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; Written by Bob Boyer and Warren A. Hunt, Jr. (some years before that)
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
; hons-help.lisp Boyer & Hunt
(in-package "ACL2")
(include-book "gentle")
(include-book "std/alists/worth-hashing" :dir :system)
(set-state-ok t)
; In this file one may find some helpful functions and lemmas in the "HONS
; School", but none of them require "under the hood" definitions. That is, the
; "user" could do all this by himself.
(defmacro all-memoized-fns (&optional show-conditions)
(if show-conditions
'(table-alist 'memoize-table (w state))
'(strip-cars (table-alist 'memoize-table (w state)))))
; FAST ALIST UTILITIES -----------------------------------------------------
(defsection make-fal
:parents (fast-alists)
:short "Make a fast alist out of an alist."
:long "<p>Note: it is usually better to use @(see make-fast-alist).</p>
<p>@('(make-fal al name)') copies the alist AL with @(see hons-acons) to make a
fast alist that ends with NAME.</p>
<p>Typically @('name') is an atom, and it becomes the final @(see cdr) of the
new fast alist. Some atoms have special meanings, e.g., they act as size
hints; see @(see hons-acons) for details.</p>
<p>However, @('name') can also be an existing fast alist. In this case, this
fast alist is extended with the new pairs from @('al'), using @(see
hons-acons). Note that @('name') will no longer be fast after the call of
@('make-fal').</p>
<p>There's nothing under-the-hood about @('make-fal'); it just repeatedly calls
@('hons-acons'). The built-in function @(see make-fast-alist) is generally
more efficient and can be nicer to reason about because logically it is just
the identity. On the other hand, @('make-fast-alist') can't be used to extend
an existing fast alist like @('make-fal').</p>"
(defn make-fal (al name)
(cond ((atom al)
name)
((atom (car al))
(make-fal (cdr al) name))
(t
(hons-acons (caar al)
(cdar al)
(make-fal (cdr al) name))))))
(defmacro ansfl (x y)
"(ANSFL x y) returns the single value X after first flushing
the fast hash table backing for Y, if Y is a fast alist. Thus
(ANSFL X Y) = X
X must be a form that returns a single value."
`((lambda (ansfl-do-not-use-elsewhere1 ansfl-do-not-use-elsewhere2)
(declare (ignore ansfl-do-not-use-elsewhere2))
ansfl-do-not-use-elsewhere1)
,x
(flush-hons-get-hash-table-link ,y)))
; [Jared]: Removing ansfl1 since I think we don't use it?
;; (defmacro ansfl1 (x)
;; `((lambda (ansfl1-do-not-use-elsewhere1)
;; ((lambda (ansfl1-do-not-use-elsewhere1
;; ansfl1-do-not-use-elsewhere2)
;; (declare (ignore ansfl1-do-not-use-elsewhere2))
;; ansfl1-do-not-use-elsewhere1)))
;; ,x))
(defmacro ansfl-list (l x)
; (ansfl-list (a b c ...) x) -- frees a, b, c, ..., returns x
(if (atom l)
x
`(ansfl (ansfl-list ,(cdr l) ,x)
,(car l))))
(defn ansfl-last-list (r bindings)
; [Jared]: BOZO please document this. It's used in het*.
; bindings is an alist. in het* the bindings are names being bound
; like in a let*.
;
; all of the names being bound are freed, then we return r.
(if (atom bindings)
r
`(ansfl ,(ansfl-last-list r (gentle-cdr bindings))
,(gentle-caar bindings))))
(defmacro het* (bindings &rest r)
; This implementation of het* is somewhat defective in that it is
; incapable of returning multiple values. We cannot see how to fix
; it.
; this is basically let*, but we try to fast-alist-free everything that gets
; bound. which works out, in a weird kind of way, for anything that
; isn't a fast alist anyway, but is really pretty gross.
`(let* ,bindings
,@(butlast r 1)
,(ansfl-last-list (car (last r)) bindings)))
(defmacro with-fast-list (var term name form)
; bind a variable to a fast-alist created by binding every element of term to t,
; with the final name name. then run form and free var.
`(let ((,var (hons-put-list
,term
t
,name)))
(ansfl ,form ,var)))
(defn hons-put-list (keys values l)
; If there are not enough values, the last atom of values is used for
; the remaining values. If there are not as many keys as values, the
; extra values are ignored.
