law dot_ordered

bendtorch-core@0.1.0.0 · src/tensor/contracts/LAWS.bend:106

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
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/dot_fold.bend as DotFold
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend as Dot
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend as FoldRecords

106# Ordered-fold family, dot instance: for every in-bounds output cell of a
107# product of a rows x inner and an inner x columns replayed matrix, the dot
108# product succeeds with `DotFold.dot_fold` of the cell's factor pairs in
109# increasing k, starting at +0.0, and both returned inputs keep every word.
110law dot_ordered:
111  for +rows: Nat
112  for +inner: Nat
113  for +columns: Nat
114  for +row: Nat
115  for row_below: {Nat.is_lt(row, rows) == True{} : Bool}
116  for +column: Nat
117  for column_below: {Nat.is_lt(column, columns) == True{} : Bool}
118  for +left: Shape.Shape
119  for left_extents: {Shape.extents(left) == [rows, inner] : List<&2, Nat>}
120  for +left_fill: F32
121  for +left_ops: List<&2, StorageLaws.Op>
122  for -left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_ops)) == Shape.logical_numel(Shape.dimensions(left)) : Nat}
123  for +right: Shape.Shape
124  for right_extents: {Shape.extents(right) == [inner, columns] : List<&2, Nat>}
125  for +right_fill: F32
126  for +right_ops: List<&2, StorageLaws.Op>
127  for -right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_ops)) == Shape.logical_numel(Shape.dimensions(right)) : Nat}
128  FoldRecords.PairFoldContract<left, right,
129    DotFold.dot_fold(factors(row, column, inner, columns, left, left_fill, left_ops, right, right_fill, right_ops, inner), 0.0),
130    other => Replayed.value(left, left_fill, left_ops, other),
131    other => Replayed.value(right, right_fill, right_ops, other),
132    Dot.dot(Dot.Cell{row, column, inner, columns},
133      Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}},
134      Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}})>