Maintainer	gatlin@niltag.net
Safe Haskell	Safe-Inferred
Language	Haskell2010

Sheet

Contents

Defining and executing sheets.
Inexhaustible streams
Tapes: bidirectional streams with a focus
References, indices, and coordinates
Reference lists
- Coordinates
- Indexed
Type-level Tape manipulation with Coordinates and Refs.
- Take
- View
- Go
Insertion
Dimensions
Utilities

Description

A Sheet is a multi-dimensional convolutional computational space. The fabric of the universe comes in sheets like this but with a higher thread- count.

Re-implementation of Kenneth Foner's ComonadSheet library. Some bug fixes and packaging upgrades have been made; additionally, for idiosyncratic reasons, where possible functional dependencies have been replaced with associated type families.

Synopsis

evaluate :: ComonadApply w => w (w a -> a) -> w a
evaluateF :: (ComonadApply w, Functor f) => w (f (w (f a) -> a)) -> w (f a)
cell :: (Comonad w, Go r w) => RefList r -> w a -> a
cells :: (Traversable t, Comonad w, Go r w) => t (RefList r) -> w a -> t a
sheet :: (InsertNested l t, Applicative t, DimensionalAs x (t a), AsDimensionalAs x (t a) ~ l a) => a -> x -> t a
change :: (InsertNested l w, ComonadApply w, DimensionalAs x (w (w a -> a)), AsDimensionalAs x (w (w a -> a)) ~ l (w a -> a)) => x -> w a -> w a
sheetFromNested :: (InsertNested (Nested fs) (Nested (NestedNTimes (NestedCount fs) Tape)), Applicative (Nested (NestedNTimes (NestedCount fs) Tape))) => a -> Nested fs a -> Nested (NestedNTimes (NestedCount fs) Tape) a
indexedSheet :: (InsertNested l (Nested ts), Applicative (Nested ts), DimensionalAs x (Nested ts a), AsDimensionalAs x (Nested ts a) ~ l a) => Coordinate (NestedCount ts) -> a -> x -> Indexed ts a
data Stream t = Cons t (Stream t)
(<:>) :: t -> Stream t -> Stream t
repeat :: t -> Stream t
zipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c
unzip :: Stream (a, b) -> (Stream a, Stream b)
iterateStream :: (value -> value) -> value -> Stream value
unfoldStream :: (state -> (value, state)) -> state -> Stream value
takeStream :: Int -> Stream value -> [value]
takeStreamNat :: Z < S n => Natural n -> Stream value -> [value]
data Tape a = Tape {
- viewL :: Stream a
- focus :: a
- viewR :: Stream a
}
tapeOf :: a -> Tape a
moveL :: Tape a -> Tape a
moveR :: Tape a -> Tape a
iterate :: (t -> t) -> (t -> t) -> t -> Tape t
enumerate :: Enum a => a -> Tape a
unfold :: (c -> (a, c)) -> (c -> a) -> (c -> (a, c)) -> c -> Tape a
data Ref (t :: RefType)
- = t ~ 'Relative => Rel Int
- | t ~ 'Absolute => Abs Int
getRef :: Ref t -> Int
class CombineRefTypes (a :: RefType) (b :: RefType) where
- type Combine a b :: RefType
- combine :: Ref a -> Ref b -> Ref (Combine a b)
data RefType
- = Relative
- | Absolute
type RefList = Conic Ref
class CombineRefLists as bs where
- (&) :: RefList as -> RefList bs -> RefList (as & bs)
merge :: ReifyNatural n => Counted n (Ref 'Relative) -> Counted n (Ref 'Absolute) -> Counted n (Ref 'Absolute)
diff :: Counted n (Either (Ref 'Relative) (Ref 'Absolute)) -> Counted n (Ref 'Absolute) -> Counted n (Ref 'Relative)
eitherFromRef :: Ref t -> Either (Ref 'Relative) (Ref 'Absolute)
getMovement :: (Length ts <= n, ((n - Length ts) + Length ts) ~ n) => RefList ts -> Counted n (Ref 'Absolute) -> Counted n (Ref 'Relative)
dimensional :: Tackable t (Replicate n 'Relative) => Natural (S n) -> Ref t -> RefList (Tack t (Replicate n 'Relative))
type Coordinate n = Counted n (Ref 'Absolute)
data Indexed ts a = Indexed {
- origin :: Coordinate (NestedCount ts)
- unindexed :: Nested ts a
}
class Cross n t where
- cross :: Counted n (t a) -> Nested (NestedNTimes n t) (Counted n a)
type Indexable ts = (Cross (NestedCount ts) Tape, ts ~ NestedNTimes (NestedCount ts) Tape)
indices :: Cross n Tape => Coordinate n -> Nested (NestedNTimes n Tape) (Coordinate n)
class Take r t where
- type ListFrom t a
- take :: RefList r -> t a -> ListFrom t a
tapeTake :: Ref 'Relative -> Tape a -> [a]
class View r t where
- type StreamFrom t a
- view :: RefList r -> t a -> StreamFrom t a
tapeView :: Ref 'Relative -> Tape a -> Stream a
class Go r t where
- go :: RefList r -> t a -> t a
tapeGo :: Ref 'Relative -> Tape a -> Tape a
data Signed f a
- = Positive (f a)
- | Negative (f a)
class InsertBase l where
- insertBase :: l a -> Tape a -> Tape a
class InsertNested l t where
- insertNested :: l a -> t a -> t a
type family AddNest x where ...
type family AsNestedAs x y where ...
class DimensionalAs (x :: Type) (y :: Type) where
- type AsDimensionalAs x y
- asDimensionalAs :: x -> y -> x `AsDimensionalAs` y
slice :: (Take r' t, Go r t) => RefList r -> RefList r' -> t a -> ListFrom t a
insert :: (DimensionalAs x (t a), InsertNested l t, AsDimensionalAs x (t a) ~ l a) => x -> t a -> t a
type Abs1 = 'Absolute :-: Nil
type Rel1 = 'Relative :-: Nil
type Nat1 = S Z
nat1 :: Natural Nat1
type Sheet1 = Nested (NestedNTimes Nat1 Tape)
type ISheet1 = Indexed (NestedNTimes Nat1 Tape)
here1 :: RefList Rel1
d1 :: CombineRefLists Rel1 x => RefList x -> RefList (Rel1 & x)
columnAt :: Int -> RefList ('Absolute :-: Nil)
column :: Z < NestedCount ts => Indexed ts x -> Int
rightBy :: Int -> RefList Rel1
leftBy :: Int -> RefList Rel1
right :: RefList Rel1
left :: RefList Rel1
type Abs2 = 'Absolute :-: Abs1
type Rel2 = 'Relative :-: Rel1
type Nat2 = S Nat1
nat2 :: Natural Nat2
type Sheet2 = Nested (NestedNTimes Nat2 Tape)
type ISheet2 = Indexed (NestedNTimes Nat2 Tape)
here2 :: RefList Rel2
d2 :: CombineRefLists Rel2 x => RefList x -> RefList (Rel2 & x)
rowAt :: Int -> RefList (Tack 'Absolute Rel1)
row :: Nat1 < NestedCount ts => Indexed ts x -> Int
belowBy :: Int -> RefList Rel2
aboveBy :: Int -> RefList Rel2
above :: RefList Rel2
below :: RefList Rel2
type Abs3 = 'Absolute :-: Abs2
type Rel3 = 'Relative :-: Rel2
type Nat3 = S Nat2
nat3 :: Natural Nat3
type Sheet3 = Nested (NestedNTimes Nat3 Tape)
type ISheet3 = Indexed (NestedNTimes Nat3 Tape)
here3 :: RefList Rel3
d3 :: CombineRefLists Rel3 x => RefList x -> RefList (Rel3 & x)
levelAt :: Int -> RefList (Tack 'Absolute Rel2)
level :: Nat2 < NestedCount ts => Indexed ts x -> Int
outwardBy :: Int -> RefList Rel3
inwardBy :: Int -> RefList Rel3
outward :: RefList Rel3
inward :: RefList Rel3
type Abs4 = 'Absolute :-: Abs3
type Rel4 = 'Relative :-: Rel3
type Nat4 = S Nat3
nat4 :: Natural Nat4
type Sheet4 = Nested (NestedNTimes Nat4 Tape)
type ISheet4 = Indexed (NestedNTimes Nat4 Tape)
here4 :: RefList Rel4
d4 :: CombineRefLists Rel4 x => RefList x -> RefList (Rel4 & x)
spaceAt :: Int -> RefList (Tack 'Absolute Rel3)
space :: Nat3 < NestedCount ts => Indexed ts x -> Int
anaBy :: Int -> RefList Rel4
cataBy :: Int -> RefList Rel4
ana :: RefList Rel4
cata :: RefList Rel4
(&&&) :: (t -> a) -> (t -> b) -> t -> (a, b)

