Hi all !
I tried to create explicit and tacit definitions of our composition
conjunctions. I think the result could possibly be used to clarify the
descriptions in NuVoc.
Opinions are welcome, there are probably still some bugs or
misunderstandings of function, there could be interesting aspects to
discuss.
The printout follows, then my project with definitions, tests and some
minor explanations.
In the end of the printout there are some performance measurements. The
explicit versions are doing bad in those. The built in versions are
slightly faster, which could be expected.
Cheers,
Erling
====Printout=======================
ts=: 6!:2 , 7!:2@] NB. Time and space
At=: 2 : 0
NB. @:
u v"_ y
:
u x v"_ y
)
<At- 1 2
┌─────┐
│_1 _2│
└─────┘
NB. < _1_2
5 <At- 1 2
┌───┐
│4 3│
└───┘
NB. < 4 3
NB. @:
AtTacit=: 2 : '[: u v'
<AtTacit- 1 2
┌─────┐
│_1 _2│
└─────┘
NB. < _1_2
5 <AtTacit- 1 2
┌───┐
│4 3│
└───┘
NB. < 4 3
NB. @:
<AtTacit-
[: < -
Atop=: 2 : 0
NB. @
u At v"v y
:
x u At v"v y
)
<Atop- 1 2
┌──┬──┐
│_1│_2│
└──┴──┘
NB. _1;_2
5 <Atop- 1 2
┌─┬─┐
│4│3│
└─┴─┘
NB. 4;3
NB. @
AtopTacit=: 2 : '([: u v)"v'
<AtopTacit- 1 2
┌──┬──┐
│_1│_2│
└──┴──┘
NB. _1;_2
5 <AtopTacit- 1 2
┌─┬─┐
│4│3│
└─┴─┘
NB. 4;3
NB. @
<AtopTacit-
([: < -)"0 0 0
<AtopTacit[
([: < [)"_ _ _
<AtopTacit i.
([: < i.)"1 _ _
Appose=: 2 : 0
NB. &:
u v"_ y
:
(v"_ x) u v"_ y
)
<Appose- 1 2
┌─────┐
│_1 _2│
└─────┘
NB. < _1 _2
5 ([:<<)Appose- 4 5
┌───┐
│1 0│
└───┘
NB. < 1 0
NB. &:
ApposeTacitMonadic=: 2 : '[: u [: v ]'
ApposeTacitDyadic=: 2 : '([: v [) u [: v ]'
<ApposeTacitMonadic- 1 2
┌─────┐
│_1 _2│
└─────┘
NB. < _1 _2
5 ([:<<)ApposeTacitDyadic- 4 5
┌───┐
│1 0│
└───┘
NB. < 1 0
NB. &:
<ApposeTacitMonadic-
[: < [: - ]
([:<<)ApposeTacitDyadic-
([: - [) ([: < <) [: - ]
Compose=: 2 : 0
NB. &
u Appose v"v y
:
x u Appose v"v y
)
<Compose- 1 2
┌──┬──┐
│_1│_2│
└──┴──┘
NB. _1;_2
5 ([:<<)Compose- 4 5
┌─┬─┐
│1│0│
└─┴─┘
NB. 1;0
NB. &
ComposeTacitMonadic=: 2 : '([: u [: v ])"v'
ComposeTacitDyadic=: 2 : '(([: v [) u [: v ])"v'
<ComposeTacitMonadic- 1 2
┌──┬──┐
│_1│_2│
└──┴──┘
NB. _1;_2
5 ([:<<)ComposeTacitDyadic- 4 5
┌─┬─┐
│1│0│
└─┴─┘
NB. 1;0
NB. &
<ComposeTacitMonadic-
([: < [: - ])"0 0 0
([:<<)ComposeTacitDyadic-
(([: - [) ([: < <) [: - ])"0 0 0
UnderRankInfinite=: 2 : 0
NB. &.:
v"_^:_1 u v"_ y
:
v"_^:_1 (v"_ x) u v"_ y
)
-UnderRankInfinite> 1 2;3 4
┌─────┐
│_1 _2│
│_3 _4│
└─────┘
NB. <2 2 $ _1 _2 -3 -4
(5;6) -UnderRankInfinite> 1 2;3 4
┌───┐
│4 3│
│3 2│
└───┘
NB. < 2 2 $ 4 3 3 2
NB. &.:
UnderRankInfiniteTacitMonadic=: 2 : '[: v^:_1 [: u [: v ]'
UnderRankInfiniteTacitDyadic=: 2 : '[: v^:_1 ([: v [) u [: v ]'
-UnderRankInfiniteTacitMonadic> 1 2;3 4
┌─────┐
│_1 _2│
│_3 _4│
└─────┘
NB. <2 2 $ _1 _2 -3 -4
(5;6) -UnderRankInfiniteTacitDyadic> 1 2;3 4
┌───┐
│4 3│
│3 2│
└───┘
NB. < 2 2 $ 4 3 3 2
NB. &.:
-UnderRankInfiniteTacitMonadic>
[: >^:_1 [: - [: > ]
-UnderRankInfiniteTacitDyadic>
[: >^:_1 ([: > [) - [: > ]
UnderRankV=: 2 : 0
NB. &.
u UnderRankInfinite v"v y
:
x u UnderRankInfinite v"v y
)
-UnderRankV> 1 2; 3 4
┌─────┬─────┐
│_1 _2│_3 _4│
└─────┴─────┘
NB. _1 _2; _3 _4
(5;6) -UnderRankV> 1 2;3 4
┌───┬───┐
│4 3│3 2│
└───┴───┘
NB. 4 3;3 2
NB. &.
