forked from min-lang/min
-
Notifications
You must be signed in to change notification settings - Fork 0
/
seq.m
282 lines (242 loc) · 11.6 KB
/
seq.m
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
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
# sequence, container, collection, generator
https://en.wikipedia.org/wiki/Collection_(abstract_data_type)
https://en.wikipedia.org/wiki/Stream_(computing)
str0 skip:N take:!N : +C? S =
Sstr n s? s
Sskip n s? str0 skip+n take s
Stake n s? str0 skip (N.opt n) s
? Fail $Fun
str_char s:+C : S = str0 0 0 s
Fact (str_char 'foo'.S.seq == 'foo')
size : +0? N =
Sskip n s? size s - n
Stake n s? N.min s.size n
Slist s? List.size s
Sstr n _? n
# Srow r s? s - r
Srow n s? n
Sfun n f? n | 0 # fixme, opt return
Slink x s? 1 + size s
Sadd r s? size r + size s
Smap _ s? size s
Sseq s? List.map_sum_nat s size
# bound : +0? N
row3 s:0,0,0 : +0 = Srow 3 s.Cast.any
Fact (size 'foo'.S.seq == 3)
Fact (Sskip 1 'foo'.S.seq . size == 2)
Fact (Stake 2 'foo'.S.seq . size == 2)
Fact (Stake 5 'foo'.S.seq . size == 3)
Fact (size (row3 2,3,5) == 3)
Fact (size Slist[13, 42] == 2)
Fact (size (Slink 3 Slist[5, 13]) == 3)
Fact (size (Smap N.tick Slist[13, 42]) == 2)
Fact (size (Sseq [Slist[1, 2], Slist[3, 5, 8]]) == 5)
do_fun f:0?Z g:Z?!0 : Z =
x = g 0
x & (f x.N.must; do_fun f g)
# producer yield
pump : +0? Z? !0 =
# Sstr n s? S.pump s : Z?!0
Sstr _ s? (S.pump s : Z?!0)
? Fail $Fun
Fact (x = pump 'foo'.S.seq; !x == N.opt \f & x 0 == N.opt \o & x 0 == N.opt \o)
do f:0?_ : +0? Z =
Sstr n s? S.do f s n
Slink x s? (f x; do f s)
Sone x? f x
Sadd r s ? (do f r; do f s)
Sseq s? List.do s (do f)
Slist s? List.do s f
Srow n s? Row.do f s n
Spair r s? (g = pump r; do ((_ f_:1,2?_ g_:Z?!1 y:2 : Z = (x = g_ 0; x & f_ x.N.must,y)) f g) s) # Rewrite.NAME_BUG
Smap g s? do (Fun.of f g) s
Skeep g s? do ((_ g_:1?B f_:0?_ x:2 : Z = g_ x & f_ x) g f) s
Sfun _ g? do_fun f g
0? 0
x? Fail.main2 $Fun x.Term.tag.N.str
Fact (x = %0; do (Ref.add x) 'foo'.S.seq; !x == \f + \o + \o)
Fact (x = %0; do (Ref.add x) Slist[2, 3, 5]; !x == 10)
Fact (x = %0; do (Ref.add x) (Sadd Slist[2, 3, 5] Slist[8, 13]); !x == 31)
Fact (x = %0; do (Ref.add x) (Sadd Slist[2, 3, 5] Slist[8, 13, 21]); !x == 52)
Fact (x = %0; do (Ref.add x) (row3 2,3,5); !x == 10)
Fact (x = %0; do (Ref.add x) (Smap N.tick Slist[2, 3]); !x == 7)
