turn lower-case characters into upper-case characters
Parent topic: PROGRAMMING Home
(Char-upcase x) is equal to #A when x is #a, #B when x is
#b, ..., and #Z when x is #z, and is x for any other character.
The guard for char-upcase requires its argument to be a character.
Char-upcase is a Common Lisp function. See any Common Lisp
documentation for more information.
less-than test for characters
Parent topic: PROGRAMMING Home
(char< x y) is true if and only if the character code of x is
less than that of y. See char-code.
The guard for char< specifies that its arguments are characters.
Char< is a Common Lisp function. See any Common Lisp
documentation for more information.
less-than-or-equal test for characters
Parent topic: PROGRAMMING Home
(char<= x y) is true if and only if the character code of x is
less than or equal to that of y. See char-code.
The guard for char<= specifies that its arguments are characters.
Char<= is a Common Lisp function. See any Common Lisp
documentation for more information.
greater-than test for characters
Parent topic: PROGRAMMING Home
(char> x y) is true if and only if the character code of x is
greater than that of y. See char-code.
The guard for char> specifies that its arguments are characters.
Char> is a Common Lisp function. See any Common Lisp
documentation for more information.
greater-than-or-equal test for characters
Parent topic: PROGRAMMING Home
(char>= x y) is true if and only if the character code of x is
greater than or equal to that of y. See char-code.
The guard for char>= specifies that its arguments are characters.
Char>= is a Common Lisp function. See any Common Lisp
documentation for more information.
recognizer for a true list of characters
Parent topic: PROGRAMMING Home
The predicate character-listp tests whether its argument is a
true list of characters.
characters in ACL2
Parent topic: PROGRAMMING Home
ACL2 accepts 256 distinct characters, which are the characters
obtained by applying the function code-char to each integer from 0
to 255. Among these, Common Lisp designates certain ones as
standard characters, namely those of the form (code-char n)
where n is from 33 to 126, together with #\Newline and #\Space. The
actual standard characters may be viewed by evaluating the
defconst *standard-chars*.
To be more precise, Common Lisp does not specify the precise
relationship between code-char and the standard characters.
However, we check that the underlying Common Lisp implementation
uses a particular relationship that extends the usual ASCII coding
of characters. We also check that Space, Tab, Newline, Page, and
Rubout correspond to characters with respective char-codes 32, 9,
10, 12, and 127.
Code-char has an inverse, char-code. Thus, when char-code is
applied to an ACL2 character, c, it returns a number n between 0 and
255 inclusive such that (code-char n) = c.
The preceding paragraph implies that there is only one ACL2 character with a given character code. CLTL allows for ``attributes'' for characters, which could allow distinct characters with the same code, but ACL2 does not allow this.
The Character Reader
ACL2 support the `#\' notation for characters provided by Common
Lisp, with some restrictions. First of all, for every character c,
the notation
#\cmay be used to denote the character object
c. That is, the user may
type in this notation and ACL2 will read it as denoting the
character object c. In this case, the character immediately
following c must be one of the following ``terminating characters'':
a Tab, a Newline, a Page character, a space, or one of the
characters:
" ' ( ) ; ` ,Other than the notation above, ACL2 accepts alternate notation for five characters.
#\Space #\Tab #\Newline #\Page #\Rubout
Again, in each of these cases the next character must be from among
the set of ``terminating characters'' described in the
single-character case. Our implementation is consistent with
IS0-8859, even though we don't provide #\ syntax for entering
characters other than that described above.