Defining and executing sheets.

evaluate :: ComonadApply w => w (w a -> a) -> w a Source #

evaluateF :: (ComonadApply w, Functor f) => w (f (w (f a) -> a)) -> w (f a) Source #

cell :: (Comonad w, Go r w) => RefList r -> w a -> a Source #

cells :: (Traversable t, Comonad w, Go r w) => t (RefList r) -> w a -> t a Source #

sheet :: (InsertNested l t, Applicative t, DimensionalAs x (t a), AsDimensionalAs x (t a) ~ l a) => a -> x -> t a Source #

Construct a sheet of values from a default value and an insertable container of values.

change :: (InsertNested l w, ComonadApply w, DimensionalAs x (w (w a -> a)), AsDimensionalAs x (w (w a -> a)) ~ l (w a -> a)) => x -> w a -> w a Source #

sheetFromNested :: (InsertNested (Nested fs) (Nested (NestedNTimes (NestedCount fs) Tape)), Applicative (Nested (NestedNTimes (NestedCount fs) Tape))) => a -> Nested fs a -> Nested (NestedNTimes (NestedCount fs) Tape) a Source #

indexedSheet :: (InsertNested l (Nested ts), Applicative (Nested ts), DimensionalAs x (Nested ts a), AsDimensionalAs x (Nested ts a) ~ l a) => Coordinate (NestedCount ts) -> a -> x -> Indexed ts a Source #

Construct an indexed sheet from an origin index, a default value, and an insertable container of values.