Fact (x = %0; do (Ref.add x) (Skeep N.odd Slist[2, 3, 5]); !x == 8)
Fact (s = %0; do (_ x,y:C,C : Z = Ref.add s y-x) (Spair 'abc'.S.seq 'def'.S.seq); !s == 9)
Fact (s = %0; do (_ x,y:C,C : Z = Ref.add s y-x) (Spair 'abc'.S.seq 'de'.S.seq); !s == 6)
Fact (s = %0; do (_ x,y:C,C : Z = Ref.add s y-x) (Spair 'ab'.S.seq 'def'.S.seq); !s == 6)
Fact (s = %0; do (_ x,y:C,C : Z = Ref.add s y-x) (Spair 'ab'.S.seq ''.S.seq); !s == 0)
Fact (do S.size (Smap List.head Slist[['foo']]); 1)
Fact (x = %0; do (Ref.add x) (Sfun 3 (tick 3)); !x == 3)
# skip/take span range slice interval
do_span0 skip:N take:!N f:0?_ : +0? Z = # do_span skip take
Sskip n s? do_span0 skip+n take f s
Stake n s? do_span0 skip (N.opt n) f s
Sstr n s? S.do f s+skip (Opt.min take n)-skip
Spair r s? (g = pump r; do_span0 skip take ((_ f_:1,2?_ g_:Z?!1 y:2 : Z = (x = g_ 0; x & f_ x.N.must,y)) f g) s) # Rewrite.NAME_BUG
Slist s? List.do s.(List.skip skip).(Opt.map2 N.must (Opt.map take (N.sub2 skip)) List.take) f
#Srow n s? Row.do f s n
Smap g s? do_span0 skip take (Fun.of f g) s
Skeep g s? do_span0 skip take ((_ g_:1?B f_:0?_ x:2 : Z = g_ x & f_ x) g f) s
Sseq s? List.do s (do_span0 skip take f)
#Sfun _ g? do_fun f g
? Fail $Fun
do_span f:0?_ s:+0 = do_span0 0 0 f s
Fact (x = %0; do_span (Ref.add x) (Sskip 1 'foo'.S.seq); !x == \o + \o)
Fact (x = %0; do_span (Ref.add x) (Stake 2 'foo'.S.seq); !x == \f + \o)
Fact (x = %0; do_span (Ref.add x) (Smap N.tick 'foo'.S.seq); !x == \f+1 + \o+1 + \o+1)
Fact (x = %0; do_span (Ref.add x) ('foo'.S.seq . Smap N.tick . Sskip 1); !x == \o+1 + \o+1)
Fact (x = %0; do_span (Ref.add x) ('foo'.S.seq . Sskip 1 . Smap N.tick); !x == \o+1 + \o+1)
Fact (x = %0; do_span (Ref.add x) (Skeep N.odd Slist[2, 3, 5]); !x == 8)
Fact (s = %0; do_span (_ x,y:C,C : Z = Ref.add s y-x) (Stake 2 (Spair 'abc'.S.seq 'def'.S.seq)); !s == 6)
Fact (s = %0; do_span (_ x,y:C,C : Z = Ref.add s y-x) (Spair 'abc'.S.seq 'def'.S.seq.(Stake 2)); !s == 6)
sum_seq f:0?1?1 a:1 s:*+0 : 1 = s & sum f (sum_seq f a s.List.tail) s.List.head | a # similar to List.flat = sum add
sum_fun f:0?1?1 a:1 g:Z?!0 : 1 =
x = g 0
x & sum_fun f (f x.N.must a) g | a
# pair/cons fold aggregate
# https://wiki.haskell.org/Foldl_as_foldr
# https://wiki.haskell.org/Foldr_Foldl_Foldl'
sum f:0?1?1 a:1 : +0? 1 =
Sstr n s? S.fold f a s n
Sone x? f x a
Sadd r s? sum f (sum f a s) r
Slist s? List.sum_right s f a
Srow n s? Row.fold f a s n
