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opentheory-prime 1.23 → 1.79

raw patch · 7 files changed

+130/−139 lines, 7 filesdep +opentheory-dividesdep +opentheory-streamdep −randomdep ~opentheorydep ~opentheory-primitive

Dependencies added: opentheory-divides, opentheory-stream

Dependencies removed: random

Dependency ranges changed: opentheory, opentheory-primitive

Files

opentheory-prime.cabal view
@@ -1,43 +1,45 @@ name: opentheory-prime-version: 1.23+version: 1.79 category: Number Theory-synopsis: Prime numbers+synopsis: Prime natural numbers license: MIT license-file: LICENSE-cabal-version: >= 1.8.0.6+cabal-version: >= 1.8.0.2 build-type: Simple author: Joe Leslie-Hurd <joe@gilith.com> maintainer: Joe Leslie-Hurd <joe@gilith.com> description:-  Prime numbers - automatically generated from the opentheory package-  haskell-prime-1.23+  Prime natural numbers - this package was automatically generated from the+  OpenTheory package natural-prime-1.79  library   build-depends:     base >= 4.0 && < 5.0,-    random >= 1.0.1.1 && < 2.0,     QuickCheck >= 2.4.0.1 && < 3.0,-    opentheory-primitive >= 1.0 && < 2.0,-    opentheory >= 1.73 && <= 1.76+    opentheory-primitive >= 1.3 && < 2.0,+    opentheory >= 1.193 && < 1.196,+    opentheory-divides >= 1.53 && < 1.56,+    opentheory-stream >= 1.42 && < 1.43    hs-source-dirs: src    ghc-options: -Wall    exposed-modules:-    OpenTheory.Number.Natural.Prime-    OpenTheory.Number.Natural.Prime.Sieve+    OpenTheory.Natural.Prime+    OpenTheory.Natural.Prime.Sieve  executable opentheory-prime-test   build-depends:     base >= 4.0 && < 5.0,-    random >= 1.0.1.1 && < 2.0,     QuickCheck >= 2.4.0.1 && < 3.0,-    opentheory-primitive >= 1.0 && < 2.0,-    opentheory >= 1.73 && <= 1.76+    opentheory-primitive >= 1.3 && < 2.0,+    opentheory >= 1.193 && < 1.196,+    opentheory-divides >= 1.53 && < 1.56,+    opentheory-stream >= 1.42 && < 1.43    hs-source-dirs: src, testsrc    ghc-options: -Wall -  main-is: Test.hs+  main-is: Main.hs
+ src/OpenTheory/Natural/Prime.hs view
@@ -0,0 +1,19 @@+{- |+module: $Header$+description: Prime natural numbers+license: MIT++maintainer: Joe Leslie-Hurd <joe@gilith.com>+stability: provisional+portability: portable+-}++module OpenTheory.Natural.Prime+where++import qualified OpenTheory.Natural.Prime.Sieve as Sieve+import qualified OpenTheory.Primitive.Natural as Natural+import qualified OpenTheory.Stream as Stream++primes :: [Natural.Natural]+primes = Stream.unfold Sieve.next Sieve.initial
+ src/OpenTheory/Natural/Prime/Sieve.hs view
@@ -0,0 +1,50 @@+{- |+module: $Header$+description: Prime natural numbers+license: MIT++maintainer: Joe Leslie-Hurd <joe@gilith.com>+stability: provisional+portability: portable+-}++module OpenTheory.Natural.Prime.Sieve+where++import qualified OpenTheory.Primitive.Natural as Natural++newtype Sieve =+  Sieve {+    unSieve ::+      (Natural.Natural,+       [(Natural.Natural, (Natural.Natural, Natural.Natural))])+  }++initial :: Sieve+initial = Sieve (1, [])++increment :: Sieve -> (Bool, Sieve)+increment =+  \s ->+    let (n, ps) = unSieve s in+    let n' = n + 1 in+    let (b, ps') = inc n' 1 ps in+    (b, Sieve (n', ps'))+  where+  {-inc ::+        Natural.Natural -> Natural.Natural ->+          [(Natural.Natural, (Natural.Natural, Natural.Natural))] ->+          (Bool, [(Natural.Natural, (Natural.Natural, Natural.Natural))])-}+    inc n _ [] = (True, (n, (0, 0)) : [])+    inc n i ((p, (k, j)) : ps) =+      let k' = (k + i) `mod` p in+      let j' = j + i in+      if k' == 0 then (False, (p, (0, j')) : ps)+      else let (b, ps') = inc n j' ps in (b, (p, (k', 0)) : ps')++perimeter :: Sieve -> Natural.Natural+perimeter s = fst (unSieve s)++next :: Sieve -> (Natural.Natural, Sieve)+next s =+  let (b, s') = increment s in if b then (perimeter s', s') else next s'
− src/OpenTheory/Number/Natural/Prime.hs 
@@ -1,18 +0,0 @@-{- |-module: $Header$-description: Prime numbers-license: MIT--maintainer: Joe Leslie-Hurd <joe@gilith.com>-stability: provisional-portability: portable--}-module OpenTheory.Number.Natural.Prime-where--import qualified OpenTheory.Data.Stream as Data.Stream-import qualified OpenTheory.Number.Natural.Prime.Sieve as Sieve-import qualified OpenTheory.Primitive.Natural as Primitive.Natural--all :: [Primitive.Natural.Natural]-all = Data.Stream.unfold Sieve.next Sieve.initial
− src/OpenTheory/Number/Natural/Prime/Sieve.hs 
@@ -1,53 +0,0 @@-{- |-module: $Header$-description: Prime numbers-license: MIT--maintainer: Joe Leslie-Hurd <joe@gilith.com>-stability: provisional-portability: portable--}-module OpenTheory.Number.Natural.Prime.Sieve-where--import qualified OpenTheory.Primitive.Natural as Primitive.Natural--newtype Sieve =-  Sieve {-    unSieve ::-      (Primitive.Natural.Natural,-       [(Primitive.Natural.Natural,-         (Primitive.Natural.Natural, Primitive.Natural.Natural))])-  }--initial :: Sieve-initial = Sieve (1, [])--increment :: Sieve -> (Bool, Sieve)-increment =-  \s ->-    let (n, ps) = unSieve s in-    let n' = n + 1 in-    let (b, ps') = inc n' 1 ps in-    (b, Sieve (n', ps'))-  where-  {-inc ::-        Primitive.Natural.Natural -> Primitive.Natural.Natural ->-          [(Primitive.Natural.Natural,-            (Primitive.Natural.Natural, Primitive.Natural.Natural))] ->-          (Bool,-           [(Primitive.Natural.Natural,-             (Primitive.Natural.Natural, Primitive.Natural.Natural))])-}-    inc n _ [] = (True, (n, (0, 0)) : [])-    inc n i ((p, (k, j)) : ps) =-      let k' = (k + i) `mod` p in-      let j' = j + i in-      if k' == 0 then (False, (p, (0, j')) : ps)-      else let (b, ps') = inc n j' ps in (b, (p, (k', 0)) : ps')--perimeter :: Sieve -> Primitive.Natural.Natural-perimeter s = fst (unSieve s)--next :: Sieve -> (Primitive.Natural.Natural, Sieve)-next s =-  let (b, s') = increment s in if b then (perimeter s', s') else next s'
+ testsrc/Main.hs view
@@ -0,0 +1,45 @@+{- |+module: Main+description: Prime natural numbers - testing+license: MIT++maintainer: Joe Leslie-Hurd <joe@gilith.com>+stability: provisional+portability: portable+-}+module Main+  ( main )+where++import qualified OpenTheory.Natural.Divides as Divides+import qualified OpenTheory.Natural.Prime as Prime+import qualified OpenTheory.Primitive.Natural as Natural+import qualified OpenTheory.Stream as Stream+import OpenTheory.Primitive.Test++assertion0 :: Bool+assertion0 = not (Stream.nth Prime.primes 0 == 0)++proposition0 :: Natural.Natural -> Natural.Natural -> Bool+proposition0 i j =+  (Stream.nth Prime.primes i <= Stream.nth Prime.primes j) == (i <= j)++proposition1 :: Natural.Natural -> Natural.Natural -> Bool+proposition1 i j =+  not+    (Divides.divides (Stream.nth Prime.primes i)+       (Stream.nth Prime.primes (i + (j + 1))))++proposition2 :: Natural.Natural -> Natural.Natural -> Bool+proposition2 n i =+  any (\p -> Divides.divides p (n + 2))+    (Stream.naturalTake Prime.primes i) ||+  Stream.nth Prime.primes i <= n + 2++main :: IO ()+main =+    do assert "Assertion 0:\n  ~(nth Prime.all 0 = 0)\n  " assertion0+       check "Proposition 0:\n  !i j. nth Prime.all i <= nth Prime.all j <=> i <= j\n  " proposition0+       check "Proposition 1:\n  !i j. ~divides (nth Prime.all i) (nth Prime.all (i + (j + 1)))\n  " proposition1+       check "Proposition 2:\n  !n i.\n    any (\\p. divides p (n + 2)) (take Prime.all i) \\/\n    nth Prime.all i <= n + 2\n  " proposition2+       return ()
− testsrc/Test.hs 
@@ -1,54 +0,0 @@-{- |-module: Main-description: Prime numbers - testing-license: MIT--maintainer: Joe Leslie-Hurd <joe@gilith.com>-stability: provisional-portability: portable--}-module Main-  ( main )-where--import qualified OpenTheory.Data.Stream as Data.Stream-import qualified OpenTheory.Number.Natural as Number.Natural-import qualified OpenTheory.Number.Natural.Geometric-  as Number.Natural.Geometric-import qualified OpenTheory.Number.Natural.Prime as Number.Natural.Prime-import qualified OpenTheory.Primitive.Random as Primitive.Random-import qualified OpenTheory.Primitive.Test as Primitive.Test--assertion0 :: Bool-assertion0 = not (Data.Stream.nth Number.Natural.Prime.all 0 == 0)--proposition0 :: Primitive.Random.Random -> Bool-proposition0 r =-  let (i, r') = Number.Natural.Geometric.fromRandom r in-  let (j, _) = Number.Natural.Geometric.fromRandom r' in-  (Data.Stream.nth Number.Natural.Prime.all i <=-   Data.Stream.nth Number.Natural.Prime.all j) == (i <= j)--proposition1 :: Primitive.Random.Random -> Bool-proposition1 r =-  let (i, r') = Number.Natural.Geometric.fromRandom r in-  let (j, _) = Number.Natural.Geometric.fromRandom r' in-  not-    (Number.Natural.divides (Data.Stream.nth Number.Natural.Prime.all i)-       (Data.Stream.nth Number.Natural.Prime.all (i + j + 1)))--proposition2 :: Primitive.Random.Random -> Bool-proposition2 r =-  let (n, r') = Number.Natural.fromRandom r in-  let (i, _) = Number.Natural.Geometric.fromRandom r' in-  any (\p -> Number.Natural.divides p (n + 2))-    (Data.Stream.take' Number.Natural.Prime.all i) ||-  Data.Stream.nth Number.Natural.Prime.all i <= n + 2--main :: IO ()-main =-    do Primitive.Test.assert "Assertion 0:\n  ~(H.nth H.Prime.all 0 = 0)\n  " assertion0-       Primitive.Test.check "Proposition 0:\n  !r.\n    let (i, r') <- H.Geometric.fromRandom r in\n    let (j, r'') <- H.Geometric.fromRandom r' in\n    H.nth H.Prime.all i <= H.nth H.Prime.all j <=> i <= j\n  " proposition0-       Primitive.Test.check "Proposition 1:\n  !r.\n    let (i, r') <- H.Geometric.fromRandom r in\n    let (j, r'') <- H.Geometric.fromRandom r' in\n    ~H.divides (H.nth H.Prime.all i) (H.nth H.Prime.all (i + j + 1))\n  " proposition1-       Primitive.Test.check "Proposition 2:\n  !r.\n    let (n, r') <- H.fromRandom r in\n    let (i, r'') <- H.Geometric.fromRandom r' in\n    any (\\p. H.divides p (n + 2)) (H.take' H.Prime.all i) \\/\n    H.nth H.Prime.all i <= n + 2\n  " proposition2-       return ()