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Naming convention for version branches (Packageversioning)

haskell-cafe - Tue, 05/19/2015 - 6:02pm
Hi all, I am currently writing a tool to automate the release and version bump of cabal projects. Currently you can call the tool by giving as argument the rank of the branch you want to bump, for example given 0.0.0.0: - `cabal-release 0` bump to `1` - `cabal-release 1` bump to `0.1` - `cabal-release 2` bump to `0.0.1` - `cabal-release 3` bump to `0.0.0.1` As we are not all robots (yet), I thought that in addition to this it would be great if the user could give a human friendly name for the rank. For now, here is what I have for the different rank: 0 == --major 1 == --major-fix 2 == --minor 3 == --minor-fix I'm curious to know what you think of those names? any suggestions or known established convention about that? Thanks
Categories: Offsite Discussion

text-icu (and FFI in general) on Windows 64 bits

haskell-cafe - Tue, 05/19/2015 - 5:51pm
I was finally successful in getting text-icu to work on Windows 64 bits. This is probably an indication of what to expect in general for packages requiring FFI on Windows 64 bits. In the past, on 32 bits, the standard Windows binary distribution from the ICU site could be used together with msys/mingw, even though it was officially only for MSVC. This no longer seems to be the case for 64 bits. When I build text-icu in that way with a 64 bit GHC and the Windows 64-bit binary ICU distribution for MSVC, the resulting EXEs segfault as soon as any function from text-icu is called. There is no official ICU download for mingw-w64 binaries. But happily, the MSYS2 project does provide a pre-built ICU binary distribution for mingw-w64. It tends to be quite up-to-date; the current version is ICU 55.1. Note, however, that I was *not* able to use the partial MSYS2 that comes with MinGHC, because pacman seems to be missing. So the solution is: 1. Download and install 64-bit MSYS2, following the instructions on the s
Categories: Offsite Discussion

Cartesian Closed Comic: Security

Planet Haskell - Tue, 05/19/2015 - 5:00pm

Categories: Offsite Blogs

Obverse and Reverse

Haskell on Reddit - Tue, 05/19/2015 - 3:15pm
Categories: Incoming News

CALL FOR PAPERS for IIT’15, IEEE Sponsored, Dubai (01-03 Nov 2015)

General haskell list - Tue, 05/19/2015 - 1:46pm
Dear Colleagues, Apologies if you receive multiple copies of this CFP. Please feel free to distribute the IIT'15 CFP to your colleagues, students and networks. CALL FOR PAPERS 2015 11th International Conference on Innovations in Information Technology (IIT'15) Special Theme: Smart Living Cities, Big Data and Sustainable Development November 01-03, 2015, Dubai, UAE http://www.it-innovations.ae/ BEST PAPER AWARDS Two best papers of the conference will be selected by the program committee. One will be awarded the "Best Research Paper Award" and another one will be awarded the “Best Application Paper Award” (for application-oriented submissions). IMPORTANT DATES Papers and Student Posters Submission 30 May 2015 Submission of Tutorials 30 May 2015 Notification for Papers and Student Posters 15 July 2015 Notification for Tutorials 15 July 2015 Final Camera-Ready 01 September 2015 PUBLICATION
Categories: Incoming News

advanced cabal configuration

haskell-cafe - Tue, 05/19/2015 - 1:06pm
Hi, I'm a maintainer of simple-sendfile and need to implement the following is to rescue 32bit Linux: - If the COff size is 8, the following FFI is used: foreign import ccall unsafe "sendfile64" c_sendfile :: Fd -> Fd -> Ptr COff -> CSize -> IO (#type ssize_t) - Otherwise, the following FFI is used: foreign import ccall unsafe "sendfile" c_sendfile :: Fd -> Fd -> Ptr COff -> CSize -> IO (#type ssize_t) How can I implement this? I guess that Setup.hs should evaluate (sizeOf (1 :: COff)) and define a C macro, say LARGE_OFFSET and write the following code. #ifdef LARGE_OFFSET foreign import ccall unsafe "sendfile64" #else foreign import ccall unsafe "sendfile" #endif I have no experience to use Build-Type: other than Simple in cabal files. Would someone explain how to implement it concretely or suggest examples which implement similar things? For more informaion, please read: https://github.com/yesodweb/wai/issues/372 Thanks. --Kazu
Categories: Offsite Discussion

PL Summer Schools forall!

Haskell on Reddit - Tue, 05/19/2015 - 12:08pm
Categories: Incoming News

Algorithm W Step by Step [PDF]

Haskell on Reddit - Tue, 05/19/2015 - 10:08am
Categories: Incoming News

Gabriel Gonzalez: Morte: an intermediate language for super-optimizing functional programs

Planet Haskell - Tue, 05/19/2015 - 8:06am

The Haskell language provides the following guarantee (with caveats): if two programs are equal according to equational reasoning then they will behave the same. On the other hand, Haskell does not guarantee that equal programs will generate identical performance. Consequently, Haskell library writers must employ rewrite rules to ensure that their abstractions do not interfere with performance.

Now suppose there were a hypothetical language with a stronger guarantee: if two programs are equal then they generate identical executables. Such a language would be immune to abstraction: no matter how many layers of indirection you might add the binary size and runtime performance would be unaffected.

Here I will introduce such an intermediate language named Morte that obeys this stronger guarantee. I have not yet implemented a back-end code generator for Morte, but I wanted to pause to share what I have completed so far because Morte uses several tricks from computer science that I believe deserve more attention.

Morte is nothing more than a bare-bones implementation of the calculus of constructions, which is a specific type of lambda calculus. The only novelty is how I intend to use this lambda calculus: as a super-optimizer.

Normalization

The typed lambda calculus possesses a useful property: every term in the lambda calculus has a unique normal form if you beta-reduce everything. If you're new to lambda calculus, normalizing an expression equates to indiscriminately inlining every function call.

