author | haftmann |
Tue, 14 Jul 2009 10:54:54 +0200 | |
changeset 32000 | 6f07563dc8a9 |
parent 31254 | 03a35fbc9dc6 |
child 33707 | 68841fb382e0 |
permissions | -rw-r--r-- |
28213 | 1 |
theory Program |
28419 | 2 |
imports Introduction |
28213 | 3 |
begin |
4 |
||
28419 | 5 |
section {* Turning Theories into Programs \label{sec:program} *} |
28213 | 6 |
|
7 |
subsection {* The @{text "Isabelle/HOL"} default setup *} |
|
8 |
||
28419 | 9 |
text {* |
10 |
We have already seen how by default equations stemming from |
|
11 |
@{command definition}/@{command primrec}/@{command fun} |
|
28447 | 12 |
statements are used for code generation. This default behaviour |
29560 | 13 |
can be changed, e.g. by providing different code equations. |
28593 | 14 |
All kinds of customisation shown in this section is \emph{safe} |
28447 | 15 |
in the sense that the user does not have to worry about |
16 |
correctness -- all programs generatable that way are partially |
|
17 |
correct. |
|
18 |
*} |
|
19 |
||
20 |
subsection {* Selecting code equations *} |
|
21 |
||
22 |
text {* |
|
23 |
Coming back to our introductory example, we |
|
29560 | 24 |
could provide an alternative code equations for @{const dequeue} |
28447 | 25 |
explicitly: |
28419 | 26 |
*} |
27 |
||
28564 | 28 |
lemma %quote [code]: |
29798 | 29 |
"dequeue (AQueue xs []) = |
30 |
(if xs = [] then (None, AQueue [] []) |
|
31 |
else dequeue (AQueue [] (rev xs)))" |
|
32 |
"dequeue (AQueue xs (y # ys)) = |
|
33 |
(Some y, AQueue xs ys)" |
|
28419 | 34 |
by (cases xs, simp_all) (cases "rev xs", simp_all) |
35 |
||
36 |
text {* |
|
28562 | 37 |
\noindent The annotation @{text "[code]"} is an @{text Isar} |
28419 | 38 |
@{text attribute} which states that the given theorems should be |
29560 | 39 |
considered as code equations for a @{text fun} statement -- |
28419 | 40 |
the corresponding constant is determined syntactically. The resulting code: |
41 |
*} |
|
42 |
||
28564 | 43 |
text %quote {*@{code_stmts dequeue (consts) dequeue (Haskell)}*} |
28419 | 44 |
|
45 |
text {* |
|
46 |
\noindent You may note that the equality test @{term "xs = []"} has been |
|
47 |
replaced by the predicate @{term "null xs"}. This is due to the default |
|
48 |
setup in the \qn{preprocessor} to be discussed further below (\secref{sec:preproc}). |
|
49 |
||
50 |
Changing the default constructor set of datatypes is also |
|
29794 | 51 |
possible. See \secref{sec:datatypes} for an example. |
28419 | 52 |
|
53 |
As told in \secref{sec:concept}, code generation is based |
|
54 |
on a structured collection of code theorems. |
|
55 |
For explorative purpose, this collection |
|
56 |
may be inspected using the @{command code_thms} command: |
|
57 |
*} |
|
58 |
||
28564 | 59 |
code_thms %quote dequeue |
28419 | 60 |
|
61 |
text {* |
|
29560 | 62 |
\noindent prints a table with \emph{all} code equations |
28419 | 63 |
for @{const dequeue}, including |
29560 | 64 |
\emph{all} code equations those equations depend |
28419 | 65 |
on recursively. |
66 |
||
67 |
Similarly, the @{command code_deps} command shows a graph |
|
29560 | 68 |
visualising dependencies between code equations. |
28419 | 69 |
*} |
70 |
||
71 |
subsection {* @{text class} and @{text instantiation} *} |
|
72 |
||
73 |
text {* |
|
28447 | 74 |
Concerning type classes and code generation, let us examine an example |
28419 | 75 |
from abstract algebra: |
76 |
*} |
|
77 |
||
29794 | 78 |
class %quote semigroup = |
28419 | 79 |
fixes mult :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixl "\<otimes>" 70) |
