SliceLAWS.narrow_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 242-254 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=242&end_line=254

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

# PyTorch's narrow(dim, start, length) is the slice start:start + length
# with step 1, once the axis is in range and start + length is at most the
# extent; a start + length past the extent is refused with OutOfRange, an
# axis past the rank as a slice refuses it.
law narrow_slices:
  for input: Core.Dynamic
  for +dim: U32
  for +start: U32
  for +length: U32
  for inside: {Nat.is_lt(U32.to_nat(dim), rank_of(input)) == True{} : Bool}
  for fits: {Nat.is_le(Nat.add(U32.to_nat(start), U32.to_nat(length)), extent_of(input, dim)) == True{} : Bool}
  {Slice.narrow(input, dim, start, length) == Slice.slice(input, dim, start, U32.add(start, length), 1) :
    Core.Dynamic & Result<&2, &1, Slice.Error, Core.Dynamic>}

Uses (22):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  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/slice.bend&name=Error
  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=narrow
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=narrow_checked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=narrow_ranged
  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=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