name: type-indexed-queues
version: 0.2.0.0
synopsis: Queues with verified and unverified versions.
description:
This library provides implementations of five different queues
(binomial, pairing, skew, leftist, and Braun), each in two
flavours: one verified, and one not.
.
At the moment, only structural invariants are maintained.
.
More information, and a walkthough of a couple implementations, can
be found at this <http://doisinkidney.com/posts/2017-04-23-verifying-data-structures-in-haskell-lhs.html blog post>.
.
/Comparisons of verified and unverified queues/
.
Both versions of each queue are provided for comparison: for
instance, compare the standard leftist queue (in
"Data.Queue.Leftist"):
.
> data Leftist a
> = Leaf
> | Node !Int
> a
> (Leftist a)
> (Leftist a)
.
To its size-indexed counterpart (in "Data.Queue.Indexed.Leftist"):
.
> data Leftist n a where
> Leaf :: Leftist 0 a
> Node :: !(The Nat (n + m + 1))
> -> a
> -> Leftist n a
> -> Leftist m a
> -> !(m <= n)
> -> Leftist (n + m + 1) a
.
The invariant here (that the size of the left queue must
always be less than that of the right) is encoded in the
proof @m '<=' n@.
.
With that in mind, compare the unverified and verified
implementatons of @merge@:
.
> merge Leaf h2 = h2
> merge h1 Leaf = h1
> merge h1@(Node w1 p1 l1 r1) h2@(Node w2 p2 l2 r2)
> | p1 < p2 =
> if ll <= lr
> then Node (w1 + w2) p1 l1 (merge r1 h2)
> else Node (w1 + w2) p1 (merge r1 h2) l1
> | otherwise =
> if rl <= rr
> then Node (w1 + w2) p2 l2 (merge r2 h1)
> else Node (w1 + w2) p2 (merge r2 h1) l2
> where
> ll = rank r1 + w2
> lr = rank l1
> rl = rank r2 + w1
> rr = rank l2
.
Verified:
.
> merge Leaf h2 = h2
> merge h1 Leaf = h1
> merge h1@(Node w1 p1 l1 r1 _) h2@(Node w2 p2 l2 r2 _)
> | p1 < p2 =
> if ll <=. lr
> then Node (w1 +. w2) p1 l1 (merge r1 h2)
> else Node (w1 +. w2) p1 (merge r1 h2) l1 . totalOrder ll lr
> | otherwise =
> if rl <=. rr
> then Node (w1 +. w2) p2 l2 (merge r2 h1)
> else Node (w1 +. w2) p2 (merge r2 h1) l2 . totalOrder rl rr
> where
> ll = rank r1 +. w2
> lr = rank l1
> rl = rank r2 +. w1
> rr = rank l2
.
/Using type families and typechecker plugins to encode the invariant/
.
The similarity is accomplished through overloading, and some
handy functions. For instance, the second if-then-else works
on boolean /singletons/, and the @<=.@ function provides a
proof of order along with its answer. The actual arithmetic
is carried out at runtime on normal integers, rather than
Peano numerals. These tricks are explained in more detail
"TypeLevel.Singletons" and "TypeLevel.Bool".
.
A typechecker plugin does most of the heavy lifting, although
there are some (small) manual proofs.
.
/Uses of verified queues/
.
The main interesting use of these sturctures is total traversable
sorting (<https://github.com/treeowl/sort-traversable sort-traversable>).
An implementation of this is provided in "Data.Traversable.Parts". I'm
interested in finding out other uses for these kinds of structures.
homepage: https://github.com/oisdk/type-indexed-queues
license: MIT
license-file: LICENSE
author: Donnacha Oisín Kidney
maintainer: mail@doisinkidney.com
copyright: 2017 Donnacha Oisín Kidney
category: Data Structures
build-type: Simple
extra-source-files: README.md
cabal-version: >=1.10
library
hs-source-dirs: src
exposed-modules: Data.Queue.Binomial
, Data.Queue.Pairing
, Data.Queue.Skew
, Data.Queue.Splay
, Data.Queue.Leftist
, Data.Queue.Braun
, Data.Queue.Class
, Data.Queue.WithDict
, Data.Queue.Indexed.Pairing
, Data.Queue.Indexed.Binomial
, Data.Queue.Indexed.Skew
, Data.Queue.Indexed.Leftist
, Data.Queue.Indexed.Braun
, Data.Queue.Indexed.Class
, Data.Queue.Indexed.Erased
, Data.Queue.Indexed.List
, Data.Queue.Indexed.Splay
, Data.Traversable.Parts
, Data.Tree.Replicate
, TypeLevel.Nat
, Data.BinaryTree
, TypeLevel.Singletons
, TypeLevel.Nat.Proofs
, TypeLevel.Bool
build-depends: base >=4.7 && <5
, ghc-typelits-natnormalise >=0.4
, deepseq >=1.4
, containers >=0.5
default-language: Haskell2010
benchmark bench
default-language: Haskell2010
type: exitcode-stdio-1.0
hs-source-dirs: bench
main-is: bench.hs
ghc-options: -O2 -rtsopts -threaded
build-depends: base >=4.8
, type-indexed-queues
, criterion >=0.1
, containers >=0.5
, random >=1.0.0.0
, pqueue >=1.0.0
test-suite type-indexed-queues-test
type: exitcode-stdio-1.0
hs-source-dirs: test
main-is: Spec.hs
build-depends: base >=4.7 && <5
, type-indexed-queues
, QuickCheck >=1.0
, doctest >=0.3.0
, containers >=0.5
, tasty >=0.1
, tasty-quickcheck >=0.1
ghc-options: -threaded -rtsopts -with-rtsopts=-N
default-language: Haskell2010
source-repository head
type: git
location: https://github.com/oisdk/type-indexed-queues