module Test.Main where

import Prelude
import Language.Bergamot.Syntax
import Language.Bergamot.Rules
import Language.Bergamot.Unifier
import Language.Bergamot.Parser
import Control.Apply
import Control.Monad.Logic.Trans
import Control.Monad.Logic.Class
import Control.Monad.Unify.Trans
import Control.Monad.Unify.Class
import Data.List (List(..), (:))
import Data.Array (fromFoldable)
import Data.Foldable
import Data.Maybe

tType et tt = Atom "type" $ et : tt : Nil
tInt = Atom "int" Nil                                      
tString = Atom "string" Nil                                
tProd t1 t2 = Atom "prod" $ t1 : t2 : Nil
tIntExpr = Atom "n" Nil                                    
tStringExpr = Atom "s" Nil
tPlusExpr et1 et2 = Atom "plus" $ et1 : et2 : Nil
tProdExpr et1 et2 = Atom "pair" $ et1 : et2 : Nil
tFstExpr et = Atom "fst" $ et : Nil
tSndExpr et = Atom "snd" $ et : Nil

toLatexExpr :: Expr String -> String
toLatexExpr (Atom "type" (t1 : t2 : Nil)) = toLatexExpr t1 <> " : " <> toLatexExpr t2
toLatexExpr (Atom "int" Nil) = "\\text{int}"
toLatexExpr (Atom "string" Nil) = "\\text{string}"
toLatexExpr (Atom "prod" (t1 : t2 : Nil)) = toLatexExpr t1 <> "\\times " <> toLatexExpr t2
toLatexExpr (Atom "n" Nil) = "n"
toLatexExpr (Atom "s" Nil) = "s"
toLatexExpr (Atom "plus" (t1 : t2 : Nil)) = toLatexExpr t1 <> " + " <> toLatexExpr t2
toLatexExpr (Atom "pair" (t1 : t2 : Nil)) = "(" <> toLatexExpr t1 <> ", " <> toLatexExpr t2 <> ")"
toLatexExpr (Atom "fst" (t : Nil)) = "\\text{fst}\\ " <> toLatexExpr t
toLatexExpr (Atom "snd" (t : Nil)) = "\\text{snd}\\ " <> toLatexExpr t
toLatexExpr (Atom s xs) = "\\text{" <> s <> "}(" <> intercalate ", " (toLatexExpr <$> xs) <> ")"
toLatexExpr (Var x) = x

toLatexRule :: Rule String -> String
toLatexRule (MkRule {head, tail}) = "\\cfrac{" <> intercalate "\\quad " (toLatexExpr <$> tail) <> "}{" <> toLatexExpr head <> "}"

toLatexProofTree :: ProofTree String -> String
toLatexProofTree (MkProofTree {claim, witnesses}) = "\\cfrac{" <> intercalate "\\quad " (toLatexProofTree <$> witnesses) <> "}{" <> toLatexExpr claim <> "}"

main :: String -> String -> Maybe String
main rs q = map (toLatexProofTree <<< map (const "?")) $ join $ lift2 runUnifier (fromFoldable <$> parseRules rs) (query <$> parseQuery q)
-- main = map toLatexProofTree $ runUnifier rules $ query $ tType (tSndExpr (tProdExpr tStringExpr (tPlusExpr tIntExpr tIntExpr))) (Var "T")