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

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||| Deriving functor instances using reflection
||| You can for instance define:
||| ```
||| data Tree a = Leaf a | Node (Tree a) (Tree a)
||| treeFunctor : Functor Tree
||| treeFunctor = %runElab derive
||| ```
module Deriving.Functor
import public Control.Monad.Either
import public Control.Monad.State
import public Data.Maybe
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
NegativeOccurrence : Name -> TTImp -> Error
NotAnApplication : TTImp -> Error
NotAFunctor : TTImp -> Error
NotABifunctor : TTImp -> Error
NotAFunctorInItsLastArg : TTImp -> Error
UnsupportedType : TTImp -> 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 (NegativeOccurrence a ty) = acc <>> ["Negative occurrence of \{show a} in \{show ty}"]
go acc (NotAnApplication s) = acc <>> ["The type \{show s} is not an application"]
go acc (NotAFunctor s) = acc <>> ["Couldn't find a `Functor' instance for the type constructor \{show s}"]
go acc (NotABifunctor s) = acc <>> ["Couldn't find a `Bifunctor' instance for the type constructor \{show s}"]
go acc (NotAFunctorInItsLastArg s) = acc <>> ["Not a functor in its last argument \{show s}"]
go acc (UnsupportedType s) = acc <>> ["Unsupported type \{show s}"]
go acc InvalidGoal = acc <>> ["Expected a goal of the form `Functor 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
------------------------------------------------------------------------------
-- Core machinery: being functorial
-- 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
public export
data Polarity = Positive | Negative
public export
not : Polarity -> Polarity
not Positive = Negative
not Negative = Positive
||| IsFunctorialIn is parametrised by
||| @ pol the polarity of the type being analysed. We start in positive polarity
||| where occurrences of x are allowed and negate the polarity every time
||| we step into the domain of a Pi type.
||| @ t the name of the data type whose constructors are being analysed
||| @ x the name of the type variable that the functioral action will change
||| @ ty the type being analysed
||| The inductive type delivers a proof that x occurs positively in ty,
||| assuming that t also is positive.
public export
data IsFunctorialIn : (pol : Polarity) -> (t, x : Name) -> (ty : TTImp) -> Type where
||| The type variable x occurs alone
FIVar : IsFunctorialIn Positive t x (IVar fc x)
||| There is a recursive subtree of type (t a1 ... an u) and u is functorial 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))
FIRec : (0 _ : IsAppView (_, t) _ f) -> IsFunctorialIn pol t x arg ->
IsFunctorialIn Positive t x (IApp fc f arg)
||| The subterm is delayed (either Inf or Lazy)
FIDelayed : IsFunctorialIn pol t x ty -> IsFunctorialIn pol t x (IDelayed fc lr ty)
||| There are nested subtrees somewhere inside a 3rd party type constructor
||| which satisfies the Bifunctor interface
FIBifun : IsFreeOf x sp -> HasImplementation Bifunctor sp ->
IsFunctorialIn pol t x arg1 -> Either (IsFunctorialIn pol t x arg2) (IsFreeOf x arg2) ->
IsFunctorialIn pol t x (IApp fc1 (IApp fc2 sp arg1) arg2)
||| There are nested subtrees somewhere inside a 3rd party type constructor
||| which satisfies the Functor interface
FIFun : IsFreeOf x sp -> HasImplementation Functor sp ->
IsFunctorialIn pol t x arg -> IsFunctorialIn pol t x (IApp fc sp arg)
||| A pi type, with no negative occurrence of x in its domain
FIPi : IsFunctorialIn (not pol) t x a -> IsFunctorialIn pol t x b ->
IsFunctorialIn pol t x (IPi fc rig pinfo nm a b)
||| A type free of x is trivially Functorial in it
FIFree : IsFreeOf x a -> IsFunctorialIn pol t x a
record Parameters where
constructor MkParameters
asFunctors : List Nat
asBifunctors : List Nat
initParameters : Parameters
initParameters = MkParameters [] []
paramConstraints : Parameters -> Nat -> Maybe TTImp
paramConstraints params pos
= IVar emptyFC `{Prelude.Interfaces.Functor} <$ guard (pos `elem` params.asFunctors)
<|> IVar emptyFC `{Prelude.Interfaces.Bifunctor} <$ guard (pos `elem` params.asBifunctors)
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 functorial in x
||| 2. or that it is free of x
||| If if it is not the case, we will use the `MonadError Error` constraint
||| to fail with an informative message.
