PointwiseProof.shift: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend as PointwiseProof
Lines 289-335 of bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&start_line=289&end_line=335

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend as Pointwise

def shift(~O: Data, ~f: O -> F32 -> F32 -> F32, ~P: Data, ~ia: P -> Nat -> Nat, ~ib: P -> Nat -> Nat,
  +rest: Nat, +operation: O, +plan: P, +left: Shape.Shape, +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>,
  +right: Shape.Shape, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>, +shape: Shape.Shape, +cursor: Nat,
  -Q: (Core.Dynamic & Core.Dynamic) & Result<&2, &1, Core.Error, Core.Dynamic> -> Type,
  next: Start(~O, ~f, ~P, ~ia, ~ib, rest, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, shape, 1n+cursor, Q)) ->
  Shaped(~O, ~f, ~P, ~ia, ~ib, rest, operation, plan, left, right, shape, 1n+cursor,
    Replayed.storage(left, left_fill, Replayed.snoc(List.append(&2, StorageLaws.Op, left_ops, Pointwise.reads(~P, ~ia, plan, cursor)),
      StorageLaws.Read{U32.from_nat(ia(plan, cursor))})),
    Replayed.storage(right, right_fill, Replayed.snoc(List.append(&2, StorageLaws.Op, right_ops, Pointwise.reads(~P, ~ib, plan, cursor)),
      StorageLaws.Read{U32.from_nat(ib(plan, cursor))})),
    Replayed.storage(shape, 0.0, Replayed.snoc(
      Pointwise.writes(~O, ~f, ~P, ~ia, ~ib, cursor, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops),
      StorageLaws.Write{U32.from_nat(cursor),
        f(operation, Replayed.value(left, left_fill, List.append(&2, StorageLaws.Op, left_ops, Pointwise.reads(~P, ~ia, plan, cursor)), U32.from_nat(ia(plan, cursor))),
          Replayed.value(right, right_fill, List.append(&2, StorageLaws.Op, right_ops, Pointwise.reads(~P, ~ib, plan, cursor)), U32.from_nat(ib(plan, cursor))))})),
    Q):
  +left_read = {StorageLaws.Read{U32.from_nat(ia(plan, cursor))} : StorageLaws.Op}
  +right_read = {StorageLaws.Read{U32.from_nat(ib(plan, cursor))} : StorageLaws.Op}
  +left_seen = List.append(&2, StorageLaws.Op, left_ops, Pointwise.reads(~P, ~ia, plan, cursor))
  +right_seen = List.append(&2, StorageLaws.Op, right_ops, Pointwise.reads(~P, ~ib, plan, cursor))
  +x = Replayed.value(left, left_fill, left_seen, U32.from_nat(ia(plan, cursor)))
  +y = Replayed.value(right, right_fill, right_seen, U32.from_nat(ib(plan, cursor)))
  +left_word = Replayed.value(left, left_fill, left_ops, U32.from_nat(ia(plan, cursor)))
  +right_word = Replayed.value(right, right_fill, right_ops, U32.from_nat(ib(plan, cursor)))
  +history = Pointwise.writes(~O, ~f, ~P, ~ia, ~ib, cursor, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops)
  -left_after = Replayed.storage(left, left_fill, Replayed.snoc(left_seen, left_read))
  -right_after = Replayed.storage(right, right_fill, Replayed.snoc(right_seen, right_read))
  -output_after = Replayed.storage(shape, 0.0, Replayed.snoc(history, StorageLaws.Write{U32.from_nat(cursor), f(operation, x, y)}))
  %Equal.cong(List<&2, StorageLaws.Op>, Storage.Storage, ops => Replayed.storage(left, left_fill, ops),
    List.append(&2, StorageLaws.Op, left_ops, Replayed.snoc(Pointwise.reads(~P, ~ia, plan, cursor), left_read)), Replayed.snoc(left_seen, left_read),
    append_snoc(left_ops, Pointwise.reads(~P, ~ia, plan, cursor), left_read)) :
    Shaped(~O, ~f, ~P, ~ia, ~ib, rest, operation, plan, left, right, shape, 1n+cursor, _, right_after, output_after, Q)
  %Equal.cong(List<&2, StorageLaws.Op>, Storage.Storage, ops => Replayed.storage(right, right_fill, ops),
    List.append(&2, StorageLaws.Op, right_ops, Replayed.snoc(Pointwise.reads(~P, ~ib, plan, cursor), right_read)), Replayed.snoc(right_seen, right_read),
    append_snoc(right_ops, Pointwise.reads(~P, ~ib, plan, cursor), right_read)) :
    Shaped(~O, ~f, ~P, ~ia, ~ib, rest, operation, plan, left, right, shape, 1n+cursor,
      input_storage(~P, ~ia, plan, left, left_fill, left_ops, 1n+cursor), _, output_after, Q)
  %Equal.cong(F32, Storage.Storage, word => Replayed.storage(shape, 0.0, Replayed.snoc(history, StorageLaws.Write{U32.from_nat(cursor), word})),
    f(operation, left_word, right_word), f(operation, x, y),
    Equal.trans(F32, f(operation, left_word, right_word), f(operation, x, right_word), f(operation, x, y),
      Equal.cong(F32, F32, word => f(operation, word, right_word), left_word, x,
        Equal.sym(F32, x, left_word, value_reads(~P, ~ia, plan, cursor, left, left_fill, left_ops, U32.from_nat(ia(plan, cursor))))),
      Equal.cong(F32, F32, word => f(operation, x, word), right_word, y,
        Equal.sym(F32, y, right_word, value_reads(~P, ~ib, plan, cursor, right, right_fill, right_ops, U32.from_nat(ib(plan, cursor))))))) :
    Shaped(~O, ~f, ~P, ~ia, ~ib, rest, operation, plan, left, right, shape, 1n+cursor,
      input_storage(~P, ~ia, plan, left, left_fill, left_ops, 1n+cursor), input_storage(~P, ~ib, plan, right, right_fill, right_ops, 1n+cursor), _, Q)
  next

Uses (25):
  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=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  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/storage/main.bend&name=Storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=reads
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=writes
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=Shaped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=Start
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=append_snoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=input_storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=value_reads
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=snoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=storage
  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/core.bend&name=Dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Error