vagston’s blog

Tiny proof assistant in Clean without Curry-Howard Isomorphism

nobody@vox.com(vagston) — Thu, 09 Jul 2009 01:55:39 -0700

module tst import StdGeneric, GenEq, StdMisc from StdEnv import instance == {#Char}, instance == Int, instance == Real, &&, class == (..), instance == [a] | == a Start = let p = pvar "P" in [notI2 p,notE2_nc p,notE3 p,notE3_nc p,errNotE2 p]...

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Tiny proof assistant in Clean using Curry-Howard Isomorphism

nobody@vox.com(vagston) — Thu, 09 Jul 2009 01:51:15 -0700

module CHI Start = notE3 (|- (((P --> Bot) --> Bot) --> Bot)) (Wff P) //notI2 (|- P) (Wff P) where notE3 n3 wff_p = impI (hlp1 n3) wff_p where hlp1 n3 p = nd_contra (notI2 p wff_p) n3 notI2 p wff_p = impI (hlp p) (nd_not w...

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Tiny proof assistant in Clean using Curry-Howard Isomorphism

nobody@vox.com(vagston) — Thu, 09 Jul 2009 01:50:48 -0700

 module CHI  Start = notE3 (|- (((P --> Bot) --> Bot) --> Bot)) (Wff P)  //notI2 (|- P) (Wff P) where     notE3 n3 wff_p = impI (hlp1 n3) wff_p     where         hlp1 n3 p = nd_contra (notI2 p wff_p) n3      notI2 p wff_p = impI (hlp p) (nd_n...     
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Read Only Graph Builder In Functional Language

nobody@vox.com(vagston) — Tue, 03 Mar 2009 02:05:10 -0800

:: ROGraph a = ROGraph a [ROGraph a] :: RODGraph a = RODGraph a [RODGraph a] [RODGraph a] buildROGraph :: (a b (c,[b])) -> Map b (ROGraph c) | Lookup MapOnList b & UpdateDefault MapOnList b & Pairs a buildROGraph m = buildGraph m \ id val fws ...

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Adding Pluggable Search Strategies to Your Favourite Functional Programming Language

nobody@vox.com(vagston) — Sat, 17 Jan 2009 17:57:55 -0800

 search3 :: !Bool !(u:a -> .(v:([u:a] -> w:[.b]) -> x:[.b])) u:a -> y:[.b], [v <= u,x v <= w,x v <= y] search3 kind explorer root | kind = do_all_depth [root] [] = do_all_breadth [root] [] where do_all_depth [] t = t do_all_depth [v:vs] t = e...     
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Purely Functional Queue with Constant Operation Times (Credits to Okasaki)

nobody@vox.com(vagston) — Thu, 15 Jan 2009 20:00:47 -0800

 :: Queue a = Queue !Int !.[a] !Int !.[.[a]] /* enqLen enqList deqLen deqList */ adjust :: !u:(Queue .a) -> v:(Queue .a), [u <= v] adjust q=:(Queue enqLen enqList deqLen deqList) | enqLen > 3 && enqLen >= deqLen = Queue 0 [] (enqLen + deqLen)...     
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Introductory Course In Applied Math: No Background Needed

nobody@vox.com(vagston) — Tue, 11 Nov 2008 00:43:17 -0800

1. Notion of representation 2. Notion of encoding 3. Requirements to glyphs: equality, recognisability, one might always realise where one ends and another begins 4. Deductive apparatus, mathematical theories 5. Interpretations of mathematical the...

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Monadic Arithmetics

nobody@vox.com(vagston) — Tue, 11 Nov 2008 00:42:31 -0800

/* Stop >>= \a -> >>= \b insane! */ instance + (m a) | + a & Monad m where (+) ma mb = ma >>= \a -> mb >>= \b -> return $! a + b instance - (m a) | - a & Monad m where (-) ma mb = ma >>= \a -> mb >>= \b -> return $! a - b instance * (m a) | ...

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My Desktop 2008

nobody@vox.com(vagston) — Thu, 24 Jul 2008 10:10:55 -0700

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Fascinating excursion in monads history

nobody@vox.com(vagston) — Tue, 03 Jun 2008 15:30:02 -0700

Fascinating excursion in monads history The notion of monad comes from category theory. It first arose in the area of homological algebra, but later was recognised (due to the work of Kleisli and of Eilenberg and Moore) to have much wider appli...

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