Reorganize Data.NumIdr.Array.Coords
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@ -8,6 +8,23 @@ import Data.NP
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%default total
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-- A Nat-based range function with better semantics
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public export
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range : Nat -> Nat -> List Nat
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range x y = if x < y then assert_total $ takeBefore (>= y) (countFrom x S)
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else []
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-- helpful theorems for working with ranges
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export
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rangeLen : (x,y : Nat) -> length (range x y) = minus y x
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rangeLen x y = believe_me $ Refl {x = minus y x}
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export
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rangeLenZ : (x : Nat) -> length (range 0 x) = x
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rangeLenZ x = rangeLen 0 x `trans` minusZeroRight x
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--------------------------------------------------------------------------------
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-- Array coordinate types
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--------------------------------------------------------------------------------
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@ -26,6 +43,44 @@ toNB [] = []
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toNB (i :: is) = finToNat i :: toNB is
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namespace Strict
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public export
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data CRange : Nat -> Type where
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One : Fin n -> CRange n
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All : CRange n
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StartBound : Fin (S n) -> CRange n
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EndBound : Fin (S n) -> CRange n
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Bounds : Fin (S n) -> Fin (S n) -> CRange n
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Indices : List (Fin n) -> CRange n
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Filter : (Fin n -> Bool) -> CRange n
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infix 0 ...
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public export
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(...) : Fin (S n) -> Fin (S n) -> CRange n
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(...) = Bounds
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public export
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CoordsRange : (s : Vect rk Nat) -> Type
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CoordsRange = NP CRange
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namespace NB
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public export
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data CRangeNB : Type where
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All : CRangeNB
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StartBound : Nat -> CRangeNB
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EndBound : Nat -> CRangeNB
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Bounds : Nat -> Nat -> CRangeNB
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Indices : List Nat -> CRangeNB
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Filter : (Nat -> Bool) -> CRangeNB
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--------------------------------------------------------------------------------
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-- Indexing helper functions
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--------------------------------------------------------------------------------
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public export
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Vects : Vect rk Nat -> Type -> Type
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Vects [] a = a
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@ -38,7 +93,7 @@ collapse {s=_::_} = concat . map collapse
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export
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mapWithIndex : {s : Vect rk Nat} -> (Vect rk Nat -> a -> b) -> Vects {rk} s a -> Vects s b
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mapWithIndex : {s : Vect rk Nat} -> (Vect rk Nat -> a -> b) -> Vects s a -> Vects s b
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mapWithIndex {s=[]} f x = f [] x
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mapWithIndex {s=_::_} f v = mapWithIndex' (\i => mapWithIndex (\is => f (i::is))) v
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where
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@ -58,86 +113,73 @@ getLocation : Vect rk Nat -> Coords {rk} s -> Nat
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getLocation sts is = getLocation' sts (toNB is)
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--------------------------------------------------------------------------------
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-- Array coordinate types
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--------------------------------------------------------------------------------
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namespace Strict
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public export
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cRangeToList : {n : Nat} -> CRange n -> Either Nat (List Nat)
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cRangeToList (One x) = Left (cast x)
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cRangeToList All = Right $ range 0 n
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cRangeToList (StartBound x) = Right $ range (cast x) n
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cRangeToList (EndBound x) = Right $ range 0 (cast x)
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cRangeToList (Bounds x y) = Right $ range (cast x) (cast y)
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cRangeToList (Indices xs) = Right $ map cast xs
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cRangeToList (Filter p) = Right $ map cast $ filter p $ toList Fin.range
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-- A Nat-based range function with better semantics
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public export
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range : Nat -> Nat -> List Nat
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range x y = if x < y then assert_total $ takeBefore (>= y) (countFrom x S)
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else []
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public export
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newRank : {s : _} -> CoordsRange s -> Nat
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newRank [] = 0
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newRank (r :: rs) = case cRangeToList r of
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Left _ => newRank rs
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Right _ => S (newRank rs)
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-- helpful theorems for working with ranges
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export
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rangeLen : (x,y : Nat) -> length (range x y) = minus y x
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rangeLen x y = believe_me $ Refl {x = minus y x}
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export
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rangeLenZ : (x : Nat) -> length (range 0 x) = x
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rangeLenZ x = rangeLen 0 x `trans` minusZeroRight x
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||| Calculate the new shape given by a coordinate range.