; Warnings: The pairs are consed onto l in what might seem to be the
; reverse order. And redundant pairs are not even consed on to l at
; all. Unless the old value of (hons-get key l) is nil, in which case
; we do cons, even if the new val is nil.
; So if you need to control the order and/or presence of the added
; pairs, write another function.
(if (atom keys)
l
(let* ((cp (consp values))
(val (if cp (car values) values))
(next-values (if cp (cdr values) values))
(old-pair (hons-get (car keys) l))
(redundant (and old-pair (hons-equal val (cdr old-pair))))
(next-l (if redundant l (hons-acons (car keys) val l))))
(hons-put-list (cdr keys) next-values next-l))))
(defund alist-keys (x)
(declare (xargs :guard t))
(cond ((atom x)
nil)
((atom (car x))
(alist-keys (cdr x)))
(t
(cons (caar x) (alist-keys (cdr x))))))
(defund alist-vals (x)
(declare (xargs :guard t))
(cond ((atom x)
nil)
((atom (car x))
(alist-vals (cdr x)))
(t
(cons (cdar x) (alist-vals (cdr x))))))
; LIST OPERATIONS USING HONS -----------------------------------------------
(defn hons-binary-append (x y)
(mbe :logic (append x y)
:exec (if (atom x)
y
(hons (car x)
(hons-binary-append (cdr x) y)))))
(defmacro hons-append (x y &rest rst)
"APPEND using HONS instead of CONS"
(xxxjoin 'hons-binary-append (cons x (cons y rst))))
(defn hons-revappend (x y)
"REVAPPEND using HONS instead of CONS"
(mbe :logic (revappend x y)
:exec (if (atom x)
y
(hons-revappend (cdr x) (hons (car x) y)))))
(defn hons-reverse (x)
"REVERSE using HONS instead of CONS"
(mbe :logic (reverse x)
:exec (if (stringp x)
(reverse x)
(hons-revappend x nil))))
(defmacro hons-list (&rest x)
"(LIST ...) using HONS instead of CONS"
(if (atom x)
nil
(list 'hons (car x) (cons 'hons-list (cdr x)))))
(defmacro hons-list* (&rest x)
"(LIST* ...) using HONS instead of CONS"
(cond ((atom x)
x)
((atom (cdr x))
(car x))
(t
(list 'hons (car x) (cons 'hons-list* (cdr x))))))
(defsection hons-make-list
:parents (fast-alists make-list)
:short "Like @(see make-list), but produces honses."
(defn hons-make-list-acc (n val ac)
(mbe :logic (make-list-ac n val ac)
:exec (if (not (posp n))
ac
(hons-make-list-acc (1- n) val (hons val ac)))))
(defmacro hons-make-list (size &key initial-element)
`(hons-make-list-acc ,size ,initial-element nil)))
; LIST OPERATIONS USING HONS-EQUAL -----------------------------------------
(defn hons-member-equal (x y)
"MEMBER-EQUAL using HONS-EQUAL for each equality check"
; [Jared]: BOZO this is exactly the same as gentle-member-equal. Why duplicate
; it? Well, maybe gentle-member-equal should actually be changed to use equal,
; and this function should be left alone.
(mbe :logic (member-equal x y)
:exec (cond ((atom y) nil)
((hons-equal x (car y)) y)
(t (hons-member-equal x (cdr y))))))
; FAST DUPLICATE CHECKING AND REMOVAL --------------------------------------
(defn hons-dups-p1 (l tab)
"Basic duplicates check; table is a fast alist that associates already-seen
elements with t."
(cond ((atom l)
(ansfl nil tab))
((hons-get (car l) tab)
(ansfl l tab))
(t
(hons-dups-p1 (cdr l)
(hons-acons (car l) t tab)))))
(encapsulate nil
(local (defthm hons-assoc-equal-hons-put-list-t
(iff (hons-assoc-equal x (hons-put-list y t rest))
(or (hons-assoc-equal x rest)
(member x y)))
:hints (("goal" :induct (hons-put-list y t rest)))))
(defthm hons-assoc-equal-hons-put-list
(implies (atom a)
(iff (hons-assoc-equal x (hons-put-list y t a))
(member x y)))))
(defn hons-dups-p (l)
; If L has no duplicate members, then (HONS-DUPS-P L) is NIL. If L
; has equal members, then (HONS-DUPS-P l) returns the second tail of L
; whose CAR is the first member of L that occurs twice in L.
; [Jared]: BOZO stylistically, would it be better to free the table in this
; function, rather than in hons-dups-p1?