What if we built a programming language whose intermediate language was lambda calculus? What if optimization was just normalization of lambda terms (i.e. indiscriminate inlining)? If so, then we would could abstract freely, knowing that while compile times might increase, our final executable would never change.

Recursion

Normally you would not want to inline everything because infinitely recursive functions would become infinitely large expressions. Fortunately, we can often translate recursive code to non-recursive code!

I'll demonstrate this trick first in Haskell and then in Morte. Let's begin from the following recursive List type along with a recursive map function over lists:

import Prelude hiding (map, foldr)

data List a = Cons a (List a) | Nil

example :: List Int
example = Cons 1 (Cons 2 (Cons 3 Nil))

map :: (a -> b) -> List a -> List b
map f Nil = Nil
map f (Cons a l) = Cons (f a) (map f l)

-- Argument order intentionally switched
foldr :: List a -> (a -> x -> x) -> x -> x
foldr Nil c n = n
foldr (Cons a l) c n = c a (foldr l c n)

result :: Int
result = foldr (map (+1) example) (+) 0

-- result = 9

Now imagine that we disable all recursion in Haskell: no more recursive types and no more recursive functions. Now we must reject the above program because:

  • the List data type definition recursively refers to itself

  • the map and foldr functions recursively refer to themselves

Can we still encode lists in a non-recursive dialect of Haskell?

Yes, we can!

-- This is a valid Haskell program

{-# LANGUAGE RankNTypes #-}

import Prelude hiding (map, foldr)

type List a = forall x . (a -> x -> x) -> x -> x

example :: List Int
example = \cons nil -> cons 1 (cons 2 (cons 3 nil))

map :: (a -> b) -> List a -> List b
map f l = \cons nil -> l (\a x -> cons (f a) x) nil

foldr :: List a -> (a -> x -> x) -> x -> x
foldr l = l

result :: Int
result = foldr (map (+ 1) example) (+) 0

-- result = 9

Carefully note that:

  • List is no longer defined recursively in terms of itself

  • map and foldr are no longer defined recursively in terms of themselves

Yet, we somehow managed to build a list, map a function over the list, and fold the list, all without ever using recursion! We do this by encoding the list as a fold, which is why foldr became the identity function.

This trick works for more than just lists. You can take any recursive data type and mechanically transform the type into a fold and transform functions on the type into functions on folds. If you want to learn more about this trick, the specific name for it is "Boehm-Berarducci encoding". If you are curious, this in turn is equivalent to an even more general concept from category theory known as "F-algebras", which let you encode inductive things in a non-inductive way.

Non-recursive code greatly simplifies equational reasoning. For example, we can easily prove that we can optimize map id l to l:

map id l

-- Inline: map f l = \cons nil -> l (\a x -> cons (f a) x) nil
= \cons nil -> l (\a x -> cons (id a) x) nil

-- Inline: id x = x
= \cons nil -> l (\a x -> cons a x) nil

-- Eta-reduce
= \cons nil -> l cons nil

-- Eta-reduce
= l

Note that we did not need to use induction to prove this optimization because map is no longer recursive. The optimization became downright trivial, so trivial that we can automate it!

Morte optimizes programs using this same simple scheme:

  • Beta-reduce everything (equivalent to inlining)
  • Eta-reduce everything

To illustrate this, I will desugar our high-level Haskell code to the calculus of constructions. This desugaring process is currently manual (and tedious), but I plan to automate this, too, by providing a front-end high-level language similar to Haskell that compiles to Morte:

-- mapid.mt

( \(List : * -> *)
-> \( map
: forall (a : *)
-> forall (b : *)
-> (a -> b) -> List a -> List b
)
-> \(id : forall (a : *) -> a -> a)

-> \(a : *) -> map a a (id a)
)

-- List
(\(a : *) -> forall (x : *) -> (a -> x -> x) -> x -> x)

-- map
( \(a : *)
-> \(b : *)
-> \(f : a -> b)
-> \(l : forall (x : *) -> (a -> x -> x) -> x -> x)
-> \(x : *)
-> \(Cons : b -> x -> x)
-> \(Nil: x)
-> l x (\(va : a) -> \(vx : x) -> Cons (f va) vx) Nil
)

-- id
(\(a : *) -> \(va : a) -> va)

This line of code is the "business end" of the program:

\(a : *) -> map a a (id a)

The extra 'a' business is because in any polymorphic lambda calculus you explicitly accept polymorphic types as arguments and specialize functions by applying them to types. Higher-level functional languages like Haskell or ML use type inference to automatically infer and supply type arguments when possible.

We can compile this program using the morte executable, which accepts a Morte program on stdin, outputs the program's type stderr, and outputs the optimized program on stdout:

$ morte < id.mt
∀(a : *) → (∀(x : *) → (a → x → x) → x → x) → ∀(x : *) → (a
→ x → x) → x → x

λ(a : *) → λ(l : ∀(x : *) → (a → x → x) → x → x) → l

The first line is the type, which is a desugared form of:

forall a . List a -> List a

The second line is the program, which is the identity function on lists. Morte optimized away the map completely, the same way we did by hand.

Morte also optimized away the rest of the code, too. Dead-code elimination is just an emergent property of Morte's simple optimization scheme.

