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Idris2/libs/base/Deriving/Traversable.idr
G. Allais 4cd38a8c5d
[ new ] deriving Show (#2741)
2022-11-02 11:57:07 +00:00

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||| Deriving traversable instances using reflection
||| You can for instance define:
||| ```
||| data Tree a = Leaf a | Node (Tree a) (Tree a)
||| treeFoldable : Traversable Tree
||| treeFoldable = %runElab derive
||| ```
module Deriving.Traversable
import public Control.Monad.Either
import public Control.Monad.State
import public Data.List1
import public Data.Maybe
import public Data.Morphisms
import public Decidable.Equality
import public Language.Reflection
import public Deriving.Common
%language ElabReflection
%default total
------------------------------------------------------------------------------
-- Errors
||| Possible errors for the functor-deriving machinery.
public export
data Error : Type where
NotFreeOf : Name -> TTImp -> Error
NotAnApplication : TTImp -> Error
NotATraversable : TTImp -> Error
NotABitraversable : TTImp -> Error
NotTraversableInItsLastArg : TTImp -> Error
UnsupportedType : TTImp -> Error
NotAFiniteStructure : Error
NotAnUnconstrainedValue : Count -> Error
InvalidGoal : Error
ConfusingReturnType : Error
-- Contextual information
WhenCheckingConstructor : Name -> Error -> Error
WhenCheckingArg : TTImp -> Error -> Error
export
Show Error where
show = joinBy "\n" . go [<] where
go : SnocList String -> Error -> List String
go acc (NotFreeOf x ty) = acc <>> ["The term \{show ty} is not free of \{show x}"]
go acc (NotAnApplication s) = acc <>> ["The type \{show s} is not an application"]
go acc (NotATraversable s) = acc <>> ["Couldn't find a `Traversable' instance for the type constructor \{show s}"]
go acc (NotABitraversable s) = acc <>> ["Couldn't find a `Bitraversable' instance for the type constructor \{show s}"]
go acc (NotTraversableInItsLastArg s) = acc <>> ["Not traversable in its last argument \{show s}"]
go acc (UnsupportedType s) = acc <>> ["Unsupported type \{show s}"]
go acc NotAFiniteStructure = acc <>> ["Cannot traverse an infinite structure"]
go acc (NotAnUnconstrainedValue rig) = acc <>> ["Cannot traverse a \{enunciate rig} value"]
go acc InvalidGoal = acc <>> ["Expected a goal of the form `Traversable f`"]
go acc ConfusingReturnType = acc <>> ["Confusing telescope"]
go acc (WhenCheckingConstructor nm err) = go (acc :< "When checking constructor \{show nm}") err
go acc (WhenCheckingArg s err) = go (acc :< "When checking argument of type \{show s}") err
record Parameters where
constructor MkParameters
asTraversables : List Nat
asBitraversables : List Nat
initParameters : Parameters
initParameters = MkParameters [] []
paramConstraints : Parameters -> Nat -> Maybe TTImp
paramConstraints params pos
= IVar emptyFC `{Prelude.Interfaces.Traversable} <$ guard (pos `elem` params.asTraversables)
<|> IVar emptyFC `{Prelude.Interfaces.Bitraversable} <$ guard (pos `elem` params.asBitraversables)
------------------------------------------------------------------------------
-- Core machinery: being traversable
-- Not meant to be re-exported as it's using the internal notion of error
isFreeOf' :
{0 m : Type -> Type} ->
{auto elab : Elaboration m} ->
{auto error : MonadError Error m} ->
(x : Name) -> (ty : TTImp) -> m (IsFreeOf x ty)
isFreeOf' x ty = case isFreeOf x ty of
Nothing => throwError (NotFreeOf x ty)
Just prf => pure prf
||| IsTraversableIn is parametrised by
||| @ t the name of the data type whose constructors are being analysed
||| @ x the name of the type variable that the traversable action will act on
||| @ ty the type being analysed
||| The inductive type delivers a proof that x can be traversed over in ty,
||| assuming that t also is traversable.