Finally, we note that it is our intention that any object printed by ACL2's top-level-loop may be read back into ACL2. Please notify the implementors if you find a counterexample to this claim.
the character corresponding to a given numeric code
Parent topic: PROGRAMMING Home
Basic axiom:
(equal (code-char x)
(if (and (integerp x)
(>= x 0)
(< x 256))
(code-char x)
(code-char 0)))
Guard for (code-char x):
(and (integerp x)
(>= x 0)
(< x 256))
ACL2 supports 8-bit characters. Inputs not between 0 and 255
are treated as 0.
coerce a character list to a string and a string to a list
Parent topic: PROGRAMMING Home
Basic axiom:
(equal (coerce x y)
(cond
((equal y 'list)
(if (stringp x)
(coerce x 'list)
nil))
(t
(coerce (make-character-list x) 'string))))
Guard for (coerce x y):
(if (equal y 'list)
(stringp x)
(if (equal y 'string)
(character-listp x)
nil))
compiling ACL2 functions
Parent topic: PROGRAMMING Home
Example: ACL2 !>:comp app ACL2 !>:set-compile-fns t
See comp and see set-compile-fns.
create an ACL2 number
Parent topic: PROGRAMMING Home
Examples: (complex x 3) ; x + 3i, where i is the principal square root of -1 (complex x y) ; x + yi (complex x 0) ; same as x, for rational numbers xThe function
complex takes two rational number arguments and
returns an ACL2 number. This number will be of type
(complex rational) [as defined in the Common Lisp language], except
that if the second argument is zero, then complex returns its first
argument. The function complex-rationalp is a recognizer for
complex rational numbers, i.e. for ACL2 numbers that are not
rational numbers.
The reader macro #C (which is the same as #c) provides a convenient
way for typing in complex numbers. For explicit rational numbers x
and y, #C(x y) is read to the same value as (complex x y).
The functions realpart and imagpart return the real and imaginary
parts (respectively) of a complex (possibly rational) number. So
for example, (realpart #C(3 4)) = 3, (imagpart #C(3 4)) = 4,
(realpart 3/4) = 3/4, and (imagpart 3/4) = 0.
A basic axiom that shows what complex returns on arguments
violating its guard (which says that both arguments are rational
numbers) is the following.
(equal (complex x y)
(complex (if (rationalp x) x 0)
(if (rationalp y) y 0)))
recognizes complex rational numbers
Parent topic: PROGRAMMING Home
Examples: (complex-rationalp 3) ; nil, as 3 is rational, not complex rational (complex-rationalp #c(3 0)) ; nil, since #c(3 0) is the same as 3 (complex-rationalp t) ; nil (complex-rationalp #c(3 1)) ; t, as #c(3 1) is the complex number 3 + i
See complex for more about complex rationals in ACL2.
concatenate lists or strings together
Parent topic: PROGRAMMING Home
Examples: (concatenate 'string "ab" "cd" "ef") ; equals "abcdef" (concatenate 'string "ab") ; equals "ab" (concatenate 'list '(a b) '(c d) '(e f)) ; equals '(a b c d e f) (concatenate 'list) ; equals nilwhereGeneral Form: (concatenate result-type x1 x2 ... xn)
n >= 0 and either: result-type is 'string and each xi is a
string; or result-type is 'list and each xi is a true list.
Concatenate simply concatenates its arguments to form the result
string or list. Also see append and see string-append,
though concatenate is probably preferable to string-append for
efficiency.
Note: We do *not* try to comply with the Lisp language's insistence
that concatenate copies its arguments. Not only are we in an
applicative setting, where this issue shouldn't matter for the
logic, but also we do not actually modify the underlying lisp
implementation of concatenate; we merely provide a definition for
it.
Concatenate is a Common Lisp function. See any Common Lisp
documentation for more information.
conditional based on if-then-else
Parent topic: PROGRAMMING Home
Cond is the construct for IF, THEN, ELSE IF, ... The test is
against nil. The argument list for cond is a list of
``clauses'', each of which is a list. In ACL2, clauses must have
length 1 or 2.
Cond is a Common Lisp macro. See any Common Lisp
documentation for more information.
complex number conjugate
Parent topic: PROGRAMMING Home
Conjugate takes an ACL2 number as an argument, and returns its
complex conjugate (i.e., the result of negating its imaginary
part.).
