formatted printing
Major Section:  PROGRAMMING

ACL2 provides the functions fmt, fmt1, and fms as substitutes for Common Lisp's format function. Also see fmt!, see fmt1!, and see fms! for versions of these functions that write forms to files in a manner that allows them to be read, by avoiding using backslash (\) to break long lines.

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.

~xx  pretty print vx (maybe after printing a newline)
~yx  pretty print vx starting in current column; end with newline
~Xxy like ~xx but use vy as the evisceration tuple
~Yxy like ~yx but use vy as the evisceration tuple
~px  pretty print term (maybe with infix) vx
     (maybe after printing a newline)
~qx  pretty print term (maybe with infix) 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
~&x  print elements of vx with ~x, separated by commas and a
     final ``and''
~vx  print elements of vx with ~x, separated by commas and a
     final ``or''
~nx  if vx is a small positive integer, print it as a word, e.g.,
     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, ~x0 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 ~x0, 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).


(fmx "Here is v0, ~x0, and here is v1, ~x1."
     (cons 'value 0)
     (cons 'value 1))
is just an abbreviation for
(fmt "Here is v0, ~x0, and here is v1, ~x1."
     (list (cons #\0 (cons 'value 0))
           (cons #\1 (cons 'value 1)))
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~]."
       (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.''


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 "~x0 is an event~@1."
      (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:

  "Error:  The instruction ~x0 is illegal when the stack is ~x1.~%"
  (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 ~x0 is illegal when the stack is ~x1.~%"
  (#\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
  '("Error:  The instruction ~x0 is illegal when the stack is ~x1.~%"
    (#\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 ~x0 ~
              is illegal when the stack is ~
              (#\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 ensures 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 ~x0 in the error string is processed, #\0 is bound to the illegal instruction.


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
        "~x*!"           ; how to print the last element
        "~x* and "       ; how to print the 2nd to last element
        "~x*, "          ; 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 
              (list "destructor elimination using ~x0"
                    (cons #\0 'elim-rule))
              (list "generalizing the terms ~&0"
                    (cons #\0 '((rev x) (app u v))))
              (list "inducting on ~x0"
                    (cons #\0 'I))))
         "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.

We 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.

and return (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.