(hons-dups-p1 l '*hons-dups-p*))
(local (in-theory (enable alist-keys)))
(local (defthm member-alist-keys
(iff (member x (alist-keys y))
(hons-assoc-equal x y))))
(encapsulate
nil
(local (defthm intersectp-cons-second
(implies (intersectp x y)
(intersectp x (cons z y)))))
(local (defthm intersectp-cons-second-2
(implies (not (intersectp x y))
(iff (intersectp x (cons z y))
(member z x)))))
(local (defthm intersectp-cons-member
(implies (member z x)
(intersectp x (cons z y)))))
(local (defthm hons-dups-p1-no-duplicatesp
(iff (hons-dups-p1 x tab)
(or (not (no-duplicatesp x))
(intersectp x (alist-keys tab))))
:hints(("Goal" :induct (hons-dups-p1 x tab)))))
(defthm hons-dups-p-no-duplicatesp
(iff (hons-dups-p x)
(not (no-duplicatesp x)))))
(local (in-theory (disable hons-dups-p)))
(defun fast-no-duplicatesp (x)
(declare (xargs :guard (eqlable-listp x)))
(mbe :logic (no-duplicatesp-equal x)
:exec (if (< (length x) 400)
(no-duplicatesp x)
(not (hons-dups-p x)))))
(defun fast-no-duplicatesp-equal (x)
(declare (xargs :guard (true-listp x)))
(mbe :logic (no-duplicatesp-equal x)
:exec (if (< (length x) 400)
(no-duplicatesp-equal x)
(not (hons-dups-p x)))))
(defun fast-no-duplicatesp-eq (x)
(declare (xargs :guard (symbol-listp x)))
(mbe :logic (no-duplicatesp-equal x)
:exec (if (< (length x) 400)
(no-duplicatesp-eq x)
(not (hons-dups-p x)))))
(defn hons-duplicates1 (l tab)
(cond ((atom l) (ansfl nil tab))
((hons-get (car l) tab)
(cons (car l) (hons-duplicates1 (cdr l) tab)))
(t (hons-duplicates1 (cdr l) (hons-acons (car l) t tab)))))
(defn hons-duplicates (l)
(hons-duplicates1 l nil))
; SUBLIS WITH FAST ALISTS AND MEMOIZATION ----------------------------------
(defsection hons-sublis-aux
:parents (hons-sublis)
:short "Memoized core of @(see hons-sublis)."
(defun hons-sublis-aux (fal x)
(declare (xargs :guard t))
(if (atom x)
(let ((pair (hons-get x fal)))
(if pair (cdr pair) x))
(cons (hons-sublis-aux fal (car x))
(hons-sublis-aux fal (cdr x)))))
(encapsulate
()
(local (defthm lemma
(implies (alistp x)
(equal (hons-assoc-equal a x)
(assoc a x)))
:hints(("Goal" :induct (len x)))))
(defthm hons-sublis-aux-removal
(implies (alistp fal)
(equal (hons-sublis-aux fal x)
(sublis fal x)))))
(make-event
(if (hons-enabledp state)
'(memoize 'hons-sublis-aux :condition '(consp x))
'(value-triple :skipping-memoization))))
(defsection hons-sublis
:parents (hons sublis)
:short "@(tsee memoize)d version of SUBLIS which uses @(see fast-alists)."
:long "<p>@('(hons-sublis fal x)') is like @(see sublis), but may be faster
in two ways.</p>
<ol>
<li>It uses @(see hons-get) instead of @(see assoc), which may provide a
speedup when the alist in question is very long. Note that for good
performance, the fast-alist argument, @('fal'), must be a valid
fast-alist.</li>
<li>It uses a memoized auxiliary function, which may provide a speedup when the
tree argument, @('x'), contains large, shared structures.</li>
</ol>"
(defun hons-sublis (fal x)
(declare (xargs :guard t))
(let ((ret (hons-sublis-aux fal x)))
(prog2$
(clear-memoize-table 'hons-sublis-aux)
ret)))
(defthm hons-sublis-removal
(implies (alistp fal)
(equal (hons-sublis fal x)
(sublis fal x)))))
; SET OPERATIONS USING HONS ------------------------------------------------
; Some "fast" operations for "set" intersection, union, and set-diff
; intended for use on lists of ACL2 objects without duplications.