Conjugate is a Common Lisp function. See any Common Lisp
documentation for more information.
pair and list constructor
Parent topic: PROGRAMMING Home
(cons x y) is a pair whose first component is x and second
component is y. If y is a list, then (cons x y) is a list
that has an addtional element x on the front.
recognizer for cons pairs
Parent topic: PROGRAMMING Home
(consp x) is true if and only if x is a cons pair.
declarations
Parent topic: PROGRAMMING Home
Examples:
(declare (ignore x y z))
(declare (ignore x y z)
(type integer i j k)
(type (satisfies integerp) m1 m2))
(declare (xargs :guard (and (integerp i)
(<= 0 i))
:guard-hints (("Goal" :use (:instance lemma3
(x (+ i j)))))))
General Form:
(declare d1 ... dn)
where, in ACL2, each di is of one of the following forms:
(ignore v1 ... vn) -- where each vi is a variable introduced in
the immediately superior lexical environment.
(type type-spec v1 ... vn) -- where each vi is a variable
introduced in the immediately superior lexical environment and
type-spec is a type specifier (as described in the documentation
for type-spec).
(xargs :key1 val1 ... :keyn valn) -- where the legal values of the
keyi's and their respective vali's are described in the
documentation for xargs.
Declarations in ACL2 may occur only where dcl occurs below:
(DEFUN name args doc-string dcl ... dcl body) (DEFMACRO name args doc-string dcl ... dcl body) (LET ((v1 t1) ...) dcl ... dcl body) (MV-LET (v1 ...) term dcl ... dcl body)Of course, if a form macroexpands into one of these (as
let*
expands into nested lets and our er-let* expands into nested
mv-lets) then declarations are permitted as handled by the macros
involved.
Declare is defined in Common Lisp. See any Common Lisp
documentation for more information.
divisor of a ratio in lowest terms
Parent topic: PROGRAMMING Home
Basic axiom:
(equal (denominator x)
(if (rationalp x)
(denominator x)
1))
Guard for (denominator x):
(rationalp x)
the number, if any, corresponding to a given character
Parent topic: PROGRAMMING Home
(digit-char-p ch) is the integer corresponding to the character
ch in base 10. For example, (digit-char-p #\3) is equal to
the integer 3. More generally, an optional second argument
specifies the radix (default 10, as indicated above).
The guard for digit-char-p (more precisely, for the function
our-digit-char-p that calls of this macro expand to) requires its
second argument to be an integer between 2 and 36, inclusive, and
its first argument to be a character.
Digit-char-p is a Common Lisp function, though it is implemented
in the ACL2 logic as an ACL2 macro. See any Common Lisp
documentation for more information.
map a digit to a character
Parent topic: PROGRAMMING Home
Example: ACL2 !>(digit-to-char 8) #\8For an integer
n from 0 to 9, (digit-to-char n) is the
character corresponding to n in decimal notation.
The guard for digit-to-char requires its argument to be an
integer between 0 and 9, inclusive.
eighth member of the list
Parent topic: PROGRAMMING Home
See any Common Lisp documentation for details.
recognizer for empty lists
Parent topic: PROGRAMMING Home
In the ACL2 logic, (endp x) is the same as (atom x).
See atom.
Unlike atom, the guard for endp requires that x is a
cons pair or is nil. Thus, endp is typically used as a
termination test for functions that recur on a true-listp
argument. See guard for general information about guards.
Endp is a Common Lisp function. See any Common Lisp
documentation for more information.
equality of symbols
Parent topic: PROGRAMMING Home
Eq is the function for determining whether two objects are
identical (i.e., have the exact same store address in the current
von Neumann implementation of Common Lisp). It is the same as
equal in the ACL2 logic.
Eq is a Common Lisp function. In order to ensure conformance
with Common Lisp, the ACL2 guard on eq requires at least one of
the arguments to eq to be a symbol. Common Lisp guarantees that
if x is a symbol, then x is eq to y if and only if x
is equal to y. Thus, the ACL2 user should think of eq as
nothing besides a fast means for checking equal when one argument
is known to be a symbol. In particular, it is possible that an
eq test will not even require the cost of a function call but
will be as fast as a single machine instruction.
test equality (of two numbers, symbols, or characters)
Parent topic: PROGRAMMING Home
(eql x y) is logically equivalent to (equal x y).