public export
data IsTraversableIn : (t, x : Name) -> (ty : TTImp) -> Type where
||| The type variable x occurs alone
TIVar : IsTraversableIn t x (IVar fc x)
||| There is a recursive subtree of type (t a1 ... an u) and u is Traversable in x.
||| We do not insist that u is exactly x so that we can deal with nested types
||| like the following:
||| data Full a = Leaf a | Node (Full (a, a))
||| data Term a = Var a | App (Term a) (Term a) | Lam (Term (Maybe a))
TIRec : (0 _ : IsAppView (_, t) _ f) -> IsTraversableIn t x arg ->
IsTraversableIn t x (IApp fc f arg)
||| The subterm is delayed (Lazy only, we can't traverse infinite structures)
TIDelayed : IsTraversableIn t x ty -> IsTraversableIn t x (IDelayed fc LLazy ty)
||| There are nested subtrees somewhere inside a 3rd party type constructor
||| which satisfies the Bitraversable interface
TIBifold : IsFreeOf x sp -> HasImplementation Bitraversable sp ->
IsTraversableIn t x arg1 -> Either (IsTraversableIn t x arg2) (IsFreeOf x arg2) ->
IsTraversableIn t x (IApp fc1 (IApp fc2 sp arg1) arg2)
||| There are nested subtrees somewhere inside a 3rd party type constructor
||| which satisfies the Traversable interface
TIFold : IsFreeOf x sp -> HasImplementation Traversable sp ->
IsTraversableIn t x arg -> IsTraversableIn t x (IApp fc sp arg)
||| A type free of x is trivially Traversable in it
TIFree : IsFreeOf x a -> IsTraversableIn t x a
parameters
{0 m : Type -> Type}
{auto elab : Elaboration m}
{auto error : MonadError Error m}
{auto cs : MonadState Parameters m}
(t : Name)
(ps : List (Name, Nat))
(x : Name)
||| When analysing the type of a constructor for the type family t,
||| we hope to observe
||| 1. either that it is traversable in x
||| 2. or that it is free of x
||| If it is not the case, we will use the `MonadError Error` constraint
||| to fail with an informative message.
public export
TypeView : TTImp -> Type
TypeView ty = Either (IsTraversableIn t x ty) (IsFreeOf x ty)
export
fromTypeView : TypeView ty -> IsTraversableIn t x ty
fromTypeView (Left prf) = prf
fromTypeView (Right fo) = TIFree fo
||| Hoping to observe that ty is traversable
export
typeView : (ty : TTImp) -> m (TypeView ty)
||| To avoid code duplication in typeView, we have an auxiliary function
||| specifically to handle the application case
typeAppView :
{fc : FC} ->
{f : TTImp} -> IsFreeOf x f ->
(arg : TTImp) ->
m (TypeView (IApp fc f arg))
typeAppView {fc, f} isFO arg = do
chka <- typeView arg
case chka of
-- if x is present in the argument then the function better be:
-- 1. free of x
-- 2. either an occurrence of t i.e. a subterm
-- or a type constructor already known to be functorial
Left sp => do
let Just (MkAppView (_, hd) ts prf) = appView f
| _ => throwError (NotAnApplication f)
case decEq t hd of
Yes Refl => pure $ Left (TIRec prf sp)
No diff => case !(hasImplementation Traversable f) of
Just prf => pure (Left (TIFold isFO prf sp))
Nothing => case lookup hd ps of
Just n => do
-- record that the nth parameter should be functorial
ns <- gets asTraversables
let ns = ifThenElse (n `elem` ns) ns (n :: ns)
modify { asTraversables := ns }
-- and happily succeed
logMsg "derive.traversable.assumption" 10 $
"I am assuming that the parameter \{show hd} is a Traversable"
pure (Left (TIFold isFO assert_hasImplementation sp))
Nothing => throwError (NotATraversable f)
-- Otherwise it better be the case that f is also free of x so that
-- we can mark the whole type as being x-free.