Inexhaustible streams

data Stream t Source #

A 'Stream t' is an inexhaustible source of values of type t. Unlike the ordinary builtin list type '[]' a Stream cannot ever be empty or exhausted.

Constructors

Cons t (Stream t)

Instances

Instances details

Applicative Stream Source #
Instance details Defined in Sheet Methods pure :: a -> Stream a Source # (<>) :: Stream (a -> b) -> Stream a -> Stream b Source # liftA2 :: (a -> b -> c) -> Stream a -> Stream b -> Stream c Source # (>) :: Stream a -> Stream b -> Stream b Source # (<*) :: Stream a -> Stream b -> Stream a Source #
Functor Stream Source #
Instance details Defined in Sheet Methods fmap :: (a -> b) -> Stream a -> Stream b Source # (<$) :: a -> Stream b -> Stream a Source #
Monad Stream Source #
Instance details Defined in Sheet Methods (>>=) :: Stream a -> (a -> Stream b) -> Stream b Source # (>>) :: Stream a -> Stream b -> Stream b Source # return :: a -> Stream a Source #
Comonad Stream Source #
Instance details Defined in Sheet Methods extract :: Stream a -> a duplicate :: Stream a -> Stream (Stream a) extend :: (Stream a -> b) -> Stream a -> Stream b
ComonadApply Stream Source #
Instance details Defined in Sheet Methods (<@>) :: Stream (a -> b) -> Stream a -> Stream b (@>) :: Stream a -> Stream b -> Stream b (<@) :: Stream a -> Stream b -> Stream a
InsertBase Stream Source #
Instance details Defined in Sheet Methods insertBase :: Stream a -> Tape a -> Tape a Source #
Show t => Show (Stream t) Source #
Instance details Defined in Sheet Methods showsPrec :: Int -> Stream t -> ShowS Source # show :: Stream t -> String Source # showList :: [Stream t] -> ShowS Source #
InsertBase (Signed Stream) Source #
Instance details Defined in Sheet Methods insertBase :: Signed Stream a -> Tape a -> Tape a Source #

(<:>) :: t -> Stream t -> Stream t Source #

repeat :: t -> Stream t Source #

Construct an infinite 'Stream a' from a value of type a.

zipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c Source #

Combines two infinite streams element-wise using the provided function.

unzip :: Stream (a, b) -> (Stream a, Stream b) Source #

iterateStream :: (value -> value) -> value -> Stream value Source #

Repeatedly apply a step function to an initial value to generate the next value

unfoldStream :: (state -> (value, state)) -> state -> Stream value Source #

takeStream :: Int -> Stream value -> [value] Source #

Capture n values from an infinite 'Stream value'.

takeStreamNat :: Z < S n => Natural n -> Stream value -> [value] Source #

Alternate implementation of takeStream which trades the inelegance but convenience of error for the type safety and inconvenience of requiring some kind of evil type witness to convey how many items to grab from the 'Stream value'.

Tapes: bidirectional streams with a focus

data Tape a Source #

Two infinite Streams of type a joined with a center value in focus. A Tape is named for tape in a Turing machine.