80 |
assumes assoc: "(x \<otimes> y) \<otimes> z = x \<otimes> (y \<otimes> z)" |
|
81 |
||
28564 | 82 |
class %quote monoid = semigroup + |
28419 | 83 |
fixes neutral :: 'a ("\<one>") |
84 |
assumes neutl: "\<one> \<otimes> x = x" |
|
85 |
and neutr: "x \<otimes> \<one> = x" |
|
86 |
||
28564 | 87 |
instantiation %quote nat :: monoid |
28419 | 88 |
begin |
89 |
||
28564 | 90 |
primrec %quote mult_nat where |
28419 | 91 |
"0 \<otimes> n = (0\<Colon>nat)" |
92 |
| "Suc m \<otimes> n = n + m \<otimes> n" |
|
93 |
||
28564 | 94 |
definition %quote neutral_nat where |
28419 | 95 |
"\<one> = Suc 0" |
28213 | 96 |
|
28564 | 97 |
lemma %quote add_mult_distrib: |
28419 | 98 |
fixes n m q :: nat |
99 |
shows "(n + m) \<otimes> q = n \<otimes> q + m \<otimes> q" |
|
100 |
by (induct n) simp_all |
|
101 |
||
28564 | 102 |
instance %quote proof |
28419 | 103 |
fix m n q :: nat |
104 |
show "m \<otimes> n \<otimes> q = m \<otimes> (n \<otimes> q)" |
|
105 |
by (induct m) (simp_all add: add_mult_distrib) |
|
106 |
show "\<one> \<otimes> n = n" |
|
107 |
by (simp add: neutral_nat_def) |
|
108 |
show "m \<otimes> \<one> = m" |
|
109 |
by (induct m) (simp_all add: neutral_nat_def) |
|
110 |
qed |
|
111 |
||
28564 | 112 |
end %quote |
28419 | 113 |
|
114 |
text {* |
|
115 |
\noindent We define the natural operation of the natural numbers |
|
116 |
on monoids: |
|
117 |
*} |
|
118 |
||
28564 | 119 |
primrec %quote (in monoid) pow :: "nat \<Rightarrow> 'a \<Rightarrow> 'a" where |
28419 | 120 |
"pow 0 a = \<one>" |
121 |
| "pow (Suc n) a = a \<otimes> pow n a" |
|
122 |
||
123 |
text {* |
|
124 |
\noindent This we use to define the discrete exponentiation function: |
|
125 |
*} |
|
126 |
||
28564 | 127 |
definition %quote bexp :: "nat \<Rightarrow> nat" where |
28419 | 128 |
"bexp n = pow n (Suc (Suc 0))" |
129 |
||
130 |
text {* |
|
131 |
\noindent The corresponding code: |
|
132 |
*} |
|
133 |
||
28564 | 134 |
text %quote {*@{code_stmts bexp (Haskell)}*} |
28419 | 135 |
|
136 |
text {* |
|
28447 | 137 |
\noindent This is a convenient place to show how explicit dictionary construction |
28419 | 138 |
manifests in generated code (here, the same example in @{text SML}): |
139 |
*} |
|
140 |
||
28564 | 141 |
text %quote {*@{code_stmts bexp (SML)}*} |
28419 | 142 |
|
28447 | 143 |
text {* |
144 |
\noindent Note the parameters with trailing underscore (@{verbatim "A_"}) |
|
145 |
which are the dictionary parameters. |
|
146 |
*} |
|
28419 | 147 |
|
148 |
subsection {* The preprocessor \label{sec:preproc} *} |
|
149 |
||
150 |
text {* |
|
151 |
Before selected function theorems are turned into abstract |
|
152 |
code, a chain of definitional transformation steps is carried |
|
153 |
out: \emph{preprocessing}. In essence, the preprocessor |
|
154 |
consists of two components: a \emph{simpset} and \emph{function transformers}. |
|
155 |
||
32000 | 156 |
The \emph{simpset} allows to employ the full generality of the |
157 |
Isabelle simplifier. Due to the interpretation of theorems as code |
|
158 |
equations, rewrites are applied to the right hand side and the |
|
159 |
arguments of the left hand side of an equation, but never to the |
|
160 |
constant heading the left hand side. An important special case are |
|
161 |
\emph{unfold theorems} which may be declared and undeclared using |
|
162 |
the @{attribute code_unfold} or \emph{@{attribute code_unfold} del} |
|
163 |
attribute respectively. |
|
28213 | 164 |
|
28419 | 165 |
Some common applications: |
