Data.Container.Additive.Morphism.Instances

Definitions

pushIntoContinuation : (d >*< p) =%+> l -> p =%+> (pushDown (d .Shp) >-+@ l)

Totality: total
Visibility: public export

leftUnit : (UnitCont >*< c) =%+> c

Totality: total
Visibility: public export

rightUnit : (c >*< UnitCont) =%+> c

Totality: total
Visibility: public export

leftUnitInv : c =%+> (UnitCont >*< c)

Totality: total
Visibility: public export

rightUnitInv : c =%+> (c >*< UnitCont)

Totality: total
Visibility: public export

assocL : ((a >*< b) >*< c) =%+> (a >*< (b >*< c))

Totality: total
Visibility: public export

assocR : (a >*< (b >*< c)) =%+> ((a >*< b) >*< c)

Totality: total
Visibility: public export

swap : (a >*< b) =%+> (b >*< a)

Totality: total
Visibility: public export

swapMiddle : ((c1 >*< c2) >*< (c3 >*< c4)) =%+> ((c1 >*< c3) >*< (c2 >*< c4))

Totality: total
Visibility: public export

copy : c =%+> (c >*< c)

  These do not exist for ordinary containers!
  Here we need `c` not to be erased since we're using its monoid structure

Totality: total
Visibility: public export

pairMaps : c =%+> d -> c =%+> e -> c =%+> (d >*< e)

Totality: total
Visibility: public export

projLeft : (c >*< d) =%+> c

Totality: total
Visibility: public export

projRight : (c >*< d) =%+> d

Totality: total
Visibility: public export

unitor : c =%+> (Scalar >-+@ c)

  Backwards pass is ComMon-homomorphism on the nose

Totality: total
Visibility: public export

unitorInv : (Scalar >-+@ c) =%+> c

  Backwards map is a ComMon-homomorphism only through the quotient

Totality: total
Visibility: public export

multiplicator : (m >-+@ (n >-+@ c)) =%+> ((m >@ n) >-+@ c)

Totality: total
Visibility: public export

multiplicatorInv : ((m >@ n) >-+@ c) =%+> (m >-+@ (n >-+@ c))

Totality: total
Visibility: public export

actionToFree : (e >-+@ Scalar) =%+> (!*) e

  Read each position as the generator it is, with multiplicity one

Totality: total
Visibility: public export

freeToAction : (!*) e =%+> (e >-+@ Scalar)

  Expand each generator into as many copies as its multiplicity says

Totality: total
Visibility: public export

adjR : UC c =%> m -> c =%+> (m >-+@ Scalar)

  Hom-set isomorphism of the adjunction, which is the general purpose
  `addContTranspose` read through the isomorphism above

Totality: total
Visibility: public export

adjL : c =%+> (m >-+@ Scalar) -> UC c =%> m

  Inverse of the hom-set isomorphism of the adjunction

Totality: total
Visibility: public export

epsilon : UC Scalar =%> Scalar

Totality: total
Visibility: public export

leftUnit : (Scalar >+@ c) =%+> c

Totality: total
Visibility: public export

rightUnit : c =%+> (c >+@ Scalar)

Totality: total
Visibility: public export

associator : ((a >+@ b) >+@ c) =%+> (a >+@ (b >+@ c))

Totality: total
Visibility: public export

leftUnitInv : c =%+> (Scalar >+@ c)

Totality: total
Visibility: public export

elim : (c >+< c) =%+> c

Totality: total
Visibility: public export

coprodDistrOverTensor : ((a >+< b) >*< (p >*< q)) =%+> ((a >*< p) >+< (b >*< q))

Totality: total
Visibility: public export

State : AddCont -> Type

  State here differers for the one in `Cont`, because `Scalar` is different
  
        ┌─────────────┐
        │             ├──► (x : c.Shp)
        │    State    │
        │             ├◄── c.Pos x
        └─────────────┘

Totality: total
Visibility: public export

toState : c .Shp -> State c

Totality: total
Visibility: public export

Costate : AddCont -> Type

  Costate here differs from the one in `Cont`, because `Scalar` is different
                   ┌─────────────┐
   (x : c.Shp)  ──►┤             │
                   │   Costate   │
      c.Pos x   ◄──┤             │
                   └─────────────┘

Totality: total
Visibility: public export

toCostate : ((x : c .Shp) -> c .Pos x) -> Costate c

Totality: total
Visibility: public export

constantOne : InterfaceOnPositions c Num => Costate c

Totality: total
Visibility: public export

Delete : Costate c

Totality: total
Visibility: public export

sum : {auto {conArg:16178} : Num a} -> (Const a >*< Const a) =%+> Const a

Totality: total
Visibility: public export

bwSumBag : (xs : List l) -> l -> All (const l) xs

Totality: total
Visibility: public export

sumBag : {auto {conArg:16266} : ComMonoid l} -> BagAll (Const l) =%+> Const l

Totality: total
Visibility: public export

negate : {auto {conArg:16308} : Num a} -> Neg a => Const a =%+> Const a

Totality: total
Visibility: public export
Fixity Declaration: prefix operator, level 10

zero : {auto {conArg:16346} : Num a} -> c =%+> Const a

Totality: total
Visibility: public export

mul : {auto {conArg:16378} : Num a} -> (Const a >*< Const a) =%+> Const a

Totality: total
Visibility: public export

SquaredDifference : {auto {conArg:16436} : Num a} -> Neg a => (Const a >*< Const a) =%+> Const a

  Mean squared error

Totality: total
Visibility: public export

selectShape : All .Shp cs -> Fin k -> Any .Shp cs

  Select a shape from All to produce an Any at the given index
  Same as `index i (allAnies shapes)` but reduces better

Totality: total
Visibility: public export

extractPos : (i : Fin n) -> AnyShpPos (selectShape shapes i) -> (index i xs) .Pos (index i shapes)

  Extract the position from an AnyPos at a given index

Totality: total
Visibility: public export