Equality

We could double-check our answer by asking Morte to optimize the identity function on lists:

-- idlist.mt

( \(List : * -> *)
-> \(id : forall (a : *) -> a -> a)

-> \(a : *) -> id (List a)
)

-- List
(\(a : *) -> forall (x : *) -> (a -> x -> x) -> x -> x)

-- id
(\(a : *) -> \(va : a) -> va)

Sure enough, Morte outputs an alpha-equivalent result (meaning the same up to variable renaming):

$ ~/.cabal/bin/morte < idlist.mt
∀(a : *) → (∀(x : *) → (a → x → x) → x → x) → ∀(x : *) → (a
→ x → x) → x → x

λ(a : *) → λ(va : ∀(x : *) → (a → x → x) → x → x) → va

We can even use the morte library to mechanically check if two Morte expressions are alpha-, beta-, and eta- equivalent. We can parse our two Morte files into Morte's Expr type and then use the Eq instance for Expr to test for equivalence:

$ ghci
Prelude> import qualified Data.Text.Lazy.IO as Text
Prelude Text> txt1 <- Text.readFile "mapid.mt"
Prelude Text> txt2 <- Text.readFile "idlist.mt"
Prelude Text> import Morte.Parser (exprFromText)
Prelude Text Morte.Parser> let e1 = exprFromText txt1
Prelude Text Morte.Parser> let e2 = exprFromText txt2
Prelude Text Morte.Parser> import Control.Applicative (liftA2)
Prelude Text Morte.Parser Control.Applicative> liftA2 (==) e1 e2
Right True
$ -- `Right` means both expressions parsed successfully
$ -- `True` means they are alpha-, beta-, and eta-equivalent

We can use this to mechanically verify that two Morte programs optimize to the same result.

Compile-time computation

Morte can compute as much (or as little) at compile as you want. The more information you encode directly within lambda calculus, the more compile-time computation Morte will perform for you. For example, if we translate our Haskell List code entirely to lambda calculus, then Morte will statically compute the result at compile time.

-- nine.mt

( \(Nat : *)
-> \(zero : Nat)
-> \(one : Nat)
-> \((+) : Nat -> Nat -> Nat)
-> \((*) : Nat -> Nat -> Nat)
-> \(List : * -> *)
-> \(Cons : forall (a : *) -> a -> List a -> List a)
-> \(Nil : forall (a : *) -> List a)
-> \( map
: forall (a : *) -> forall (b : *)
-> (a -> b) -> List a -> List b
)
-> \( foldr
: forall (a : *)
-> List a
-> forall (r : *)
-> (a -> r -> r) -> r -> r
)
-> ( \(two : Nat)
-> \(three : Nat)
-> ( \(example : List Nat)

-> foldr Nat (map Nat Nat ((+) one) example) Nat (+) zero
)

-- example
(Cons Nat one (Cons Nat two (Cons Nat three (Nil Nat))))
)

-- two
((+) one one)

-- three
((+) one ((+) one one))
)

-- Nat
( forall (a : *)
-> (a -> a)
-> a
-> a
)

-- zero
( \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> Zero
)

-- one
( \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> Succ Zero
)

-- (+)
( \(m : forall (a : *) -> (a -> a) -> a -> a)
-> \(n : forall (a : *) -> (a -> a) -> a -> a)
-> \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> m a Succ (n a Succ Zero)
)

-- (*)
( \(m : forall (a : *) -> (a -> a) -> a -> a)
-> \(n : forall (a : *) -> (a -> a) -> a -> a)
-> \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> m a (n a Succ) Zero
)

-- List
( \(a : *)
-> forall (x : *)
-> (a -> x -> x) -- Cons
-> x -- Nil
-> x
)

-- Cons
( \(a : *)
-> \(va : a)
-> \(vas : forall (x : *) -> (a -> x -> x) -> x -> x)
-> \(x : *)
-> \(Cons : a -> x -> x)
-> \(Nil : x)
-> Cons va (vas x Cons Nil)
)

-- Nil
( \(a : *)
-> \(x : *)
-> \(Cons : a -> x -> x)
-> \(Nil : x)
-> Nil
)

-- map
( \(a : *)
-> \(b : *)
-> \(f : a -> b)
-> \(l : forall (x : *) -> (a -> x -> x) -> x -> x)
-> \(x : *)
-> \(Cons : b -> x -> x)
-> \(Nil: x)
-> l x (\(va : a) -> \(vx : x) -> Cons (f va) vx) Nil
)

-- foldr
( \(a : *)
-> \(vas : forall (x : *) -> (a -> x -> x) -> x -> x)
-> vas
)

The relevant line is:

foldr Nat (map Nat Nat ((+) one) example) Nat (+) zero

If you remove the type-applications to Nat, this parallels our original Haskell example. We can then evaluate this expression at compile time:

$ morte < nine.mt
∀(a : *) → (a → a) → a → a

λ(a : *) → λ(Succ : a → a) → λ(Zero : a) → Succ (Succ (Succ
(Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))

Morte reduces our program to a church-encoded nine.

Run-time computation

Morte does not force you to compute everything using lambda calculus at compile time. Suppose that we wanted to use machine arithmetic at run-time instead. We can do this by parametrizing our program on:

  • the Int type,
  • operations on Ints, and
  • any integer literals we use

We accept these "foreign imports" as ordinary arguments to our program:

-- foreign.mt

-- Foreign imports
\(Int : *) -- Foreign type
-> \((+) : Int -> Int -> Int) -- Foreign function
-> \((*) : Int -> Int -> Int) -- Foreign function
-> \(lit@0 : Int) -- Literal "1" -- Foreign data
-> \(lit@1 : Int) -- Literal "2" -- Foreign data
-> \(lit@2 : Int) -- Literal "3" -- Foreign data
-> \(lit@3 : Int) -- Literal "1" -- Foreign data
-> \(lit@4 : Int) -- Literal "0" -- Foreign data

-- The rest is compile-time lambda calculus
-> ( \(List : * -> *)
-> \(Cons : forall (a : *) -> a -> List a -> List a)
-> \(Nil : forall (a : *) -> List a)
-> \( map
: forall (a : *)
-> forall (b : *)
-> (a -> b) -> List a -> List b
)
-> \( foldr
: forall (a : *)
-> List a
-> forall (r : *)
-> (a -> r -> r) -> r -> r
)
-> ( \(example : List Int)

-> foldr Int (map Int Int ((+) lit@3) example) Int (+) lit@4
)

-- example
(Cons Int lit@0 (Cons Int lit@1 (Cons Int lit@2 (Nil Int))))
)

-- List
( \(a : *)
-> forall (x : *)
-> (a -> x -> x) -- Cons
-> x -- Nil
-> x
)