Unlike equal, eql has a guard requiring at least one of its
arguments to be a number, a symbol, or a character. Generally,
eql is executed more efficiently than equal.
For a discussion of the various ways to test against 0, See zero-test-idioms.
Eql is a Common Lisp function. See any Common Lisp documentation
for more information.
recognizer for a true list of pairs whose cars are suitable for eql
Parent topic: PROGRAMMING Home
The predicate eqlable-alistp tests whether its argument is a
true-listp of consp objects whose cars all satisfy
eqlablep.
recognizer for a true list of objects each suitable for eql
Parent topic: PROGRAMMING Home
The predicate eqlable-listp tests whether its argument is a
true-listp of objects satisfying eqlablep.
the guard for the function eql
Parent topic: PROGRAMMING Home
The predicate eqlablep tests whether its argument is suitable for
eql, at least one of whose arguments must satisfy this predicate
in Common Lisp. (Eqlablep x) is true if and only if its argument
is a number, a symbol, or a character.
true equality
Parent topic: PROGRAMMING Home
(equal x y) is equal to t or nil, according to whether or
not x and y are the same value.
For a discussion of the various idioms for testing against 0, See zero-test-idioms.
perform a sequence of state-changing ``error triples''
Parent topic: PROGRAMMING Home
Example:
(er-progn (check-good-foo-p (f-get-global 'my-foo state) state)
(value (* (f-get-global 'my-foo state)
(f-get-global 'bar state))))
This sequencing primitive is only useful when programming with state, something that very few users will probably want to do. See state.
Er-progn is used much the way that progn is used in Common
Lisp, except that it expects each form within it to evaluate to an
``error triple'' of the form (mv erp val state). The first such
form, if any, that evaluates to such a triple where erp is not
nil yields the error triple returned by the er-progn. If
there is no such form, then the last form returns the value of the
er-progn form.
We intend to write more about this topic, especially if there are requests to do so.
test whether an integer is even
Parent topic: PROGRAMMING Home
(evenp x) is true if and only if the integer x is even.
Actually, in the ACL2 logic (evenp x) is defined to be true when
x/2 is an integer.
The guard for evenp requires its argument to be an integer.
Evenp is a Common Lisp function. See any Common Lisp
documentation for more information.
the list of characters in the decimal form of a number
Parent topic: PROGRAMMING Home
Example: ACL2 !>(explode-nonnegative-integer 325 nil) (#3 #2 #5)For a non-negative integer
n, (explode-nonnegative-integer n nil)
is the list of characters in the decimal representation of n.
The guard for explode-nonnegative-integer requires the first
argument to be a nonnegative integer.
exponential function
Parent topic: PROGRAMMING Home
(Expt r i) is the result of raising the number r to the
integer power i.
The guard for (expt r i) is that r is a number and i
is an integer, and furthermore, if r is 0 then i is
nonnegative. When the type requirements of the guard aren't
met, (expt r i) first coerces r to a number and i to an
integer.
Expt is a Common Lisp function. See any Common Lisp
documentation for more information. Note that r can be a complex
number; this is consistent with Common lisp.
fifth member of the list
Parent topic: PROGRAMMING Home
See any Common Lisp documentation for details.
first member of the list
Parent topic: PROGRAMMING Home
See any Common Lisp documentation for details.
coerce to a number
Parent topic: PROGRAMMING Home
Fix simply returns any numeric argument unchanged, returning 0
on a non-numeric argument. Also see nfix, see ifix, and
see rfix for analogous functions that coerce to a natural
number, an integer, and a rational number, respectively.
Fix has a guard of t.
coerce to a true list
Parent topic: PROGRAMMING Home
Fix-true-list is the identity function on true-listp objects.
It converts every list to a true list by dropping the final cdr,
and it converts every atom to nil.
division returning an integer by truncating toward negative infinity
Parent topic: PROGRAMMING Home
Example Forms: ACL2 !>(floor 14 3) 4 ACL2 !>(floor -14 3) -5 ACL2 !>(floor 14 -3) -5 ACL2 !>(floor -14 -3) 4 ACL2 !>(floor -15 -3) 5
(Floor i j) returns the result of taking the quotient of i and
j and returning the greatest integer not exceeding that quotient.