public export
TypeView : Polarity -> TTImp -> Type
TypeView pol ty = Either (IsFunctorialIn pol t x ty) (IsFreeOf x ty)
export
fromTypeView : TypeView pol ty -> IsFunctorialIn pol t x ty
fromTypeView (Left prf) = prf
fromTypeView (Right fo) = FIFree fo
||| Hoping to observe that ty is functorial
export
typeView : {pol : Polarity} -> (ty : TTImp) -> m (TypeView pol ty)
||| To avoid code duplication in typeView, we have an auxiliary function
||| specifically to handle the application case
typeAppView :
{fc : FC} -> {pol : Polarity} ->
{f : TTImp} -> IsFreeOf x f ->
(arg : TTImp) ->
m (TypeView pol (IApp fc f arg))
typeAppView {fc, pol, 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 => case pol of
Positive => pure $ Left (FIRec prf sp)
Negative => throwError (NegativeOccurrence t (IApp fc f arg))
No diff => case !(hasImplementation Functor f) of
Just prf => pure (Left (FIFun isFO prf sp))
Nothing => case lookup hd ps of
Just n => do
-- record that the nth parameter should be functorial
ns <- gets asFunctors
let ns = ifThenElse (n `elem` ns) ns (n :: ns)
modify { asFunctors := ns }
-- and happily succeed
logMsg "derive.functor.assumption" 10 $
"I am assuming that the parameter \{show hd} is a Functor"
pure (Left (FIFun isFO assert_hasImplementation sp))
Nothing => throwError (NotAFunctor 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 {pol} f
| _ => throwError $ case pol of
Positive => NotAFunctorInItsLastArg (IApp fc f arg)
Negative => NegativeOccurrence x (IApp fc f arg)
pure (Right assert_IsFreeOf)
typeView {pol} tm@(IVar fc y) = case decEq x y of
Yes Refl => case pol of
Positive => pure (Left FIVar)
Negative => throwError (NegativeOccurrence x tm)
No _ => pure (Right assert_IsFreeOf)
typeView ty@(IPi fc rig pinfo nm a b) = do
va <- typeView a
vb <- typeView b
pure $ case (va, vb) of
(_, Left sp) => Left (FIPi (fromTypeView va) sp)
(Left sp, _) => Left (FIPi sp (fromTypeView vb))
(Right _, Right _) => 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 Bifunctor f) of
Just prf => pure (Left (FIBifun 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 bifunctorial
ns <- gets asBifunctors
let ns = ifThenElse (n `elem` ns) ns (n :: ns)
modify { asBifunctors := ns }
-- and happily succeed
logMsg "derive.functor.assumption" 10 $
"I am assuming that the parameter \{show hd} is a Bifunctor"
pure (Left (FIBifun isFO assert_hasImplementation sp !(typeView arg2)))
Nothing => throwError (NotABifunctor f)
typeView (IApp _ f arg) = do
isFO <- isFreeOf' x f
typeAppView isFO arg
typeView (IDelayed _ lz f) = pure $ case !(typeView f) of
Left sp => Left (FIDelayed sp)
Right _ => Right assert_IsFreeOf
typeView (IPrimVal _ _) = pure (Right assert_IsFreeOf)
typeView (IType _) = pure (Right assert_IsFreeOf)
typeView ty = throwError (UnsupportedType ty)
------------------------------------------------------------------------------
-- Core machinery: building the mapping function from an IsFunctorialIn proof
parameters (fc : FC) (mutualWith : List Name)
||| functorFun 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)`.