UnderRankVTacitMonadic=: 2 : '([: v^:_1 [: u [: v ])"v'
UnderRankVTacitDyadic=: 2 : '([: v^:_1 ([: v [) u [: v ])"v'
-UnderRankVTacitMonadic> 1 2; 3 4
┌─────┬─────┐
│_1 _2│_3 _4│
└─────┴─────┘
NB. _1 _2; _3 _4
(5;6) -UnderRankVTacitDyadic> 1 2;3 4
┌───┬───┐
│4 3│3 2│
└───┴───┘
NB. 4 3;3 2
NB. &.
-UnderRankVTacitMonadic>
([: >^:_1 [: - [: > ])"0 0 0
-UnderRankVTacitDyadic>
([: >^:_1 ([: > [) - [: > ])"0 0 0
n=.500000
v=.?~n
$v
500000
10{.v
415593 299586 376558 161399 308885 477430 286004 354448 123594 75795
ts'-AtTacit-AtTacit-AtTacit-AtTacit-@- v'
0.240852 1.32199e8
ts'-AtTacit-AtTacit-AtTacit-AtTacit-AtopTacit- v'
0.2369 1.322e8
ts'-At-At-At-At-Atop- v'
2.96161 1.32204e8
ts'-@:-@:-@:-@:-@- v'
0.158078 1.32197e8
====================== Project =======================================
ts=: 6!:2 , 7!:2@] NB. Time and space
At=: 2 : 0
NB. @:
u v"_ y
:
u x v"_ y
)
<At- 1 2
NB. < _1_2
5 <At- 1 2
NB. < 4 3
NB. @:
AtTacit=: 2 : '[: u v'
<AtTacit- 1 2
NB. < _1_2
5 <AtTacit- 1 2
NB. < 4 3
NB. @:
<AtTacit-
Atop=: 2 : 0
NB. @
u At v"v y
:
x u At v"v y
)
<Atop- 1 2
NB. _1;_2
5 <Atop- 1 2
NB. 4;3
NB. @
AtopTacit=: 2 : '([: u v)"v'
<AtopTacit- 1 2
NB. _1;_2
5 <AtopTacit- 1 2
NB. 4;3
NB. @
<AtopTacit-
<AtopTacit[
<AtopTacit i.
Appose=: 2 : 0
NB. &:
u v"_ y
:
(v"_ x) u v"_ y
)
<Appose- 1 2
NB. < _1 _2
5 ([:<<)Appose- 4 5
NB. < 1 0
NB. &:
ApposeTacitMonadic=: 2 : '[: u [: v ]'
ApposeTacitDyadic=: 2 : '([: v [) u [: v ]'
<ApposeTacitMonadic- 1 2
NB. < _1 _2
5 ([:<<)ApposeTacitDyadic- 4 5
NB. < 1 0
NB. &:
<ApposeTacitMonadic-
([:<<)ApposeTacitDyadic-
Compose=: 2 : 0
NB. &
u Appose v"v y
:
x u Appose v"v y
)
<Compose- 1 2
NB. _1;_2
5 ([:<<)Compose- 4 5
NB. 1;0
NB. &
ComposeTacitMonadic=: 2 : '([: u [: v ])"v'
ComposeTacitDyadic=: 2 : '(([: v [) u [: v ])"v'
<ComposeTacitMonadic- 1 2
NB. _1;_2
5 ([:<<)ComposeTacitDyadic- 4 5
NB. 1;0
NB. &
<ComposeTacitMonadic-
([:<<)ComposeTacitDyadic-
UnderRankInfinite=: 2 : 0
NB. &.:
v"_^:_1 u v"_ y
:
v"_^:_1 (v"_ x) u v"_ y
)
-UnderRankInfinite> 1 2;3 4
NB. <2 2 $ _1 _2 -3 -4
(5;6) -UnderRankInfinite> 1 2;3 4
NB. < 2 2 $ 4 3 3 2
NB. &.:
UnderRankInfiniteTacitMonadic=: 2 : '[: v^:_1 [: u [: v ]'
UnderRankInfiniteTacitDyadic=: 2 : '[: v^:_1 ([: v [) u [: v ]'
-UnderRankInfiniteTacitMonadic> 1 2;3 4
NB. <2 2 $ _1 _2 -3 -4
(5;6) -UnderRankInfiniteTacitDyadic> 1 2;3 4
NB. < 2 2 $ 4 3 3 2
NB. &.:
-UnderRankInfiniteTacitMonadic>
-UnderRankInfiniteTacitDyadic>
UnderRankV=: 2 : 0
NB. &.
u UnderRankInfinite v"v y
:
x u UnderRankInfinite v"v y
)
-UnderRankV> 1 2; 3 4
NB. _1 _2; _3 _4
(5;6) -UnderRankV> 1 2;3 4
NB. 4 3;3 2
NB. &.
UnderRankVTacitMonadic=: 2 : '([: v^:_1 [: u [: v ])"v'
UnderRankVTacitDyadic=: 2 : '([: v^:_1 ([: v [) u [: v ])"v'
-UnderRankVTacitMonadic> 1 2; 3 4
NB. _1 _2; _3 _4
(5;6) -UnderRankVTacitDyadic> 1 2;3 4
NB. 4 3;3 2
NB. &.
-UnderRankVTacitMonadic>
-UnderRankVTacitDyadic>
n=.500000
v=.?~n
$v
10{.v
ts'-AtTacit-AtTacit-AtTacit-AtTacit-@- v'
ts'-AtTacit-AtTacit-AtTacit-AtTacit-AtopTacit- v'
ts'-At-At-At-At-Atop- v'
ts'-@:-@:-@:-@:-@- v'
----------------------------------------------------------------------
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