-
Notifications
You must be signed in to change notification settings - Fork 1
/
ex333.lisp
342 lines (309 loc) · 14.7 KB
/
ex333.lisp
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
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
; Answers for 3-3-3
(defun set-cdr! (x y)
(setf (cdr x) y))
(defun set-car! (x y)
(setf (car x) y))
(defun lookup (key table)
(let ((record (my-assoc key (cdr table))))
(if record
(cdr record)
nil)))
(defun my-assoc (key records)
(cond ((null records) nil)
((equal key (caar records)) (car records))
(t (my-assoc key (cdr records)))))
(defun insert! (key value table)
(let ((record (my-assoc key (cdr table))))
(if record
(set-cdr! record value)
(set-cdr! table
(cons (cons key value) (cdr table))))
'ok))
(defun make-table ()
'(*table*))
(defun lookup-2d (key-1 key-2 table)
(let ((subtable (my-assoc key-1 (cdr table))))
(if subtable
(let ((record (my-assoc key-2 (cdr subtable))))
(if record
(cdr record)
nil))
nil)))
(defun insert-2d! (key-1 key-2 value table)
(let ((subtable (my-assoc key-1 (cdr table))))
(if subtable
(let ((record (my-assoc key-2 (cdr subtable))))
(if record
(set-cdr! record value)
(set-cdr! subtable
(cons (cons key-2 value)
(cdr subtable)))))
(set-cdr! table
(cons (list key-1
(cons key-2 value))
(cdr table))))
'ok))
(defun make-table-proc ()
(let ((local-table (list '*table*)))
(labels ((lookup (key-1 key-2)
(let ((subtable (my-assoc key-1 (cdr local-table))))
(if subtable
(let ((record (my-assoc key-2 (cdr subtable))))
(if record
(cdr record)
nil))
nil)))
(insert! (key-1 key-2 value)
(let ((subtable (my-assoc key-1 (cdr local-table))))
(if subtable
(let ((record (my-assoc key-2 (cdr subtable))))
(if record
(set-cdr! record value)
(set-cdr! subtable
(cons (cons key-2 value)
(cdr subtable)))))
(set-cdr! local-table
(cons (list key-1
(cons key-2 value))
(cdr local-table))))
'ok))
(dispatch (m)
(case m
(lookup-proc #'lookup)
(insert-proc! #'insert!)
(t (error "Unknown operation -- TABLE ~a" m)))))
#'dispatch)))
; Exercise 3.24
(defun make-table-proc-2 (same-key?)
(let ((local-table (list '*table*)))
(labels ((my-assoc (key records)
(cond ((null records) nil)
((funcall same-key? key (caar records)) (car records))
(t (my-assoc key (cdr records)))))
(lookup (key-1 key-2)
(let ((subtable (my-assoc key-1 (cdr local-table))))
(if subtable
(let ((record (my-assoc key-2 (cdr subtable))))
(if record
(cdr record)
nil))
nil)))
(insert! (key-1 key-2 value)
(let ((subtable (my-assoc key-1 (cdr local-table))))
(if subtable
(let ((record (my-assoc key-2 (cdr subtable))))
(if record
(set-cdr! record value)
(set-cdr! subtable
(cons (cons key-2 value)
(cdr subtable)))))
(set-cdr! local-table
(cons (list key-1
(cons key-2 value))
(cdr local-table))))
'ok))
(dispatch (m)
(case m
(lookup-proc #'lookup)
(insert-proc! #'insert!)
(t (error "Unknown operation -- TABLE ~a" m)))))
#'dispatch)))
; Exercise 3.25
(defun make-table-3 (&optional (same-key? #'equal))
(let ((local-table (list '*table*)))
(labels ((my-assoc (key records)
(cond ((null records) nil)
((funcall same-key? key (caar records)) (car records))
(t (my-assoc key (cdr records)))))
(lookup (keys)
(labels ((iter (table keys)
(cond ((null table) nil)
((null keys) (cdr table))
(t (iter (my-assoc (car keys) (cdr table))
(cdr keys))))))
(iter local-table keys)))
(insert! (keys value)
(labels ((iter (keys table)
(if (null keys)
(set-cdr! table value)
(let ((subtable (my-assoc (car keys) (cdr table))))
(if subtable
(iter (cdr keys) subtable)
(append-item! keys value table)))))
(append-item! (keys value table)
(if (null keys)
(set-cdr! table value)
(let ((new-record (list (car keys))))
(set-cdr! table (cons new-record (cdr table)))
(append-item! (cdr keys) value new-record)))))
(iter keys local-table)))
(dispatch (m)
(case m
(lookup #'lookup)
(insert! #'insert!)
(t (error "Unknown operation -- TABLE ~a" m)))))
#'dispatch)))
(defun insert-table! (table keys value)
(funcall (funcall table 'insert!) keys value))
(defun lookup-table (table keys)
(funcall (funcall table 'lookup) keys))
; Exercise 3.26
;; Even better, I'll implement it.