Spair r s? (z = pump r; sum ((_ f_:1,2?3?3 z_:Z?!1 y:2 a_:3 : 3 = (x = z_ 0; x & f_ x.N.must,y a_ | a_)) f z) a s)
Smap g s? sum ((_ g_:2?0 f_:0?1?1 x:2 a_:1 : 1 = f_ (g_ x) a_) g f) a s
Skeep g s? sum ((_ g_:1?B f_:0?1?1 x:2 a_:1 : 1 = g_ x & f_ x a_ | a_) g f) a s
Sfun _ g? sum_fun f a g
Sseq s? sum_seq f a s
# Snil _? a
0? a
x? Fail.main2 $Fun x.Term.tag.N.str
Fact (sum N.add 0 'foo'.S.seq == \f + \o + \o)
Fact (sum N.add 0 Slist[2, 3, 5] == 10)
Fact (sum N.add 0 (row3 2,3,5) == 10)
Fact (sum N.min N.max3 Slist[3, 2, 13, 5] == 2)
Fact (sum N.max 0 Slist[2, 3, 13, 5] == 13)
Fact (sum N.add 0 (Skeep N.odd Slist[2, 3, 5]) == 8)
Fact (sum (_ x,y:C,C s:N : N = s + y-x) 0 (Spair 'abc'.S.seq 'def'.S.seq) == 9)
# http://okmij.org/ftp/Streams.html#1enum2iter Parallel composition of iteratees: one source to several sinks
sum_size f:0?1?1 a:1 s:+0 : 1, N = sum ((_ f_:0?1?1 x:0 a,n:1,N : 1, N = f_ x a, n+1) f) a,0 s
# Fact (sum_size N.add 42 Slist[] == 42,0) # FIX_TYPE_ANNOTATE
Fact (sum_size N.add 42 Slist([]:*N) == 42,0)
Fact (sum_size N.add 0 Slist[2, 3, 5] == 10,3)
sum_nat s:+N : N = sum N.add 0 s
Fact (sum_nat Slist[2, 3, 5] == 10)
sum_size_nat s:+N : N, N = sum_size N.add 0 s
Fact (sum_size_nat Slist[2, 3, 5] == 10,3)
#mean s:+N : R = sum_nat s / size s
Fact (sum_nat Slist[2, 3, 5] == 10)
# while/break, short circuit, early termination
# todo - need another function for returning B,1
# list anamorphism [Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire]
sum_opt f:1?0?!1 a:1 opt:1?!1 must:!1?1 : +0? !1 =
Sstr _ s? S.sum_opt f a s opt must
Slist s? List.sum_opt f a s opt must
Smap g s? sum_opt ((_ g_:2?0 f_:1?0?!1 a_:1 x:2 : !1 = f_ a_ (g_ x)) g f) a opt must s
Skeep g s? sum_opt ((_ g_:0?B f_:1?0?!1 opt_:1?!1 a_:1 x:0 : !1 = g_ x & f_ a_ x | opt_ a_) g f opt) a opt must s
# Sfun _ g? sum_fun f a g
# Sseq s? sum2 f a s
? Fail $Fun
# Fact (sum_opt N.even.bit_opt 0 Slist[2, 4, 10] == Opt 0) # todo - Opt.eq
Fact (Opt.eq_by Z.eq (sum_opt N.even.bit_opt 0 Z.opt Z.must Slist[2, 4, 10]) !Z.opt)
Fact (sum_opt N.even.bit_opt 0 Z.opt Z.must Slist[2, 4, 7, 10] == 0)
# paramorphisms
sum_key f:1?0?!1 a:1 must:!1?1 : +0? B, 1 =
#Sstr _ s? S.sum_key f a s
Slist s? List.sum_key f a s must
#Smap g s? sum_key ((_ g_:2?0 f_:1?0?!1 a_:1 x:2 : !1 = f_ a_ (g_ x)) g f) a s
#Skeep g s? sum_key ((_ g_:1?B f_:0?1?!1 x:2 a_:1 : !1 = g_ x & f_ x a_ | a_) g f) a s
