commit 93ea6443db84c52dbe11fa3176526859fc617f2f
parent 39ac8f8ce0ce5f77ba9ba20b4ab4df5201fa75ad
Author: Andres Navarro <canavarro82@gmail.com>
Date: Wed, 1 Jun 2011 19:02:48 -0300
Completed the pairs & lists module in the manual.
Diffstat:
5 files changed, 307 insertions(+), 28 deletions(-)
diff --git a/manual/html/Index.html b/manual/html/Index.html
@@ -42,7 +42,10 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Control.html#index-g_t_0024sequence-29"><code>$sequence</code></a>: <a href="Control.html#Control">Control</a></li>
<li><a href="Booleans.html#index-and_003f-15"><code>and?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Pairs-and-lists.html#index-append-80"><code>append</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-append_0021-88"><code>append!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="A-Sample-Applicative-Description.html#index-applicative-descriptions-8">applicative descriptions</a>: <a href="A-Sample-Applicative-Description.html#A-Sample-Applicative-Description">A Sample Applicative Description</a></li>
+<li><a href="Pairs-and-lists.html#index-assoc-83"><code>assoc</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-assq-90"><code>assq</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Booleans.html#index-boolean_003f-13"><code>boolean?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Booleans.html#index-booleans-12">booleans</a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Pairs-and-lists.html#index-caaaar-58"><code>caaaar</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -77,7 +80,9 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Pairs-and-lists.html#index-cdr-45"><code>cdr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-cons-38"><code>cons</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Control.html#index-control-26">control</a>: <a href="Control.html#Control">Control</a></li>
+<li><a href="Pairs-and-lists.html#index-copy_002des-89"><code>copy-es</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-copy_002des_002dimmutable_0021-41"><code>copy-es-immutable!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-countable_002dlist_003f-86"><code>countable-list?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Format-of-Descriptions.html#index-description-format-7">description format</a>: <a href="Format-of-Descriptions.html#Format-of-Descriptions">Format of Descriptions</a></li>
<li><a href="Evaluation-Notation.html#index-documentation-notation-4">documentation notation</a>: <a href="Evaluation-Notation.html#Evaluation-Notation">Evaluation Notation</a></li>
<li><a href="Pairs-and-lists.html#index-empty-list-34">empty list</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -87,6 +92,8 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Equivalence.html#index-equivalence-19">equivalence</a>: <a href="Equivalence.html#Equivalence">Equivalence</a></li>
<li><a href="Error-Messages.html#index-error-message-notation-6">error message notation</a>: <a href="Error-Messages.html#Error-Messages">Error Messages</a></li>
<li><a href="Evaluation-Notation.html#index-evaluation-notation-3">evaluation notation</a>: <a href="Evaluation-Notation.html#Evaluation-Notation">Evaluation Notation</a></li>
+<li><a href="Pairs-and-lists.html#index-filter-82"><code>filter</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-finite_002dlist_003f-85"><code>finite-list?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Some-Terms.html#index-fonts-2">fonts</a>: <a href="Some-Terms.html#Some-Terms">Some Terms</a></li>
<li><a href="A-Sample-Applicative-Description.html#index-foo-11"><code>foo</code></a>: <a href="A-Sample-Applicative-Description.html#A-Sample-Applicative-Description">A Sample Applicative Description</a></li>
<li><a href="Control.html#index-for_002deach-31"><code>for-each</code></a>: <a href="Control.html#Control">Control</a></li>
@@ -96,10 +103,13 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Pairs-and-lists.html#index-length-78"><code>length</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list-42"><code>list</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list_002a-43"><code>list*</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-list_002dneighbors-81"><code>list-neighbors</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list_002dref-79"><code>list-ref</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list_002dtail-75"><code>list-tail</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-lists-35">lists</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-map-77"><code>map</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-member_003f-84"><code>member?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Pairs-and-lists.html#index-memq_003f-91"><code>memq?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-nil-33">nil</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Booleans.html#index-not_003f-14"><code>not?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Pairs-and-lists.html#index-null_003f-37"><code>null?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -109,6 +119,7 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Pairs-and-lists.html#index-pair_003f-36"><code>pair?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-pairs-32">pairs</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Printing-Notation.html#index-printing-notation-5">printing notation</a>: <a href="Printing-Notation.html#Printing-Notation">Printing Notation</a></li>
+<li><a href="Pairs-and-lists.html#index-reduce-87"><code>reduce</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-set_002dcar_0021-39"><code>set-car!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-set_002dcdr_0021-40"><code>set-cdr!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Symbols.html#index-string_002d_003esymbol-25"><code>string->symbol</code></a>: <a href="Symbols.html#Symbols">Symbols</a></li>
diff --git a/manual/html/index.html b/manual/html/index.html
@@ -37,10 +37,10 @@ Up: <a rel="up" accesskey="u" href="../index.html#dir">(dir)</a>
<li><a accesskey="1" href="License.html#License">License</a>: Conditions for copying and changing klisp.
