module Language.Symantic.Lib.Function where
import Prelude hiding (const, flip, id)
import qualified Data.Function as Fun
import qualified Data.MonoTraversable as MT
import Language.Symantic
type instance Sym (->) = Sym_Function
class Sym_Function term where
comp :: term (b -> c) -> term (a -> b) -> term (a -> c); infixr 9 `comp`
const :: term a -> term b -> term a
flip :: term (a -> b -> c) -> term (b -> a -> c)
id :: term a -> term a
default comp :: Sym_Function (UnT term) => Trans term => term (b -> c) -> term (a -> b) -> term (a -> c)
default const :: Sym_Function (UnT term) => Trans term => term a -> term b -> term a
default flip :: Sym_Function (UnT term) => Trans term => term (a -> b -> c) -> term (b -> a -> c)
default id :: Sym_Function (UnT term) => Trans term => term a -> term a
comp = trans2 comp
const = trans2 const
flip = trans1 flip
id = trans1 id
instance Sym_Function Eval where
comp = eval2 (Fun..)
const = eval2 Fun.const
flip = eval1 Fun.flip
id = eval1 Fun.id
instance Sym_Function View where
comp = viewInfix "." (infixR 9)
const = view2 "const"
flip = view1 "flip"
id = view1 "id"
instance (Sym_Function r1, Sym_Function r2) => Sym_Function (Dup r1 r2) where
comp = dup2 @Sym_Function comp
const = dup2 @Sym_Function const
flip = dup1 @Sym_Function flip
id = dup1 @Sym_Function id
instance (Sym_Function term, Sym_Lambda term) => Sym_Function (BetaT term)
instance NameTyOf (->) where
nameTyOf _c = [] `Mod` "->"
instance ClassInstancesFor (->) where
proveConstraintFor _c (TyApp _ q (TyApp _ z _r))
| Just HRefl <- proj_ConstKiTy @_ @(->) z
= case () of
_ | Just HRefl <- proj_ConstKiTy @_ @Functor q -> Just Dict
| Just HRefl <- proj_ConstKiTy @_ @Applicative q -> Just Dict
| Just HRefl <- proj_ConstKiTy @_ @Monad q -> Just Dict
_ -> Nothing
proveConstraintFor _c (TyApp _ q (TyApp _ (TyApp _ z _a) b))
| Just HRefl <- proj_ConstKiTy @_ @(->) z
= case () of
_ | Just HRefl <- proj_ConstKiTy @_ @Monoid q
, Just Dict <- proveConstraint (q `tyApp` b) -> Just Dict
| Just HRefl <- proj_ConstKiTy @_ @MT.MonoFunctor q -> Just Dict
_ -> Nothing
proveConstraintFor _c _q = Nothing
instance TypeInstancesFor (->)
instance Gram_Term_AtomsFor src ss g (->)
instance (Source src, SymInj ss (->)) => ModuleFor src ss (->) where
moduleFor = ["Function"] `moduleWhere`
[ "const" := teFunction_const
, "flip" := teFunction_flip
, "id" := teFunction_id
, "." `withInfixR` 9 := teFunction_compose
]
tyFun :: Source src => LenInj vs => Type src vs (->)
tyFun = tyConst @(K (->)) @(->)
a0 :: Source src => LenInj vs => KindInj (K a) =>
Type src (Proxy a ': vs) a
a0 = tyVar "a" varZ
b1 :: Source src => LenInj vs => KindInj (K b) =>
Type src (a ': Proxy b ': vs) b
b1 = tyVar "b" $ VarS varZ
c2 :: Source src => LenInj vs => KindInj (K c) =>
Type src (a ': b ': Proxy c ': vs) c
c2 = tyVar "c" $ VarS $ VarS varZ
teFunction_compose :: TermDef (->) '[Proxy a, Proxy b, Proxy c] (() #> ((b -> c) -> (a -> b) -> (a -> c)))
teFunction_compose = Term noConstraint ((b1 ~> c2) ~> (a0 ~> b1) ~> (a0 ~> c2)) $ teSym @(->) $ lam2 comp
teFunction_const :: TermDef (->) '[Proxy a, Proxy b] (() #> (a -> b -> a))
teFunction_const = Term noConstraint (a0 ~> b1 ~> a0) $ teSym @(->) $ lam2 const
teFunction_flip :: TermDef (->) '[Proxy a, Proxy b, Proxy c] (() #> ((a -> b -> c) -> (b -> a -> c)))
teFunction_flip = Term noConstraint ((a0 ~> b1 ~> c2) ~> (b1 ~> a0 ~> c2)) $ teSym @(->) $ lam1 flip
teFunction_id :: TermDef (->) '[Proxy a] (() #> (a -> a))
teFunction_id = Term noConstraint (a0 ~> a0) $ teSym @(->) $ lam1 id