-- | -- Module : Data.Express.Hole -- Copyright : (c) 2019-2021 Rudy Matela -- License : 3-Clause BSD (see the file LICENSE) -- Maintainer : Rudy Matela <rudy@matela.com.br> -- -- Utilities for manipulating variables and typed holes encoded as 'Expr's. {-# LANGUAGE CPP #-} module Data.Express.Hole ( -- * Creating variables varAsTypeOf , listVars , listVarsAsTypeOf -- * Typed holes , hole , isHole , hasHole , isComplete , holes , nubHoles , holeAsTypeOf , fill ) where import Data.Express.Core import Data.Dynamic import Data.Maybe (fromMaybe) import Data.Express.Utils.Typeable (tyArity) import Data.Express.Utils.List (nubSort) import Data.Express.Utils.String (variableNamesFromTemplate) -- | /O(1)/. -- Creates a 'var'iable with the same type as the given 'Expr'. -- -- > > let one = val (1::Int) -- > > "x" `varAsTypeOf` one -- > x :: Int -- -- > > "p" `varAsTypeOf` val False -- > p :: Bool varAsTypeOf :: String -> Expr -> Expr varAsTypeOf :: String -> Expr -> Expr varAsTypeOf String n = String -> Dynamic -> Expr Value (Char '_'Char -> String -> String forall a. a -> [a] -> [a] :String n) (Dynamic -> Expr) -> (Expr -> Dynamic) -> Expr -> Expr forall b c a. (b -> c) -> (a -> b) -> a -> c . Dynamic -> Dynamic undefine (Dynamic -> Dynamic) -> (Expr -> Dynamic) -> Expr -> Dynamic forall b c a. (b -> c) -> (a -> b) -> a -> c . Dynamic -> Maybe Dynamic -> Dynamic forall a. a -> Maybe a -> a fromMaybe Dynamic forall a. a err (Maybe Dynamic -> Dynamic) -> (Expr -> Maybe Dynamic) -> Expr -> Dynamic forall b c a. (b -> c) -> (a -> b) -> a -> c . Expr -> Maybe Dynamic toDynamic where err :: a err = String -> a forall a. HasCallStack => String -> a error String "varAsTypeOf: could not compile Dynamic value, type error?" undefine :: Dynamic -> Dynamic #if __GLASGOW_HASKELL__ >= 806 undefine :: Dynamic -> Dynamic undefine (Dynamic TypeRep a t a v) = (TypeRep a -> a -> Dynamic forall a. TypeRep a -> a -> Dynamic Dynamic TypeRep a t a forall a. HasCallStack => a undefined) #else undefine = id -- there's no way to do this using the old Data.Dynamic API. #endif -- | /O(1)/. -- Creates an 'Expr' representing a typed hole with the type of the given -- 'Expr'. (cf. 'hole') -- -- > > val (1::Int) -- > 1 :: Int -- > > holeAsTypeOf $ val (1::Int) -- > _ :: Int holeAsTypeOf :: Expr -> Expr holeAsTypeOf :: Expr -> Expr holeAsTypeOf = (String "" String -> Expr -> Expr `varAsTypeOf`) -- | /O(1)/. -- Creates an 'Expr' representing a typed hole of the given argument type. -- -- > > hole (undefined :: Int) -- > _ :: Int -- -- > > hole (undefined :: Maybe String) -- > _ :: Maybe [Char] -- -- A hole is represented as a variable with no name or -- a value named @"_"@: -- -- > hole x = var "" x -- > hole x = value "_" x hole :: Typeable a => a -> Expr hole :: a -> Expr hole a a = String -> a -> Expr forall a. Typeable a => String -> a -> Expr var String "" (a forall a. HasCallStack => a undefined a -> a -> a forall a. a -> a -> a `asTypeOf` a a) -- | /O(1)/. -- Checks if an 'Expr' represents a typed hole. -- (cf. 