def loop_success

bendtorch-core@0.1.0.0 · src/tensor/elementwise_PROOF.bend:813

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/elementwise.bend as Elementwise
import bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformProof

813def loop_success(fuel: Nat, +operation: Elementwise.Operation, +plan: Shape.BroadcastPlan, +cursor: Nat,
814  state: Elementwise.State<Shape.output_shape(plan)>,
815  -fits: FittingSources<plan, step_left_owner(Shape.output_shape(plan), Elementwise.Continue{state}), step_right_owner(Shape.output_shape(plan), Elementwise.Continue{state})>,
816  -within: {Nat.is_le(Nat.add(fuel, cursor), Shape.elements(Shape.output_shape(plan))) == True{} : Bool}) ->
817  Totality.Success<Elementwise.loop(fuel, operation, plan, cursor, state)>:
818  match fuel:
819    case 0n:
820      Elementwise.State{left, right, output} = state
821      Totality.Success{{==}}
822    case 1n+remaining:
823      loop_finish_success(remaining, operation, plan, cursor,
824        step_left_owner(Shape.output_shape(plan), Elementwise.Continue{state}), step_right_owner(Shape.output_shape(plan), Elementwise.Continue{state}),
825        Elementwise.natural_step(operation, plan, cursor, state),
826        {\{NaturalSuccess: successful => successful} : NaturalSuccess<Shape.output_shape(plan), cursor, Elementwise.natural_step(operation, plan, cursor, state)> ->
827          {natural_succeeded(Shape.output_shape(plan), cursor, Elementwise.natural_step(operation, plan, cursor, state)) == True{} : Bool}}(
828            natural_success(operation, plan, cursor, state, fits,
829              Arith.lt_le_trans(cursor, 1n+Nat.add(remaining, cursor), Shape.elements(Shape.output_shape(plan)),
830                Arith.lt_succ(cursor, Nat.add(remaining, cursor), TransformProof.add_cursor_le(remaining, cursor)), within))),
831        natural_decided_retains(operation, plan, cursor, U32.from_nat(cursor), Shape.bool_case(Nat.is_eq(U32.to_nat(U32.from_nat(cursor)), cursor)), state), fits,
832        state => next_fits => loop_success(remaining, operation, plan, 1n+cursor, state, next_fits,
833          %Equal.sym(Nat, Nat.add(remaining, 1n+cursor), 1n+Nat.add(remaining, cursor), Arith.add_succ(remaining, cursor)) :
834            {Nat.is_le(_, Shape.elements(Shape.output_shape(plan))) == True{} : Bool}
835          within))