(defconst *magic-number-for-hashing*
18
"Assoc is sometimes faster than gethash.~/
Lisp folklore says it is faster to use ASSOC than GETHASH on a list
if the list has length 18 or less.~/~/")
; [Jared] BOZO it would be nice to prove these equivalent to simple set
; operations with no fast alist stuff.
(defn hons-int1 (l1 al2)
(cond ((atom l1)
nil)
((hons-get (car l1) al2)
(cons (car l1) (hons-int1 (cdr l1) al2)))
(t
(hons-int1 (cdr l1) al2))))
(defn hons-intersection2 (l1 l2)
(cond ((atom l1)
nil)
((hons-member-equal (car l1) l2)
(cons (car l1) (hons-intersection2 (cdr l1) l2)))
(t
(hons-intersection2 (cdr l1) l2))))
(defn hons-intersection (l1 l2) ; preserves order of members in l1
(cond ((worth-hashing l2)
(with-fast-list fl2 l2 '*hons-intersection-alist*
(hons-int1 l1 fl2)))
(t
(hons-intersection2 l1 l2))))
(encapsulate
nil
(local
(defthm hons-int1-is-intersection-equal
(implies (atom atom)
(equal (hons-int1 x (hons-put-list y t atom))
(intersection-equal x y)))
:hints(("Goal" :in-theory (enable intersection-equal)))))
(local
(defthm hons-intersection2-is-intersection-equal
(equal (hons-intersection2 x y)
(intersection-equal x y))
:hints(("Goal" :in-theory (enable intersection-equal)))))
(defthm hons-intersection-is-intersection-equal
(equal (hons-intersection a b)
(intersection-equal a b))))
(defn hons-intersect-p1 (l1 al2)
(cond ((atom l1)
nil)
((hons-get (car l1) al2)
t)
(t
(hons-intersect-p1 (cdr l1) al2))))
(defn hons-intersect-p2 (l1 l2)
(cond ((atom l1) nil)
((hons-member-equal (car l1) l2)
t)
(t
(hons-intersect-p2 (cdr l1) l2))))
(defn hons-intersect-p (l1 l2) ; returns T or NIL
(cond ((and (worth-hashing l1)
(worth-hashing l2))
(with-fast-list fl2 l2 '*hons-intersect-p-alist*
(hons-intersect-p1 l1 fl2)))
(t
(hons-intersect-p2 l1 l2))))
(encapsulate
nil
(local
(defthm hons-intersect-p1-is-intersectp
(implies (atom atom)
(equal (hons-intersect-p1 x (hons-put-list y t atom))
(intersectp x y)))
:hints(("Goal" :in-theory (enable intersectp)))))
(local
(defthm hons-intersect-p2-is-intersectp
(equal (hons-intersect-p2 x y)
(intersectp x y))
:hints(("Goal" :in-theory (enable intersectp)))))
(defthm hons-intersect-p-is-intersectp
(equal (hons-intersect-p a b)
(intersectp a b))))
(defn hons-sd1 (l1 al2)
(cond ((atom l1) nil)
((hons-get (car l1) al2)
(hons-sd1 (cdr l1) al2))
(t (cons (car l1) (hons-sd1 (cdr l1) al2)))))
(defn hons-set-diff2 (l1 l2)
(cond ((atom l1) nil)
((hons-member-equal (car l1) l2)
(hons-set-diff2 (cdr l1) l2))
(t (cons (car l1) (hons-set-diff2 (cdr l1) l2)))))
(defn hons-set-diff (l1 l2) ; preserves order of members in l1
(cond ((worth-hashing l2)
(with-fast-list fl2 l2 '*hons-set-diff-alist*
(hons-sd1 l1 fl2)))
(t (hons-set-diff2 l1 l2))))
(encapsulate
nil
(local
(defthm hons-sd1-is-set-difference$
(implies (atom atom)
(equal (hons-sd1 x (hons-put-list y t atom))
(set-difference$ x y)))
:hints(("Goal" :in-theory (enable set-difference$)))))
(local
(defthm hons-set-diff2-is-set-difference$
(equal (hons-set-diff2 x y)
(set-difference$ x y))
:hints(("Goal" :in-theory (enable set-difference$)))))
(defthm hons-set-diff-is-set-difference$
(equal (hons-set-diff a b)
(set-difference$ a b))))
(defn hons-union1 (l1 al2 acc)
(cond ((atom l1) acc)
((hons-get (car l1) al2)
(hons-union1 (cdr l1) al2 acc))
(t (hons-union1 (cdr l1) al2 (cons (car l1) acc)))))
(defn hons-union2 (l1 l2 acc)
(cond ((atom l1) acc)
((hons-member-equal (car l1) l2)
(hons-union2 (cdr l1) l2 acc))
(t (hons-union2 (cdr l1) l2 (cons (car l1) acc)))))
;; variant like hons-sd1, hons-int1 where fl2 doubles as the accumulator,
;; and therefore does not collect duplicates; useful for unioning together many lists
(defn hons-un1 (l1 fl2)
(cond ((atom l1) fl2)
((hons-get (car l1) fl2)
(hons-un1 (cdr l1) fl2))
(t (hons-un1 (cdr l1) (hons-acons (car l1) t fl2)))))
(defn hons-union (l1 l2)
; HONS-UNION may run faster if L1 and L2 are lists of atoms or honsps,
; since HONS-MEMBER-EQUAL and HONS-GET may be used.