# Sfun _ g? sum_fun f a g
# Sseq s? sum2 f a s
? Fail $Fun
Fact (sum_key N.even.bit_opt 0 Z.must Slist[2, 4, 10] == 1,0)
Fact (sum_key N.even.bit_opt 0 Z.must Slist[2, 4, 7, 10] == 0,0)
sum_at f:1?0?!1 a:1 opt:0?!0 s:+0 : N, !0, 1 =
sum_key ((_ f_:1?0?!1 opt_:1?!1 i,x0,a:N,!0,1 x:0 : !(N, !0, 1) = (x0 & (i, x0, a) | (b = f_ a x; i+1, (!b & opt_ x):!0, b:1))) f opt) 0,0,a Opt.must s . Row.at1
Fact (sum_at N.even.bit_opt 0 N.opt Slist[2, 4, 7, 10] == 3,7.N.opt,0)
# find
get opt:0?!0 must:!1?1 f:0?B s:+0 : !(N, 0) =
i, x, _ = sum_at f.not.bit_opt 0 opt s
x & (i, must x):!(N, 0)
Fact (get N.opt N.must N.odd Slist[2, 4, 7, 10] == 3,7)
bit_opt f:0?B : f:Z?0?!Z = (_ f_:0?B _:Z x:0 : !Z = f_ x . Opt.of) f
bit_and f:0?B : f:0?B?B = (_ f_:0?B x:0 y:B : B = f_ x & y) f
#not f:0?B : 0?B = (_ f_:0?B x:0 : B = !(f_ x)) f
not f:0?B : 0?B = (_ f:0?B x:0 : B = !(f x)) f
all f:0?B s:+0 : B = sum_opt f.bit_opt 0 Z.opt Z.must s . Opt.bit
Fact (all C.is_lower 'foo'.S.seq)
Fact !(all C.is_upper 'foo'.S.seq)
Fact (all N.odd Slist[1, 3, 5])
Fact !(all N.odd Slist[1, 2, 5])
Fact !(all (N.le 5) (Skeep N.odd Slist[3, 10, 5]))
Fact (all (N.gt 7) Slist[3, 5])
Fact (all (N.gt 7) (Skeep N.odd Slist[3, 10, 5]))
Fact (all S.bit (Skeep S.bit Slist['foo', '']))
Fact !(all (_ x:Z?N : B = N.lt !x 3) Slist[(_ _ : N = 2), (_ _ : N = 5), (_ _ : N = !Fail.nil)])
Fact (Job.err (? all_full (_ x:Z?N : B = N.lt (x 0) 3) Slist[(_ _ : N = 2), (_ _ : N = 5), (_ _ : N = Fail 'foo')] . Z) == "foo: error \.")
all_full f:0?B s:+0 : B = sum f.bit_and 1 s
Fact (all_full N.odd Slist[1, 3, 5])
Fact !(all_full N.odd Slist[1, 2, 5])
# in has mem member
any f:0?B s:+0 : B = sum_opt f.not.bit_opt 0 Z.opt Z.must s . Opt.bit . B.not
Fact (any C.is_lower 'Foo'.S.seq)
Fact !(any C.is_upper 'foo'.S.seq)
Fact (any N.even Slist[1, 2, 5])
Fact !(any N.even Slist[1, 3, 5])
Fact (any (N.eq 5) (Skeep N.odd Slist[3, 10, 5]))
Fact (any (_ x:Z?N : B = N.gt !x 3) Slist[(_ _ : N = 2), (_ _ : N = 5), (_ _ : N = !Fail.nil)])
Fact (any (N.lt 3) (Smap Fun.do (Slist[(_ _ : N = 2), (_ _ : N = 5), (_ _ : N = !Fail.nil)])))
any_full f:0?B s:+0 : B = sum f.not.bit_and 1 s . B.not
Fact (any_full N.even Slist[1, 2, 5])
Fact !(any_full N.even Slist[1, 3, 5])
Fact (Job.err (? any_full (_ x:Z?N : B = N.gt !x 3) Slist[(_ _ : N = 2), (_ _ : N = 5), (_ _ : N = Fail 'foo')] . Z) == "foo: error \.")