Right fo => do
Right _ <- typeView f
| _ => throwError $ NotTraversableInItsLastArg (IApp fc f arg)
pure (Right assert_IsFreeOf)
typeView tm@(IVar fc y) = case decEq x y of
Yes Refl => pure (Left TIVar)
No _ => pure (Right assert_IsFreeOf)
typeView fab@(IApp _ (IApp fc1 f arg1) arg2) = do
chka1 <- typeView arg1
case chka1 of
Right _ => do isFO <- isFreeOf' x (IApp _ f arg1)
typeAppView {f = assert_smaller fab (IApp _ f arg1)} isFO arg2
Left sp => do
isFO <- isFreeOf' x f
case !(hasImplementation Bitraversable f) of
Just prf => pure (Left (TIBifold isFO prf sp !(typeView arg2)))
Nothing => do
let Just (MkAppView (_, hd) ts prf) = appView f
| _ => throwError (NotAnApplication f)
case lookup hd ps of
Just n => do
-- record that the nth parameter should be bitraversable
ns <- gets asBitraversables
let ns = ifThenElse (n `elem` ns) ns (n :: ns)
modify { asBitraversables := ns }
-- and happily succeed
logMsg "derive.traversable.assumption" 10 $
"I am assuming that the parameter \{show hd} is a Bitraversable"
pure (Left (TIBifold isFO assert_hasImplementation sp !(typeView arg2)))
Nothing => throwError (NotABitraversable f)
typeView (IApp _ f arg) = do
isFO <- isFreeOf' x f
typeAppView isFO arg
typeView (IDelayed _ lz f) = case !(typeView f) of
Left sp => case lz of
LLazy => pure (Left (TIDelayed sp))
_ => throwError NotAFiniteStructure
Right _ => pure (Right assert_IsFreeOf)
typeView (IPrimVal _ _) = pure (Right assert_IsFreeOf)
typeView (IType _) = pure (Right assert_IsFreeOf)
typeView ty = case isFreeOf x ty of
Nothing => throwError (UnsupportedType ty)
Just prf => pure (Right prf)
------------------------------------------------------------------------------
-- Core machinery: building the traverse function from an IsTraversableIn proof
parameters (fc : FC) (mutualWith : List Name)
||| traverseFun takes
||| @ mutualWith a list of mutually defined type constructors. Calls to their
||| respective mapping functions typically need an assert_total because the
||| termination checker is not doing enough inlining to see that things are
||| terminating
||| @ assert records whether we should mark recursive calls as total because
||| we are currently constructing the argument to a higher order function
||| which will obscure the termination argument. Starts as `Nothing`, becomes
||| `Just False` if an `assert_total` has already been inserted.
||| @ ty the type being transformed by the mapping function
||| @ rec the name of the mapping function being defined (used for recursive calls)
||| @ f the name of the function we're mapping
||| @ arg the (optional) name of the argument being mapped over. This lets us use
||| Nothing when generating arguments to higher order functions so that we generate
||| the eta contracted `map (mapTree f)` instead of `map (\ ts => mapTree f ts)`.
traverseFun : (assert : Maybe Bool) -> {ty : TTImp} -> IsTraversableIn t x ty ->
(rec, f : Name) -> (arg : Maybe TTImp) -> TTImp
traverseFun assert TIVar rec f t = apply fc (IVar fc f) (toList t)
traverseFun assert (TIRec y sp) rec f t
-- only add assert_total if it is declared to be needed
= ifThenElse (fromMaybe False assert) (IApp fc (IVar fc (UN $ Basic "assert_total"))) id
$ apply fc (IVar fc rec) (traverseFun (Just False) sp rec f Nothing :: toList t)
traverseFun assert (TIDelayed sp) rec f Nothing
-- here we need to eta-expand to avoid "Lazy t does not unify with t" errors
= let nm = UN $ Basic "eta" in
ILam fc MW ExplicitArg (Just nm) (IDelayed fc LLazy (Implicit fc False))
$ apply fc `((<$>))
[ `(delay)
, traverseFun assert sp rec f (Just (IVar fc nm))
]
traverseFun assert (TIDelayed sp) rec f (Just t)
= apply fc `((<$>))
[ `(delay)
, traverseFun assert sp rec f (Just t)
]
traverseFun assert {ty = IApp _ ty _} (TIFold _ _ sp) rec f t
-- only add assert_total if we are calling a mutually defined Traversable implementation.