Constructors

Tape
Fields viewL :: Stream a focus :: a viewR :: Stream a

Instances

Instances details

Representable Tape Source #
Instance details Defined in Sheet Associated Types type Rep Tape Methods tabulate :: (Rep Tape -> a) -> Tape a index :: Tape a -> Rep Tape -> a
Applicative Tape Source #
Instance details Defined in Sheet Methods pure :: a -> Tape a Source # (<>) :: Tape (a -> b) -> Tape a -> Tape b Source # liftA2 :: (a -> b -> c) -> Tape a -> Tape b -> Tape c Source # (>) :: Tape a -> Tape b -> Tape b Source # (<*) :: Tape a -> Tape b -> Tape a Source #
Functor Tape Source #
Instance details Defined in Sheet Methods fmap :: (a -> b) -> Tape a -> Tape b Source # (<$) :: a -> Tape b -> Tape a Source #
Comonad Tape Source #
Instance details Defined in Sheet Methods extract :: Tape a -> a duplicate :: Tape a -> Tape (Tape a) extend :: (Tape a -> b) -> Tape a -> Tape b
ComonadApply Tape Source #
Instance details Defined in Sheet Methods (<@>) :: Tape (a -> b) -> Tape a -> Tape b (@>) :: Tape a -> Tape b -> Tape b (<@) :: Tape a -> Tape b -> Tape a
Distributive Tape Source #
Instance details Defined in Sheet Methods distribute :: Functor f => f (Tape a) -> Tape (f a) collect :: Functor f => (a -> Tape b) -> f a -> Tape (f b) distributeM :: Monad m => m (Tape a) -> Tape (m a) collectM :: Monad m => (a -> Tape b) -> m a -> Tape (m b)
InsertBase Tape Source #
Instance details Defined in Sheet Methods insertBase :: Tape a -> Tape a -> Tape a Source #
(Take Nil (Nested ts), Functor (Nested ts)) => Take Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList Nil -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
View Nil (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList Nil -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(View Nil (Nested ts), Functor (Nested ts)) => View Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList Nil -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
InsertBase l => InsertNested (Nested (F l) :: Type -> Type) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (F l) a -> Nested (F Tape) a -> Nested (F Tape) a Source #
(InsertBase l, InsertNested (Nested ls) (Nested ts), Functor (Nested ls), Applicative (Nested ts)) => InsertNested (Nested (N ls l) :: Type -> Type) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (N ls l) a -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
Go ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: Nil) -> Nested (F Tape) a -> Nested (F Tape) a Source #
(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
Take ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (F Tape)) a Source # Methods take :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> ListFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), Take rs (Nested ts)) => Take ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
View ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
type Rep Tape Source #
Instance details Defined in Sheet type Rep Tape = Int
type ListFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (F Tape)) a = [a]
type ListFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (N ts Tape)) a = ListFrom (Nested ts) [a]
type ListFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (N ts Tape)) a = ListFrom (Nested ts) [a]
type StreamFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (F Tape)) a = Stream a
type StreamFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (F Tape)) a = Stream a
type StreamFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (N ts Tape)) a = StreamFrom (Nested ts) (Stream a)
type StreamFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (N ts Tape)) a = StreamFrom (Nested ts) (Stream a)

tapeOf :: a -> Tape a Source #

Tape unit.

moveL :: Tape a -> Tape a Source #

Utilities to move a Tape one cell to the left or right.

moveR :: Tape a -> Tape a Source #

Utilities to move a Tape one cell to the left or right.

iterate :: (t -> t) -> (t -> t) -> t -> Tape t Source #

Builds a Tape out of two generator functions and an initial seed value. prev will generate the left-hand Stream while next will generate the right-hand Stream.

enumerate :: Enum a => a -> Tape a Source #

Constructs a Tape from any Enumerable type.

unfold :: (c -> (a, c)) -> (c -> a) -> (c -> (a, c)) -> c -> Tape a Source #

Unfolds a Tape from two Stream unfold functions, a function to generate the initial focus, and a seed value.

References, indices, and coordinates

data Ref (t :: RefType) Source #

A Ref is indexed by a RefType kind (confusing name, to be sure) and represents some unique value. Here that unique value is carried by an Int property. An absolute reference denotes a coordinate in a fixed frame of reference. A relative reference denotes some distance to be applied to another anchor reference (relative or absolute).

