SliceLAWS.select_slices: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend as SliceLAWS
Lines 293-305 of bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend&start_line=293&end_line=305

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/tensor/slice.bend as Slice

# PyTorch's select(dim, index) is the slice index:index + 1 with step 1,
# reshaped to the input's dimensions without the axis, once the axis is in
# range and the index below the extent; an index at or past the extent is
# refused with OutOfRange, an axis past the rank as a slice refuses it.
law select_slices:
  for input: Core.Dynamic
  for +dim: U32
  for +index: U32
  for inside: {Nat.is_lt(U32.to_nat(dim), rank_of(input)) == True{} : Bool}
  for below: {Nat.is_lt(U32.to_nat(index), extent_of(input, dim)) == True{} : Bool}
  {Slice.select(input, dim, index) ==
    reshaped(Slice.dropped(Shape.dimensions(Totality.dynamic_shape(input)), U32.to_nat(dim)), Slice.slice(input, dim, index, U32.add(index, 1), 1)) :
    Core.Dynamic & Result<&2, &1, Slice.Error, Core.Dynamic>}

Uses (24):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=rank_dimensions
  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/elementwise_totality.bend&name=dynamic_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=dropped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=extent_at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=refused
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=select
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=select_checked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=select_ranged
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=slice
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend&name=extent_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend&name=rank_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend&name=reshaped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&name=reshaped_as