-- |
-- Module      : Data.Express.Fold
-- Copyright   : (c) 2019-2021 Rudy Matela
-- License     : 3-Clause BSD  (see the file LICENSE)
-- Maintainer  : Rudy Matela <rudy@matela.com.br>
--
-- Defines utilities for folding and unfolding 'Expr's.
{-# LANGUAGE CPP #-}
#if __GLASGOW_HASKELL__ == 708
{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-}
#endif
module Data.Express.Fold
  ( fold
  , unfold
  , foldPair
  , unfoldPair
  , foldTrio
  , unfoldTrio
  , foldApp
  , unfoldApp
  )
where

import Data.Express.Core
import Data.Express.Utils.Typeable

data ExprPair = ExprPair

-- | /O(n)/.
-- Folds a list of 'Expr' with function application (':$').
-- This reverses the effect of 'unfoldApp'.
--
-- > foldApp [e0]           =  e0
-- > foldApp [e0,e1]        =  e0 :$ e1
-- > foldApp [e0,e1,e2]     =  e0 :$ e1 :$ e2
-- > foldApp [e0,e1,e2,e3]  =  e0 :$ e1 :$ e2 :$ e3
--
-- Remember ':$' is left-associative, so:
--
-- > foldApp [e0]           =    e0
-- > foldApp [e0,e1]        =   (e0 :$ e1)
-- > foldApp [e0,e1,e2]     =  ((e0 :$ e1) :$ e2)
-- > foldApp [e0,e1,e2,e3]  = (((e0 :$ e1) :$ e2) :$ e3)
--
-- This function /may/ produce an ill-typed expression.
foldApp :: [Expr] -> Expr
foldApp :: [Expr] -> Expr
foldApp = (Expr -> Expr -> Expr) -> [Expr] -> Expr
forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
foldl1 Expr -> Expr -> Expr
(:$)

-- | /O(1)/.
-- Folds a pair of 'Expr' values into a single 'Expr'.
-- (cf. 'unfoldPair')
--
-- This /always/ generates an ill-typed expression,
-- as it uses a fake pair constructor.
--
-- > > foldPair (val False, val (1::Int))
-- > (False,1) :: ill-typed # ExprPair $ Bool #
--
-- > > foldPair (val (0::Int), val True)
-- > (0,True) :: ill-typed # ExprPair $ Int #
--
-- This is useful when applying transformations on pairs of 'Expr's, such as
-- 'Data.Express.Canon.canonicalize',
-- 'Data.Express.Map.mapValues' or
-- 'Data.Express.Canon.canonicalVariations'.
--
-- > > let ii = var "i" (undefined::Int)
-- > > let kk = var "k" (undefined::Int)
-- > > unfoldPair $ canonicalize $ foldPair (ii,kk)
-- > (x :: Int,y :: Int)
foldPair :: (Expr,Expr) -> Expr
foldPair :: (Expr, Expr) -> Expr
foldPair (Expr
e1,Expr
e2)  =  String -> ExprPair -> Expr
forall a. Typeable a => String -> a -> Expr
value String
"," (ExprPair
forall a. HasCallStack => a
undefined :: ExprPair) Expr -> Expr -> Expr
:$ Expr
e1 Expr -> Expr -> Expr
:$ Expr
e2

-- | /O(1)/.
-- Unfolds an 'Expr' representing a pair.
-- This reverses the effect of 'foldPair'.
--
-- > > value "," ((,) :: Bool->Bool->(Bool,Bool)) :$ val True :$ val False
-- > (True,False) :: (Bool,Bool)
-- > > unfoldPair $ value "," ((,) :: Bool->Bool->(Bool,Bool)) :$ val True :$ val False
-- > (True :: Bool,False :: Bool)
unfoldPair :: Expr -> (Expr,Expr)
unfoldPair :: Expr -> (Expr, Expr)
unfoldPair (Value String
"," Dynamic
_ :$ Expr
e1 :$ Expr
e2) = (Expr
e1,Expr
e2)
unfoldPair (Value String
"(,)" Dynamic
_ :$ Expr
e1 :$ Expr
e2) = (Expr
e1,Expr
e2)
unfoldPair Expr
_  =  String -> (Expr, Expr)
forall a. HasCallStack => String -> a
error String
"unfoldPair: not an Expr pair"