166 |
*} |
|
167 |
||
168 |
text_raw {* |
|
169 |
\begin{itemize} |
|
170 |
*} |
|
171 |
||
172 |
text {* |
|
173 |
\item replacing non-executable constructs by executable ones: |
|
174 |
*} |
|
175 |
||
32000 | 176 |
lemma %quote [code_inline]: |
28419 | 177 |
"x \<in> set xs \<longleftrightarrow> x mem xs" by (induct xs) simp_all |
178 |
||
179 |
text {* |
|
180 |
\item eliminating superfluous constants: |
|
181 |
*} |
|
182 |
||
32000 | 183 |
lemma %quote [code_inline]: |
28419 | 184 |
"1 = Suc 0" by simp |
185 |
||
186 |
text {* |
|
187 |
\item replacing executable but inconvenient constructs: |
|
188 |
*} |
|
189 |
||
32000 | 190 |
lemma %quote [code_inline]: |
28419 | 191 |
"xs = [] \<longleftrightarrow> List.null xs" by (induct xs) simp_all |
192 |
||
193 |
text_raw {* |
|
194 |
\end{itemize} |
|
195 |
*} |
|
196 |
||
197 |
text {* |
|
28447 | 198 |
\noindent \emph{Function transformers} provide a very general interface, |
28419 | 199 |
transforming a list of function theorems to another |
200 |
list of function theorems, provided that neither the heading |
|
201 |
constant nor its type change. The @{term "0\<Colon>nat"} / @{const Suc} |
|
202 |
pattern elimination implemented in |
|
203 |
theory @{text Efficient_Nat} (see \secref{eff_nat}) uses this |
|
204 |
interface. |
|
205 |
||
206 |
\noindent The current setup of the preprocessor may be inspected using |
|
31254 | 207 |
the @{command print_codeproc} command. |
28419 | 208 |
@{command code_thms} provides a convenient |
209 |
mechanism to inspect the impact of a preprocessor setup |
|
29560 | 210 |
on code equations. |
28419 | 211 |
|
212 |
\begin{warn} |
|
32000 | 213 |
|
214 |
Attribute @{attribute code_unfold} also applies to the |
|
215 |
preprocessor of the ancient @{text "SML code generator"}; in case |
|
216 |
this is not what you intend, use @{attribute code_inline} instead. |
|
28419 | 217 |
\end{warn} |
218 |
*} |
|
219 |
||
220 |
subsection {* Datatypes \label{sec:datatypes} *} |
|
221 |
||
222 |
text {* |
|
223 |
Conceptually, any datatype is spanned by a set of |
|
29794 | 224 |
\emph{constructors} of type @{text "\<tau> = \<dots> \<Rightarrow> \<kappa> \<alpha>\<^isub>1 \<dots> \<alpha>\<^isub>n"} where @{text |
225 |
"{\<alpha>\<^isub>1, \<dots>, \<alpha>\<^isub>n}"} is exactly the set of \emph{all} type variables in |
|
226 |
@{text "\<tau>"}. The HOL datatype package by default registers any new |
|
227 |
datatype in the table of datatypes, which may be inspected using the |
|
228 |
@{command print_codesetup} command. |
|
28419 | 229 |
|
29794 | 230 |
In some cases, it is appropriate to alter or extend this table. As |
231 |
an example, we will develop an alternative representation of the |
|
232 |
queue example given in \secref{sec:intro}. The amortised |
|
233 |
representation is convenient for generating code but exposes its |
|
234 |
\qt{implementation} details, which may be cumbersome when proving |
|
235 |
theorems about it. Therefore, here a simple, straightforward |
|
236 |
representation of queues: |
|
28419 | 237 |
*} |
238 |
||
29794 | 239 |
datatype %quote 'a queue = Queue "'a list" |
240 |
||
241 |
definition %quote empty :: "'a queue" where |
|
242 |
"empty = Queue []" |
|
28419 | 243 |
|
29794 | 244 |
primrec %quote enqueue :: "'a \<Rightarrow> 'a queue \<Rightarrow> 'a queue" where |
245 |
"enqueue x (Queue xs) = Queue (xs @ [x])" |
|
246 |
||
247 |
fun %quote dequeue :: "'a queue \<Rightarrow> 'a option \<times> 'a queue" where |
|
248 |
"dequeue (Queue []) = (None, Queue [])" |