For example, the quotient of -14 by 3 is -4 2/3, and the largest
integer not exceeding that rational number is -5.
The guard for (floor i j) requires that i and j are
rational numbers and j is non-zero.
Floor is a Common Lisp function. See any Common Lisp
documentation for more information.
:(str alist co-channel state evisc) => state
Parent topic: PROGRAMMING Home
See fmt for further explanation.
The tilde-directives are
~px pretty print vx (maybe after printing a newline)
~qx pretty print vx starting in current column; end with newline
~Pxy like ~px but use vy as the evisceration tuple
~Qxy like ~qx but use vy as the evisceration tuple
~@x if vx is a string, "str", recursively format "str"
if vx is ("str" . a), recursively format "str" under a+
~#x~[...~/...~/ ... ~/...~] cases on vx
^ ^ ... ^ if 0<=vx<=k, choose vxth alternative
0 1 ... k if vx is a list of length 1, case 0; else 1
~*x iterator: vx must be of the form
("str0" "str1" "str2" "str3" lst . a);
if lst is initially empty, format "str0" under a+; otherwise,
bind #\* successively to the elements of lst and then
recursively format "stri" under a+, where i=1 if there is one
element left to process, i=2 if there are two left, and i=3
otherwise.
~&x print elements of vx with ~p, separated by commas and a
final ``and''
~vx print elements of vx with ~p, separated by commas and a
final ``or''
~nx if vx is a small positive integer, print it as a word, e.g.,
seven;
if vx is a singleton containing a small positive integer, print
the corresponding ordinal as a word, e.g., seventh
~Nx like ~nx but the word is capitalized, e.g., Seven or Seventh
~tx tab out to column vx; newline first if at or past column vx
~cx vx is (n . w), print integer n right justified in field of
width w
~fx print object vx flat over as many lines as necessary
~Fx same as ~f, except that subsequent lines are indented to
start one character to the right of the first character printed
~sx if vx is a symbol, print vx, breaking on hyphens; if vx is a
string, print the characters in it, breaking on hyphens
~ tilde space: print a space
~_x print vx spaces
~
tilde newline: skip following whitespace
~% output a newline
~| output a newline unless already on left margin
~~ print a tilde
~- if close to rightmargin, output a hyphen and newline; else
skip this char
formatted printing
Parent topic: PROGRAMMING Home
ACL2 provides the functions fmt, fmt1, and fms as substitutes for Common
Lisp's format function.
All three print a given string under an alist pairing character
objects with values, interpreting certain ``tilde-directives'' in
the string. Channel must be a character output channel (e.g.,
*standard-co*).
General Forms: result (fms string alist channel state evisc-tuple) ; state (fmt string alist channel state evisc-tuple) ; (mv col state) (fmt1 string alist column channel state evisc-tuple) ; (mv col state)
Fms and fmt print an initial newline to put channel in column 0;
Fmt1 requires the current column as input. Columns are numbered
from 0. The current column is the column into which the next
character will be printed. (Thus, the current column number is also
the number of characters printed since the last newline.) The col
returned by fmt and fmt1 is the current column at the conclusion of
the formatting. Evisc-tuple must be either nil (meaning no
abbreviations are used when objects are printed) or an
``evisceration tuple'' such as that returned by
(default-evisc-tuple state).We list the tilde-directives below. The notation is explained after the chart.
~px pretty print vx (maybe after printing a newline)
~qx pretty print vx starting in current column; end with newline
~Pxy like ~px but use vy as the evisceration tuple
~Qxy like ~qx but use vy as the evisceration tuple
~@x if vx is a string, "str", recursively format "str"
if vx is ("str" . a), recursively format "str" under a+
~#x~[...~/...~/ ... ~/...~] cases on vx
^ ^ ... ^ if 0<=vx<=k, choose vxth alternative
0 1 ... k if vx is a list of length 1, case 0; else 1
~*x iterator: vx must be of the form
("str0" "str1" "str2" "str3" lst . a);
if lst is initially empty, format "str0" under a+; otherwise,
bind #\* successively to the elements of lst and then
recursively format "stri" under a+, where i=1 if there is one
element left to process, i=2 if there are two left, and i=3
otherwise.
