FoldProof.pair_shift: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend as FoldProof
Lines 173-214 of bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend&start_line=173&end_line=214

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
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend as PointwiseProof
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold.bend as Fold

def pair_shift(~O: Data, ~g: O -> F32 -> 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>, +cursor: Nat,
  -Q: (Core.Dynamic & Core.Dynamic) & Result<&2, &1, Core.Error, F32> -> Type,
  next: PairStart(~O, ~g, ~P, ~ia, ~ib, rest, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, 1n+cursor, Q)) ->
  PairShaped(~O, ~g, ~P, ~ia, ~ib, rest, operation, plan, left, right, 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))})),
    g(operation, Fold.pair_total(~O, ~g, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, cursor),
      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))
  +before = Fold.pair_total(~O, ~g, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, 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)))
  -right_after = Replayed.storage(right, right_fill, Replayed.snoc(right_seen, right_read))
  %Equal.cong(List<&2, StorageLaws.Op>, Storage.Storage, history => Replayed.storage(left, left_fill, history),
    List.append(&2, StorageLaws.Op, left_ops, Replayed.snoc(Pointwise.reads(~P, ~ia, plan, cursor), left_read)), Replayed.snoc(left_seen, left_read),
    PointwiseProof.append_snoc(left_ops, Pointwise.reads(~P, ~ia, plan, cursor), left_read)) :
    PairShaped(~O, ~g, ~P, ~ia, ~ib, rest, operation, plan, left, right, 1n+cursor, _, right_after, g(operation, before, x, y), Q)
  %Equal.cong(List<&2, StorageLaws.Op>, Storage.Storage, history => Replayed.storage(right, right_fill, history),
    List.append(&2, StorageLaws.Op, right_ops, Replayed.snoc(Pointwise.reads(~P, ~ib, plan, cursor), right_read)), Replayed.snoc(right_seen, right_read),
    PointwiseProof.append_snoc(right_ops, Pointwise.reads(~P, ~ib, plan, cursor), right_read)) :
    PairShaped(~O, ~g, ~P, ~ia, ~ib, rest, operation, plan, left, right, 1n+cursor,
      PointwiseProof.input_storage(~P, ~ia, plan, left, left_fill, left_ops, 1n+cursor), _, g(operation, before, x, y), Q)
  %Equal.trans(F32, g(operation, before, left_word, right_word), g(operation, before, x, right_word), g(operation, before, x, y),
    Equal.cong(F32, F32, w => g(operation, before, w, right_word), left_word, x,
      Equal.sym(F32, x, left_word, PointwiseProof.value_reads(~P, ~ia, plan, cursor, left, left_fill, left_ops, U32.from_nat(ia(plan, cursor))))),
    Equal.cong(F32, F32, w => g(operation, before, x, w), right_word, y,
      Equal.sym(F32, y, right_word, PointwiseProof.value_reads(~P, ~ib, plan, cursor, right, right_fill, right_ops, U32.from_nat(ib(plan, cursor)))))) :
    PairShaped(~O, ~g, ~P, ~ia, ~ib, rest, operation, plan, left, right, 1n+cursor,
      PointwiseProof.input_storage(~P, ~ia, plan, left, left_fill, left_ops, 1n+cursor),
      PointwiseProof.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/fold.bend&name=pair_total
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend&name=PairShaped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend&name=PairStart
  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_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