= let isMutual = fromMaybe False (appView ty >>= \ v => pure (snd v.head `elem` mutualWith)) in
ifThenElse isMutual (IApp fc (IVar fc (UN $ Basic "assert_total"))) id
$ apply fc (IVar fc (UN $ Basic "traverse"))
(traverseFun ((False <$ guard isMutual) <|> assert <|> Just True) sp rec f Nothing
:: toList t)
traverseFun assert (TIBifold _ _ sp1 (Left sp2)) rec f t
= apply fc (IVar fc (UN $ Basic "bitraverse"))
(traverseFun (assert <|> Just True) sp1 rec f Nothing
:: traverseFun (assert <|> Just True) sp2 rec f Nothing
:: toList t)
traverseFun assert (TIBifold _ _ sp (Right _)) rec f t
= apply fc (IVar fc (UN $ Basic "bitraverseFst"))
(traverseFun (assert <|> Just True) sp rec f Nothing
:: toList t)
traverseFun assert (TIFree y) rec f t = `(mempty)
------------------------------------------------------------------------------
-- User-facing: Traversable deriving
applyA : FC -> TTImp -> List (Either (Argument TTImp) TTImp) -> TTImp
applyA fc c [] = `(pure ~(c))
applyA fc c (Right a :: as) = applyA fc (IApp fc c a) as
applyA fc c as =
let (pref, suff) = spanBy canBeApplied ([<] <>< as) in
let (lams, args, vals) = preEta 0 (pref <>> []) in
let eta = foldr (\ x => ILam fc MW ExplicitArg (Just x) (Implicit fc False)) (apply c args) lams in
fire eta (map Left vals ++ (suff <>> []))
where
canBeApplied : Either (Argument TTImp) TTImp -> Maybe (Either TTImp TTImp)
canBeApplied (Left (Arg _ t)) = pure (Left t)
canBeApplied (Right t) = pure (Right t)
canBeApplied _ = Nothing
preEta : Nat -> List (Either (Argument TTImp) TTImp) ->
(List Name, List (Argument TTImp), List TTImp)
preEta n [] = ([], [], [])
preEta n (a :: as) =
let (n, ns, args, vals) = the (Nat, List Name, List (Argument TTImp), List _) $
let x = UN (Basic ("y" ++ show n)); vx = IVar fc x in case a of
Left (Arg fc t) => (S n, [x], [Arg fc vx], [t])
Left (NamedArg fc nm t) => (S n, [x], [NamedArg fc nm vx], [t])
Left (AutoArg fc t) => (S n, [x], [AutoArg fc vx], [t])
Right t => (n, [], [Arg fc t], [])
in
let (nss, argss, valss) = preEta n as in
(ns ++ nss, args ++ argss, vals ++ valss)
go : TTImp -> List (Either TTImp TTImp) -> TTImp
go f [] = f
go f (Left a :: as) = go (apply fc `((<*>)) [f, a]) as
go f (Right a :: as) = go (apply fc `((<*>)) [f, IApp fc `(pure) a]) as
fire : TTImp -> List (Either TTImp TTImp) -> TTImp
fire f [] = f
fire f (a :: as) = go (apply fc `((<$>)) [f, either id id a]) as
namespace Traversable
derive' : (Elaboration m, MonadError Error m) =>
{default Private vis : Visibility} ->
{default Total treq : TotalReq} ->
{default [] mutualWith : List Name} ->
m (Traversable f)
derive' = do
-- expand the mutualwith names to have the internal, fully qualified, names
mutualWith <- map concat $ for mutualWith $ \ nm => do
ntys <- getType nm
pure (fst <$> ntys)
-- The goal should have the shape (Traversable t)
Just (IApp _ (IVar _ traversable) t) <- goal
| _ => throwError InvalidGoal
when (`{Prelude.Interfaces.Traversable} /= traversable) $
logMsg "derive.traversable" 1 "Expected to derive Traversable but got \{show traversable}"
-- t should be a type constructor
logMsg "derive.traversable" 1 "Deriving Traversable for \{showPrec App $ mapTTImp cleanup t}"
MkIsType f params cs <- isType t
