def ParallelFinal

bendtorch-core@0.1.0.0 · src/tensor/contracts/product_proof.bend:201

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/contracts/product_parallel_proof.bend as Par

201# The parallel product over replayed inputs, in transport form: P holds for
202# the product if it holds for both inputs replayed with histories that keep
203# their words, next to the output replayed with the writes of every cell.
204def ParallelFinal(+lo: Matrix.Order, +ro: Matrix.Order, +left: Shape.Shape, +right: Shape.Shape, +output: Shape.Shape, +rows: U32, +inner: U32, +columns: U32,
205  +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>,
206  -s: Storage.Storage, -P: Result<&2, &1, Matrix.Error, Core.Dynamic & Core.Dynamic & Core.Dynamic> -> Type) -> Type:
207  @+left_kept: List<&2, StorageLaws.Op> ->
208  @left_values: (@+other: U32 -> {Replayed.value(left, left_fill, left_kept, other) == Replayed.value(left, left_fill, left_ops, other) : F32}) ->
209  @left_words: {Laws.words(left, left_fill, left_kept, Shape.logical_numel(Shape.dimensions(left))) ==
210    Laws.words(left, left_fill, left_ops, Shape.logical_numel(Shape.dimensions(left))) : List<&2, F32>} ->
211  @-left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_kept)) == Shape.logical_numel(Shape.dimensions(left)) : Nat} ->
212  @+right_kept: List<&2, StorageLaws.Op> ->
213  @right_values: (@+other: U32 -> {Replayed.value(right, right_fill, right_kept, other) == Replayed.value(right, right_fill, right_ops, other) : F32}) ->
214  @right_words: {Laws.words(right, right_fill, right_kept, Shape.logical_numel(Shape.dimensions(right))) ==
215    Laws.words(right, right_fill, right_ops, Shape.logical_numel(Shape.dimensions(right))) : List<&2, F32>} ->
216  @-right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_kept)) == Shape.logical_numel(Shape.dimensions(right)) : Nat} ->
217  @-output_fits: {Lifecycle.logical_length(StorageLaws.replay(Par.writes(lo, ro, U32.to_nat(inner), U32.to_nat(rows), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output))), s)) == Shape.logical_numel(Shape.dimensions(output)) : Nat} ->
218    P(Done{(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_kept), left_fits}},
219      Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_kept), right_fits}},
220      Core.Packed{output, Core.TTensor{StorageLaws.replay(Par.writes(lo, ro, U32.to_nat(inner), U32.to_nat(rows), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output))), s), output_fits}})})