<li><a accesskey="2" href="Introduction.html#Introduction">Introduction</a>: Introduction and conventions used.
<!-- TODO lisp types and other introductions -->
-<li><a accesskey="3" href="Booleans.html#Booleans">Booleans</a>: Boolean module features.
+<li><a accesskey="3" href="Booleans.html#Booleans">Booleans</a>: Booleans module features.
<li><a accesskey="4" href="Equivalence.html#Equivalence">Equivalence</a>: Equivalence under mutation & Equivalence up to
mutation module features.
-<li><a accesskey="5" href="Symbols.html#Symbols">Symbols</a>: Symbol module features.
+<li><a accesskey="5" href="Symbols.html#Symbols">Symbols</a>: Symbols module features.
<li><a accesskey="6" href="Control.html#Control">Control</a>: Control module features.
<li><a accesskey="7" href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a>: Pairs and lists and Pair mutation module features.
<!-- TODO complete -->
diff --git a/manual/klisp.info b/manual/klisp.info
@@ -26,10 +26,10 @@ in part.
* License:: Conditions for copying and changing klisp.
* Introduction:: Introduction and conventions used.
-* Booleans:: Boolean module features.
+* Booleans:: Booleans module features.
* Equivalence:: Equivalence under mutation & Equivalence up to
mutation module features.
-* Symbols:: Symbol module features.
+* Symbols:: Symbols module features.
* Control:: Control module features.
* Pairs and lists:: Pairs and lists and Pair mutation module features.
* Index:: Index including concepts, functions, variables,
@@ -736,6 +736,120 @@ output using, modulo whitespace, external representation `(1 2 3)'.
(append () h . t) == (append h . t)
(append (cons a b) h . t) == (cons a (append b h . t))
+ -- Applicative: list-neighbors (list-neighbors list)
+ The `list-neighbors' applicative constructs and returns a list of
+ all the consecutive sublists of `list' of length 2, in order. If
+ `list' is nil, the result is nil. If `list' is non-nil, the
+ length of the result is one less than the length of `list'. If
+ `list' is cyclic, the result is structurally isomorphic to it
+ (i.e., has the same acyclic prefix length and cycle length).
+
+ For example:
+ (list-neighbors (list 1 2 3 4)) => ((1 2) (2 3) (3 4))
+
+ -- Applicative: filter (filter applicative list)
+ Applicative `filter' passes each of the elements of `list' as an
+ argument to `applicative', one at a time in no particular order,
+ using a fresh empty environment for each call. The result of each
+ call to `applicative' must be boolean, otherwise an error is
+ signaled. `filter' constructs and returns a list of all elements
+ of `list' on which `applicative' returned true, in the same order
+ as in `list'. `applicative' is called exactly as many times as
+ there are pairs in `list'. The resultant list has a cycle
+ containing exactly those elements accepted by `applicative' that
+ were in the cycle of `list'; if there were no such elements, the
+ result is acyclic.
+
+ -- Applicative: assoc (assoc object pairs)
+ Applicative `assoc' returns the first element of `pairs' whose car
+ is `equal?' to `object'. If there is no such element in `pairs',
+ nil is returned.
+
+ -- Applicative: member? (member? object list)
+ Applicative `member?' is a predicate that returns true iff some
+ element of `list' is `equal?' to `object'.
+
+ -- Applicative: finite-list? (finite-list? . objects)
+ This is the type predicate for type finite-list. `finite-list?'