'hole') -- -- > > isHole $ hole (undefined :: Int) -- > True -- -- > > isHole $ value "not" not :$ val True -- > False -- -- > > isHole $ val 'a' -- > False isHole :: Expr -> Bool isHole :: Expr -> Bool isHole (Value String "_" Dynamic _) = Bool True isHole Expr _ = Bool False -- | /O(n)/. -- Lists all holes in an expression, in order and with repetitions. -- (cf. 'nubHoles') -- -- > > holes $ hole (undefined :: Bool) -- > [_ :: Bool] -- -- > > holes $ value "&&" (&&) :$ hole (undefined :: Bool) :$ hole (undefined :: Bool) -- > [_ :: Bool,_ :: Bool] -- -- > > holes $ hole (undefined :: Bool->Bool) :$ hole (undefined::Bool) -- > [_ :: Bool -> Bool,_ :: Bool] holes :: Expr -> [Expr] holes :: Expr -> [Expr] holes = (Expr -> Bool) -> [Expr] -> [Expr] forall a. (a -> Bool) -> [a] -> [a] filter Expr -> Bool isHole ([Expr] -> [Expr]) -> (Expr -> [Expr]) -> Expr -> [Expr] forall b c a. (b -> c) -> (a -> b) -> a -> c . Expr -> [Expr] values -- | /O(n^2)/. -- Lists all holes in an expression without repetitions. -- (cf. 'holes') -- -- > > nubHoles $ hole (undefined :: Bool) -- > [_ :: Bool] -- -- > > nubHoles $ value "&&" (&&) :$ hole (undefined :: Bool) :$ hole (undefined :: Bool) -- > [_ :: Bool] -- -- > > nubHoles $ hole (undefined :: Bool->Bool) :$ hole (undefined::Bool) -- > [_ :: Bool,_ :: Bool -> Bool] -- -- Runtime averages to -- /O(n log n)/ on evenly distributed expressions -- such as @(f x + g y) + (h z + f w)@; -- and to /O(n^2)/ on deep expressions -- such as @f (g (h (f (g (h x)))))@. nubHoles :: Expr -> [Expr] nubHoles :: Expr -> [Expr] nubHoles = [Expr] -> [Expr] forall a. Ord a => [a] -> [a] nubSort ([Expr] -> [Expr]) -> (Expr -> [Expr]) -> Expr -> [Expr] forall b c a. (b -> c) -> (a -> b) -> a -> c . Expr -> [Expr] holes -- | /O(n)/. -- Returns whether an expression contains a hole -- -- > > hasHole $ hole (undefined :: Bool) -- > True -- -- > > hasHole $ value "not" not :$ val True -- > False -- -- > > hasHole $ value "not" not :$ hole (undefined :: Bool) -- > True hasHole :: Expr -> Bool hasHole :: Expr -> Bool hasHole = (Expr -> Bool) -> [Expr] -> Bool forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool any Expr -> Bool isHole ([Expr] -> Bool) -> (Expr -> [Expr]) -> Expr -> Bool forall b c a. (b -> c) -> (a -> b) -> a -> c . Expr -> [Expr] values -- | /O(n)/. -- Returns whether an expression is complete. -- A complete expression is one without holes. -- -- > > isComplete $ hole (undefined :: Bool) -- > False -- -- > > isComplete $ value "not" not :$ val True -- > True -- -- > > isComplete $ value "not" not :$ hole (undefined :: Bool) -- > False -- -- 'isComplete' is the negation of 'hasHole'. -- -- > isComplete = not . hasHole -- -- 'isComplete' is to 'hasHole' what -- 'isGround' is to 'hasVar'. isComplete :: Expr -> Bool isComplete :: Expr -> Bool isComplete = Bool -> Bool not (Bool -> Bool) -> (Expr -> Bool) -> Expr -> Bool forall b c a. (b -> c) -> (a -> b) -> a -> c . Expr -> Bool hasHole -- | -- Generate an infinite list of variables -- based on a template and a given type. -- (cf. 