; To prove someday:
; (defthm hons-union-thm
; (equal (gentle-member x (hons-union l1 l2))
; (or (gentle-member x l1)
; (gentle-member x l2))))
(cond ((atom l1) l2)
((atom l2) l1)
((atom (cdr l1))
(if (hons-member-equal (car l1) l2)
l2
(cons (car l1) l2)))
((atom (cdr l2))
(if (hons-member-equal (car l2) l1)
l1
(cons (car l2) l1)))
(t
;; [Jared]: calling len on both lists seems inefficient; we could
;; write a cdr-both style function that determines which is longer
;; BOZO This is a very messy optimization, and the benchmarks below
;; suggest that it might be backward. What is our goal? If we want
;; to produce the shortest list containing the union of our elements,
;; then we're going about it all wrong in any case. If we just want
;; any list containing the union, and we want to get it as fast as
;; possible, we're better off putting only the shorter list into the
;; fal; here we're using the longer list instead.
(let ((len1 (len l1))
(len2 (len l2)))
(cond ((and (>= len2 len1)
(>= len1 *magic-number-for-hashing*))
(with-fast-list
fl2 l2 '*hons-union*
(hons-union1 l1 fl2 l2)))
((and (>= len1 len2)
(>= len2 *magic-number-for-hashing*))
(with-fast-list
fl1 l1 '*hons-union*
(hons-union1 l2 fl1 l1)))
(t (hons-union2 l1 l2 l2)))))))
;; (let ((l1 (loop for i from 1 to 10 collect i))
;; (l2 (loop for i from 1 to 1000 collect i)))
;; (progn
;; (time$ (loop for i from 1 to 1000 collect
;; (with-fast-list fl2 l2 '*hons-union*
;; (hons-union1 l1 fl2 l2))))
;; nil)) ;; 0.43 seconds, 102 MB
;; (let ((l1 (loop for i from 1 to 10 collect i))
;; (l2 (loop for i from 1 to 1000 collect i)))
;; (progn
;; (time$ (loop for i from 1 to 1000 collect
;; (with-fast-list fl1 l1 '*hons-union*
;; (hons-union1 l2 fl1 l1))))
;; nil)) ;; 0.10 seconds, 18 MB (!!)
;; (let ((l1 (loop for i from 1 to 10 collect i))
;; (l2 (loop for i from 1 to 1000 collect i)))
;; (progn
;; (time$ (loop for i from 1 to 1000 collect
;; (with-fast-list fl1 l1 '*hons-union*
;; (hons-un1 l2 fl1))))
;; nil)) ;; 0.42 seconds, 101 MB
;; (let ((l1 (loop for i from 1 to 10 collect i))
;; (l2 (loop for i from 1 to 1000 collect i)))
;; (progn
;; (time$ (loop for i from 1 to 1000 collect
;; (with-fast-list fl2 l2 '*hons-union*
;; (hons-un1 l1 fl2))))
;; nil)) ;; 0.43 seconds, 102 MB
;; (let ((l1 (loop for i from 1 to 10 collect i))
;; (l2 (loop for i from 1 to 20 nconc
;; (loop for i from 1 to 50 collect i))))
;; (progn
;; (time$ (loop for i from 1 to 1000 collect
;; (with-fast-list fl2 l2 '*hons-union*
;; (hons-union1 l1 fl2 l2))))
;; nil)) ;; 0.11 seconds, 3.3 MB
;; (let ((l1 (loop for i from 1 to 10 collect i))
;; (l2 (loop for i from 1 to 20 nconc
;; (loop for i from 1 to 50 collect i))))
;; (progn
;; (time$ (loop for i from 1 to 1000 collect
;; (with-fast-list fl1 l1 '*hons-union*
;; (hons-union1 l2 fl1 l1))))
;; nil)) ;; 0.10 seconds, 15 MB
;; Note that because hons-union1 and 2 accumulate the first arg onto the second
;; arg in reverse order, it's not the same as union$.