functorFun : (assert : Maybe Bool) -> {ty : TTImp} -> IsFunctorialIn pol t x ty ->
(rec, f : Name) -> (arg : Maybe TTImp) -> TTImp
functorFun assert FIVar rec f t = apply fc (IVar fc f) (toList t)
functorFun assert (FIRec 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) (functorFun (Just False) sp rec f Nothing :: toList t)
functorFun assert (FIDelayed 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) (Implicit fc False)
$ IDelay fc
$ functorFun assert sp rec f (Just (IVar fc nm))
functorFun assert (FIDelayed sp) rec f (Just t)
= IDelay fc
$ functorFun assert sp rec f (Just t)
functorFun assert {ty = IApp _ ty _} (FIFun _ _ sp) rec f t
-- only add assert_total if we are calling a mutually defined Functor 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 "map"))
(functorFun ((False <$ guard isMutual) <|> assert <|> Just True) sp rec f Nothing
:: toList t)
functorFun assert (FIBifun _ _ sp1 (Left sp2)) rec f t
= apply fc (IVar fc (UN $ Basic "bimap"))
(functorFun (assert <|> Just True) sp1 rec f Nothing
:: functorFun (assert <|> Just True) sp2 rec f Nothing
:: toList t)
functorFun assert (FIBifun _ _ sp (Right _)) rec f t
= apply fc (IVar fc (UN $ Basic "mapFst"))
(functorFun (assert <|> Just True) sp rec f Nothing
:: toList t)
functorFun assert (FIPi {rig, pinfo, nm} dn sp) rec f t
= optionallyEta fc t $ \ arg =>
let nm = fromMaybe (UN $ Basic "x") nm in
-- /!\ We cannot use the type stored in FIPi here because it could just
-- be a name that will happen to be different when bound on the LHS!
-- Cf. the Free test case in reflection017
ILam fc rig pinfo (Just nm) (Implicit fc False) $
functorFun assert sp rec f
$ Just $ IApp fc arg
$ functorFun assert dn rec f (Just (IVar fc nm))
functorFun assert (FIFree y) rec f t = fromMaybe `(id) t
------------------------------------------------------------------------------
-- User-facing: Functor deriving
namespace Functor
derive' : (Elaboration m, MonadError Error m) =>
{default Private vis : Visibility} ->
{default Total treq : TotalReq} ->
{default [] mutualWith : List Name} ->
m (Functor 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 (Functor t)
Just (IApp _ (IVar _ functor) t) <- goal
| _ => throwError InvalidGoal
when (`{Prelude.Interfaces.Functor} /= functor) $
logMsg "derive.functor" 1 "Expected to derive Functor but got \{show functor}"
-- t should be a type constructor
logMsg "derive.functor" 1 "Deriving Functor for \{showPrec App $ mapTTImp cleanup t}"
MkIsType f params cs <- isType t
logMsg "derive.functor.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 mapName = un ("map" ++ 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.functor.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)
-- only keep the arguments that are either:
-- 1. modified by map
-- 2. explicit
recs <- for (zip vars args) $ \ (v, (rig, arg)) => do
res <- withError (WhenCheckingArg (mapTTImp cleanup $ unArg arg)) $
typeView {pol = Positive} f paras para (unArg arg)
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
pure (v, functorFun fc mutualWith useTot sp mapName funName . Just <$> v)
Right free => do ignore $ isExplicit v
pure (v, v)
let (vars, recs) = unzip (catMaybes recs)
pure $ PatClause fc
(apply fc (IVar fc mapName) [ fun, apply (IVar fc cName) vars])
(apply (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 va = IVar fc a
let vb = IVar fc b
logMsg "derive.functor.parameters" 20 $ unlines
[ "Functors: \{show ns.asFunctors}"
, "Bifunctors: \{show ns.asBifunctors}"
, "Parameters: \{show (map (mapFst unArg) params)}"
]
let ty = MkTy fc fc mapName $ withParams fc (paramConstraints ns) params
$ IPi fc M0 ImplicitArg (Just a) (IType fc)
$ IPi fc M0 ImplicitArg (Just b) (IType fc)
$ `((~(va) -> ~(vb)) -> ~(t) ~(va) -> ~(t) ~(vb))
logMsg "derive.functor.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 mapName cls
] `(MkFunctor {f = ~(t)} ~(IVar fc mapName))
||| Derive an implementation of Functor for a type constructor.
||| This can be used like so:
||| ```
||| data Tree a = Leaf a | Node (Tree a) (Tree a)
||| treeFunctor : Functor Tree
||| treeFunctor = %runElab derive
||| ```
export
derive : {default Private vis : Visibility} ->
{default Total treq : TotalReq} ->
{default [] mutualWith : List Name} ->
Elab (Functor 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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