~&x print elements of vx with ~p, separated by commas and a
final ``and''
~vx print elements of vx with ~p, separated by commas and a
final ``or''
~nx if vx is a small positive integer, print it as a word, e.g.,
seven;
if vx is a singleton containing a small positive integer, print
the corresponding ordinal as a word, e.g., seventh
~Nx like ~nx but the word is capitalized, e.g., Seven or Seventh
~tx tab out to column vx; newline first if at or past column vx
~cx vx is (n . w), print integer n right justified in field of
width w
~fx print object vx flat over as many lines as necessary
~Fx same as ~f, except that subsequent lines are indented to
start one character to the right of the first character printed
~sx if vx is a symbol, print vx, breaking on hyphens; if vx is a
string, print the characters in it, breaking on hyphens
~ tilde space: print a space
~_x print vx spaces
~
tilde newline: skip following whitespace
~% output a newline
~| output a newline unless already on left margin
~~ print a tilde
~- if close to rightmargin, output a hyphen and newline; else
skip this char
If x is a character, then vx is the value of #\x under the
current alist. When we say ``format str under a+'' we mean
recursively process the given string under an alist obtained by
appending a to the current alist.
ACL2's formatting functions print to the indicated channel, keeping
track of which column they are in. Fmt1 can be used if the caller
knows which column the channel is in (i.e., how many characters have
been printed since the last newline). Otherwise, fmt or fms must be
used, both of which output a newline so as to establish the column
position at 0. Unlike Common Lisp's format routine, fmt and its
relatives break the output into lines so as to try to avoid printing
past column 77. That number is built-into the definitions of ACL2's
formatting functions. Line breaks are automatically inserted as
necessary in place of spaces and after hyphens in the text being
printed.
The formatting functions scan the string from left to right,
printing each successive character unless it is a tilde (~). Upon
encountering tildes the formatters take action determined by the
character or characters immediately following the tilde. The
typical tilde-directive is a group of three successive characters
from the string being printed. For example, ~p0 is a 3 character
tilde-directive. The first character in a tilde-directive is always
the tilde character itself. The next character is called the
``command'' character. The character after that is usually taken as
the name of a ``format variable'' that is bound in the alist under
which the string is being printed. Format variables are, by
necessity, characters. The objects actually printed by a
tilde-directive are the objects obtained by looking up the command's
format variables in the alist. Typical format variable names are 0,
1, 2, ..., 9, a, b, c, etc., and if a tilde-directive uses the
format variable 0, as in ~p0, then the character #\0 must be bound
in the alist. Some tilde commands take no arguments and others take
more than one, so some directives are of length two and others are
longer.
It should be noted that this use of characters in the string to
denote arguments is another break from Common Lisp's format routine.
In Common Lisp, the directives refer implicitly to the ``next item
to be printed.'' But in ACL2 the directives name each item
explicitly with our format variables.
The following text contains examples that can be evaluated. To make
this process easier, we use a macro which is defined as part of ACL2
just for this documentation. The macro is named fmx and it takes up
to eleven arguments, the first of which is a format string, str, and
the others of which are taken as the values of format variables.
The variables used are #\0 through #\9. The macro constructs an
appropriate alist, a, and then evaluates
(fmt str a *standard-co* state nil).
Thus,
(fmx "Here is v0, ~p0, and here is v1, ~p1."
(cons 'value 0)
(cons 'value 1))
is just an abbreviation for
(fmt "Here is v0, ~p0, and here is v1, ~p1."
(list (cons #\0 (cons 'value 0))
(cons #\1 (cons 'value 1)))
*standard-co*
state
nil)
which returns (mv 53 state) after printing the line
Here is v0, (VALUE . 0), and here is v1, (VALUE . 1).We now devote special attention to three of the tilde-directives whose use is non-obvious.
