def halves_equal

bendtorch-core@0.1.0.0 · src/autograd/reduce_parallel_proof.bend:700

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel
import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce

700# A split hands each half the contribution array.
701def halves_equal(+d: Nat, -A: Array<F32>, pair: Array<F32> & Array<F32>, -exact: {pair == Array.clone(F32, A) : Array<F32> & Array<F32>},
702  -valid: Model.Balanced(F32, d, A)) ->
703  Parallel.Fact<({Pair.fst(Array<F32> & Unit, Array<F32> & Unit, Reduce.halves(pair)) == (A, Unit{}) : Array<F32> & Unit} &
704    {Pair.snd(Array<F32> & Unit, Array<F32> & Unit, Reduce.halves(pair)) == (A, Unit{}) : Array<F32> & Unit})>:
705  (first, second) = pair
706  Parallel.Fact{(
707    Equal.cong(Array<F32>, Array<F32> & Unit, a => (a, Unit{}), first, A,
708      {\{Parallel.Fact: p => p} : Parallel.Fact<({Pair.fst(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>})> ->
709        {Pair.fst(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>}}(Parallel.clone_first(d, A, A, (first, second), exact, {==}, valid))),
710    Equal.cong(Array<F32>, Array<F32> & Unit, a => (a, Unit{}), second, A,
711      {\{Parallel.Fact: p => p} : Parallel.Fact<({Pair.snd(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>})> ->
712        {Pair.snd(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>}}(Parallel.clone_second(d, A, A, (first, second), exact, {==}, valid))))}