{-# OPTIONS_GHC -Wno-overlapping-patterns #-}
{-# LANGUAGE RankNTypes      #-}
{-# LANGUAGE GADTs           #-}
{-# LANGUAGE KindSignatures  #-}

{-@ LIQUID "--reflection" @-}

-- Z3 encoding cannot be used until this is fixed:
-- https://github.com/Z3Prover/z3/issues/3930
{- LIQUID "--no-adt"         @-}
{-@ LIQUID "--ple-local"      @-}
{-@ LIQUID "--prune-unsorted" @-}

module T1649MeasuresDef where



{-@ assume injectiveEqRTFun :: x:(a->b) -> y:(a->b) -> d:{EqRT (a->b) {x} {y} | isEqFun d}
                         -> {x = eqFunX d && y = eqFunY d} @-}
injectiveEqRTFun :: (a->b) -> (a->b) -> EqT (a->b) -> ()
injectiveEqRTFun _ _ _ = ()


{-@ measure isEqFun @-}
isEqFun :: EqT a -> Bool
isEqFun (EqFun _ _ _) = True
isEqFun _             = False

{-@ reflect eqFunX @-}
{-@ eqFunX :: {d:EqT (a -> b) | isEqFun d} -> (a -> b) @-}
eqFunX :: EqT (a -> b) ->  (a -> b)
eqFunX (EqFun x _ _) = x

{-@ reflect eqFunY @-}
{-@ eqFunY :: {d:EqT (a -> b) | isEqFun d} -> (a -> b) @-}
eqFunY :: EqT (a -> b) ->  (a -> b)
eqFunY (EqFun _ y _) = y


{-@ ple     eqFunP @-}
{-@ reflect eqFunP @-}
{-@ eqFunP :: d:{EqT (a -> b) | isEqFun d} -> (x:a -> EqRT b {eqFunX d x} {eqFunY d x}) @-}
eqFunP :: EqT (a -> b) ->  (a -> EqT b)
eqFunP (EqFun _ _ p) = p


data EqT  :: * -> *  where
   EqFun  :: (a -> b) -> (a -> b) -> (a -> EqT b) -> EqT (a -> b)

{-@ data EqT  :: * -> *  where
     EqFun  :: ff:(a -> b) -> gg:(a -> b) -> (x:a -> EqRT b {ff x} {gg x}) -> EqRT (a -> b) {ff} {gg}
@-}


{-@ type EqRT a E1 E2 = {v:EqT a | E1 = E2} @-}