'listVarsAsTypeOf') -- -- > > putL 10 $ listVars "x" (undefined :: Int) -- > [ x :: Int -- > , y :: Int -- > , z :: Int -- > , x' :: Int -- > , y' :: Int -- > , z' :: Int -- > , x'' :: Int -- > , ... -- > ] -- -- > > putL 10 $ listVars "p" (undefined :: Bool) -- > [ p :: Bool -- > , q :: Bool -- > , r :: Bool -- > , p' :: Bool -- > , q' :: Bool -- > , r' :: Bool -- > , p'' :: Bool -- > , ... -- > ] listVars :: Typeable a => String -> a -> [Expr] listVars :: String -> a -> [Expr] listVars String s a a = (String -> Expr) -> [String] -> [Expr] forall a b. (a -> b) -> [a] -> [b] map (String -> a -> Expr forall a. Typeable a => String -> a -> Expr `var` a a) (String -> [String] variableNamesFromTemplate String s) -- | -- Generate an infinite list of variables -- based on a template -- and the type of a given 'Expr'. -- (cf. 'listVars') -- -- > > let one = val (1::Int) -- > > putL 10 $ "x" `listVarsAsTypeOf` one -- > [ x :: Int -- > , y :: Int -- > , z :: Int -- > , x' :: Int -- > , ... -- > ] -- -- > > let false = val False -- > > putL 10 $ "p" `listVarsAsTypeOf` false -- > [ p :: Bool -- > , q :: Bool -- > , r :: Bool -- > , p' :: Bool -- > , ... -- > ] listVarsAsTypeOf :: String -> Expr -> [Expr] listVarsAsTypeOf :: String -> Expr -> [Expr] listVarsAsTypeOf String s Expr e = (String -> Expr) -> [String] -> [Expr] forall a b. (a -> b) -> [a] -> [b] map (String -> Expr -> Expr `varAsTypeOf` Expr e) (String -> [String] variableNamesFromTemplate String s) -- | Fill holes in an expression with the given list. -- -- > > let i_ = hole (undefined :: Int) -- > > let e1 -+- e2 = value "+" ((+) :: Int -> Int -> Int) :$ e1 :$ e2 -- > > let xx = var "x" (undefined :: Int) -- > > let yy = var "y" (undefined :: Int) -- -- > > fill (i_ -+- i_) [xx, yy] -- > x + y :: Int -- -- > > fill (i_ -+- i_) [xx, xx] -- > x + x :: Int -- -- > > let one = val (1::Int) -- -- > > fill (i_ -+- i_) [one, one -+- one] -- > 1 + (1 + 1) :: Int -- -- This function silently remaining expressions: -- -- > > fill i_ [xx, yy] -- > x :: Int -- -- This function silently keeps remaining holes: -- -- > > fill (i_ -+- i_ -+- i_) [xx, yy] -- > (x + y) + _ :: Int -- -- This function silently skips remaining holes -- if one is not of the right type: -- -- > > fill (i_ -+- i_ -+- i_) [xx, val 'c', yy] -- > (x + _) + _ :: Int fill :: Expr -> [Expr] -> Expr fill :: Expr -> [Expr] -> Expr fill Expr e = (Expr, [Expr]) -> Expr forall a b. (a, b) -> a fst ((Expr, [Expr]) -> Expr) -> ([Expr] -> (Expr, [Expr])) -> [Expr] -> Expr forall b c a. (b -> c) -> (a -> b) -> a -> c . Expr -> [Expr] -> (Expr, [Expr]) fill' Expr e where fill' :: Expr -> [Expr] -> (Expr,[Expr]) fill' :: Expr -> [Expr] -> (Expr, [Expr]) fill' (Expr e1 :$ Expr e2) [Expr] es = let (Expr e1',[Expr] es') = Expr -> [Expr] -> (Expr, [Expr]) fill' Expr e1 [Expr] es (Expr e2',[Expr] es'') = Expr -> [Expr] -> (Expr, [Expr]) fill' Expr e2 [Expr] es' in (Expr e1' Expr -> Expr -> Expr :$ Expr e2', [Expr] es'') fill' Expr eh (Expr e:[Expr] es) | Expr -> Bool isHole Expr eh Bool -> Bool -> Bool && Expr -> TypeRep typ Expr eh TypeRep -> TypeRep -> Bool forall a. Eq a => a -> a -> Bool == Expr -> TypeRep typ Expr e = (Expr e,[Expr] es) fill' Expr e [Expr] es = (Expr e,[Expr] es)