Constructors

t ~ 'Relative => Rel Int
t ~ 'Absolute => Abs Int

Instances

Instances details

Enum (Ref 'Absolute) Source #
Instance details Defined in Sheet Methods succ :: Ref 'Absolute -> Ref 'Absolute Source # pred :: Ref 'Absolute -> Ref 'Absolute Source # toEnum :: Int -> Ref 'Absolute Source # fromEnum :: Ref 'Absolute -> Int Source # enumFrom :: Ref 'Absolute -> [Ref 'Absolute] Source # enumFromThen :: Ref 'Absolute -> Ref 'Absolute -> [Ref 'Absolute] Source # enumFromTo :: Ref 'Absolute -> Ref 'Absolute -> [Ref 'Absolute] Source # enumFromThenTo :: Ref 'Absolute -> Ref 'Absolute -> Ref 'Absolute -> [Ref 'Absolute] Source #
Enum (Ref 'Relative) Source #
Instance details Defined in Sheet Methods succ :: Ref 'Relative -> Ref 'Relative Source # pred :: Ref 'Relative -> Ref 'Relative Source # toEnum :: Int -> Ref 'Relative Source # fromEnum :: Ref 'Relative -> Int Source # enumFrom :: Ref 'Relative -> [Ref 'Relative] Source # enumFromThen :: Ref 'Relative -> Ref 'Relative -> [Ref 'Relative] Source # enumFromTo :: Ref 'Relative -> Ref 'Relative -> [Ref 'Relative] Source # enumFromThenTo :: Ref 'Relative -> Ref 'Relative -> Ref 'Relative -> [Ref 'Relative] Source #
Num (Ref 'Absolute) Source #
Instance details Defined in Sheet Methods (+) :: Ref 'Absolute -> Ref 'Absolute -> Ref 'Absolute Source # (-) :: Ref 'Absolute -> Ref 'Absolute -> Ref 'Absolute Source # (*) :: Ref 'Absolute -> Ref 'Absolute -> Ref 'Absolute Source # negate :: Ref 'Absolute -> Ref 'Absolute Source # abs :: Ref 'Absolute -> Ref 'Absolute Source # signum :: Ref 'Absolute -> Ref 'Absolute Source # fromInteger :: Integer -> Ref 'Absolute Source #
Num (Ref 'Relative) Source #
Instance details Defined in Sheet Methods (+) :: Ref 'Relative -> Ref 'Relative -> Ref 'Relative Source # (-) :: Ref 'Relative -> Ref 'Relative -> Ref 'Relative Source # (*) :: Ref 'Relative -> Ref 'Relative -> Ref 'Relative Source # negate :: Ref 'Relative -> Ref 'Relative Source # abs :: Ref 'Relative -> Ref 'Relative Source # signum :: Ref 'Relative -> Ref 'Relative Source # fromInteger :: Integer -> Ref 'Relative Source #
Show (Ref t) Source #
Instance details Defined in Sheet Methods showsPrec :: Int -> Ref t -> ShowS Source # show :: Ref t -> String Source # showList :: [Ref t] -> ShowS Source #
Eq (Ref t) Source #
Instance details Defined in Sheet Methods (==) :: Ref t -> Ref t -> Bool Source # (/=) :: Ref t -> Ref t -> Bool Source #
Ord (Ref t) Source #
Instance details Defined in Sheet Methods compare :: Ref t -> Ref t -> Ordering Source # (<) :: Ref t -> Ref t -> Bool Source # (<=) :: Ref t -> Ref t -> Bool Source # (>) :: Ref t -> Ref t -> Bool Source # (>=) :: Ref t -> Ref t -> Bool Source # max :: Ref t -> Ref t -> Ref t Source # min :: Ref t -> Ref t -> Ref t Source #

getRef :: Ref t -> Int Source #

For when we want to throw away the type information and access the raw Int value beneath the Ref.

class CombineRefTypes (a :: RefType) (b :: RefType) where Source #

Associated Types

type Combine a b :: RefType Source #

Methods

combine :: Ref a -> Ref b -> Ref (Combine a b) Source #

Instances

Instances details

CombineRefTypes 'Absolute 'Relative Source #
Instance details Defined in Sheet Associated Types type Combine 'Absolute 'Relative :: RefType Source # Methods combine :: Ref 'Absolute -> Ref 'Relative -> Ref (Combine 'Absolute 'Relative) Source #
CombineRefTypes 'Relative 'Absolute Source #
Instance details Defined in Sheet Associated Types type Combine 'Relative 'Absolute :: RefType Source # Methods combine :: Ref 'Relative -> Ref 'Absolute -> Ref (Combine 'Relative 'Absolute) Source #
CombineRefTypes 'Relative 'Relative Source #
Instance details Defined in Sheet Associated Types type Combine 'Relative 'Relative :: RefType Source # Methods combine :: Ref 'Relative -> Ref 'Relative -> Ref (Combine 'Relative 'Relative) Source #

data RefType Source #

There are two kinds reference types: Relative and Absolute.

Constructors

Relative
Absolute

Instances

Instances details

Go ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: Nil) -> Nested (F Tape) a -> Nested (F Tape) a Source #
(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
Take ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (F Tape)) a Source # Methods take :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> ListFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), Take rs (Nested ts)) => Take ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
View ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
(CombineRefTypes a b, CombineRefLists as bs) => CombineRefLists (a :-: as) (b :-: bs) Source #
Instance details Defined in Sheet Methods (&) :: RefList (a :-: as) -> RefList (b :-: bs) -> RefList ((a :-: as) & (b :-: bs)) Source #

Reference lists

type RefList = Conic Ref Source #

A RefList is a Conic list of references.

class CombineRefLists as bs where Source #

We can combine lists of references if their corresponding elements can be combined. When combining two lists of references, any trailing elements from the longer list will be preserved at the end.

Methods

(&) :: RefList as -> RefList bs -> RefList (as & bs) infixr 4 Source #

Instances

Instances details

CombineRefLists Nil Nil Source #
Instance details Defined in Sheet Methods (&) :: RefList Nil -> RefList Nil -> RefList (Nil & Nil) Source #
CombineRefLists Nil (b :-: bs) Source #
Instance details Defined in Sheet Methods (&) :: RefList Nil -> RefList (b :-: bs) -> RefList (Nil & (b :-: bs)) Source #
CombineRefLists (a :-: as) Nil Source #
Instance details Defined in Sheet Methods (&) :: RefList (a :-: as) -> RefList Nil -> RefList ((a :-: as) & Nil) Source #
(CombineRefTypes a b, CombineRefLists as bs) => CombineRefLists (a :-: as) (b :-: bs) Source #
Instance details Defined in Sheet Methods (&) :: RefList (a :-: as) -> RefList (b :-: bs) -> RefList ((a :-: as) & (b :-: bs)) Source #

merge :: ReifyNatural n => Counted n (Ref 'Relative) -> Counted n (Ref 'Absolute) -> Counted n (Ref 'Absolute) Source #