|
249 |
| "dequeue (Queue (x # xs)) = (Some x, Queue xs)" |
|
28213 | 250 |
|
28419 | 251 |
text {* |
29794 | 252 |
\noindent This we can use directly for proving; for executing, |
253 |
we provide an alternative characterisation: |
|
28419 | 254 |
*} |
255 |
||
29794 | 256 |
definition %quote AQueue :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a queue" where |
257 |
"AQueue xs ys = Queue (ys @ rev xs)" |
|
258 |
||
259 |
code_datatype %quote AQueue |
|
260 |
||
29798 | 261 |
text {* |
262 |
\noindent Here we define a \qt{constructor} @{const "AQueue"} which |
|
263 |
is defined in terms of @{text "Queue"} and interprets its arguments |
|
264 |
according to what the \emph{content} of an amortised queue is supposed |
|
265 |
to be. Equipped with this, we are able to prove the following equations |
|
266 |
for our primitive queue operations which \qt{implement} the simple |
|
267 |
queues in an amortised fashion: |
|
268 |
*} |
|
29794 | 269 |
|
270 |
lemma %quote empty_AQueue [code]: |
|
271 |
"empty = AQueue [] []" |
|
272 |
unfolding AQueue_def empty_def by simp |
|
273 |
||
274 |
lemma %quote enqueue_AQueue [code]: |
|
275 |
"enqueue x (AQueue xs ys) = AQueue (x # xs) ys" |
|
276 |
unfolding AQueue_def by simp |
|
28419 | 277 |
|
29794 | 278 |
lemma %quote dequeue_AQueue [code]: |
279 |
"dequeue (AQueue xs []) = |
|
29798 | 280 |
(if xs = [] then (None, AQueue [] []) |
281 |
else dequeue (AQueue [] (rev xs)))" |
|
29794 | 282 |
"dequeue (AQueue xs (y # ys)) = (Some y, AQueue xs ys)" |
283 |
unfolding AQueue_def by simp_all |
|
284 |
||
29798 | 285 |
text {* |
286 |
\noindent For completeness, we provide a substitute for the |
|
287 |
@{text case} combinator on queues: |
|
288 |
*} |
|
29794 | 289 |
|
30227 | 290 |
lemma %quote queue_case_AQueue [code]: |
291 |
"queue_case f (AQueue xs ys) = f (ys @ rev xs)" |
|
292 |
unfolding AQueue_def by simp |
|
29794 | 293 |
|
29798 | 294 |
text {* |
295 |
\noindent The resulting code looks as expected: |
|
296 |
*} |
|
29794 | 297 |
|
298 |
text %quote {*@{code_stmts empty enqueue dequeue (SML)}*} |
|
28419 | 299 |
|
300 |
text {* |
|
29794 | 301 |
\noindent From this example, it can be glimpsed that using own |
302 |
constructor sets is a little delicate since it changes the set of |
|
303 |
valid patterns for values of that type. Without going into much |
|
304 |
detail, here some practical hints: |
|
28419 | 305 |
|
306 |
\begin{itemize} |
|
29794 | 307 |
|
308 |
\item When changing the constructor set for datatypes, take care |
|
30227 | 309 |
to provide alternative equations for the @{text case} combinator. |
29794 | 310 |
|
311 |
\item Values in the target language need not to be normalised -- |
|
312 |
different values in the target language may represent the same |
|
313 |
value in the logic. |
|
314 |
||
315 |
\item Usually, a good methodology to deal with the subtleties of |
|
316 |
pattern matching is to see the type as an abstract type: provide |
|
317 |
a set of operations which operate on the concrete representation |
|
318 |
of the type, and derive further operations by combinations of |
|
319 |
these primitive ones, without relying on a particular |
|
320 |
representation. |
|
321 |
||
28419 | 322 |
\end{itemize} |
323 |
*} |
|
324 |
||
28213 | 325 |
|
30938
c6c9359e474c
wellsortedness is no issue for a user manual any more
haftmann
parents:
30227
diff
changeset
|
326 |
subsection {* Equality *} |
28213 | 327 |
|
28419 | 328 |
text {* |
329 |