(defun symbol> (a b)
(not (null (string> (symbol-name a)
(symbol-name b)))))
(defun make-tree (&optional (after? #'symbol>) (key #'identity) (equal? #'equal))
(let ((tree '()))
(labels ((make-node (value left right)
(list value left right))
(left (node)
(cadr node))
(right (node)
(caddr node))
(set-left! (node tree)
(setf (cadr node) tree))
(set-right! (node tree)
(setf (caddr node) tree))
(value (node)
(car node))
(insert! (x)
(let ((new-node (make-node x '() '())))
(labels ((iter (node)
(if (funcall after? (funcall key x) (funcall key (value node)))
(if (null (right node))
(set-right! node new-node)
(iter (right node)))
(if (null (left node))
(set-left! node new-node)
(iter (left node))))))
(if (null tree)
(setf tree new-node)
(iter tree)))))
(lookup (x)
(labels ((iter (node)
(if (null node)
nil
(let ((node-val (value node)))
(if (funcall equal? x (funcall key node-val))
node-val
(iter (if (funcall after? x (funcall key node-val))
(right node)
(left node))))))))
(iter tree)))
(dispatch (m)
(case m
(insert! #'insert!)
(lookup #'lookup)
(t (error "Bad message for tree ~a" m)))))
#'dispatch)))
(defun tree-insert! (tree a)
(funcall (funcall tree 'insert!) a))
(defun tree-lookup (tree a)
(funcall (funcall tree 'lookup) a))
(defun make-table-4 (&optional (same-key? #'equal) (key-after? #'symbol>))
(let ((local-table (cons '*table* (make-tree key-after? #'car same-key?))))
(labels ((my-assoc (key records)
(tree-lookup records key))
(lookup (keys)
(labels ((iter (table keys)
(cond ((null table) nil)
((null keys) (cdr table))
(t (iter (my-assoc (car keys) (cdr table))
(cdr keys))))))
(iter local-table keys)))
(insert! (keys value)
(labels ((iter (keys table)
(if (null keys)
(set-cdr! table value)
(let ((subtable (my-assoc (car keys) (cdr table))))
(if subtable
(iter (cdr keys) subtable)
(append-item! keys value table)))))
(append-item! (keys value table)
(if (null keys)
(set-cdr! table value)
(let ((new-record (list (car keys)))
(new-subtree (make-tree key-after? #'car same-key?)))
(tree-insert! new-subtree new-record)
(set-cdr! table new-subtree)
(append-item! (cdr keys) value new-record)))))
(iter keys local-table)))
(dispatch (m)
(case m
(lookup #'lookup)
(insert! #'insert!)
(t (error "Unknown operation -- TABLE ~a" m)))))
#'dispatch)))
; Exercise 3.27
; a)
;; Ignoring all the calls to the table functions except lookup. They are all bound to global env.
;; +------------------------------------------------------------------+
;; global --> | memo-fib: ----------------------------------+
;; env | memoize: |
;; +-------|-------------------------------------+--------------------+
;; v ^ ^ |
;; .--- ---. | | |
;; | 0 | 0-+------------+ | +---+---+
;; `-|-^---' +-----------+ | 0 | 0 +------------+
;; | | +-|-+---+ |
;; v | | |
;; parameters: f | v |
;; body: ... | parameters: n |
;; | body: (cond ... ) |
;; (memoize (lambda (n)) .. | |
;; +------------------+--+ (let ((table (make-table))) v
;; E1-->| f: (lambda (n) ... |<--------+ +----------------------+
;; +---------------------+ +-----------+ table: (new table) |<--- E2
;; +-----^---------^------+
;; | |
;; | +----+---+
;; | | x: 3 |<------ E3
;; | +--------+ (memo-fib 3)
;; |
;; | +--------+
;; +----+ x: 2 |<------ E6
;; | +--------+ (memo-fib (- n 1))
;; |
;; | +--------+
;; +----+ x: 1 |<------ E9
;; | +--------+ (memo-fib (- n 1))
;; |
;; | +--------+
;; +----+ x: 0 |<------ E12
;; | +--------+ (memo-fib (- n 2))
;; |
;; | +--------+
;; +----+ x: 1 |<------ E15
;; +--------+ (memo-fib (- n 2))
;; ---------------------------------------------------+
;; Lookup make-table |
;; insert! | <-- global env
;; ----------^----------^-----------^-----------------+
;; (f x) | | | (lookup x table)
;; +----+----+ | +-----+----+
;; E5 ->| n: 3 | | | key: 3 |<------ E4
;; +---------+ | +----------+
;; (f x) | (lookup x table)
;; +---------+ | +----------+
;; E8 ->| n: 2 +-----+-----| key: 2 |<------ E7
;; +---------+ | +----------+
;; (f x) | (lookup x table)
;; +---------+ | +----------+
;; E11->| n: 1 +-----+-----| key: 1 |<------ E10
;; +---------+ | +----------+
;; (f x) | (lookup x table)
;; +---------+ | +----------+
;; E14->| n: 0 +-----+-----| key: 0 |<------ E13
;; +---------+ | +----------+
;; | (lookup x table)
;; | +----------+
;; +-----| key: 1 |<------ E16
;; +----------+
; b)
; Because it does not have to recurse all the way down the structure. If a
; value has previously been computed it will be immediately returned, whereas
; in the original recursive procedure, the two recursive calls redo a lot of
; work.
; c)
; No, because fib's recursions refer to the 'fib' procedure itself, so it would
; only use the memoized procedure on the first level of recursion.