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public export
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newShape : {s : _} -> (rs : CoordsRange s) -> Vect (newRank rs) Nat
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newShape [] = []
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newShape (r :: rs) with (cRangeToList r)
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newShape (r :: rs) | Left _ = newShape rs
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newShape (r :: rs) | Right xs = length xs :: newShape rs
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public export
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data CRange : Nat -> Type where
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One : Fin n -> CRange n
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All : CRange n
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StartBound : Fin (S n) -> CRange n
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EndBound : Fin (S n) -> CRange n
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Bounds : Fin (S n) -> Fin (S n) -> CRange n
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Indices : List (Fin n) -> CRange n
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Filter : (Fin n -> Bool) -> CRange n
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getNewPos : {s : _} -> (rs : CoordsRange {rk} s) -> Vect rk Nat -> Vect (newRank rs) Nat
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getNewPos [] [] = []
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getNewPos (r :: rs) (i :: is) with (cRangeToList r)
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_ | Left _ = getNewPos rs is
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_ | Right xs = cast (assert_total $ case findIndex (==i) xs of Just x => x)
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:: getNewPos rs is
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infix 0 ...
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public export
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(...) : Fin (S n) -> Fin (S n) -> CRange n
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(...) = Bounds
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export
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getCoordsList : {s : Vect rk Nat} -> (rs : CoordsRange s) -> List (Vect rk Nat, Vect (newRank rs) Nat)
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getCoordsList rs = map (\is => (is, getNewPos rs is)) $ go rs
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where
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go : {0 rk : _} -> {s : Vect rk Nat} -> CoordsRange s -> List (Vect rk Nat)
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go [] = [[]]
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go (r :: rs) = [| (either pure id (cRangeToList r)) :: go rs |]
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public export
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CoordsRange : (s : Vect rk Nat) -> Type
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CoordsRange = NP CRange
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namespace NB
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export
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cRangeNBToList : Nat -> CRangeNB -> List Nat
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cRangeNBToList s All = range 0 s
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cRangeNBToList s (StartBound x) = range x s
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cRangeNBToList s (EndBound x) = range 0 x
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cRangeNBToList s (Bounds x y) = range x (minimum y s)
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cRangeNBToList s (Indices xs) = filter (<s) xs
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cRangeNBToList s (Filter p) = filter p $ range 0 s
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public export
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cRangeToList : {n : Nat} -> CRange n -> Either Nat (List Nat)
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cRangeToList (One x) = Left (cast x)
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cRangeToList All = Right $ range 0 n
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cRangeToList (StartBound x) = Right $ range (cast x) n
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cRangeToList (EndBound x) = Right $ range 0 (cast x)
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cRangeToList (Bounds x y) = Right $ range (cast x) (cast y)
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cRangeToList (Indices xs) = Right $ map cast xs
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cRangeToList (Filter p) = Right $ map cast $ filter p $ toList Fin.range
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export
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newShape : Vect rk Nat -> Vect rk CRangeNB -> Vect rk Nat
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newShape = zipWith (length .: cRangeNBToList)
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export
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getNewPos : Vect rk Nat -> Vect rk CRangeNB -> Vect rk Nat -> Vect rk Nat
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getNewPos = zipWith3 (\d,r,i => assert_total $
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case findIndex (==i) (cRangeNBToList d r) of Just x => cast x)
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public export
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newRank : {s : _} -> CoordsRange s -> Nat
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newRank [] = 0
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newRank (r :: rs) = case cRangeToList r of
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Left _ => newRank rs
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Right _ => S (newRank rs)
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||| Calculate the new shape given by a coordinate range.
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public export
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newShape : {s : _} -> (rs : CoordsRange s) -> Vect (newRank rs) Nat
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newShape [] = []
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newShape (r :: rs) with (cRangeToList r)
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newShape (r :: rs) | Left _ = newShape rs
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newShape (r :: rs) | Right xs = length xs :: newShape rs
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getNewPos : {s : _} -> (rs : CoordsRange {rk} s) -> Vect rk Nat -> Vect (newRank rs) Nat
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getNewPos [] [] = []
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getNewPos (r :: rs) (i :: is) with (cRangeToList r)
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_ | Left _ = getNewPos rs is
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_ | Right xs = cast (assert_total $ case findIndex (==i) xs of Just x => x)
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:: getNewPos rs is
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export
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getCoordsList : {s : Vect rk Nat} -> (rs : CoordsRange s) -> List (Vect rk Nat, Vect (newRank rs) Nat)
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getCoordsList rs = map (\is => (is, getNewPos rs is)) $ go rs
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where
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go : {0 rk : _} -> {s : Vect rk Nat} -> CoordsRange s -> List (Vect rk Nat)
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go [] = pure []
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go (r :: rs) = [| (either pure id (cRangeToList r)) :: go rs |]
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export
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getCoordsList : Vect rk Nat -> Vect rk CRangeNB -> List (Vect rk Nat, Vect rk Nat)
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getCoordsList s rs = map (\is => (is, getNewPos s rs is)) $ go s rs
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where
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go : {0 rk : _} -> Vect rk Nat -> Vect rk CRangeNB -> List (Vect rk Nat)
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go [] [] = [[]]
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go (d :: s) (r :: rs) = [| cRangeNBToList d r :: go s rs |]
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