def summed_is

bendtorch-core@0.1.0.0 · src/tensor/gather_PROOF.bend:463

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/storage/refinement.bend as Refinement
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend as Generic

463def summed_is(+i: Nat, +at: Nat, +slot: Nat, +acc: F32, +dg: Nat, -G: Array<F32>, +di: Nat, -I: Array<U32>, index: Array<U32>, +j: U32,
464  -kept: {index == I : Array<U32>}, -seen: {Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(slot))) == Some{j} : Maybe<&2, U32>},
465  hit: Bool, -told: {Nat.is_eq(U32.to_nat(j), i) == hit : Bool}, -valid: Model.Balanced(F32, dg, G)) ->
466  Generic.Fact<Stepped<dg, G, di, I, i, at, slot, acc, Gather.summed(hit, at, acc, G, index)>>:
467  match hit:
468    case False{}:
469      Generic.Fact{Skipped{j, seen, told, Equal.cong(Array<U32>, F32 & (Array<F32> & Array<U32>), b => (acc, (G, b)), index, I, kept)}}
470    case True{}:
471      Generic.Fact{Taken{j, seen, told, Refinement.second(F32, Array.get(F32, G, U32.from_nat(at))),
472        Equal.sym(Maybe<&2, F32>, Some{Refinement.second(F32, Array.get(F32, G, U32.from_nat(at)))},
473          Model.observe(F32, dg, G, Refinement.route(dg, U32.from_nat(at))), Refinement.law_get_refines(F32, dg, G, U32.from_nat(at), valid)),
474        Equal.trans(F32 & (Array<F32> & Array<U32>), Gather.accumulate(acc, index, Array.get(F32, G, U32.from_nat(at))),
475          (F32.add(acc, Refinement.second(F32, Array.get(F32, G, U32.from_nat(at)))), (Refinement.first(F32, Array.get(F32, G, U32.from_nat(at))), index)),
476          (F32.add(acc, Refinement.second(F32, Array.get(F32, G, U32.from_nat(at)))), (G, I)),
477          accumulated(acc, index, Array.get(F32, G, U32.from_nat(at))),
478          triple(acc, Refinement.second(F32, Array.get(F32, G, U32.from_nat(at))), Refinement.first(F32, Array.get(F32, G, U32.from_nat(at))), index, G, I,
479            Refinement.law_get_retains(F32, dg, G, U32.from_nat(at), valid), kept))}}