Surely you have already noticed how equality is treated |
|
330 |
by the code generator: |
|
331 |
*} |
|
332 |
||
28564 | 333 |
primrec %quote collect_duplicates :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list \<Rightarrow> 'a list" where |
28447 | 334 |
"collect_duplicates xs ys [] = xs" |
28419 | 335 |
| "collect_duplicates xs ys (z#zs) = (if z \<in> set xs |
336 |
then if z \<in> set ys |
|
337 |
then collect_duplicates xs ys zs |
|
338 |
else collect_duplicates xs (z#ys) zs |
|
339 |
else collect_duplicates (z#xs) (z#ys) zs)" |
|
340 |
||
341 |
text {* |
|
28428 | 342 |
\noindent The membership test during preprocessing is rewritten, |
28419 | 343 |
resulting in @{const List.member}, which itself |
344 |
performs an explicit equality check. |
|
345 |
*} |
|
346 |
||
28564 | 347 |
text %quote {*@{code_stmts collect_duplicates (SML)}*} |
28419 | 348 |
|
349 |
text {* |
|
350 |
\noindent Obviously, polymorphic equality is implemented the Haskell |
|
351 |
way using a type class. How is this achieved? HOL introduces |
|
352 |
an explicit class @{class eq} with a corresponding operation |
|
353 |
@{const eq_class.eq} such that @{thm eq [no_vars]}. |
|
28447 | 354 |
The preprocessing framework does the rest by propagating the |
29560 | 355 |
@{class eq} constraints through all dependent code equations. |
28419 | 356 |
For datatypes, instances of @{class eq} are implicitly derived |
357 |
when possible. For other types, you may instantiate @{text eq} |
|
358 |
manually like any other type class. |
|
359 |
||
360 |
Though this @{text eq} class is designed to get rarely in |
|
30938
c6c9359e474c
wellsortedness is no issue for a user manual any more
haftmann
parents:
30227
diff
changeset
|
361 |
the way, in some cases the automatically derived code equations |
28419 | 362 |
for equality on a particular type may not be appropriate. |
363 |
As example, watch the following datatype representing |
|
364 |
monomorphic parametric types (where type constructors |
|
365 |
are referred to by natural numbers): |
|
366 |
*} |
|
367 |
||
28564 | 368 |
datatype %quote monotype = Mono nat "monotype list" |
28419 | 369 |
(*<*) |
370 |
lemma monotype_eq: |
|
28462 | 371 |
"eq_class.eq (Mono tyco1 typargs1) (Mono tyco2 typargs2) \<equiv> |
372 |
eq_class.eq tyco1 tyco2 \<and> eq_class.eq typargs1 typargs2" by (simp add: eq) |
|
28419 | 373 |
(*>*) |
374 |
||
375 |
text {* |
|
28462 | 376 |
\noindent Then code generation for SML would fail with a message |
28419 | 377 |
that the generated code contains illegal mutual dependencies: |
378 |
the theorem @{thm monotype_eq [no_vars]} already requires the |
|
379 |
instance @{text "monotype \<Colon> eq"}, which itself requires |
|
380 |
@{thm monotype_eq [no_vars]}; Haskell has no problem with mutually |
|
28462 | 381 |
recursive @{text instance} and @{text function} definitions, |
28593 | 382 |
but the SML serialiser does not support this. |
28419 | 383 |
|
28447 | 384 |
In such cases, you have to provide your own equality equations |
28419 | 385 |
involving auxiliary constants. In our case, |
386 |
@{const [show_types] list_all2} can do the job: |
|
387 |
*} |
|
388 |
||
28564 | 389 |
lemma %quote monotype_eq_list_all2 [code]: |
28419 | 390 |
"eq_class.eq (Mono tyco1 typargs1) (Mono tyco2 typargs2) \<longleftrightarrow> |
28462 | 391 |
eq_class.eq tyco1 tyco2 \<and> list_all2 eq_class.eq typargs1 typargs2" |
28419 | 392 |
by (simp add: eq list_all2_eq [symmetric]) |
393 |
||
394 |
text {* |
|
395 |
\noindent does not depend on instance @{text "monotype \<Colon> eq"}: |