+ returns true iff all the objects in `objects' are acyclic lists.
+
+ -- Applicative: countable-list? (countable-list? . objects)
+ This is the type predicate for type list. `countable-list?'
+ returns true iff all the objects in `objects' are lists.
+
+ -- Applicative: reduce (reduce list binary identity [precycle incycle
+ postcycle])
+ `binary' should be an applicative. If the short form is used,
+ `list' should be an acyclic. If the long form is used, `precycle',
+ `incycle', and `postcycle' should be applicatives.
+
+ If `list' is empty, applicative `reduce' returns `identity'. If
+ `list' is nonempty but acyclic, applicative `reduce' uses binary
+ operation `binary' to merge all the elements of `list' into a
+ single object, using any associative grouping of the elements.
+ That is, the sequence of objects initially found in `list' is
+ repeatedly decremented in length by applying `binary' to a list of
+ any two consecutive objects, replacing those two objects with the
+ result at the point in the sequence where they occurred; and when
+ the sequence contains only one object, that object is returned.
+ If `list' is cyclic, the long form must be used. The elements of
+ the cycle are passed, one at a time (but just once for each
+ position in the cycle), as arguments to unary applicative
+ `precycle'; the finite, cyclic sequence of results from `precycle'
+ is reduced using binary applicative `incycle'; and the result from
+ reducing the cycle is passed as an argument to unary applicative
+ `postcycle'. Binary operation `binary' is used to reduce the
+ sequence consisting of the elements of the acyclic prefix of
+ `list' followed by the result returned by `postcycle'. The only
+ constraint on the order of calls to the applicatives is that each
+ call must be made before its result is needed (thus, parts of the
+ reduction of the acyclic prefix may occur before the contribution
+ from the cycle has been completed).
+
+ Each call to `binary', `precycle', `incycle', or `postcycle' uses
+ the dynamic environment of the call to `reduce'.
+
+ If `list' is acyclic with length `n >= 1', `binary' is called `n -
+ 1' times. If `list' is cyclic with acyclic prefix length `a' and
+ cycle length `c', `binary' is called `a' times; `precycle', `c'
+ times; `incycle', `c - 1' times; and `postcycle', once.
+
+ -- Applicative: append! (append! . lists)
+ `lists' must be a nonempty list; its first element must be an
+ acyclic nonempty list, and all of its elements except the last
+ element (if any) must be acyclic lists.
+
+ The `append!' applicative sets the cdr of the last pair in each
+ nonempty list argument to refer to the next non-nil argument,
+ except that if there is a last non-nil argument, it isn’t mutated.
+ It is an error for any two of the list arguments to have the same
+ last pair. The result returned by this applicative is inert.
+
+ The following equivalences hold:
+ (append! v) == #inert
+ (append! u v . w) == ($sequence (append! u v) (append! u . w))
+
+ -- Applicative: copy-es (copy-es object)
+ Briefly, applicative `copy-es' returns an object initially
+ `equal?' to `object' with a freshly constructed evaluation
+ structure made up of mutable pairs. If `object' is not a pair,
+ the applicative returns `object'. If `object' is a pair, the
+ applicative returns a freshly constructed pair whose car and cdr
+ would be suitable results for `(copy-es (car object))' and
+ `(copy-es (cdr object))', respectively. Further, the evaluation
+ structure of the returned value is structurally isomorphic to that
+ of `object' at the time of copying, with corresponding non-pair
+ referents being `eq?'.
+
+ -- Applicative: assq (assq object pairs)
+ Applicative `assq' returns the first element of `pairs' whose car
+ is `eq?' to `object'. If there is no such element in `pairs', nil
+ is returned.
+
+ -- Applicative: memq? (memq? object list)
+ Applicative `memq?' is a predicate that returns true iff some
+ element of `list' is `eq?' to `object'.
+
File: klisp.info, Node: Index, Next: (dir), Prev: Pairs and lists, Up: Top
@@ -752,8 +866,11 @@ Index
* $sequence: Control. (line 23)
* and?: Booleans. (line 20)
* append: Pairs and lists. (line 208)
+* append!: Pairs and lists. (line 306)
* applicative descriptions: A Sample Applicative Description.