data ExprTrio = ExprTrio

-- | /O(1)/.
-- Folds a trio/triple of 'Expr' values into a single 'Expr'.
-- (cf. 'unfoldTrio')
--
-- This /always/ generates an ill-typed expression
-- as it uses a fake trio/triple constructor.
--
-- > > foldTrio (val False, val (1::Int), val 'a')
-- > (False,1,'a') :: ill-typed # ExprTrio $ Bool #
--
-- > > foldTrio (val (0::Int), val True, val 'b')
-- > (0,True,'b') :: ill-typed # ExprTrio $ Int #
--
-- This is useful when applying transformations on pairs of 'Expr's, such as
-- 'Data.Express.Canon.canonicalize',
-- 'Data.Express.Map.mapValues' or
-- 'Data.Express.Canon.canonicalVariations'.
--
-- > > let ii = var "i" (undefined::Int)
-- > > let kk = var "k" (undefined::Int)
-- > > let zz = var "z" (undefined::Int)
-- > > unfoldPair $ canonicalize $ foldPair (ii,kk,zz)
-- > (x :: Int,y :: Int,z :: Int)
foldTrio :: (Expr,Expr,Expr) -> Expr
foldTrio :: (Expr, Expr, Expr) -> Expr
foldTrio (Expr
e1,Expr
e2,Expr
e3)  =  String -> ExprTrio -> Expr
forall a. Typeable a => String -> a -> Expr
value String
",," (ExprTrio
forall a. HasCallStack => a
undefined :: ExprTrio) Expr -> Expr -> Expr
:$ Expr
e1 Expr -> Expr -> Expr
:$ Expr
e2 Expr -> Expr -> Expr
:$ Expr
e3

-- | /O(1)/.
-- Unfolds an 'Expr' representing a trio/triple.
-- This reverses the effect of 'foldTrio'.
--
-- > > value ",," ((,,) :: Bool->Bool->Bool->(Bool,Bool,Bool)) :$ val True :$ val False :$ val True
-- > (True,False,True) :: (Bool,Bool,Bool)
-- > > unfoldTrio $ value ",," ((,,) :: Bool->Bool->Bool->(Bool,Bool,Bool)) :$ val True :$ val False :$ val True
-- > (True :: Bool,False :: Bool,True :: Bool)
--
-- (cf. 'unfoldPair')
unfoldTrio :: Expr -> (Expr,Expr,Expr)
unfoldTrio :: Expr -> (Expr, Expr, Expr)
unfoldTrio (Value String
",," Dynamic
_ :$ Expr
e1 :$ Expr
e2 :$ Expr
e3) = (Expr
e1,Expr
e2,Expr
e3)
unfoldTrio (Value String
"(,,)" Dynamic
_ :$ Expr
e1 :$ Expr
e2 :$ Expr
e3) = (Expr
e1,Expr
e2,Expr
e3)
unfoldTrio Expr
_  =  String -> (Expr, Expr, Expr)
forall a. HasCallStack => String -> a
error String
"unfoldTrio: not an Expr trio"

data ExprList = ExprList

-- | /O(n)/.
-- Folds a list of 'Expr's into a single 'Expr'.
-- (cf. 'unfold')
--
-- This /always/ generates an ill-typed expression.
--
-- > fold [val False, val True, val (1::Int)]
-- > [False,True,1] :: ill-typed # ExprList $ Bool #
--
-- This is useful when applying transformations on lists of 'Expr's, such as
-- 'Data.Express.Canon.canonicalize',
-- 'Data.Express.Map.mapValues' or
-- 'Data.Express.Canon.canonicalVariations'.
--
-- > > let ii = var "i" (undefined::Int)
-- > > let kk = var "k" (undefined::Int)
-- > > let qq = var "q" (undefined::Bool)
-- > > let notE = value "not" not
-- > > unfold . canonicalize . fold $ [ii,kk,notE :$ qq, notE :$ val False]
-- > [x :: Int,y :: Int,not p :: Bool,not False :: Bool]
fold :: [Expr] -> Expr
fold :: [Expr] -> Expr
fold []      =  String -> ExprList -> Expr
forall a. Typeable a => String -> a -> Expr
value String
"[]" ExprList
ExprList
fold (Expr
e:[Expr]
es)  =  String -> ExprList -> Expr
forall a. Typeable a => String -> a -> Expr
value String
":"  ExprList
ExprList Expr -> Expr -> Expr
:$ Expr
e Expr -> Expr -> Expr
:$ [Expr] -> Expr
fold [Expr]
es

-- | /O(n)/.
-- Unfolds an 'Expr' representing a list into a list of 'Expr's.
-- This reverses the effect of 'fold'.
--
-- > > expr [1,2,3::Int]
-- > [1,2,3] :: [Int]
-- > > unfold $ expr [1,2,3::Int]
-- > [1 :: Int,2 :: Int,3 :: Int]
unfold :: Expr -> [Expr]
unfold :: Expr -> [Expr]
unfold (Value String
"[]" Dynamic
_)             =  []
unfold (Value String
":"  Dynamic
_ :$ Expr
e :$ Expr
es)  =  Expr
e Expr -> [Expr] -> [Expr]
forall a. a -> [a] -> [a]
: Expr -> [Expr]
unfold Expr
es
unfold Expr
e  =  String -> [Expr]
forall a. HasCallStack => String -> a
error (String -> [Expr]) -> String -> [Expr]
forall a b. (a -> b) -> a -> b
$ String
"unfold: cannot unfold expression: " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Expr -> String
forall a. Show a => a -> String
show Expr
e

#if __GLASGOW_HASKELL__ == 708
deriving instance Typeable ExprPair
deriving instance Typeable ExprTrio
deriving instance Typeable ExprList
#endif