def preserved_read

bendtorch-core@0.1.0.0 · src/tensor/reduction_PROOF.bend:174

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/reduction.bend as Reduction
import bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend as Laws

174def preserved_read(+fuel: Nat, -shape: Shape.Shape, -original: Core.Tensor<shape>, +cursor: Nat, +accumulator: F32,
175  tensor: Core.Tensor<shape>, result: Result<&2, &2, Core.Error, F32>,
176  -rec: @tensor: Core.Tensor<shape> -> @+value: F32 -> Laws.Preserved<shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value)>,
177  -kept: @+other: U32 -> {Core.checked_observe(shape, tensor, other) == Core.checked_observe(shape, original, other) : Maybe<&2, F32>}) ->
178  Laws.Preserved<shape, original, Reduction.read_step(shape,
179    tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, (tensor, result))>:
180  match result:
181    case Fail{error}:
182      Laws.Preserved{other => {==}}
183    case Done{+value}:
184      Laws.Preserved{other =>
185        claim : @certificate: Laws.Preserved<shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value))> ->
186          {Laws.retained_observe(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other) ==
187            Laws.successful_observe(shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other) : Maybe<&2, F32>} =
188          \{Laws.Preserved: kept => kept(other)}
189        Equal.trans(Maybe<&2, F32>,
190          Laws.retained_observe(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other),
191          Laws.successful_observe(shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other),
192          Laws.successful_observe(shape, original, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other),
193          claim(rec(tensor, F32.add(accumulator, value))), success_keeps(shape, original, tensor,
194            Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other, kept(other)))}