-- Cons
( \(a : *)
-> \(va : a)
-> \(vas : forall (x : *) -> (a -> x -> x) -> x -> x)
-> \(x : *)
-> \(Cons : a -> x -> x)
-> \(Nil : x)
-> Cons va (vas x Cons Nil)
)

-- Nil
( \(a : *)
-> \(x : *)
-> \(Cons : a -> x -> x)
-> \(Nil : x)
-> Nil
)

-- map
( \(a : *)
-> \(b : *)
-> \(f : a -> b)
-> \(l : forall (x : *) -> (a -> x -> x) -> x -> x)
-> \(x : *)
-> \(Cons : b -> x -> x)
-> \(Nil: x)
-> l x (\(va : a) -> \(vx : x) -> Cons (f va) vx) Nil
)

-- foldr
( \(a : *)
-> \(vas : forall (x : *) -> (a -> x -> x) -> x -> x)
-> vas
)

We can use Morte to optimize the above program and Morte will reduce the program to nothing but foreign types, operations, and values:

$ morte < foreign.mt
∀(Int : *) → (Int → Int → Int) → (Int → Int → Int) → Int →
Int → Int → Int → Int → Int

λ(Int : *) → λ((+) : Int → Int → Int) → λ((*) : Int → Int →
Int) → λ(lit : Int) → λ(lit@1 : Int) → λ(lit@2 : Int) →
λ(lit@3 : Int) → λ(lit@4 : Int) → (+) ((+) lit@3 lit) ((+)
((+) lit@3 lit@1) ((+) ((+) lit@3 lit@2) lit@4))

If you study that closely, Morte adds lit@3 (the "1" literal) to each literal of the list and then adds them up. We can then pass this foreign syntax tree to our machine arithmetic backend to transform those foreign operations to efficient operations.

Morte lets you choose how much information you want to encode within lambda calculus. The more information you encode in lambda calculus the more Morte can optimize your program, but the slower your compile times will get, so it's a tradeoff.

Corecursion

Corecursion is the dual of recursion. Where recursion works on finite data types, corecursion works on potentially infinite data types. An example would be the following infinite Stream in Haskell:

data Stream a = Cons a (Stream a)

numbers :: Stream Int
numbers = go 0
where
go n = Cons n (go (n + 1))

-- numbers = Cons 0 (Cons 1 (Cons 2 (...

map :: (a -> b) -> Stream a -> Stream b
map f (Cons a l) = Cons (f a) (map f l)

example :: Stream Int
example = map (+ 1) numbers

-- example = Cons 1 (Cons 2 (Cons 3 (...

Again, pretend that we disable any function from referencing itself so that the above code becomes invalid. This time we cannot reuse the same trick from previous sections because we cannot encode numbers as a fold without referencing itself. Try this if you don't believe me.

However, we can still encode corecursive things in a non-corecursive way. This time, we encode our Stream type as an unfold instead of a fold:

-- This is also valid Haskell code

{-# LANGUAGE ExistentialQuantification #-}

data Stream a = forall s . MkStream
{ seed :: s
, step :: s -> (a, s)
}

numbers :: Stream Int
numbers = MkStream 0 (\n -> (n, n + 1))

map :: (a -> b) -> Stream a -> Stream b
map f (MkStream s0 k) = MkStream s0 k'
where
k' s = (f a, s')
where (a, s') = k s

In other words, we store an initial seed of some type s and a step function of type s -> (a, s) that emits one element of our Stream. The type of our seed s can be anything and in our numbers example, the type of the internal state is Int. Another stream could use a completely different internal state of type (), like this:

-- ones = Cons 1 ones

ones :: Stream Int
ones = MkStream () (\_ -> (1, ()))

The general name for this trick is an "F-coalgebra" encoding of a corecursive type.

Once we encode our infinite stream non-recursively, we can safely optimize the stream by inlining and eta reduction:

map id l

-- l = MkStream s0 k
= map id (MkStream s0 k)

-- Inline definition of `map`
= MkStream s0 k'
where
k' = \s -> (id a, s')
where
(a, s') = k s

-- Inline definition of `id`
= MkStream s0 k'
where
k' = \s -> (a, s')
where
(a, s') = k s

-- Inline: (a, s') = k s
= MkStream s0 k'
where
k' = \s -> k s

-- Eta reduce
= MkStream s0 k'
where
k' = k

-- Inline: k' = k
= MkStream s0 k

-- l = MkStream s0 k
= l

Now let's encode Stream and map in Morte and compile the following four expressions:

map id

id

map f . map g

map (f . g)

Save the following Morte file to stream.mt and then uncomment the expression you want to test:

( \(id : forall (a : *) -> a -> a)
-> \( (.)
: forall (a : *)
-> forall (b : *)
-> forall (c : *)
-> (b -> c)
-> (a -> b)
-> (a -> c)
)
-> \(Pair : * -> * -> *)
-> \(P : forall (a : *) -> forall (b : *) -> a -> b -> Pair a b)
-> \( first
: forall (a : *)
-> forall (b : *)
-> forall (c : *)
-> (a -> b)
-> Pair a c
-> Pair b c
)

-> ( \(Stream : * -> *)
-> \( map
: forall (a : *)
-> forall (b : *)
-> (a -> b)
-> Stream a
-> Stream b
)

-- example@1 = example@2
-> ( \(example@1 : forall (a : *) -> Stream a -> Stream a)
-> \(example@2 : forall (a : *) -> Stream a -> Stream a)

-- example@3 = example@4
-> \( example@3
: forall (a : *)
-> forall (b : *)
-> forall (c : *)
-> (b -> c)
-> (a -> b)
-> Stream a
-> Stream c
)

-> \( example@4
: forall (a : *)
-> forall (b : *)
-> forall (c : *)
-> (b -> c)
-> (a -> b)
-> Stream a
-> Stream c
)

-- Uncomment the example you want to test
-> example@1
-- -> example@2
-- -> example@3
-- -> example@4
)