(line 6)
+* assoc: Pairs and lists. (line 252)
+* assq: Pairs and lists. (line 333)
* boolean?: Booleans. (line 12)
* booleans: Booleans. (line 6)
* caaaar: Pairs and lists. (line 101)
@@ -788,7 +905,9 @@ Index
* cdr: Pairs and lists. (line 86)
* cons: Pairs and lists. (line 35)
* control: Control. (line 6)
+* copy-es: Pairs and lists. (line 321)
* copy-es-immutable!: Pairs and lists. (line 49)
+* countable-list?: Pairs and lists. (line 265)
* description format: Format of Descriptions.
(line 6)
* documentation notation: Evaluation Notation. (line 6)
@@ -799,6 +918,8 @@ Index
* equivalence: Equivalence. (line 6)
* error message notation: Error Messages. (line 6)
* evaluation notation: Evaluation Notation. (line 6)
+* filter: Pairs and lists. (line 239)
+* finite-list?: Pairs and lists. (line 261)
* fonts: Some Terms. (line 13)
* foo: A Sample Applicative Description.
(line 15)
@@ -809,10 +930,13 @@ Index
* length: Pairs and lists. (line 191)
* list: Pairs and lists. (line 72)
* list*: Pairs and lists. (line 78)
+* list-neighbors: Pairs and lists. (line 228)
* list-ref: Pairs and lists. (line 198)
* list-tail: Pairs and lists. (line 147)
* lists: Pairs and lists. (line 6)
* map: Pairs and lists. (line 169)
+* member?: Pairs and lists. (line 257)
+* memq?: Pairs and lists. (line 338)
* nil: Pairs and lists. (line 6)
* not?: Booleans. (line 16)
* null?: Pairs and lists. (line 31)
@@ -824,6 +948,7 @@ Index
* pair?: Pairs and lists. (line 27)
* pairs: Pairs and lists. (line 6)
* printing notation: Printing Notation. (line 6)
+* reduce: Pairs and lists. (line 270)
* set-car!: Pairs and lists. (line 41)
* set-cdr!: Pairs and lists. (line 42)
* string->symbol: Symbols. (line 20)
@@ -835,23 +960,23 @@ Index
Tag Table:
Node: Top302
-Node: License1209
-Node: Introduction2880
-Node: Caveats5703
-Node: Kernel History6489
-Node: Conventions7934
-Node: Some Terms8605
-Node: Evaluation Notation9276
-Node: Printing Notation10297
-Node: Error Messages10773
-Node: Format of Descriptions11421
-Node: A Sample Applicative Description11985
-Node: Acknowledgements13748
-Node: Booleans14134
-Node: Equivalence16676
-Node: Symbols17469
-Node: Control18834
-Node: Pairs and lists21151
-Node: Index32148
+Node: License1211
+Node: Introduction2882
+Node: Caveats5705
+Node: Kernel History6491
+Node: Conventions7936
+Node: Some Terms8607
+Node: Evaluation Notation9278
+Node: Printing Notation10299
+Node: Error Messages10775
+Node: Format of Descriptions11423
+Node: A Sample Applicative Description11987
+Node: Acknowledgements13750
+Node: Booleans14136
+Node: Equivalence16678
+Node: Symbols17471
+Node: Control18836
+Node: Pairs and lists21153
+Node: Index38167
End Tag Table
diff --git a/manual/src/klisp.texi b/manual/src/klisp.texi
@@ -72,10 +72,10 @@ in part.
* License:: Conditions for copying and changing klisp.
* Introduction:: Introduction and conventions used.
@c TODO lisp types and other introductions
-* Booleans:: Boolean module features.
+* Booleans:: Booleans module features.
* Equivalence:: Equivalence under mutation & Equivalence up to
mutation module features.
-* Symbols:: Symbol module features.
+* Symbols:: Symbols module features.
* Control:: Control module features.
* Pairs and lists:: Pairs and lists and Pair mutation module features.
@c TODO complete
diff --git a/manual/src/pairs_lists.texi b/manual/src/pairs_lists.texi
@@ -105,12 +105,10 @@ operand tree, regardless of whether that tree is or is not a list.