The Case Statement
~#x is essentially a ``case statement'' in the language of fmt.
The proper form of the statement is
~#x~[case-0~/case-1~/ ... ~/case-k~],where each of the
case-i is a format string. In the most common
use, the variable x has an integer value, vx, between 0 and k,
inclusive. The effect of formatting the directive is to format
case-vx.For example
(fmx "Go ~#0~[North~/East~/South~/West~].~%" 1)will print ``Go East.'' followed by a newline and will return
(mv 0 state), while if you change the 1 above to 3 (the
maximum legal value), it will print ``Go West.''
In order to make it easier to print such phrases as ``there are
seven cases'' requiring agreement between subject and verb based on
the number of elements of a list, the case statement allows its
variable to take a list as its value and selects case-0 if the list
has length 1 and case-1 otherwise.
(let ((cases '(a b c)))
(fmx "There ~#0~[is ~n1 case~/are ~n1 cases~]."
cases
(length cases)))
will print ``There are three cases.'' but if you change the
'(a b c) above simply to '(a) it will print ``There is one
case.'' and if you change it to nil it will print ``There are
zero cases.''
Indirection
Roughly speaking, ~@ will act as though the value of its argument
is a format string and splice it into the current string at the
current position. It is often used when the phrase to be printed
must be computed. For example,
(let ((ev 'DEFUN))
(fmx "~p0 is an event~@1."
'foo
(if (member-eq ev '(defun defstub encapsulate))
" that may introduce a function symbol"
"")))
will print ``foo is an event that may introduce a function
symbol,'' but if the value of ev is changed from 'defun to 'defthm,
it prints ``foo is an event.'' The ~@ directive ``splices'' in the
computed phrase (which might be empty). Of course, this particular
example could be done with the case statement
~#1~[~/ that may introduce a function symbol~]where the value of
#\1 is appropriately computed to be 0 or 1.
If the argument to ~@ is a pair, it is taken to be a format string
consed onto an alist, i.e., ("str" . a), and the alist, a, is used
to extend the current one before "str" is recursively processed.
This feature of fmt can be used to pass around ``phrases'' that
contain computed contextual information in a. The most typical use
is as ``error messages.'' For example, suppose you are writing a
function which does not have access to state and so cannot print an
error message. It may nevertheless be necessary for it to signal an
error to its caller, say by returning two results, the first of
which is interpreted as an error message if non-nil. Our convention
is to use a ~@ pair to represent such messages. For example, the
error value might be produced by the code:
(cons
"Error: The instruction ~p0 is illegal when the stack is ~p1.~%"
(list (cons #\0 (current-instruction st))
(cons #\1 (i-stack st))))
If the current-instruction and i-stack (whatever they are) are
'(popi 3) and '(a b) when the cons above is evaluated, then it
produces
'("Error: The instruction ~p0 is illegal when the stack is ~p1.~%"
(#\0 POPI 3)
(#\1 A B))
and if this pair is made the value of the fmt variable 0, then
~@0 will print
Error: The instruction (POPI 3) is illegal when the stack is (A B).For example, evaluate
(let
((pair
'("Error: The instruction ~p0 is illegal when the stack is ~p1.~%"
(#\0 POPI 3)
(#\1 A B))))
(fmx "~@0" pair)).
Thus, even though the function that produced the ``error'' could
not print it, it could specify exactly what error message and data
are to be printed.
This example raises another issue. Sometimes it is desirable to
break lines in your format strings so as to make your source code
more attractive. That is the purpose of the tilde-newline
directive. The following code produces exactly the same output as
described above.
(let ((pair '("Error: The instruction ~p0 ~
is illegal when the stack is ~
~p1.~%"
(#\0 POPI 3)
(#\1 A B))))
(fmx "~@0" pair)).
