std/Number/Unary.bruijn


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163

# MIT License, Copyright (c) 2022 Marvin Borner
# with help from Justine Tunney
# classic Church style numerals

:import std/Logic .
:import std/Combinator .
:import std/Pair .

# returns true if a unary number is zero
zero? [0 [(+0u)] true] ⧗ Unary → Boolean

=?‣ zero?

:test (=?(+0u)) (true)
:test (=?(+42u)) (false)

# adds 1 to a unary number
inc [[[1 (2 1 0)]]] ⧗ Unary → Unary

++‣ inc

:test (++(+0u)) ((+1u))
:test (++(+1u)) ((+2u))
:test (++(+42u)) ((+43u))

# subs 1 from a unary number
dec [[[2 [[0 (1 3)]] [1] [0]]]] ⧗ Unary → Unary

--‣ dec

:test (--(+0u)) ((+0u))
:test (--(+1u)) ((+0u))
:test (--(+42u)) ((+41u))

# adds two unary numbers
add [[[[3 1 (2 1 0)]]]] ⧗ Unary → Unary → Unary

…+… add

:test ((+0u) + (+2u)) ((+2u))
:test ((+5u) + (+3u)) ((+8u))

# subs two unary numbers
sub [[0 dec 1]] ⧗ Unary → Unary → Unary

…-… sub

:test ((+2u) - (+2u)) ((+0u))
:test ((+5u) - (+3u)) ((+2u))

# returns true if number is less than or equal to other number
leq? [[=?(1 - 0)]] ⧗ Unary → Unary → Boolean

…≤?… leq?

:test ((+1u) ≤? (+2u)) (true)
:test ((+2u) ≤? (+2u)) (true)
:test ((+3u) ≤? (+2u)) (false)

# returns true if number is greater than or equal to other number
geq? \leq? ⧗ Unary → Unary → Boolean

…≥?… geq?

:test ((+1u) ≥? (+2u)) (false)
:test ((+2u) ≥? (+2u)) (true)
:test ((+3u) ≥? (+2u)) (true)

# returns true if number is greater than other number
# larger numbers should be second argument (performance)
gre? [[¬(1 ≤? 0)]] ⧗ Unary → Unary → Boolean

…>?… gre?

:test ((+1u) >? (+2u)) (false)
:test ((+2u) >? (+2u)) (false)
:test ((+3u) >? (+2u)) (true)

# returns true if number is less than other number
# smaller numbers should be second argument (performance)
les? \gre? ⧗ Unary → Unary → Boolean

…<?… les?

:test ((+1u) <? (+2u)) (true)
:test ((+2u) <? (+2u)) (false)
:test ((+3u) <? (+2u)) (false)

# returns true if two balanced ternary numbers are equal
eq? [[(0 ≥? 1) ⋀? (0 ≤? 1)]] ⧗ Unary → Unary → Boolean

…=?… eq?

:test ((+1u) =? (+0u)) (false)
:test ((+1u) =? (+1u)) (true)
:test ((+42u) =? (+42u)) (true)

# returns true if two balanced ternary numbers are not equal
not-eq? not! ∘∘ eq? ⧗ Unary → Unary → Boolean

…≠?… not-eq?

:test ((+1u) ≠? (+0u)) (true)
:test ((+1u) ≠? (+1u)) (false)
:test ((+42u) ≠? (+42u)) (false)

# muls two unary numbers
mul …∘… ⧗ Unary → Unary → Unary

…⋅… mul

:test ((+0u) ⋅ (+2u)) ((+0u))
:test ((+2u) ⋅ (+3u)) ((+6u))

# divs two unary numbers
div [[[[3 [[0 1]] [1] (3 [3 [[0 1]] [3 (0 1)] [0]] 0)]]]] ⧗ Unary → Unary → Unary

…/… div

:test ((+8u) / (+4u)) ((+2u))
:test ((+2u) / (+1u)) ((+2u))
:test ((+2u) / (+2u)) ((+1u))
:test ((+2u) / (+3u)) ((+0u))

# slower div
div* [z rec ++0] ⧗ Unary → Unary → Unary
	rec [[[[[[=?0 ((+0u) 2 1) (2 (5 0 3 2 1))] (3 - 2)]]]]]

# returns remainder of integer division
mod [[[[3 [0 [[1]]] (3 [3 [[[0 (2 (5 1)) 1]]] [1] 1] [1]) [[0]]]]]] ⧗ Unary → Unary → Unary

…%… mod

:test ((+10u) % (+3u)) ((+1u))
:test ((+3u) % (+5u)) ((+3u))

# slower mod
mod* [[1 [0 [[(0 ⋀? (3 ≤? 1)) case-rec case-end]]] (1 : true) [[1]]]] ⧗ Unary → Unary → Unary
	case-rec (1 - 3) : true
	case-end 1 : false

# exponentiates two unary number
# doesn't give correct results for x^0
pow* [[1 0]] ⧗ Unary → Unary → Unary

# exponentiates two unary numbers
pow [[0 [[3 (1 0)]] [[1 0]]]] ⧗ Unary → Unary → Unary

…^… pow

:test ((+2u) ^ (+3u)) ((+8u))
:test ((+3u) ^ (+2u)) ((+9u))

# fibonacci sequence
# index +1 vs std/Math fib
fib [0 [[[2 0 [2 (1 0)]]]] [[1]] [0]] ⧗ Unary → Unary

:test (fib (+6u)) ((+8u))

# factorial function
fac [[1 [[0 (1 [[2 1 (1 0)]])]] [1] [0]]] ⧗ Unary → Unary

:test (fac (+3u)) ((+6u))