list s:+0 : *0 = sum List.main 0 s
Fact (list 'foo'.S.seq == [\f, \o, \o])
Fact (list Slist[2, 3, 5] == [2, 3, 5])
Fact (list (Smap N.tick Slist[13, 42]) == [14, 43])
Fact (list (Sseq [Slist[1, 2], Slist[3, 5, 8], Slist[11, 13]]) == [1, 2, 3, 5, 8, 11, 13])
Fact (list (Sfun 3 (tick 3)) == [2, 1, 0])
Fact (list (Smap Fun.do Slist[(_ _ : N = 2), (_ _ : N = 5)]) == [2, 5])
Fact (list (Skeep N.odd Slist[2, 3, 5, 8]) == [3, 5])
tick n:N : Z? !N =
i = %0
(_ n_:N i_:%N _:Z : !N = (!i_ < n_ & Ref.tick0 i_ . N.opt)) n i
Fact (f = tick 3; !f == N.opt 0 & !f == N.opt 1 & !f == N.opt 2 & !f == 0)
row s:+0 : Mem = (n = s.size; r, f = Row.init n; do f s; r)
Fact (row Slist[2, 3, 5] . Row.mem_eq3 2,3,5)
Fact (row (Sseq [Slist[1, 2], Slist[3], Slist[5, 8]]) . Row.mem_eq5 1,2,3,5,8)
Fact (row (Sfun 3 (tick 3)) . Row.mem_eq3 0,1,2)
pop : +0? !(0, +0) =
# Sstr n s? (S.pop s . (x, r? (x, (Sstr n-1 r : +0))))
Sstr n s? (S.pop s . (x, r? (x:0, (Sstr n-1 r : +0)))) # FIX_TYPE_ANNOTATE
Slist s? (List.pop s . (x, r? x, Slist r))
# Srow n s? Row.do f s n
# Spair r s? (z = pump r; do ((_ f_:1,2?_ z_:Z?!1 y:2 : Z = (x = z_ 0; x & f_ x.Opt.un,y)) f z) s) # FIXME - failed if [p] not [z]
# Smap g s? do (Fun.of f g) s
# Skeep g s? do ((_ g_:1?B f_:0?_ x:2 : Z = g_ x & f_ x) g f) s
# Sseq s? List.do s (do f)
# Sfun _ g? do_fun f g
? Fail $Fun
Fact (x, s = pop Slist[13, 42]; x == 13 & list s == [42])
#Fact (pop 'foo'.S.seq == \f,'oo'.S.seq) # todo Seq.eq_by
peek s:+0 : !0 = pop s . Opt.at0
# Fact (peek Slist[] == 0)
Fact (peek Slist([]:*N) == 0)
Fact (peek Slist[13, 42] == 13)
cores f:0?_ s:+0 opt:0?!0 must:!0?0 : Z =
r = % list s
Thread.all (_ _:N = Ref.do f r opt must)
0
Fact (s = %0; cores (_ x:N = Ref.padd s x) 100.List.nat.Slist N.opt N.must; !s == 4950) # n(n+1)/2 = (99*100)/2 = 4950
add r:+0 s:+0 : +0 = Sadd r s
Fact (add Slist[2, 3, 5] Slist[8, 13] . list == [2, 3, 5, 8, 13])
Fact (Slist[2, 3, 5]+Slist[8, 13] . list == [2, 3, 5, 8, 13])
adds s:*+0 : +0 = List.sum add 0 s
Fact (adds [Slist[2, 3, 5], Slist[8, 13]] . list == [2, 3, 5, 8, 13])
eq r:+0 s:+0 : B = N.eq r.Cast.any s.Cast.any
Fact (eq 0 0)
eq_by f:0?0?B r:+0 s:+0 : B = Fail $Fun # TODO
map_line s:+0 f:0?S : S = List.map_line s.list f
str_by f:0?S s:+0 : S = List.str_by f s.list