|
396 |
*} |
|
397 |
||
28564 | 398 |
text %quote {*@{code_stmts "eq_class.eq :: monotype \<Rightarrow> monotype \<Rightarrow> bool" (SML)}*} |
28419 | 399 |
|
400 |
||
28462 | 401 |
subsection {* Explicit partiality *} |
402 |
||
403 |
text {* |
|
404 |
Partiality usually enters the game by partial patterns, as |
|
405 |
in the following example, again for amortised queues: |
|
406 |
*} |
|
407 |
||
29798 | 408 |
definition %quote strict_dequeue :: "'a queue \<Rightarrow> 'a \<times> 'a queue" where |
409 |
"strict_dequeue q = (case dequeue q |
|
410 |
of (Some x, q') \<Rightarrow> (x, q'))" |
|
411 |
||
412 |
lemma %quote strict_dequeue_AQueue [code]: |
|
413 |
"strict_dequeue (AQueue xs (y # ys)) = (y, AQueue xs ys)" |
|
414 |
"strict_dequeue (AQueue xs []) = |
|
415 |
(case rev xs of y # ys \<Rightarrow> (y, AQueue [] ys))" |
|
416 |
by (simp_all add: strict_dequeue_def dequeue_AQueue split: list.splits) |
|
28462 | 417 |
|
418 |
text {* |
|
419 |
\noindent In the corresponding code, there is no equation |
|
29798 | 420 |
for the pattern @{term "AQueue [] []"}: |
28462 | 421 |
*} |
422 |
||
28564 | 423 |
text %quote {*@{code_stmts strict_dequeue (consts) strict_dequeue (Haskell)}*} |
28462 | 424 |
|
425 |
text {* |
|
426 |
\noindent In some cases it is desirable to have this |
|
427 |
pseudo-\qt{partiality} more explicitly, e.g.~as follows: |
|
428 |
*} |
|
429 |
||
28564 | 430 |
axiomatization %quote empty_queue :: 'a |
28462 | 431 |
|
29798 | 432 |
definition %quote strict_dequeue' :: "'a queue \<Rightarrow> 'a \<times> 'a queue" where |
433 |
"strict_dequeue' q = (case dequeue q of (Some x, q') \<Rightarrow> (x, q') | _ \<Rightarrow> empty_queue)" |
|
28213 | 434 |
|
29798 | 435 |
lemma %quote strict_dequeue'_AQueue [code]: |
436 |
"strict_dequeue' (AQueue xs []) = (if xs = [] then empty_queue |
|
437 |
else strict_dequeue' (AQueue [] (rev xs)))" |
|
438 |
"strict_dequeue' (AQueue xs (y # ys)) = |
|
439 |
(y, AQueue xs ys)" |
|
440 |
by (simp_all add: strict_dequeue'_def dequeue_AQueue split: list.splits) |
|
28462 | 441 |
|
442 |
text {* |
|
29798 | 443 |
Observe that on the right hand side of the definition of @{const |
444 |
"strict_dequeue'"} the constant @{const empty_queue} occurs |
|
445 |
which is unspecified. |
|
28462 | 446 |
|
29798 | 447 |
Normally, if constants without any code equations occur in a |
448 |
program, the code generator complains (since in most cases this is |
|
449 |
not what the user expects). But such constants can also be thought |
|
450 |
of as function definitions with no equations which always fail, |
|
451 |
since there is never a successful pattern match on the left hand |
|
452 |
side. In order to categorise a constant into that category |
|
453 |
explicitly, use @{command "code_abort"}: |
|
28462 | 454 |
*} |
455 |
||
28564 | 456 |
code_abort %quote empty_queue |
28462 | 457 |
|
458 |
text {* |
|
459 |
\noindent Then the code generator will just insert an error or |
|
460 |
exception at the appropriate position: |
|
461 |
*} |
|
462 |
||
28564 | 463 |
text %quote {*@{code_stmts strict_dequeue' (consts) empty_queue strict_dequeue' (Haskell)}*} |
28462 | 464 |
|
465 |
text {* |
|
466 |
\noindent This feature however is rarely needed in practice. |
|
467 |
Note also that the @{text HOL} default setup already declares |
|
468 |
@{const undefined} as @{command "code_abort"}, which is most |
|
469 |
likely to be used in such situations. |
|
470 |
*} |
|
28213 | 471 |
|
472 |
end |
|
28462 | 473 |