(encapsulate nil
(local (defthm hons-union1-revappend-set-difference
(equal (hons-union1 x tab y)
(revappend (set-difference$ x (alist-keys tab)) y))))
(local (defthm hons-union2-revappend-set-difference
(equal (hons-union2 x l y)
(revappend (set-difference$ x l) y))))
;; bozo prove something about hons-union, but maybe fix it first
)
(defn hons-union-list (l)
(if (atom l)
nil
(hons-union (car l)
(hons-union-list (cdr l)))))
(defn hons-subset1 (l al)
(or (atom l)
(and (hons-get (car l) al)
(hons-subset1 (cdr l) al))))
(defn hons-subset2 (l1 l2)
(cond ((atom l1) t)
((hons-member-equal (car l1) l2)
(hons-subset2 (cdr l1) l2))))
(defn hons-subset (l1 l2)
(cond ((worth-hashing l2)
(with-fast-list fl2 l2 '*hons-subset-alist*
(hons-subset1 l1 fl2)))
(t (hons-subset2 l1 l2))))
(defn hons-set-equal (l1 l2)
(and (hons-subset l1 l2)
(hons-subset l2 l1)))
; DEFHONST -----------------------------------------------------------------
;; [Jared]: bozo new hons means defhonst changes...
;; Defhonst is like defconst.
;; The record for all defhonst values is kept in the ACL2 global
;; 'defhonst. To flush all defhonst records manually, one may:
;; (f-put-global 'defhonst nil state).
; [Jared]: if defhonst is really like defconst, then why have it? What's the
; difference? Why is it desirable? We should have some documentation for it.
; It seems there are a couple of consequences of using defhonst, e.g.,
; persistent hons table, evisceration, etc.
;; [Jared]: removed this, but not sure what it was for.
;; (defmacro update-defhonst (f r)
;; `(let ((f ,f) (r ,r))
;; (pprogn
;; (f-put-global
;; 'defhonst
;; (hons (hons (cadr r)
;; (concatenate 'string "," (symbol-name f)))
;; (if (boundp-global 'defhonst state)
;; (get-global 'defhonst state)
;; nil))
;; state)
;; (value f))))
(defmacro defhonst (name form &key (evisc 'nil eviscp) check doc)
; From Matt Mon Sep 29 09:53:49 CDT 2008
`(with-output
:off summary
(progn
;; [Jared]: switched to hons-copy-persistent
(defconst ,name (hons-copy-persistent ,form) ,doc)
(table evisc-table
,name
,(if eviscp
evisc
(let ((str (symbol-name name)))
(if (may-need-slashes str)
(concatenate 'string "#.|" str "|")
(concatenate 'string "#." str)))))
;; [Jared]: removed the table event
;; (table persistent-hons-table
;; (let ((x ,name))
;; (if (or (consp x) (stringp x))
;; ; honsp-check without check
;; x
;; nil))
;; t)
,@(and check
`((assert-event ,check)))
(value-triple ',name))))
; UNRELATED TO HONS --------------------------------------------------------
; [Jared]: BOZO why is this stuff in hons-help.lisp? What does any of this
; have to do with hons? Can we move this elsewhere?
; [Jared]: moved plev stuff to tools/plev.lisp
; [Jared] removing FAIL from the manual to discourage its use. I generally
; think we should encourage the use of ER or IMPOSSIBLE instead.
;; "There are no axioms about FAIL except the equality axioms.
;; One can prove:
;; (thm (implies (and (equal x1 x2) (equal y1 y2))
;; (equal (fail x1 y1) (fail x2 y2))))
;; However, if FAIL is called at run-time, an error occurs.
;; FAIL can perhaps be understood in analogy with the notion of a
;; 'resource error'. Though one can prove:
;; (thm (implies (posp n) (consp (make-list n))))
;; what will happen if one invokes (make-list (expt 2 2000))? It is
;; hard to predict, but eventually, something like an error will
;; occur."
(defstub fail (x y)
; [Jared]: find a better place for this?
t)
|