def cell_keeps

bendtorch-core@0.1.0.0 · src/tensor/batched_matmul_PROOF.bend:232

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul.bend as Batched
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel

232# Every cell hands both input arrays back.
233def cell_keeps(+lo: Matrix.Order, +ro: Matrix.Order, +inner: Nat, +rows: Nat, +columns: Nat, +l1: Nat, +l2: Nat, +r1: Nat, +r2: Nat, +o2: Nat,
234  +position: Nat, +dl: Nat, +dr: Nat, A: Array<F32>, B: Array<F32>, inside: Bool,
235  -left_valid: Model.Balanced(F32, dl, A), -right_valid: Model.Balanced(F32, dr, B)) ->
236  Parallel.Fact<{Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, inside)) == (A, B) : Array<F32> & Array<F32>}>:
237  match inside:
238    case False{}:
239      Parallel.Fact{{==}}
240    case True{}:
241      Parallel.Fact{{\{StridedRun: values => logical => fold => left_kept => right_kept =>
242        Equal.trans(Array<F32> & Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{})),
243          (Pair.fst(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{}))),
244            Pair.snd(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{})))),
245          (A, B),
246          eta(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{}))),
247          Parallel.pair_equal(Pair.fst(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{}))),
248            Pair.snd(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{}))),
249            A, B, left_kept, right_kept))} :
250        StridedRun<inner, dl, dr, A, B, Matrix.stride(lo, rows), Matrix.stride(ro, columns),
251          Batched.left_start(Laws.layout_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2), position),
252          Batched.right_start(Laws.layout_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2), position), 0.0,
253          cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{})> ->
254        {Pair.snd(F32, Array<F32> & Array<F32>, cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{})) == (A, B) : Array<F32> & Array<F32>}}(
255        {\{Parallel.Fact: p => p} :
256          Parallel.Fact<StridedRun<inner, dl, dr, A, B, Matrix.stride(lo, rows), Matrix.stride(ro, columns),
257            Batched.left_start(Laws.layout_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2), position),
258            Batched.right_start(Laws.layout_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2), position), 0.0,
259            cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{})>> ->
260          StridedRun<inner, dl, dr, A, B, Matrix.stride(lo, rows), Matrix.stride(ro, columns),
261            Batched.left_start(Laws.layout_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2), position),
262            Batched.right_start(Laws.layout_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2), position), 0.0,
263            cell_of(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, A, B, True{})>}(
264          dot_run(lo, ro, inner, rows, columns, l1, l2, r1, r2, o2, position, dl, dr, A, B, left_valid, right_valid)))}