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Strengthen Cons and Snoc interfaces

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This commit is contained in:
Kiana Sheibani 2023-04-25 12:39:52 -04:00
parent e1da48721e
commit e980b3602d
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
3 changed files with 57 additions and 9 deletions
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25
src/Control/Lens/Cons.idr
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@ -4,6 +4,7 @@ import Data.Profunctor
import Control.Lens.Optic
import Control.Lens.Iso
import Control.Lens.Prism
import Control.Lens.Review
import Control.Lens.Optional
%default total
@ -13,9 +14,15 @@ import Control.Lens.Optional
||| left side of a sequence.
public export
interface Cons s t a b | s where
||| This is a prism that can attach or detach a value from the left side of a
||| An isomorphism that can inspact the left side of a sequence.
consIso : Iso s t (Maybe (a, s)) (Maybe (b, t))
||| A prism that can attach or detach a value from the left side of a
||| sequence.
cons_ : Prism s t (a, s) (b, t)
cons_ = consIso . prism Just (\case
Nothing => Left Nothing
Just x => Right x)
||| Access the head (left-most element) of a sequence, if it is non-empty.
public export
@ -28,14 +35,25 @@ public export
tail_ : Cons s s a a => Optional' s s
tail_ @{_} @{MkIsOptional _} = cons_ . second
||| Use a `Cons` implementation to construct an empty sequence.
public export
nil : Cons s s a a => s
nil = review consIso Nothing
||| An interface that provides a way to detach and inspect elements from the
||| right side of a sequence.
public export
interface Snoc s t a b | s where
||| An isomorphism that can inspact the right side of a sequence.
snocIso : Iso s t (Maybe (s, a)) (Maybe (t, b))
||| This is a prism that can attach or detach a value from the right side of a
||| sequence.
snoc_ : Prism s t (s, a) (t, b)
snoc_ = snocIso . prism Just (\case
Nothing => Left Nothing
Just x => Right x)
||| Access all but the right-most element of a sequence, if it is non-empty.
public export
@ -46,3 +64,8 @@ init_ @{_} @{MkIsOptional _} = snoc_ . first
public export
last_ : Snoc s s a a => Optional' s a
last_ @{_} @{MkIsOptional _} = snoc_ . second
||| Use a `Snoc` implementation to construct an empty sequence.
public export
nil' : Snoc s s a a => s
nil' = review snocIso Nothing