/usr/share/acl2-6.3/books/cutil/defmapappend.cert is in acl2-books-certs 6.3-5.
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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 | (IN-PACKAGE "ACL2")
"ACL2 Version 6.3"
:BEGIN-PORTCULLIS-CMDS
(INCLUDE-BOOK "portcullis")
:END-PORTCULLIS-CMDS
:EXPANSION-ALIST
((2 RECORD-EXPANSION (DEFXDOC CUTIL::DEFMAPAPPEND :PARENTS (CUTIL) :SHORT "Append transformations of list elements." :LONG "<p>Defmapappend allows you to quickly introduce a function like</p>
@({
(loop for elem in x append (f elem))
})
<p>and produces some basic theorems about this new function.</p>
<p>General form:</p>
@({
(defmapappend name formals
transform
&key guard ; t by default
verify-guards ; t by default
transform-exec ; nil by default
transform-true-list-p ; nil by default
mode ; default defun-mode by default
parents ; '(undocumented) by default
short ; nil by default
long ; nil by default
rest ; nil by default
)
})
<p>For instance,</p>
@({
(defmapappend append-square-lists (x)
(square-lists x)
:guard (integer-list-listp x))
})
<p>would introduce a new function, @('append-square-lists'), that applies
@('square-lists') to every element of its argument and appends together all of
the results.</p>
<p>Note that <b>x</b> is treated in a special way: it refers to the whole list
in the formals and guards, but refers to the individual elements of the list in
the @('element') portion. This is similar to how other macros like @(see
deflist), @(see defalist), and @(see defprojection) handle @('x').</p>
<h3>Usage and Arguments</h3>
<p>Let @('pkg') be the package of @('name'). All functions, theorems, and
variables are created in this package. One of the formals must be @('pkg::x'),
and this argument represents the list that will be transformed. Otherwise, the
only restriction on formals is that you may not use the names @('pkg::a'),
@('pkg::y'), and @('pkg::acc'), because we use these variables in the theorems
we generate.</p>
<p>The @('transform') should indicate an element transforming function that
produces a list of some kind as its output. Adopting an ML-like syntax,
@('transform') should have a signature such as the following:</p>
@({
transform : elem -> A list
})
<p>We produce a new function of the given @('name'), which has the
signature:</p>
@({
name : elem list -> A list
})
<p>Our new function applies @('transform') to every element in its input list,
and appends together all of the results. That is, the logical definition of
the new function we introduce is as follows:</p>
@({
(defun name (x)
(if (atom x)
nil
(append (transform (car x))
(name (cdr x)))))
})
<p>The new function will be more efficient than the above. In particular, we
write a @('mappappend-exec') function that builds the answer in reverse using
revappend and reverses it at the end. An even more efficient version is
possible when the @(':transform-exec') option is provided; see below for
details.</p>
<p>The optional @(':guard') and @(':verify-guards') are given to the
@('defund') event that we introduce. Often @(see deflist) is convenient for
introducing the necessary guard.</p>
<p>The optional @(':mode') keyword can be set to @(':logic') or @(':program')
to introduce the recognizer in logic or program mode. The default is whatever
the current default defun-mode is for ACL2, i.e., if you are already in program
mode, it will default to program mode, etc.</p>
<p>The optional @(':transform-true-list-p') argument can be set to @('t')
whenever the transformation is known to unconditionally produce a true list,
and allows us to slightly optimize our function.</p>
<h4>The :transform-exec argument</h4>
<p>When provided, the optional @(':transform-exec') argument should be the name
of a function that satisfies the following property:</p>
@({
(equal (transform-exec x acc)
(revappend (transform x)))
})
<p>Note that such functions are automatically introduced by @(see
defprojection). For instance,</p>
@({
(defprojection square-list (x)
(square x))
})
<p>generates a suitable function named @('square-list-exec'). Amusingly,
suitable functions are also generated by defmapappend, itself.</p>
<p>When such a function is provided, we can use it to generate a more efficient
implementation, which uses the tail-recursive function to build the answer in
reverse, and then reverses it at the very end, avoiding even the intermediate
computation of the lists emitted by @('transform').</p>
<p>The optional @(':parents'), @(':short'), and @(':long') options are as in
@(see xdoc), and are analagous to those of @(see deflist) or @(see
defprojection).</p>
<p>The optional @(':rest') option is as in @(see deflist), and allows you to