-- example@1
(\(a : *) -> map a a (id a))

-- example@2
(\(a : *) -> id (Stream a))

-- example@3
( \(a : *)
-> \(b : *)
-> \(c : *)
-> \(f : b -> c)
-> \(g : a -> b)
-> map a c ((.) a b c f g)
)

-- example@4
( \(a : *)
-> \(b : *)
-> \(c : *)
-> \(f : b -> c)
-> \(g : a -> b)
-> (.) (Stream a) (Stream b) (Stream c) (map b c f) (map a b g)
)
)

-- Stream
( \(a : *)
-> forall (x : *)
-> (forall (s : *) -> s -> (s -> Pair a s) -> x)
-> x
)

-- map
( \(a : *)
-> \(b : *)
-> \(f : a -> b)
-> \( st
: forall (x : *)
-> (forall (s : *) -> s -> (s -> Pair a s) -> x)
-> x
)
-> \(x : *)
-> \(S : forall (s : *) -> s -> (s -> Pair b s) -> x)
-> st
x
( \(s : *)
-> \(seed : s)
-> \(step : s -> Pair a s)
-> S
s
seed
(\(seed@1 : s) -> first a b s f (step seed@1))
)
)
)

-- id
(\(a : *) -> \(va : a) -> va)

-- (.)
( \(a : *)
-> \(b : *)
-> \(c : *)
-> \(f : b -> c)
-> \(g : a -> b)
-> \(va : a)
-> f (g va)
)

-- Pair
(\(a : *) -> \(b : *) -> forall (x : *) -> (a -> b -> x) -> x)

-- P
( \(a : *)
-> \(b : *)
-> \(va : a)
-> \(vb : b)
-> \(x : *)
-> \(P : a -> b -> x)
-> P va vb
)

-- first
( \(a : *)
-> \(b : *)
-> \(c : *)
-> \(f : a -> b)
-> \(p : forall (x : *) -> (a -> c -> x) -> x)
-> \(x : *)
-> \(Pair : b -> c -> x)
-> p x (\(va : a) -> \(vc : c) -> Pair (f va) vc)
)

Both example@1 and example@2 will generate alpha-equivalent code:

$ morte < example1.mt
∀(a : *) → (∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) → (a →
s → x) → x) → x) → x) → ∀(x : *) → (∀(s : *) → s → (s → ∀(x
: *) → (a → s → x) → x) → x) → x

λ(a : *) → λ(st : ∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) →
(a → s → x) → x) → x) → x) → st

$ morte < example2.mt
∀(a : *) → (∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) → (a →
s → x) → x) → x) → x) → ∀(x : *) → (∀(s : *) → s → (s → ∀(x
: *) → (a → s → x) → x) → x) → x

λ(a : *) → λ(va : ∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) →
(a → s → x) → x) → x) → x) → va

Similarly, example@3 and example@4 will generate alpha-equivalent code:

$ morte < example3.mt
∀(a : *) → ∀(b : *) → ∀(c : *) → (b → c) → (a → b) → (∀(x :
*) → (∀(s : *) → s → (s → ∀(x : *) → (a → s → x) → x) → x) →
x) → ∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) → (c → s → x)
→ x) → x) → x

λ(a : *) → λ(b : *) → λ(c : *) → λ(f : b → c) → λ(g : a → b)
→ λ(st : ∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) → (a → s
→ x) → x) → x) → x) → λ(x : *) → λ(S : ∀(s : *) → s → (s → ∀
(x : *) → (c → s → x) → x) → x) → st x (λ(s : *) → λ(seed :
s) → λ(step : s → ∀(x : *) → (a → s → x) → x) → S s seed (λ(
seed@1 : s) → λ(x : *) → λ(Pair : c → s → x) → step seed@1 x
(λ(va : a) → Pair (f (g va)))))

$ morte < example4.mt
∀(a : *) → ∀(b : *) → ∀(c : *) → (b → c) → (a → b) → (∀(x :
*) → (∀(s : *) → s → (s → ∀(x : *) → (a → s → x) → x) → x) →
x) → ∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) → (c → s → x)
→ x) → x) → x

λ(a : *) → λ(b : *) → λ(c : *) → λ(f : b → c) → λ(g : a → b)
→ λ(va : ∀(x : *) → (∀(s : *) → s → (s → ∀(x : *) → (a → s
→ x) → x) → x) → x) → λ(x : *) → λ(S : ∀(s : *) → s → (s → ∀
(x : *) → (c → s → x) → x) → x) → va x (λ(s : *) → λ(seed :
s) → λ(step : s → ∀(x : *) → (a → s → x) → x) → S s seed (λ(
seed@1 : s) → λ(x : *) → λ(Pair : c → s → x) → step seed@1 x
(λ(va : a) → Pair (f (g va))))

We inadvertently proved stream fusion for free, but we're still not done, yet! Everything we learn about recursive and corecursive sequences can be applied to model recursive and corecursive effects!

Effects

I will conclude this post by showing how to model both recursive and corecursive programs that have side effects. The recursive program will echo ninety-nine lines from stdin to stdout. The equivalent Haskell program is in the comment header:

-- recursive.mt

-- The Haskell code we will translate to Morte:
--
-- import Prelude hiding (
-- (+), (*), IO, putStrLn, getLine, (>>=), (>>), return )
--
-- -- Simple prelude
--
-- data Nat = Succ Nat | Zero
--
-- zero :: Nat
-- zero = Zero
--
-- one :: Nat
-- one = Succ Zero
--
-- (+) :: Nat -> Nat -> Nat
-- Zero + n = n
-- Succ m + n = m + Succ n
--
-- (*) :: Nat -> Nat -> Nat
-- Zero * n = Zero
-- Succ m * n = n + (m * n)
--
-- foldNat :: Nat -> (a -> a) -> a -> a
-- foldNat Zero f x = x
-- foldNat (Succ m) f x = f (foldNat m f x)
--
-- data IO r
-- = PutStrLn String (IO r)
-- | GetLine (String -> IO r)
-- | Return r
--
-- putStrLn :: String -> IO U
-- putStrLn str = PutStrLn str (Return Unit)
--
-- getLine :: IO String
-- getLine = GetLine Return
--
-- return :: a -> IO a
-- return = Return
--
-- (>>=) :: IO a -> (a -> IO b) -> IO b
-- PutStrLn str io >>= f = PutStrLn str (io >>= f)
-- GetLine k >>= f = GetLine (\str -> k str >>= f)
-- Return r >>= f = f r
--
-- -- Derived functions
--
-- (>>) :: IO U -> IO U -> IO U
-- m >> n = m >>= \_ -> n
--
-- two :: Nat
-- two = one + one
--
-- three :: Nat
-- three = one + one + one
--
-- four :: Nat
-- four = one + one + one + one
--
-- five :: Nat
-- five = one + one + one + one + one
--
-- six :: Nat
-- six = one + one + one + one + one + one
--
-- seven :: Nat
-- seven = one + one + one + one + one + one + one
--
-- eight :: Nat
-- eight = one + one + one + one + one + one + one + one
--
-- nine :: Nat
-- nine = one + one + one + one + one + one + one + one + one
--
-- ten :: Nat
-- ten = one + one + one + one + one + one + one + one + one + one
--
-- replicateM_ :: Nat -> IO U -> IO U
-- replicateM_ n io = foldNat n (io >>) (return Unit)
--
-- ninetynine :: Nat
-- ninetynine = nine * ten + nine
--
-- main_ :: IO U
-- main_ = replicateM_ ninetynine (getLine >>= putStrLn)

-- "Free" variables
( \(String : * )
-> \(U : *)
-> \(Unit : U)

-- Simple prelude
-> ( \(Nat : *)
-> \(zero : Nat)
-> \(one : Nat)
-> \((+) : Nat -> Nat -> Nat)
-> \((*) : Nat -> Nat -> Nat)
-> \(foldNat : Nat -> forall (a : *) -> (a -> a) -> a -> a)
-> \(IO : * -> *)
-> \(return : forall (a : *) -> a -> IO a)
-> \((>>=)
: forall (a : *)
-> forall (b : *)
-> IO a
-> (a -> IO b)
-> IO b
)
-> \(putStrLn : String -> IO U)
-> \(getLine : IO String)

-- Derived functions
-> ( \((>>) : IO U -> IO U -> IO U)
-> \(two : Nat)
-> \(three : Nat)
-> \(four : Nat)
-> \(five : Nat)
-> \(six : Nat)
-> \(seven : Nat)
-> \(eight : Nat)
-> \(nine : Nat)
-> \(ten : Nat)
-> ( \(replicateM_ : Nat -> IO U -> IO U)
-> \(ninetynine : Nat)

-> replicateM_ ninetynine ((>>=) String U getLine putStrLn)
)

-- replicateM_
( \(n : Nat)
-> \(io : IO U)
-> foldNat n (IO U) ((>>) io) (return U Unit)
)

-- ninetynine
((+) ((*) nine ten) nine)
)

-- (>>)
( \(m : IO U)
-> \(n : IO U)
-> (>>=) U U m (\(_ : U) -> n)
)

-- two
((+) one one)

-- three
((+) one ((+) one one))

-- four
((+) one ((+) one ((+) one one)))

-- five
((+) one ((+) one ((+) one ((+) one one))))

-- six
((+) one ((+) one ((+) one ((+) one ((+) one one)))))

-- seven
((+) one ((+) one ((+) one ((+) one ((+) one ((+) one one))))))

-- eight
((+) one ((+) one ((+) one ((+) one ((+) one ((+) one ((+) one one)))))))
-- nine
((+) one ((+) one ((+) one ((+) one ((+) one ((+) one ((+) one ((+) one one))))))))

-- ten
((+) one ((+) one ((+) one ((+) one ((+) one ((+) one ((+) one ((+) one ((+) one one)))))))))
)

-- Nat
( forall (a : *)
-> (a -> a)
-> a
-> a
)

-- zero
( \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> Zero
)

-- one
( \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> Succ Zero
)

-- (+)
( \(m : forall (a : *) -> (a -> a) -> a -> a)
-> \(n : forall (a : *) -> (a -> a) -> a -> a)
-> \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> m a Succ (n a Succ Zero)
)

-- (*)
( \(m : forall (a : *) -> (a -> a) -> a -> a)
-> \(n : forall (a : *) -> (a -> a) -> a -> a)
-> \(a : *)
-> \(Succ : a -> a)
-> \(Zero : a)
-> m a (n a Succ) Zero
)

-- foldNat
( \(n : forall (a : *) -> (a -> a) -> a -> a)
-> n
)

-- IO
( \(r : *)
-> forall (x : *)
-> (String -> x -> x)
-> ((String -> x) -> x)
-> (r -> x)
-> x
)

-- return
( \(a : *)
-> \(va : a)
-> \(x : *)
-> \(PutStrLn : String -> x -> x)
-> \(GetLine : (String -> x) -> x)
-> \(Return : a -> x)
-> Return va
)

-- (>>=)
( \(a : *)
-> \(b : *)
-> \(m : forall (x : *)
-> (String -> x -> x)
-> ((String -> x) -> x)
-> (a -> x)
-> x
)
-> \(f : a
-> forall (x : *)
-> (String -> x -> x)
-> ((String -> x) -> x)
-> (b -> x)
-> x
)
-> \(x : *)
-> \(PutStrLn : String -> x -> x)
-> \(GetLine : (String -> x) -> x)
-> \(Return : b -> x)
-> m x PutStrLn GetLine (\(va : a) -> f va x PutStrLn GetLine Return)
)

-- putStrLn
( \(str : String)
-> \(x : *)
-> \(PutStrLn : String -> x -> x )
-> \(GetLine : (String -> x) -> x)
-> \(Return : U -> x)
-> PutStrLn str (Return Unit)
)

