# FUNCTION

# Public

# *V (&REST XS)

Constrains its arguments to be numbers. If called with no arugments,
returns 1. If called with a single argument, returns its value. If called with
more than two arguments, behaves as nested sequence of two-argument calls:
(*V X1 X2 ... Xn) = (*V X1 (*V X2 (*V ...)))
When called with two arguments, if both arguments are bound, returns the
product of their values. If either argument is known to equal zero, returns
zero. If either argument is known to equal one, returns the value of the other.
Otherwise returns number variable V.
* Product of X1 and X2 is constrained to equal V. This includes constraining
their bounds appropriately. If it becomes known that cannot be true, FAIL
is called.
* If both arguments are known to be reals, V is constrained to be real.
* If both arguments are known to be integers, V is constained to be integer.
* If V is known to be an integer, and either X1 or X2 is known to be real,
both X1 and X2 are constrained to be integers.
* If V is known to be an reals, and either X1 or X2 is known to be real,
both X1 and X2 are constrained to be reals.
Note: Numeric contagion rules of Common Lisp are not applied if either
argument equals zero or one.

# +V (&REST XS)

Constrains its arguments to be numbers. Returns 0 if called with no
arguments. If called with a single argument, returns its value. If called with
more than two arguments, behaves as nested sequence of two-argument calls:
(+V X1 X2 ... Xn) = (+V X1 (+V X2 (+V ...)))
When called with two arguments, if both arguments are bound, returns the sum
of their values. If either argument is known to be zero, returns the value of
the remaining argument. Otherwise returns number variable V.
* Sum of X1 and X2 is constrained to equal V. This includes constraining
their bounds appropriately. If it becomes known that cannot be true, FAIL
is called.
* If both arguments are known to be reals, V is constrained to be real.
* If both arguments are known to be integers, V is constained to be integer.
* If one argument is known to be a non-integer, and the other is known to
be a real, V is constrained to be a non-integer.
* If one argument is known to be a non-real, and the other is known
to be a real, V is constrained to be non-real.
Note: Numeric contagion rules of Common Lisp are not applied if either
argument equals zero.

# -V (X &REST XS)

Constrains its arguments to be numbers. If called with a single argument,
behaves as if the two argument call:
(-V 0 X)
If called with more than two arguments, behaves as nested sequence of
two-argument calls:
(-V X1 X2 ... Xn) = (-V X1 (-V X2 (-V ...)))
When called with two arguments, if both arguments are bound, returns the
difference of their values. If X2 is known to be zero, returns the value of
X1. Otherwise returns number variable V.
* Difference of X1 and X2 is constrained to equal V. This includes
constraining their bounds appropriately. If it becomes known that cannot
be true, FAIL is called.
* If both arguments are known to be reals, V is constrained to be real.
* If both arguments are known to be integers, V is constained to be integer.
* If one argument is known to be a non-integer, and the other is known to
be a real, V is constrained to be a non-integer.
* If one argument is known to be a non-real, and the other is known
to be a real, V is constrained to be non-real.
Note: Numeric contagion rules of Common Lisp are not applied if X2 equals zero.

# /=V (X &REST XS)

Returns a boolean value which is constrained to be T if no two arguments
are numerically equal, and constrained to be NIL if any two or more arguments
are numerically equal.
This function takes one or more arguments. All of the arguments are restricted
to be numeric.
Returns T when called with one argument. A call such as (/=V X1 X2 ... Xn)
with more than two arguments behaves like a conjunction of two argument calls:
(ANDV (/=V X1 X2) ... (/=V X1 Xn)
(/=V X2 X3) ... (/=V X2 Xn)
...
(/=V Xi Xi+1 ... (/=V Xi Xn)
...
(/=V Xn-1 xn))
When called with two arguments, returns T if X1 is known not to be equal to X2
at the time of call, NIL if X1 is known to be equal to X2 at the time of
call, and otherwise a new boolean variable V.
Two numeric values are known not to be equal when their domains are disjoint.
Two real values are known not to be equal when their ranges are disjoint, i.e.
the upper bound of one is greater than the lower bound of the other.
Two numeric values are known to be equal only when they are both bound and
equal according to the Common Lisp function =.
When a new variable is created, the values of X1, X2 and V are mutually
constrained via noticers so that V is equal to T if and only if X1 is known
not to be equal to X2 and V is equal to NIL if and only if X1 is known to be
equal to X2.
* If it later becomes known that X1 is not equal to X2, noticers attached to
X1 and X2 restrict V to equal T. Likewise, if it later becomes known that X1
is equal to X2, noticers attached to X1 and X2 restrict V to equal NIL.
* If V ever becomes known to equal T then a noticer attached to V restricts X1
to not be equal to X2. Likewise, if V ever becomes known to equal NIL then a
noticer attached to V restricts X1 to be equal to X2.
Restricting two values X1 and X2 to be equal is performed by attaching
noticers to X1 and X2. These noticers continually restrict the domains of X1
and X2 to be equivalent sets (using the Common Lisp function = as a test
function) as their domains are restricted. Furthermore, if X1 is known to be
real then the noticer attached to X2 continually restrict the upper bound of
X1 to be no higher than the upper bound of X2 and the lower bound of X1 to be
no lower than the lower bound of X2. The noticer of X2 performs a symmetric
restriction on the bounds of X1 if it is known to be real.
Restricting two values X1 and X2 to not be equal is also performed by
attaching noticers to X1 and X2. These noticers however, do not restrict the
domains or ranges of X1 or X2. They simply monitor their continually
restrictions and fail when any assertion causes X1 to be known to be equal to
X2.

