Get a rule search engine working with hardcoded rules
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@ -104,9 +104,9 @@ let upstream =
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in upstream
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with logict.repo = "https://dev.danilafe.com/Everything-I-Know-About-Types/logict.git"
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with logict.version = "24298710fa940bfcf2d272bc6d5c7417f2bfccfe"
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with logict.version = "c2088a696727d26cb41b2553d24f3909f0525e12"
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with logict.dependencies = [ "control", "lists", "maybe", "prelude", "transformers", "tuples" ]
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with unifyt.repo = "https://dev.danilafe.com/Everything-I-Know-About-Types/unifyt.git"
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with unifyt.version = "d1e227dbed5e5af63510872b95a9417200c0d7c7"
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with unifyt.version = "014d9b38c8a1742dc3039227f84e3ba06acea51b"
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with unifyt.dependencies = [ "control", "foldable-traversable", "lazy", "maybe", "newtype", "ordered-collections", "prelude", "transformers", "tuples" ]
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@ -5,23 +5,23 @@ 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 (gets, modify)
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import Control.Apply (class Apply, apply)
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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.Applicative (class Applicative, pure, (*>))
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import Control.Bind (class Bind, bind, (>>=))
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import Control.MonadPlus (class MonadPlus)
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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(..))
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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.Unify.Trans (UnifyT(..), runUnifyT)
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import Control.Monad.Logic.Trans (SFKT(..), runSFKT)
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import Data.List (List(..), (:))
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import Control.Monad.Logic.Trans (SFKT(..), runSFKTOnce)
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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)
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import Data.Foldable (class Foldable, foldr, foldl, foldMap, any)
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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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@ -39,25 +39,10 @@ data 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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instance Foldable Expr where
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foldr f b (Var x) = f x b
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foldr f b (Atom _ xs) = foldr (\x b' -> foldr f b' x) b xs
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foldl f b (Var x) = f b x
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foldl f b (Atom _ xs) = foldl (foldl f) b xs
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foldMap f (Var x) = f x
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foldMap f (Atom _ xs) = foldl (<>) mempty (foldMap f <$> xs)
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instance Traversable Expr where
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sequence (Var f) = Var <$> f
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sequence (Atom name fs) = Atom name <$> sequence (sequence <$> fs)
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traverse f e = sequence (f <$> e)
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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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@ -80,22 +65,119 @@ instance UnificationVariable k => Unifiable k Expr where
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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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newtype Unifier a = MkUnifier (UnifyT IntVar Expr (SFKT Maybe) a)
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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 (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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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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-- >:(
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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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runUnifier :: forall a. Unifier a -> Maybe a
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runUnifier m = runSFKT (runUnifyT $ un MkUnifier m) (const <<< Just) Nothing
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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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rules :: Array (Rule Metavariable)
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rules =
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[ MkRule { name: "TInt", head: tType tIntExpr tInt, tail: Nil }
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, MkRule { name: "TString", head: tType tStringExpr tString, tail: Nil }
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, MkRule { name: "TPlusInt", head: tType (tPlusExpr (Var "e1") (Var "e2")) tInt, tail: fromFoldable
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[ tType (Var "e1") tInt
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, tType (Var "e2") tInt
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] }
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, MkRule { name: "TPlusString", head: tType (tPlusExpr (Var "e1") (Var "e2")) tString, tail: fromFoldable
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[ tType (Var "e1") tString
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, tType (Var "e2") tString
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] }
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, MkRule { name: "TPair", head: tType (tProdExpr (Var "e1") (Var "e2")) (tProd (Var "t1") (Var "t2")), tail: fromFoldable
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[ tType (Var "e1") (Var "t1")
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, tType (Var "e2") (Var "t2")
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] }
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, MkRule { name: "TFst", head: tType (tFstExpr (Var "e")) (Var "t1"), tail: fromFoldable
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[ tType (Var "e") (tProd (Var "t1") (Var "t2"))
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] }
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, MkRule { name: "TSnd", head: tType (tSndExpr (Var "e")) (Var "t2"), tail: fromFoldable
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[ tType (Var "e") (tProd (Var "t1") (Var "t2"))
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] }
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]
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tType et tt = Atom "type" $ et : tt : Nil
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tInt = Atom "int" Nil
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tString = Atom "string" Nil
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tProd t1 t2 = Atom "prod" $ t1 : t2 : Nil
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tIntExpr = Atom "n" Nil
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tStringExpr = Atom "s" Nil
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tPlusExpr et1 et2 = Atom "plus" $ et1 : et2 : Nil
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tProdExpr et1 et2 = Atom "pair" $ et1 : et2 : Nil
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tFstExpr et = Atom "fst" $ et : Nil
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tSndExpr et = Atom "snd" $ et : Nil
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toLatexExpr :: Expr IntVar -> String
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toLatexExpr (Atom "type" (t1 : t2 : Nil)) = toLatexExpr t1 <> " : " <> toLatexExpr t2
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toLatexExpr (Atom "int" Nil) = "\\text{int}"
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toLatexExpr (Atom "string" Nil) = "\\text{string}"
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toLatexExpr (Atom "prod" (t1 : t2 : Nil)) = toLatexExpr t1 <> "\\times" <> toLatexExpr t2
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toLatexExpr (Atom "n" Nil) = "n"
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toLatexExpr (Atom "s" Nil) = "s"
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toLatexExpr (Atom "plus" (t1 : t2 : Nil)) = toLatexExpr t1 <> " + " <> toLatexExpr t2
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toLatexExpr (Atom "pair" (t1 : t2 : Nil)) = "(" <> toLatexExpr t1 <> ", " <> toLatexExpr t2 <> ")"
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toLatexExpr (Atom "fst" (t : Nil)) = "\\text{fst}\\ " <> toLatexExpr t
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toLatexExpr (Atom "snd" (t : Nil)) = "\\text{snd}\\ " <> toLatexExpr t
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toLatexExpr (Atom s xs) = "\\text{" <> s <> "}(" <> intercalate ", " (toLatexExpr <$> xs) <> ")"
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toLatexExpr (Var _) = "?"
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toLatexProofTree :: ProofTree IntVar -> String
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toLatexProofTree (MkProofTree {claim, rule, witnesses}) = "\\cfrac{" <> intercalate "\\quad" (toLatexProofTree <$> witnesses) <> "}{" <> toLatexExpr claim <> "}"
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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 = instantiate e >>= match rules >>= reifyProofTree
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runUnifier :: forall a. Unifier a -> List a
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runUnifier m = runSFKTOnce (fst <$> (runUnifyT $ un MkUnifier m))
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@ -9,15 +9,5 @@ import Control.Monad.Unify.Class
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import Data.List
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import Data.Maybe
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runSomeComputation :: forall m. MonadLogic m => MonadUnify IntVar Expr m => m (Expr IntVar)
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runSomeComputation = do
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x1 <- fresh
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x2 <- fresh
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let binPred = Atom "hello" $ fromFoldable [variable x1, variable x2]
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let realBinPred = Atom "hello" $ fromFoldable [Atom "first" $ fromFoldable [], Atom "second" $ fromFoldable []]
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unify binPred realBinPred
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(unify (variable x1) (variable x2) >>= const (reify (variable x1))) `interleave` (unify (variable x1) (variable x1) >>= const (reify (variable x2)))
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main :: Maybe (Expr IntVar)
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main = runUnifier runSomeComputation
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main :: List String
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main = map toLatexProofTree $ runUnifier $ query $ tType (tSndExpr (tProdExpr tStringExpr (tPlusExpr tIntExpr tIntExpr))) (Var "T")
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