-- getLine
( \(x : *)
-> \(PutStrLn : String -> x -> x )
-> \(GetLine : (String -> x) -> x)
-> \(Return : String -> x)
-> GetLine Return
)
)

This program will compile to a completely unrolled read-write loop, as most recursive programs will:

$ morte < recursive.mt
∀(String : *) → ∀(U : *) → U → ∀(x : *) → (String → x → x) →
((String → x) → x) → (U → x) → x

λ(String : *) → λ(U : *) → λ(Unit : U) → λ(x : *) → λ(PutStr
Ln : String → x → x) → λ(GetLine : (String → x) → x) → λ(Ret
urn : U → x) → GetLine (λ(va : String) → PutStrLn va (GetLin
e (λ(va@1 : String) → PutStrLn va@1 (GetLine (λ(va@2 : Strin
g) → PutStrLn va@2 (GetLine (λ(va@3 : String) → PutStrLn ...
<snip>
... GetLine (λ(va@92 : String) → PutStrLn va@92 (GetLine (λ(
va@93 : String) → PutStrLn va@93 (GetLine (λ(va@94 : String)
→ PutStrLn va@94 (GetLine (λ(va@95 : String) → PutStrLn va@
95 (GetLine (λ(va@96 : String) → PutStrLn va@96 (GetLine (λ(
va@97 : String) → PutStrLn va@97 (GetLine (λ(va@98 : String)
→ PutStrLn va@98 (Return Unit))))))))))))))))))))))))))))))
))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
))))))))))))))))))))))))))))))))))))))))))))))))

In contrast, if we encode the effects corecursively we can express a program that echoes indefinitely from stdin to stdout:

-- corecursive.mt

-- data IOF r s
-- = PutStrLn String s
-- | GetLine (String -> s)
-- | Return r
--
-- data IO r = forall s . MkIO s (s -> IOF r s)
--
-- main = MkIO
-- Nothing
-- (maybe (\str -> PutStrLn str Nothing) (GetLine Just))

( \(String : *)
-> ( \(Maybe : * -> *)
-> \(Just : forall (a : *) -> a -> Maybe a)
-> \(Nothing : forall (a : *) -> Maybe a)
-> \( maybe
: forall (a : *)
-> Maybe a
-> forall (x : *)
-> (a -> x)
-> x
-> x
)
-> \(IOF : * -> * -> *)
-> \( PutStrLn
: forall (r : *)
-> forall (s : *)
-> String
-> s
-> IOF r s
)
-> \( GetLine
: forall (r : *)
-> forall (s : *)
-> (String -> s)
-> IOF r s
)
-> \( Return
: forall (r : *)
-> forall (s : *)
-> r
-> IOF r s
)
-> ( \(IO : * -> *)
-> \( MkIO
: forall (r : *)
-> forall (s : *)
-> s
-> (s -> IOF r s)
-> IO r
)
-> ( \(main : forall (r : *) -> IO r)
-> main
)

-- main
( \(r : *)
-> MkIO
r
(Maybe String)
(Nothing String)
( \(m : Maybe String)
-> maybe
String
m
(IOF r (Maybe String))
(\(str : String) ->
PutStrLn
r
(Maybe String)
str
(Nothing String)
)
(GetLine r (Maybe String) (Just String))
)
)
)

-- IO
( \(r : *)
-> forall (x : *)
-> (forall (s : *) -> s -> (s -> IOF r s) -> x)
-> x
)

-- MkIO
( \(r : *)
-> \(s : *)
-> \(seed : s)
-> \(step : s -> IOF r s)
-> \(x : *)
-> \(k : forall (s : *) -> s -> (s -> IOF r s) -> x)
-> k s seed step
)
)

-- Maybe
(\(a : *) -> forall (x : *) -> (a -> x) -> x -> x)

-- Just
( \(a : *)
-> \(va : a)
-> \(x : *)
-> \(Just : a -> x)
-> \(Nothing : x)
-> Just va
)

-- Nothing
( \(a : *)
-> \(x : *)
-> \(Just : a -> x)
-> \(Nothing : x)
-> Nothing
)

-- maybe
( \(a : *)
-> \(m : forall (x : *) -> (a -> x) -> x-> x)
-> m
)

-- IOF
( \(r : *)
-> \(s : *)
-> forall (x : *)
-> (String -> s -> x)
-> ((String -> s) -> x)
-> (r -> x)
-> x
)

-- PutStrLn
( \(r : *)
-> \(s : *)
-> \(str : String)
-> \(vs : s)
-> \(x : *)
-> \(PutStrLn : String -> s -> x)
-> \(GetLine : (String -> s) -> x)
-> \(Return : r -> x)
-> PutStrLn str vs
)

-- GetLine
( \(r : *)
-> \(s : *)
-> \(k : String -> s)
-> \(x : *)
-> \(PutStrLn : String -> s -> x)
-> \(GetLine : (String -> s) -> x)
-> \(Return : r -> x)
-> GetLine k
)

-- Return
( \(r : *)
-> \(s : *)
-> \(vr : r)
-> \(x : *)
-> \(PutStrLn : String -> s -> x)
-> \(GetLine : (String -> s) -> x)
-> \(Return : r -> x)
-> Return vr
)

)

This compiles to a state machine that we can unfold one step at a time:

$ morte < corecursive.mt
∀(String : *) → ∀(r : *) → ∀(x : *) → (∀(s : *) → s → (s → ∀
(x : *) → (String → s → x) → ((String → s) → x) → (r → x) →
x) → x) → x