Given a homogenous list of length n containing relative references, we can merge those relative positions with a homogenous list of absolute references.

diff :: Counted n (Either (Ref 'Relative) (Ref 'Absolute)) -> Counted n (Ref 'Absolute) -> Counted n (Ref 'Relative) Source #

Finds the relative movement necessary to move from a given absolute coordinate to the location specified by a list of a relative and absolute coordinates.

eitherFromRef :: Ref t -> Either (Ref 'Relative) (Ref 'Absolute) Source #

Given a Ref, forget the type-level information about whether it's absolute or relative by casting it into an Either type, with the left branch holding relative reference and the right branch absolute.

getMovement :: (Length ts <= n, ((n - Length ts) + Length ts) ~ n) => RefList ts -> Counted n (Ref 'Absolute) -> Counted n (Ref 'Relative) Source #

Given a list of relative and absolute references (an n-dimensional reference) and an n-dimensional coordinate, we can obtain the relative movement necessary to get from the coordinate to the location specified by the references given.

dimensional :: Tackable t (Replicate n 'Relative) => Natural (S n) -> Ref t -> RefList (Tack t (Replicate n 'Relative)) Source #

Given a number n greater than zero and some reference, prepend (n - 1) relative references of value zero to the reference given, thus creating an n-dimensional reference where the references refers to the nth dimension.

Coordinates

type Coordinate n = Counted n (Ref 'Absolute) Source #

data Indexed ts a Source #

A Nested functor paired with a valid index to one of its members.

Constructors

Indexed
Fields origin :: Coordinate (NestedCount ts) unindexed :: Nested ts a

Instances

Instances details

(Go (Replicate (NestedCount ts) 'Relative) (Nested ts), Length r <= NestedCount ts, ((NestedCount ts - Length r) + Length r) ~ NestedCount ts, ReifyNatural (NestedCount ts)) => Go r (Indexed ts :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList r -> Indexed ts a -> Indexed ts a Source #
InsertNested l (Nested ts) => InsertNested (l :: Type -> Type) (Indexed ts :: Type -> Type) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). l a -> Indexed ts a -> Indexed ts a Source #
(Take (Replicate (NestedCount ts) 'Relative) (Nested ts), Length r <= NestedCount ts, ((NestedCount ts - Length r) + Length r) ~ NestedCount ts) => Take r (Indexed ts) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Indexed ts) a Source # Methods take :: RefList r -> Indexed ts a -> ListFrom (Indexed ts) a Source #
(View (Replicate (NestedCount ts) 'Relative) (Nested ts), Length r <= NestedCount ts, ((NestedCount ts - Length r) + Length r) ~ NestedCount ts) => View r (Indexed ts) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Indexed ts) a Source # Methods view :: RefList r -> Indexed ts a -> StreamFrom (Indexed ts) a Source #
NestedAs x (Nested ts y) => DimensionalAs x (Indexed ts y) Source #
Instance details Defined in Sheet Associated Types type AsDimensionalAs x (Indexed ts y) Source # Methods asDimensionalAs :: x -> Indexed ts y -> AsDimensionalAs x (Indexed ts y) Source #
(ComonadApply (Nested ts), ReifyNatural (NestedCount ts), Cross (NestedCount ts) Tape, ts ~ NestedNTimes (NestedCount ts) Tape, Go (Replicate (NestedCount ts) 'Relative) (Nested ts)) => Representable (Indexed ts) Source #
Instance details Defined in Sheet Associated Types type Rep (Indexed ts) Methods tabulate :: (Rep (Indexed ts) -> a) -> Indexed ts a index :: Indexed ts a -> Rep (Indexed ts) -> a
Functor (Nested ts) => Functor (Indexed ts) Source #
Instance details Defined in Sheet Methods fmap :: (a -> b) -> Indexed ts a -> Indexed ts b Source # (<$) :: a -> Indexed ts b -> Indexed ts a Source #
(ComonadApply (Nested ts), Indexable ts) => Comonad (Indexed ts) Source #
Instance details Defined in Sheet Methods extract :: Indexed ts a -> a duplicate :: Indexed ts a -> Indexed ts (Indexed ts a) extend :: (Indexed ts a -> b) -> Indexed ts a -> Indexed ts b
(ComonadApply (Nested ts), Indexable ts) => ComonadApply (Indexed ts) Source #
Instance details Defined in Sheet Methods (<@>) :: Indexed ts (a -> b) -> Indexed ts a -> Indexed ts b (@>) :: Indexed ts a -> Indexed ts b -> Indexed ts b (<@) :: Indexed ts a -> Indexed ts b -> Indexed ts a
(ComonadApply (Nested ts), ReifyNatural (NestedCount ts), Cross (NestedCount ts) Tape, ts ~ NestedNTimes (NestedCount ts) Tape, Go (Replicate (NestedCount ts) 'Relative) (Nested ts)) => Distributive (Indexed ts) Source #
Instance details Defined in Sheet Methods distribute :: Functor f => f (Indexed ts a) -> Indexed ts (f a) collect :: Functor f => (a -> Indexed ts b) -> f a -> Indexed ts (f b) distributeM :: Monad m => m (Indexed ts a) -> Indexed ts (m a) collectM :: Monad m => (a -> Indexed ts b) -> m a -> Indexed ts (m b)
type AsDimensionalAs x (Indexed ts y) Source #
Instance details Defined in Sheet type AsDimensionalAs x (Indexed ts y) = AsNestedAs x (Nested ts y)
type Rep (Indexed ts) Source #
Instance details Defined in Sheet type Rep (Indexed ts) = Counted (NestedCount ts) Int
type ListFrom (Indexed ts) a Source #
Instance details Defined in Sheet type ListFrom (Indexed ts) a = ListFrom (Nested ts) a
type StreamFrom (Indexed ts) a Source #
Instance details Defined in Sheet type StreamFrom (Indexed ts) a = StreamFrom (Nested ts) a