@deffnx Applicative cdr (cdr pair)
These applicatives return, respectively, the car and cdr of @code{pair}.
@end deffn
-@c 2 levels
@deffn Applicative caar (caar pair)
@deffnx Applicative cadr (cadr pair)
@deffnx Applicative cdar (cdar pair)
@deffnx Applicative cddr (cddr pair)
-@c 3 levels
@deffnx Applicative caaar (caaar pair)
@deffnx Applicative caadr (caadr pair)
@deffnx Applicative cadar (cadar pair)
@@ -119,7 +117,6 @@ These applicatives return, respectively, the car and cdr of @code{pair}.
@deffnx Applicative cdadr (cdadr pair)
@deffnx Applicative cddar (cddar pair)
@deffnx Applicative cdddr (cdddr pair)
-@c 3 levels
@deffnx Applicative caaaar (caaaar pair)
@deffnx Applicative caaadr (caaadr pair)
@deffnx Applicative caadar (caadar pair)
@@ -128,7 +125,6 @@ These applicatives return, respectively, the car and cdr of @code{pair}.
@deffnx Applicative cadadr (cadadr pair)
@deffnx Applicative caddar (caddar pair)
@deffnx Applicative cadddr (cadddr pair)
-
@deffnx Applicative cdaaar (cdaaar pair)
@deffnx Applicative cdaadr (cdaadr pair)
@deffnx Applicative cdadar (cdadar pair)
@@ -269,4 +265,151 @@ The following equivalences hold:
(append () h . t) @equiv{} (append h . t)
(append (cons a b) h . t) @equiv{} (cons a (append b h . t))
@end example
+@c TODO add xref/comp to append
+@end deffn
+
+@deffn Applicative list-neighbors (list-neighbors list)
+ The @code{list-neighbors} applicative constructs and returns a list
+of all the consecutive sublists of @code{list} of length 2, in order.
+If @code{list} is nil, the result is nil. If @code{list} is non-nil,
+the length of the result is one less than the length of
+@code{list}. If @code{list} is cyclic, the result is structurally
+isomorphic to it (i.e., has the same acyclic prefix length and cycle
+length).
+@c TODO add xref to isomorphic
+
+ For example:
+@example
+(list-neighbors (list 1 2 3 4)) @result{} ((1 2) (2 3) (3 4))
+@end example
+@end deffn
+
+@deffn Applicative filter (filter applicative list)
+ Applicative @code{filter} passes each of the elements of @code{list}
+as an argument to @code{applicative}, one at a time in no particular
+order, using a fresh empty environment for each call. The result of
+each call to @code{applicative} must be boolean, otherwise an error is
+signaled. @code{filter} constructs and returns a list of all elements
+of @code{list} on which @code{applicative} returned true, in the same
+order as in @code{list}. @code{applicative} is called exactly as many
+times as there are pairs in @code{list}. The resultant list has a
+cycle containing exactly those elements accepted by @code{applicative}
+that were in the cycle of @code{list}; if there were no such elements,
+the result is acyclic.
+@end deffn
+
+@deffn Applicative assoc (assoc object pairs)
+ Applicative @code{assoc} returns the first element of @code{pairs}
+whose car is @code{equal?} to @code{object}. If there is no such
+element in @code{pairs}, nil is returned.
+@c TODO add xref/comp to assq
+@c TODO add xref to equal?
+@end deffn
+
+@deffn Applicative member? (member? object list)
+ Applicative @code{member?} is a predicate that returns true iff some
+element of @code{list} is @code{equal?} to @code{object}.
+@c TODO add xref/comp to memq
+@c TODO add xref to equal?
+@end deffn
+
+@deffn Applicative finite-list? (finite-list? . objects)
+ This is the type predicate for type finite-list.
+@code{finite-list?} returns true iff all the objects in
+@code{objects} are acyclic lists.
+@end deffn
+
+@deffn Applicative countable-list? (countable-list? . objects)
+This is the type predicate for type list. @code{countable-list?}
+returns true iff all the objects in @code{objects} are lists.
