1	import Base
2	import ../shape/core.bend as Shape
3	import ./layout.bend as Layout
4	import ./transpose_spec.bend as Transpose
5	import ./permute_values_records.bend as Records
6	import ../storage/LAWS.bend as StorageLaws
7	import ./core.bend as Core
8	import ./lifecycle.bend as Lifecycle
9	import ./transforms.bend as Transforms
10	import ./contracts/replayed.bend as Replayed
11	
12	# `permute_copy` of a `Core.from_values(input, values)` tensor by a valid
13	# permutation succeeds with dimensions `Axis.order(dims, axes)`; output index i
14	# holds `values[permute_source(input, axes, i)]`, and the returned source
15	# still holds `values[j]` at every j.
16	law permute_contract:
17	  for +input: Shape.Shape
18	  for +values: List<&2, F32>
19	  for counted: {List.length(&2, F32, values) == Shape.logical_numel(Shape.dimensions(input)) : Nat}
20	  for +axes: List<&2, U32>
21	  for valid: {True{} == Layout.bijective(input, axes) : Bool}
22	  Records.PermuteContract<input, values, axes>
23	
24	# `transpose_copy(a, b)` of a `Core.from_values` tensor with both axes in
25	# range is the permute contract with the axes that swap a and b.
26	law transpose_contract:
27	  for +input: Shape.Shape
28	  for +values: List<&2, F32>
29	  for counted: {List.length(&2, F32, values) == Shape.logical_numel(Shape.dimensions(input)) : Nat}
30	  for +a: U32
31	  for +b: U32
32	  for inside: {True{} == Transpose.valid(input, a, b) : Bool}
33	  Records.TransposeContract<input, values, a, b>
34	
35	# `permute_dynamic` of a replayed tensor, once `Layout.permutation` gives the
36	# plan, in the transport form of `broadcast_to_replayed`: for every P, if P
37	# holds for every result that hands the source back with the same words and
38	# gives an output of the plan's shape, replayed over +0.0, whose cell i holds
39	# the source's word at `permute_source(input, axes, i)`, then P holds for the
40	# call. The output is a replayed tensor, so a later family law applies to it.
41	law permute_replayed:
42	  for +input: Shape.Shape
43	  for +fill: F32
44	  for +ops: List<&2, StorageLaws.Op>
45	  for -fits: {Lifecycle.logical_length(Replayed.storage(input, fill, ops)) == Shape.logical_numel(Shape.dimensions(input)) : Nat}
46	  for +axes: List<&2, U32>
47	  for +plan: Layout.Plan<input, axes>
48	  for laid: {Layout.permutation(input, axes) == Done{plan} : Result<&2, &2, Layout.Error, Layout.Plan<input, axes>>}
49	  for -P: Core.Dynamic & Result<&2, &1, Transforms.Error, Core.Dynamic> -> Type
50	  for h: Records.PermutedWith(input, fill, ops, axes, plan, P)
51	  P(Transforms.permute_dynamic(Core.Packed{input, Core.TTensor{Replayed.storage(input, fill, ops), fits}}, axes))
52	
53	# `transpose_dynamic(a, b)` of a replayed tensor with both axes in range is the
54	# permute of `permute_replayed` by the swapped axes, in the same transport form.
55	law transpose_replayed:
56	  for +input: Shape.Shape
57	  for +fill: F32
58	  for +ops: List<&2, StorageLaws.Op>
59	  for -fits: {Lifecycle.logical_length(Replayed.storage(input, fill, ops)) == Shape.logical_numel(Shape.dimensions(input)) : Nat}
60	  for +a: U32
61	  for +b: U32
62	  for inside: {True{} == Transpose.valid(input, a, b) : Bool}
63	  for +plan: Layout.Plan<input, Transpose.swapped_axes(input, a, b)>
64	  for laid: {Layout.permutation(input, Transpose.swapped_axes(input, a, b)) == Done{plan} :
65	    Result<&2, &2, Layout.Error, Layout.Plan<input, Transpose.swapped_axes(input, a, b)>>}
66	  for -P: Core.Dynamic & Result<&2, &1, Transforms.Error, Core.Dynamic> -> Type
67	  for h: Records.PermutedWith(input, fill, ops, Transpose.swapped_axes(input, a, b), plan, P)
68	  P(Transforms.transpose_dynamic(Core.Packed{input, Core.TTensor{Replayed.storage(input, fill, ops), fits}}, a, b))