class Cross n t where Source #

Methods

cross :: Counted n (t a) -> Nested (NestedNTimes n t) (Counted n a) Source #

Instances

Instances details

(Cross (S n) t, Functor t, Functor (Nested (NestedNTimes (S n) t))) => Cross (S (S n)) t Source #
Instance details Defined in Sheet Methods cross :: Counted (S (S n)) (t a) -> Nested (NestedNTimes (S (S n)) t) (Counted (S (S n)) a) Source #
Functor t => Cross (S Z) t Source #
Instance details Defined in Sheet Methods cross :: Counted (S Z) (t a) -> Nested (NestedNTimes (S Z) t) (Counted (S Z) a) Source #

Indexed

type Indexable ts = (Cross (NestedCount ts) Tape, ts ~ NestedNTimes (NestedCount ts) Tape) Source #

indices :: Cross n Tape => Coordinate n -> Nested (NestedNTimes n Tape) (Coordinate n) Source #

Type-level `Tape` manipulation with `Coordinate`s and `Ref`s.

Take

class Take r t where Source #

Associated Types

type ListFrom t a Source #

Methods

take :: RefList r -> t a -> ListFrom t a Source #

Instances

Instances details

(Take Nil (Nested ts), Functor (Nested ts)) => Take Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList Nil -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
(Take (Replicate (NestedCount ts) 'Relative) (Nested ts), Length r <= NestedCount ts, ((NestedCount ts - Length r) + Length r) ~ NestedCount ts) => Take r (Indexed ts) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Indexed ts) a Source # Methods take :: RefList r -> Indexed ts a -> ListFrom (Indexed ts) a Source #
Take ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (F Tape)) a Source # Methods take :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> ListFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), Take rs (Nested ts)) => Take ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #

tapeTake :: Ref 'Relative -> Tape a -> [a] Source #

Take all the items between the current focus and the item specified by the Relative Reference and return them as a list '[a]'.

View

class View r t where Source #

Associated Types

type StreamFrom t a Source #

Type of an n-dimensional stream extracted from an n-dimensional sheet.

Methods

view :: RefList r -> t a -> StreamFrom t a Source #

Instances

Instances details

View Nil (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList Nil -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(View Nil (Nested ts), Functor (Nested ts)) => View Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList Nil -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
(View (Replicate (NestedCount ts) 'Relative) (Nested ts), Length r <= NestedCount ts, ((NestedCount ts - Length r) + Length r) ~ NestedCount ts) => View r (Indexed ts) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Indexed ts) a Source # Methods view :: RefList r -> Indexed ts a -> StreamFrom (Indexed ts) a Source #
View ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #

tapeView :: Ref 'Relative -> Tape a -> Stream a Source #

Go

class Go r t where Source #

Methods

go :: RefList r -> t a -> t a Source #

Move to the location specified by the given RefList.

Instances

Instances details

Go Nil (Nested ts :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList Nil -> Nested ts a -> Nested ts a Source #
(Go (Replicate (NestedCount ts) 'Relative) (Nested ts), Length r <= NestedCount ts, ((NestedCount ts - Length r) + Length r) ~ NestedCount ts, ReifyNatural (NestedCount ts)) => Go r (Indexed ts :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList r -> Indexed ts a -> Indexed ts a Source #
Go ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: Nil) -> Nested (F Tape) a -> Nested (F Tape) a Source #
(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #

tapeGo :: Ref 'Relative -> Tape a -> Tape a Source #

data Signed f a Source #

A Signed f is an 'f a' annotated with a sign: either Positive or Negative. This is a useful type for specifying direction when inserting into sheets. By wrapping a list or stream in Negative and then inserting it into a sheet, you insert it in the opposite direction of the usual one.

