of the book "ML for the working programmer" by L.C. Paulson. Thanks! Byung-Jae

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re: infinite types
by blaat blaat 16 Jul '03

16 Jul '03

Sorry if this mail starts a new thread. I am not subscribed to haskell-cafe and am new to hotmail. Uhm, as far as the example goes. I was trying to define a small (shallow encoding of) a reactive systems language. Because I wanted to try something else than monads I defined the following recursive type for a reactive system. type R m = m -> Maybe (R m, [m]) Supposedly a reactive system is a system which may not take a message (the Maybe), or do take it and respond with an updated version of itself, and a sequence of outgoing messages. For example, a copying machine might be defined as: id:R m id m = Just (id, [m]) A version for a ?Meally? machine embedding (always take an incoming message, and respond with one outgoing message) could be written as type Meally i o = i -> (Meally i o, o) where id is defined as id::Meally a a id m = (id, m) I like the formalization because (a) it is concise, (b) structural composition operators can be defined trivially, (c) hides the state of a machine, (d) might possibly, in the long run, somewhere, even work out equally well as a monadic approach. Does it make sense? Are there any known references to this approach? Cheers, l4t3r PS: Actually, I just realized this might be the co-algebraic approach, so I guess I am asking for a haskell which allows co-algebraic types. _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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infinite types
by blaat blaat 16 Jul '03

16 Jul '03

Hi al! In my holliday I like to hobby a bit with haskell. For a small formalization I wanted to try out a specification which uses infinite types. Does a (extended) haskel compiler exist which allows infinite types? Chees, l4t3r _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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