vagston’s blog

Tiny proof assistant in Clean without Curry-Howard Isomorphism

2009-07-09T08:55:39Z

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

2009-07-09T08:51:15Z

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

2009-07-09T08:50:48Z

 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

2009-03-03T10:05:10Z

:: 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

2009-01-18T01:57:55Z

 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)

2009-01-16T04:00:47Z

 :: 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

2008-11-11T08:43:17Z

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

2008-11-11T08:42:31Z

/* 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

2008-07-24T17:10:55Z

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Fascinating excursion in monads history

2008-06-03T22:30:02Z

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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