def target_split

bendtorch-core@0.1.0.0 · src/tensor/slice_PROOF.bend:809

import Base
import bendtorch-core@0.1.0.0/src/tensor/slice.bend as Slice
import bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedProof

809# Position (o * extent + i) * inner + r splits into row o * extent + i and
810# remainder r, and the row into o and i.
811def target_split(+outer: Nat, +extent: Nat, +inner: Nat, +start: Nat, +step: Nat, +length: Nat, +o: Nat, +i: Nat, +r: Nat,
812  +i_below: {Nat.is_lt(i, extent) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}) ->
813  {Slice.target(Slice.Plan{outer, extent, inner, start, step, length}, Laws.position(extent, inner, o, i, r)) ==
814    picked_at(outer, extent, inner, start, step, length, Nat.add(Nat.mul(o, extent), i), r, i) : Maybe<&2, Nat>}:
815  +row = Nat.add(Nat.mul(o, extent), i)
816  +pos = Laws.position(extent, inner, o, i, r)
817  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
818    {target_of(outer, extent, inner, start, step, length, _, Nat.mod(pos, inner)) ==
819      picked_at(outer, extent, inner, start, step, length, row, r, i) : Maybe<&2, Nat>}
820  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
821    {target_of(outer, extent, inner, start, step, length, row, _) == picked_at(outer, extent, inner, start, step, length, row, r, i) : Maybe<&2, Nat>}
822  %Equal.sym(Nat, Nat.mod(row, extent), i, BatchedProof.mod_exact(o, extent, i, i_below)) :
823    {picked_at(outer, extent, inner, start, step, length, row, r, _) == picked_at(outer, extent, inner, start, step, length, row, r, i) : Maybe<&2, Nat>}
824  {==}