SumProof.total_words: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend as SumProof
Lines 25-40 of bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend&start_line=25&end_line=40

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/reduction.bend as Reduction
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold.bend as Fold
import bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend as Sum
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Laws

def total_words(+shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +count: Nat) ->
  {Fold.total(~Unit, ~Sum.add, ~Unit, ~Sum.position, ~Sum.every, Unit{}, Unit{}, shape, fill, ops, count) ==
    Reduction.sequential_sum(Laws.words(shape, fill, ops, count), 0.0) : F32}:
  match count:
    case 0n:
      {==}
    case 1n+previous:
      +word = Replayed.value(shape, fill, ops, U32.from_nat(previous))
      %Equal.sym(F32, Reduction.sequential_sum(List.append(&2, F32, Laws.words(shape, fill, ops, previous), [word]), 0.0),
        F32.add(Reduction.sequential_sum(Laws.words(shape, fill, ops, previous), 0.0), word),
        sequential_snoc(Laws.words(shape, fill, ops, previous), word, 0.0)) :
        {F32.add(Fold.total(~Unit, ~Sum.add, ~Unit, ~Sum.position, ~Sum.every, Unit{}, Unit{}, shape, fill, ops, previous), word) == _ : F32}
      Equal.cong(F32, F32, total => F32.add(total, word),
        Fold.total(~Unit, ~Sum.add, ~Unit, ~Sum.position, ~Sum.every, Unit{}, Unit{}, shape, fill, ops, previous),
        Reduction.sequential_sum(Laws.words(shape, fill, ops, previous), 0.0),
        total_words(shape, fill, ops, previous))

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=words
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold.bend&name=total
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=every
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=position
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend&name=sequential_snoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=sequential_sum