+@end deffn
+
+@deffn Applicative reduce (reduce list binary identity [precycle incycle postcycle])
+ @code{binary} should be an applicative. If the short form is used,
+@code{list} should be an acyclic. If the long form is used,
+@code{precycle}, @code{incycle}, and @code{postcycle} should be
+applicatives.
+
+ If @code{list} is empty, applicative @code{reduce} returns
+@code{identity}. If @code{list} is nonempty but acyclic, applicative
+@code{reduce} uses binary operation @code{binary} to merge all the
+elements of @code{list} into a single object, using any associative
+grouping of the elements. That is, the sequence of objects initially
+found in @code{list} is repeatedly decremented in length by applying
+@code{binary} to a list of any two consecutive objects, replacing
+those two objects with the result at the point in the sequence where
+they occurred; and when the sequence contains only one object, that
+object is returned. If @code{list} is cyclic, the long form must be
+used. The elements of the cycle are passed, one at a time (but just
+once for each position in the cycle), as arguments to unary
+applicative @code{precycle}; the finite, cyclic sequence of results
+from @code{precycle} is reduced using binary applicative
+@code{incycle}; and the result from reducing the cycle is passed as an
+argument to unary applicative @code{postcycle}. Binary operation
+@code{binary} is used to reduce the sequence consisting of the
+elements of the acyclic prefix of @code{list} followed by the result
+returned by @code{postcycle}. The only constraint on the order of
+calls to the applicatives is that each call must be made before its
+result is needed (thus, parts of the reduction of the acyclic prefix
+may occur before the contribution from the cycle has been completed).
+
+ Each call to @code{binary}, @code{precycle}, @code{incycle}, or
+@code{postcycle} uses the dynamic environment of the call to
+@code{reduce}.
+
+ If @code{list} is acyclic with length @code{n >= 1},
+@code{binary} is called @code{n - 1} times. If @code{list} is cyclic
+with acyclic prefix length @code{a} and cycle length @code{c},
+@code{binary} is called @code{a} times; @code{precycle}, @code{c}
+times; @code{incycle}, @code{c - 1} times; and @code{postcycle}, once.
+@end deffn
+
+@deffn Applicative append! (append! . lists)
+ @code{lists} must be a nonempty list; its first element must be an
+acyclic nonempty list, and all of its elements except the last element
+(if any) must be acyclic lists.
+
+ The @code{append!} applicative sets the cdr of the last pair in each
+nonempty list argument to refer to the next non-nil argument, except
+that if there is a last non-nil argument, it isn’t mutated. It is an
+error for any two of the list arguments to have the same last pair.
+The result returned by this applicative is inert.
+
+ The following equivalences hold:
+@example
+(append! v) @equiv{} #inert
+(append! u v . w) @equiv{} ($sequence (append! u v) (append! u . w))
+@end example
+@end deffn
+
+@deffn Applicative copy-es (copy-es object)
+ Briefly, applicative @code{copy-es} returns an object initially
+@code{equal?} to @code{object} with a freshly constructed evaluation
+@c TODO add xref to evaluation structure
+structure made up of mutable pairs. If @code{object} is not a pair,
+the applicative returns @code{object}. If @code{object} is a pair,
+the applicative returns a freshly constructed pair whose car and cdr
+would be suitable results for @code{(copy-es (car object))} and
+@code{(copy-es (cdr object))}, respectively. Further, the evaluation
+@c TODO add xref to isomorphic
+structure of the returned value is structurally isomorphic to that of
+@code{object} at the time of copying, with corresponding non-pair
+referents being @code{eq?}.
+@c TODO add xref/comp to copy-es-immutable and the reverse too!
+@c TODO add xref to eq?/equal?
+@end deffn
+
+@deffn Applicative assq (assq object pairs)
+ Applicative @code{assq} returns the first element of @code{pairs}
+whose car is @code{eq?} to @code{object}. If there is no such element
+in @code{pairs}, nil is returned.
+@c TODO add xref/comp to assoc
+@c TODO add xref to eq?
+@end deffn
+
+@deffn Applicative memq? (memq? object list)
+ Applicative @code{memq?} is a predicate that returns true iff some
+element of @code{list} is @code{eq?} to @code{object}.
+@c TODO add xref/comp to member?
+@c TODO add xref to eq?
@end deffn