λ(String : *) → λ(r : *) → λ(x : *) → λ(k : ∀(s : *) → s → (
s → ∀(x : *) → (String → s → x) → ((String → s) → x) → (r →
x) → x) → x) → k (∀(x : *) → (String → x) → x → x) (λ(x : *)
→ λ(Just : String → x) → λ(Nothing : x) → Nothing) (λ(m : ∀
(x : *) → (String → x) → x → x) → m (∀(x : *) → (String → (∀
(x : *) → (String → x) → x → x) → x) → ((String → ∀(x : *) →
(String → x) → x → x) → x) → (r → x) → x) (λ(str : String)
→ λ(x : *) → λ(PutStrLn : String → (∀(x : *) → (String → x)
→ x → x) → x) → λ(GetLine : (String → ∀(x : *) → (String → x
) → x → x) → x) → λ(Return : r → x) → PutStrLn str (λ(x : *)
→ λ(Just : String → x) → λ(Nothing : x) → Nothing)) (λ(x :
*) → λ(PutStrLn : String → (∀(x : *) → (String → x) → x → x)
→ x) → λ(GetLine : (String → ∀(x : *) → (String → x) → x →
x) → x) → λ(Return : r → x) → GetLine (λ(va : String) → λ(x
: *) → λ(Just : String → x) → λ(Nothing : x) → Just va))

I don't expect you to understand that output other than to know that we can translate the output to any backend that provides functions, and primitive read/write operations.

Conclusion

If you would like to use Morte, you can find the library on both Github and Hackage. I also provide a Morte tutorial that you can use to learn more about the library.

Morte is dependently typed in theory, but in practice I have not exercised this feature so I don't understand the implications of this. If this turns out to be a mistake then I will downgrade Morte to System Fw, which has higher-kinds and polymorphism, but no dependent types.

Additionally, Morte might be usable to transmit code in a secure and typed way in distributed environment or to share code between diverse functional language by providing a common intermediate language. However, both of those scenarios require additional work, such as establishing a shared set of foreign primitives and creating Morte encoders/decoders for each target language.

Also, there are additional optimizations which Morte might implement in the future. For example, Morte could use free theorems (equalities you deduce from the types) to simplify some code fragments even further, but Morte currently does not do this.

My next goals are:

  • Add a back-end to compile Morte to LLVM
  • Add a front-end to desugar a medium-level Haskell-like language to Morte

Once those steps are complete then Morte will be a usable intermediate language for writing super-optimizable programs.

Also, if you're wondering, the name Morte is a tribute to a talking skull from the game Planescape: Torment, since the Morte library is a "bare-bones" calculus of constructions.

Literature

If this topic interests you more, you may find the following links helpful, in roughly increasing order of difficulty:

Categories: Offsite Blogs

The Notes of GHC

Haskell on Reddit - Tue, 05/19/2015 - 7:25am
Categories: Incoming News

FP Complete: PSA: GHC 7.10, cabal, and Windows

Planet Haskell - Tue, 05/19/2015 - 2:20am

Since we've received multiple bug reports on this, and there are many people suffering from it reporting on the cabal issue, Neil and I decided a more public announcement was warranted.

There is an as-yet undiagnosed bug in cabal which causes some packages to fail to install. Packages known to be affected are blaze-builder-enumerator, data-default-instances-old-locale, vector-binary-instances, and data-default-instances-containers. The output looks something like:

Resolving dependencies... Configuring data-default-instances-old-locale-0.0.1... Building data-default-instances-old-locale-0.0.1... Failed to install data-default-instances-old-locale-0.0.1 Build log ( C:\Users\gl67\AppData\Roaming\cabal\logs\data-default-instances-old-locale-0.0.1.log ): Building data-default-instances-old-locale-0.0.1... Preprocessing library data-default-instances-old-locale-0.0.1... [1 of 1] Compiling Data.Default.Instances.OldLocale ( Data\Default\Instances\OldLocale.hs, dist\build\Data\Default\Instances\OldLocale.o ) C:\Users\gl67\repos\MinGHC\7.10.1\ghc-7.10.1\mingw\bin\ar.exe: dist\build\libHSdata-default-instances-old-locale-0.0.1-6jcjjaR25tK4x3nJhHHjFM.a-11336\libHSdata-default-instances-old-locale-0.0.1-6jcjjaR25tK4x3nJhHHjFM.a: No such file or directory cabal.exe: Error: some packages failed to install: data-default-instances-old-locale-0.0.1 failed during the building phase. The exception was: ExitFailure 1

There are two workarounds I know of at this time:

  • You can manually unpack and install the package which seems to work, e.g.:

    cabal unpack data-default-instances-old-locale-0.0.1 cabal install .\data-default-instances-old-locale-0.0.1
  • Drop down to GHC 7.8.4 until the cabal bug is fixed

For normal users, you can stop reading here. If you're interested in more details and may be able to help fix it, here's a summary of the research I've done so far:

As far as I can tell, this is a bug in cabal-install, not the Cabal library. Despite reports to the contrary, it does not seem to be that the parallelization level (-j option) has any impact. The only thing that seems to affect the behavior is whether cabal-install unpacks and installs in one step, or does it in two steps. That's why unpacking and then installing works around the bug.

I've stared at cabal logs on this quite a bit, but don't see a rhyme or reason to what's happening here. The bug is easily reproducible, so hopefully someone with more cabal expertise will be able to look at this soon, as this bug has high severity and has been affecting Windows users for almost two months.

Categories: Offsite Blogs

Is it efficient to use foldMap for the List monoid?

Haskell on Reddit - Tue, 05/19/2015 - 2:15am

Let t be an instance of Foldable and suppose we are given a value of type t a for some a. Suppose also we intend to map every element of type a in this t a to a list and concatenate the results.

Since List is a Monoid (with signature ((++), [])), a very clean approach to this is to simply call foldMap. However, since foldMap exploits (or may exploit) the associativity of the monoidal operation, we could end up with an inefficient sequencing of concatenations, unlike the use of foldr, which would allow us to keep the accumulating parameter on the right.

Does GHC apply some optimization (such as a rewrite rule) to rend this matter moot, or should the somewhat more cumbersome usage of foldr be preferred?

submitted by n-simplex
[link] [12 comments]
Categories: Incoming News