first commit

Example.hs

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+{-# LANGUAGE
+ FlexibleContexts,
+ TypeOperators
+ #-}
+module Example where
+
+import Types.Nats
+import Types.Step
+import Types.Terms
+
+import Types.Isomorphic
+
+
+
+true = Lam $ Lam $ Var $ S Z
+false = Lam $ Lam $ Var $ Z
+
+ifThenElse a b c = App (App a b) c
+
+land a b = ifThenElse a b false
+lor a b = App (ifThenElse a (Lam $ true) (Lam $ Var Z)) b
+
+-- magic. try :t infer_implicit
+infer_implicit = stepVar $ App (Lam $ Var Z) (lor false true)
+
+-- Type operators make the heart grow warmer! 
+infixr 0 :$
+type m :$ a = m a
+
+-- EVEN MORE MAGIC
+infer_explicit = val :: (Step (App (Lam :$ Var Z) :$ Var :$ S :$ S Z) b => Term b)
+
+main = do
+  putStrLn $ show infer_implicit
+  putStrLn $ show infer_explicit

LICENSE

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README

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+<h1>Dependently typed logic programming in meta-haskell!</h1>
+
+<h2>Overview: </h2>
+<p>
+An example of using dependently typed logic programming in haskell's 
+type system to do theorem proved template black magic without templates.
+</p>
+
+<h2>Details: </h2>
+<p>
+A big step semantics for lazy lambda 
+calculus on types used on class logic programming, 
+and an Isomorphism class which forces a class and 
+instances under different data types to be isomorphic 
+to a GADT with constructors such that we the class 
+can not be instanced elsewhere with more datatypes.
+</p>

Types/Isomorphic.hs

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+{-# LANGUAGE
+ MultiParamTypeClasses,
+ FunctionalDependencies
+ #-}
+module Types.Isomorphic ( Iso(..) 
+                        ) where 
+
+-- | @'Iso'@ is a class which allows for a proof that a is of "type" m
+class Iso m a | a -> m where
+  tp :: a
+  val :: m a
+
+  into :: a -> m a
+  into = const val
+
+  outof :: m a -> a
+  outof = const tp