Data.Container.Additive.Morphism.Instances

Definitions

State : AddCont -> Type

  "State" as defined in https://arxiv.org/abs/2403.13001 and open games 
  
        ┌─────────────┐
        │             ├──► (x : c.Shp)
        │    State    │
        │             ├◄── c.Pos x
        └─────────────┘

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toState : c .Shp -> State c

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fromState : State c -> c .Shp

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Costate : AddCont -> Type

  "Costate" as defined in https://arxiv.org/abs/2403.13001 and open games 
  
                   ┌─────────────┐
   (x : c.Shp)  ──►┤             │
                   │   Costate   │
      c.Pos x   ◄──┤             │
                   └─────────────┘

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

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

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constantOne : InterfaceOnPositions c Num => Costate c

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Delete : Costate c

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pushDown : AddCont -> AddCont

  If we model the idea of a container (S !> P) as a box
   ┌──────┐
   │ s:S  │
   ├──────┤
   │  Ps  │
   └──────┘
  then `pushDown` is interpreted as pushing down the container,
  pruning anything that goes out of the box, and using `Unit` for
  anything new that appears:
   ┌──────┐
   │ Unit │
   ├──────┤
   │ s:S  │
   └──────┘
      Ps
  For additive containers we need to take the free monoid

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pushIntoContinuationList : (d >< p) =%> l -> p =%> (pushDown d >@ List l)

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

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leftUnit : (Scalar >< c) =%> c

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rightUnit : (c >< Scalar) =%> c

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leftUnitInv : c =%> (Scalar >< c)

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rightUnitInv : c =%> (c >< Scalar)

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

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

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swap : (a >< b) =%> (b >< a)

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

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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

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PairMaps : c =%> d -> c =%> e -> c =%> (d >< e)

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ProjLeft : (c >< d) =%> c

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ProjRight : (c >< d) =%> d

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leftUnit : (Scalar >@ c) =%> c

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rightUnit : (c >@ Scalar) =%> c

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leftUnitInv : c =%> (Scalar >@ c)

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rightUnitInv : c =%> (c >@ Scalar)

  Right unit inverse: c =%> c >@ I

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elim : (c >+< c) =%> c

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duoidal : ((c >@ d) >< (e >@ f)) =%> ((c >< e) >@ (d >< f))

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

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rebracketcomptensor : ((e >@ y) >< y) =%> (e >@ (y >< y))

  Not an isomorphism, arising from duoidal structure between >@ and ><

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distribute : (c >< e) =%> s -> (c >< (e >@ g)) =%> (s >@ g)

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extractEffect : (d >< (e >@ f)) =%> (e >@ (d >< f))

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Sum : {auto {conArg:18521} : Num a} -> (Const a >< Const a) =%> Const a

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bwSumList : ComMonoid l => (xs : List l) -> l -> All (const l) xs

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SumList : {auto {conArg:18621} : ComMonoid l} -> List (Const l) =%> Const l

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Negate : {auto {conArg:18653} : Num a} -> Neg a => Const a =%> Const a

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Zero : {auto {conArg:18693} : Num a} -> c =%> Const a

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Mul : {auto {conArg:18726} : Num a} -> (Const a >< Const a) =%> Const a

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SquaredDifference : {auto {conArg:18787} : Num a} -> Neg a => (Const a >< Const a) =%> Const a

  Mean squared error

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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

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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

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