logMsg "derive.traversable.constructors" 1 $
joinBy "\n" $ "" :: map (\ (n, ty) => " \{showPrefix True $ dropNS n} : \{show $ mapTTImp cleanup ty}") cs
-- Generate a clause for each data constructor
let fc = emptyFC
let un = UN . Basic
let traverseName = un ("traverse" ++ show (dropNS f))
let funName = un "f"
let fun = IVar fc funName
(ns, cls) <- runStateT {m = m} initParameters $ for cs $ \ (cName, ty) =>
withError (WhenCheckingConstructor cName) $ do
-- Grab the types of the constructor's explicit arguments
let Just (MkConstructorView (paraz :< (para, _)) args) = constructorView ty
| _ => throwError ConfusingReturnType
let paras = paraz <>> []
logMsg "derive.traversable.clauses" 10 $
"\{showPrefix True (dropNS cName)} (\{joinBy ", " (map (showPrec Dollar . mapTTImp cleanup . unArg . snd) args)})"
let vars = map (map (IVar fc . un . ("x" ++) . show . (`minus` 1)))
$ zipWith (<$) [1..length args] (map snd args)
recs <- for (zip vars args) $ \ (v, (rig, arg)) => do
res <- withError (WhenCheckingArg (mapTTImp cleanup (unArg arg))) $ do
res <- typeView f paras para (unArg arg)
case res of
Left _ => case rig of
MW => pure ()
_ => throwError (NotAnUnconstrainedValue rig)
_ => pure ()
pure res
pure $ case res of
Left sp => -- do not bother with assert_total if you're generating
-- a covering/partial definition
let useTot = False <$ guard (treq /= Total) in
Just (v, Left (traverseFun fc mutualWith useTot sp traverseName funName . Just <$> v))
Right free => do ignore $ isExplicit v
Just (v, Right (unArg v))
let (vars, recs) = unzip (catMaybes recs)
pure $ PatClause fc
(apply fc (IVar fc traverseName) [ fun, apply (IVar fc cName) vars])
(applyA fc (IVar fc cName) recs)
-- Generate the type of the mapping function
let paramNames = unArg . fst <$> params
let a = un $ freshName paramNames "a"
let b = un $ freshName paramNames "b"
let f = un $ freshName paramNames "f"
let va = IVar fc a
let vb = IVar fc b
let vf = IVar fc f
let ty = MkTy fc fc traverseName $ withParams fc (paramConstraints ns) params
$ IPi fc M0 ImplicitArg (Just a) (IType fc)
$ IPi fc M0 ImplicitArg (Just b) (IType fc)
$ IPi fc M0 ImplicitArg (Just f) (IPi fc MW ExplicitArg Nothing (IType fc) (IType fc))
$ `(Applicative ~(vf) => (~(va) -> ~(vf) ~(vb)) -> ~(t) ~(va) -> ~(vf) (~(t) ~(vb)))
logMsg "derive.traversable.clauses" 1 $
joinBy "\n" ("" :: (" " ++ show (mapITy cleanup ty))
:: map ((" " ++) . showClause InDecl . mapClause cleanup) cls)
-- Define the instance
check $ ILocal fc
[ IClaim fc MW vis [Totality treq] ty
, IDef fc traverseName cls
] `(MkTraversable {t = ~(t)} ~(IVar fc traverseName))
||| Derive an implementation of Traversable for a type constructor.
||| This can be used like so:
||| ```
||| data Tree a = Leaf a | Node (Tree a) (Tree a)
||| treeTraversable : Traversable Tree
||| treeTraversable = %runElab derive
||| ```
export
derive : {default Private vis : Visibility} ->
{default Total treq : TotalReq} ->
{default [] mutualWith : List Name} ->
Elab (Traversable f)
derive = do
res <- runEitherT {e = Error, m = Elab} (derive' {vis, treq, mutualWith})
case res of
Left err => fail (show err)
Right prf => pure prf
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