144 lines
5.7 KiB
Plaintext
144 lines
5.7 KiB
Plaintext
module Language.Bergamot.Syntax where
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import Prelude (Unit, ($), (<<<), unit, (/=), const, flip, (+))
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import Control.Plus (class Plus, empty)
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import Control.Monad (class Monad)
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import Control.Monad.State.Trans (StateT, runStateT)
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import Control.Monad.State.Class (class MonadState, gets, modify)
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import Control.Apply (class Apply, apply, lift2)
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import Control.Alt (class Alt, alt)
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import Control.Alternative (class Alternative)
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import Control.Applicative (class Applicative, pure, (*>))
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import Control.Bind (class Bind, bind, join, (>>=))
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import Control.MonadPlus (class MonadPlus)
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import Control.Monad.Reader.Class (class MonadReader, class MonadAsk, local, ask)
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import Control.Monad.Logic.Class (class MonadLogic, msplit, interleave)
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import Control.Monad.Unify.Class (class MonadUnify, class Unifiable, class UnificationVariable, Stream(..), squash, alongside, ComparisonAction(..), fresh, unify, reify)
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import Control.Monad.Reader.Trans (ReaderT, runReaderT)
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import Control.Monad.Unify.Trans (UnifyT(..), runUnifyT)
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import Control.Monad.Logic.Trans (SFKT(..), runSFKTOnce)
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import Control.Monad.State.Trans (StateT(..), runStateT)
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import Data.List (List(..), (:), fromFoldable)
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import Data.Functor (class Functor, (<$>), map)
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import Data.Eq (class Eq)
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import Data.Ord (class Ord)
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import Data.Traversable (class Traversable, sequence, traverse, oneOf)
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import Data.Foldable (class Foldable, foldr, foldl, foldMap, any, intercalate)
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import Data.Monoid ((<>), mempty)
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import Data.Map (Map, lookup, insert)
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import Data.Map as Map
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import Data.Set (Set, singleton, union)
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import Data.Tuple (Tuple(..), fst)
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import Data.Tuple.Nested ((/\))
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import Data.Lazy (Lazy, defer, force)
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import Data.Newtype (class Newtype, un, over2)
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import Data.Maybe (Maybe(..), fromMaybe, isJust)
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import Data.Bifunctor (rmap)
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data Expr v
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= Var v
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| Atom String (List (Expr v))
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derive instance Eq v => Eq (Expr v)
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derive instance Functor Expr
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derive instance Foldable Expr
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derive instance Traversable Expr
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newtype IntVar = MkIntVar Int
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derive instance Eq IntVar
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derive instance Ord IntVar
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instance UnificationVariable IntVar where
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variables = mkVarList 0
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where mkVarList n = StreamCons (MkIntVar n) $ defer $ \_ -> mkVarList (n+1)
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instance UnificationVariable k => Unifiable k Expr where
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variable = Var
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squash (Var f) = f
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squash (Atom name args) = Atom name $ squash <$> args
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alongside (Var k1) (Var k2) = Var (Merge k1 k2)
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alongside (Var k) f = Var (Store k f)
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alongside f (Var k) = Var (Store k f)
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alongside (Atom n1 _) (Atom n2 _) | n1 /= n2 = Var Fail
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alongside (Atom n1 args1) (Atom _ args2) = Atom n1 $ combine args1 args2
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where
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combine Nil Nil = Nil
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combine (_:_) Nil = (Var Fail) : Nil
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combine Nil (_:_) = (Var Fail) : Nil
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combine (x:xs) (y:ys) = alongside x y : combine xs ys
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-- note: unification expression ef not the same as functor-to-instantiate f, this way we can instantiate
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-- things that contain expression etc.
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instantiate :: forall k f ef m. Traversable f => MonadUnify k ef m => f Metavariable -> m (f k)
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instantiate f = map fst $ runStateT (traverse metavariable f) Map.empty
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newtype Rule k = MkRule { name :: String, head :: Expr k, tail :: List (Expr k) }
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derive instance Newtype (Rule k) _
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derive instance Functor Rule
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derive instance Foldable Rule
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derive instance Traversable Rule
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newtype Unifier a = MkUnifier (UnifyT IntVar Expr (ReaderT (Array (Rule Metavariable)) (SFKT List)) a)
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derive instance Newtype (Unifier a) _
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derive newtype instance Functor Unifier
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derive newtype instance Apply Unifier
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derive newtype instance Applicative Unifier
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derive newtype instance Alt Unifier
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derive newtype instance Plus Unifier
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derive newtype instance Alternative Unifier
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derive newtype instance Bind Unifier
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derive newtype instance Monad Unifier
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derive newtype instance MonadPlus Unifier
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derive newtype instance MonadUnify IntVar Expr Unifier
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-- >:(
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instance MonadAsk (Array (Rule Metavariable)) Unifier where
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ask = MkUnifier $ MkUnifyT ask
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-- >:(
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instance MonadReader (Array (Rule Metavariable)) Unifier where
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local f m = MkUnifier $ MkUnifyT $ StateT $ \s -> local f (runStateT (un MkUnifyT $ un MkUnifier m) s)
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-- >:(
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instance MonadLogic Unifier where
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msplit m = MkUnifier $ MkUnifyT $ map (map (rmap (MkUnifier <<< MkUnifyT))) $ msplit $ un MkUnifyT $ un MkUnifier m
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interleave = over2 MkUnifier (over2 MkUnifyT interleave)
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type Metavariable = String
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type Metavariables k = Map Metavariable k
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metavariable :: forall k f m. MonadState (Metavariables k) m => MonadUnify k f m => Metavariable -> m k
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metavariable s = do
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r <- gets (lookup s)
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case r of
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Just v -> pure v
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Nothing -> do
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v <- fresh
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modify (insert s v) *> pure v
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newtype ProofTree k = MkProofTree { claim :: Expr k, rule :: Rule Metavariable, witnesses :: List (ProofTree k) }
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match :: Array (Rule Metavariable) -> Expr IntVar -> Unifier (ProofTree IntVar)
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match rs e = oneOf $ map (matchSingle e) rs
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where
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matchSingle e' rule = do
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MkRule {head, tail} <- instantiate rule
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_ <- unify e' head
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witnesses <- traverse (match rs) tail
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pure $ MkProofTree { claim: e, rule: rule, witnesses: witnesses }
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reifyProofTree :: ProofTree IntVar -> Unifier (ProofTree IntVar)
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reifyProofTree (MkProofTree {claim, rule, witnesses}) = do
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claim' <- reify claim
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witnesses' <- traverse reifyProofTree witnesses
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pure $ MkProofTree $ { claim: claim', rule: rule, witnesses: witnesses' }
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query :: Expr Metavariable -> Unifier (ProofTree IntVar)
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query e = (join $ lift2 match ask (instantiate e)) >>= reifyProofTree
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runUnifier :: forall a. Array (Rule Metavariable) -> Unifier a -> List a
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runUnifier rs m = runSFKTOnce (fst <$> (runReaderT (runUnifyT $ un MkUnifier m) rs))
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