Constructors

Positive (f a)
Negative (f a)

Instances

Instances details

InsertBase (Signed Stream) Source #
Instance details Defined in Sheet Methods insertBase :: Signed Stream a -> Tape a -> Tape a Source #
InsertBase (Signed []) Source #
Instance details Defined in Sheet Methods insertBase :: Signed [] a -> Tape a -> Tape a Source #
Show (f a) => Show (Signed f a) Source #
Instance details Defined in Sheet Methods showsPrec :: Int -> Signed f a -> ShowS Source # show :: Signed f a -> String Source # showList :: [Signed f a] -> ShowS Source #
Eq (f a) => Eq (Signed f a) Source #
Instance details Defined in Sheet Methods (==) :: Signed f a -> Signed f a -> Bool Source # (/=) :: Signed f a -> Signed f a -> Bool Source #
Ord (f a) => Ord (Signed f a) Source #
Instance details Defined in Sheet Methods compare :: Signed f a -> Signed f a -> Ordering Source # (<) :: Signed f a -> Signed f a -> Bool Source # (<=) :: Signed f a -> Signed f a -> Bool Source # (>) :: Signed f a -> Signed f a -> Bool Source # (>=) :: Signed f a -> Signed f a -> Bool Source # max :: Signed f a -> Signed f a -> Signed f a Source # min :: Signed f a -> Signed f a -> Signed f a Source #

Insertion

class InsertBase l where Source #

Methods

insertBase :: l a -> Tape a -> Tape a Source #

Instances

Instances details

InsertBase Stream Source #
Instance details Defined in Sheet Methods insertBase :: Stream a -> Tape a -> Tape a Source #
InsertBase Tape Source #
Instance details Defined in Sheet Methods insertBase :: Tape a -> Tape a -> Tape a Source #
InsertBase [] Source #
Instance details Defined in Sheet Methods insertBase :: [a] -> Tape a -> Tape a Source #
InsertBase (Signed Stream) Source #
Instance details Defined in Sheet Methods insertBase :: Signed Stream a -> Tape a -> Tape a Source #
InsertBase (Signed []) Source #
Instance details Defined in Sheet Methods insertBase :: Signed [] a -> Tape a -> Tape a Source #

class InsertNested l t where Source #

Methods

insertNested :: l a -> t a -> t a Source #

Instances

Instances details

InsertNested l (Nested ts) => InsertNested (l :: Type -> Type) (Indexed ts :: Type -> Type) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). l a -> Indexed ts a -> Indexed ts a Source #
InsertBase l => InsertNested (Nested (F l) :: Type -> Type) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (F l) a -> Nested (F Tape) a -> Nested (F Tape) a Source #
(InsertBase l, InsertNested (Nested ls) (Nested ts), Functor (Nested ls), Applicative (Nested ts)) => InsertNested (Nested (N ls l) :: Type -> Type) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (N ls l) a -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #

type family AddNest x where ... Source #

Equations

AddNest (Nested fs (f x)) = Nested (N fs f) x

type family AsNestedAs x y where ... Source #

Equations

AsNestedAs (f x) (Nested (F g) b) = Nested (F f) x
AsNestedAs x y = AddNest (x `AsNestedAs` UnNest y)

Dimensions

class DimensionalAs (x :: Type) (y :: Type) where Source #

DimensionalAs provides a mechanism to "lift" an n-deep nested structure into an explicit Nested type. This is the way in which raw lists-of-lists-of-lists-, etc. can be inserted (without manual annotation of nesting depth) into a sheet.

Associated Types

type AsDimensionalAs x y Source #

Methods

asDimensionalAs :: x -> y -> x `AsDimensionalAs` y Source #

Instances

Instances details

(NestedAs x (Nested ts y), AsDimensionalAs x (Nested ts y) ~ AsNestedAs x (Nested ts y)) => DimensionalAs x (Nested ts y) Source #
Instance details Defined in Sheet Associated Types type AsDimensionalAs x (Nested ts y) Source # Methods asDimensionalAs :: x -> Nested ts y -> AsDimensionalAs x (Nested ts y) Source #
NestedAs x (Nested ts y) => DimensionalAs x (Indexed ts y) Source #
Instance details Defined in Sheet Associated Types type AsDimensionalAs x (Indexed ts y) Source # Methods asDimensionalAs :: x -> Indexed ts y -> AsDimensionalAs x (Indexed ts y) Source #

slice :: (Take r' t, Go r t) => RefList r -> RefList r' -> t a -> ListFrom t a Source #

Combination of go and take: moves to the location specified by the first argument, then takes the amount specified by the second argument.

insert :: (DimensionalAs x (t a), InsertNested l t, AsDimensionalAs x (t a) ~ l a) => x -> t a -> t a Source #

Insert a (possibly nested) list-like structure into a (possibly many-dimensional) sheet. The depth of the nesting structure being inserted must match the number of dimensions of the sheet into which it is being inserted. The structure being inserted need not be a Nested type: it need only have enough levels of structure (ie, number of nested lists) to match the dimensionality of the sheet.