add theorems into the same section.</p>") (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::DEFMAPAPPEND) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS CUTIL) (:SHORT . "Append transformations of list elements.") (:LONG . "<p>Defmapappend allows you to quickly introduce a function like</p>
@({
(loop for elem in x append (f elem))
})
<p>and produces some basic theorems about this new function.</p>
<p>General form:</p>
@({
(defmapappend name formals
transform
&key guard ; t by default
verify-guards ; t by default
transform-exec ; nil by default
transform-true-list-p ; nil by default
mode ; default defun-mode by default
parents ; '(undocumented) by default
short ; nil by default
long ; nil by default
rest ; nil by default
)
})
<p>For instance,</p>
@({
(defmapappend append-square-lists (x)
(square-lists x)
:guard (integer-list-listp x))
})
<p>would introduce a new function, @('append-square-lists'), that applies
@('square-lists') to every element of its argument and appends together all of
the results.</p>
<p>Note that <b>x</b> is treated in a special way: it refers to the whole list
in the formals and guards, but refers to the individual elements of the list in
the @('element') portion. This is similar to how other macros like @(see
deflist), @(see defalist), and @(see defprojection) handle @('x').</p>
<h3>Usage and Arguments</h3>
<p>Let @('pkg') be the package of @('name'). All functions, theorems, and
variables are created in this package. One of the formals must be @('pkg::x'),
and this argument represents the list that will be transformed. Otherwise, the
only restriction on formals is that you may not use the names @('pkg::a'),
@('pkg::y'), and @('pkg::acc'), because we use these variables in the theorems
we generate.</p>
<p>The @('transform') should indicate an element transforming function that
produces a list of some kind as its output. Adopting an ML-like syntax,
@('transform') should have a signature such as the following:</p>
@({
transform : elem -> A list
})
<p>We produce a new function of the given @('name'), which has the
signature:</p>
@({
name : elem list -> A list
})
<p>Our new function applies @('transform') to every element in its input list,
and appends together all of the results. That is, the logical definition of
the new function we introduce is as follows:</p>
@({
(defun name (x)
(if (atom x)
nil
(append (transform (car x))
(name (cdr x)))))
})
<p>The new function will be more efficient than the above. In particular, we
write a @('mappappend-exec') function that builds the answer in reverse using
revappend and reverses it at the end. An even more efficient version is
possible when the @(':transform-exec') option is provided; see below for
details.</p>
<p>The optional @(':guard') and @(':verify-guards') are given to the
@('defund') event that we introduce. Often @(see deflist) is convenient for
introducing the necessary guard.</p>
<p>The optional @(':mode') keyword can be set to @(':logic') or @(':program')
to introduce the recognizer in logic or program mode. The default is whatever
the current default defun-mode is for ACL2, i.e., if you are already in program
mode, it will default to program mode, etc.</p>
<p>The optional @(':transform-true-list-p') argument can be set to @('t')
whenever the transformation is known to unconditionally produce a true list,
and allows us to slightly optimize our function.</p>
<h4>The :transform-exec argument</h4>
<p>When provided, the optional @(':transform-exec') argument should be the name
of a function that satisfies the following property:</p>
@({
(equal (transform-exec x acc)
(revappend (transform x)))
})
<p>Note that such functions are automatically introduced by @(see
defprojection). For instance,</p>
@({
(defprojection square-list (x)
(square x))
})
<p>generates a suitable function named @('square-list-exec'). Amusingly,
suitable functions are also generated by defmapappend, itself.</p>
<p>When such a function is provided, we can use it to generate a more efficient
implementation, which uses the tail-recursive function to build the answer in
reverse, and then reverses it at the very end, avoiding even the intermediate
computation of the lists emitted by @('transform').</p>
<p>The optional @(':parents'), @(':short'), and @(':long') options are as in
@(see xdoc), and are analagous to those of @(see deflist) or @(see
defprojection).</p>
<p>The optional @(':rest') option is as in @(see deflist), and allows you to
add theorems into the same section.</p>") (:FROM . "[books]/cutil/defmapappend.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::DEFMAPAPPEND)))))))
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