Finally, observe that when ~@0 extends the current alist, alist,
with the one, a, in its argument, the bindings from a are added to
the front of alist, overriding the current values of any shared
variables. This insures that the variable values seen by the
recursively processed string, "str", are those from a, but if
"str" uses variables not bound in a, their values are as specified
in the original alist. Intuitively, variables bound in a are local
to the processing of ("str" . a) but "str" may use ``global
variables.'' The example above illustrates this because when the
~@0 is processed, #\0 is bound to the error message pair. But
when the ~p0 in the error string is processed, #\0 is bound to the
illegal instruction.Iteration
The ~* directive is used to process each element of a list. For
example,
(let ((lst '(a b c d e f g h))) ; a true-list whose elements we exhibit
(fmx "~*0"
`("Whoa!" ; what to print if there's nothing to print
"~p*!" ; how to print the last element
"~p* and " ; how to print the 2nd to last element
"~p*, " ; how to print all other elements
,lst))) ; the list of elements to print
will print ``A, B, C, D, E, F, G and H!''. Try this example with
other true list values of lst, such as '(a b), '(a), and nil. The
tilde-directives ~&0 and ~v0, which take a true list argument and
display its elements separated by commas and a final ``and'' or
``or,'' are implemented in terms of the more general ~*.
The ~* directive allows the 5-tuple to specify in its final cdr an
alist with which to extend the current one before processing the
individual elements.
We often use ~* to print a series of phrases, separated by suitable
punctuation, whitespace and noise words. In such use, the ~*
handles the separation of the phrases and each phrase is generally
printed by ~@.
Here is a complex example. In the let*, below, we bind phrases to a
list of ~@ pairs and then we create a ~* 5-tuple to print out the
conjunction of the phrases with a parenthetical ``finally!'' if the
series is longer than 3.
(let* ((phrases
(list (list "simplifying with the replacement rules ~&0"
(cons #\0 '(rewrite-rule1
rewrite-rule2
rewrite-rule3)))
(list "destructor elimination using ~p0"
(cons #\0 'elim-rule))
(list "generalizing the terms ~&0"
(cons #\0 '((rev x) (app u v))))
(list "inducting on ~p0"
(cons #\0 'I))))
(5-tuple
(list
"magic" ; no phrases
"~@*" ; last phrase
"~@*, and~#f~[~/ (finally!)~] " ; second to last phrase
"~@*, " ; other phrases
phrases ; the phrases themselves
(cons #\f
(if (>(length phrases) 3) 1 0))))) ;print ``finally''?
(fmx "We did it by ~*0." 5-tuple))
This let* prints
We did it by simplifying with the replacement rules REWRITE-RULE1, REWRITE-RULE2 and REWRITE-RULE3, destructor elimination using ELIM- RULE, generalizing the terms (REV X) and (APP U V), and (finally!) inducting on I.You might wish to try evaluating the
let* after removing elements
of phrases.
Most of the output produced by ACL2 is produced via fmt statements.
Thus, inspection of the source code will yield many examples. A
complicated example is the code that explains the simplifier's work.
See :pc simplify-clause-msg1. An ad hoc example is provided by the
function fmt-doc-example, which takes two arguments: an arbitrary
true list and state. To see how fmt-doc-example works, :pe
fmt-doc-example.
(fmt-doc-example '(a b c d e f g h i j k l m n o p) state)will produce the output
Here is a true list: (A B C D E F G H I J K L M N O P). It has 16 elements, the third of which is C.and returnWe could print each element in square brackets: ([A], [B], [C], [D], [E], [F], [G], [H], [I], [J], [K], [L], [M], [N], [almost there: O], [the end: P]). And if we wished to itemize them into column 15 we could do it like this 0123456789012345 0 (zeroth) A 1 (first) B 2 (second) C 3 (third) D 4 (fourth) E 5 (fifth) F 6 (sixth) G 7 (seventh) H 8 (eighth) I 9 (ninth) J 10 (tenth) K 11 (eleventh) L 12 (twelfth) M 13 (thirteenth) N 14 (14th) O 15 (15th) P End of example.
(mv 15 state).
Finally, we should remind the reader that fmt and its subfunctions,
most importantly fmt0, are written entirely in ACL2. We make this
comment for two reasons. First, it illustrates the fact that quite
low level code can be efficiently written in the language. Second,
it means that as a last resort for documentation purposes you can
read the source code without changing languages.