# /V (X &REST XS)

Constrains its arguments to be numbers. If called with a single argument,
behaves as the two argument call:
(/V 1 X)
If called with more than two arguments, behaves as nested sequence of
two-argument calls:
(/V X1 X2 ... Xn) = (/V ... (/V (/V X1 X2) X3) ... Xn)
When called with two arguments, if both arguments are bound, returns the
division of their values. If X1 is known to equal zero, returns 0. If X2 is
known to equal zero, FAIL is called. If X2 is known to equal one, returns the
value of X1. Otherwise returns number variable V.
* Division of X1 and X2 is constrained to equal V. This includes
constraining their bounds appropriately. If it becomes known that cannot
be true, FAIL is called.
* If both arguments are known to be reals, V is constrained to be real.
* If both arguments are known to be integers, V is constained to be integer.
* If V is known to be an integer, and either X1 or X2 is known to be real,
both X1 and X2 are constrained to be integers.
* If V is known to be an reals, and either X1 or X2 is known to be real,
both X1 and X2 are constrained to be reals.
Note: Numeric contagion rules of Common Lisp are not applied if X1 equals zero
or X2 equals one.

# <=V (X &REST XS)

All arguments are constrained to be real. Returns T when called with one
argument. A call such as (<=V X1 X2 ... Xn) with more than two arguments
behaves like a conjunction of two argument calls:
(ANDV (<=V X1 X2) ... (<=V Xi Xi+1) ... (<=V Xn-1 Xn))
When called with two arguments, returns T if X1 is know to be less than or equal to X2
at the time of the call, NIL if X1 is known to be greater than X2, and otherwise a new
boolean variable V.
Values of V, X1, and X2 are mutually constrained:
* V is equal to T iff X1 is known to be less than or equal to X2.
* V is equal to NIL iff X2 is known to be greater than X2.
* If V is known to be T, X1 is constrained to be less than or equal to X2.
* If V is known to be NIL, X1 is constrained to be greater than X2.

# <V (X &REST XS)

Returns a boolean value which is constrained to be T if each argument Xi is
less than the following argument Xi+1 and constrained to be NIL if some
argument Xi is greater than or equal to the following argument Xi+1.
This function takes one or more arguments. All of the arguments are restricted
to be real.
Returns T when called with one argument. A call such as (<V X1 X2 ... Xn)
with more than two arguments behaves like a conjunction of two argument calls:
(ANDV (<V X1 X2) ... (<V Xi Xi+1 ) ... (<V Xn-1 Xn))
When called with two arguments, returns T if X1 is known to be less than X2 at
the time of call, NIL if X1 is known to be greater than or equal to X2 at the
time of call, and otherwise a new boolean variable V.
A real value X1 is known to be less than a real value X2 if X1 has an upper
bound, X2 has a lower bound and the upper bound of X1 is less than the lower
bound of X2.
A real value X1 is known to be greater than or equal to a real value X2 if X1
has a lower bound, X2 has an upper bound and the lower bound of X1 is greater
than or equal to the upper bound of X2.
When a new variable is created, the values of X1, X2 and v are mutually
constrained via noticers so that V is equal to T if and only if X1 is known to
be less than X2 and V is equal to NIL if and only if X1 is known to be greater
than or equal to X2.
* If it later becomes known that X1 is less than X2, noticers attached to X1
and X2 restrict V to equal T. Likewise, if it later becomes known that X1 is
greater than or equal to X2, noticers attached to X1 and X2 restrict V to
equal NIL.
* If V ever becomes known to equal T then a noticer attached to V restricts X1
to be less than X2. Likewise, if V ever becomes known to equal NIL then a
noticer attached to V restricts X1 to be greater than or equal to X2.
Restricting a real value X1 to be less than a real value X2 is performed by
attaching noticers to X1 and X2. The noticer attached to X1 continually
restricts the lower bound of X2 to be no lower than the upper bound of X1 if
X1 has an upper bound. The noticer attached to X2 continually restricts the
upper bound of X1 to be no higher than the lower bound of X2 if X2 has a lower
bound. Since these restrictions only guarantee that X1 be less than or equal
to X2, the constraint that X1 be strictly less than X2 is enforced by having
the noticers fail when both X1 and X2 become known to be equal.
Restricting a real value X1 to be greater than or equal to a real value X2 is
performed by an analogous set of noticers without this last equality check.

# =V (X &REST XS)

Returns a boolean value which is constrained to be T if all of the
arguments are numerically equal, and constrained to be NIL if two or more of
the arguments numerically differ.
This function takes one or more arguments. All of the arguments are restricted
to be numeric.
Returns T when called with one argument. A call such as (=V X1 X2 ... Xn)
with more than two arguments behaves like a conjunction of two argument calls:
(ANDV (=V X1 X2) ... (=V Xi Xi+1) ... (=V Xn-1 Xn))
When called with two arguments, returns T if X1 is known to be equal to X2 at
the time of call, NIL if X1 is known not to be equal to X2 at the time of
call, and a new boolean variable V if is not known if the two values are
equal.
Two numeric values are known to be equal only when they are both bound and
equal according to the Common Lisp function =.
Two numeric values are known not to be equal when their domains are disjoint.
Furthermore, two real values are known not to be equal when their ranges are
disjoint, i.e. the upper bound of one is greater than the lower bound of the
other.
When a new variable is created, the values of X1, X2, and V are mutually
constrained via noticers so that V is equal to T if and only if X1 is known to
be equal to X2, and V is equal to NIL if and only if X1 is known not to be
equal to X2.
* If it later becomes known that X1 is equal to X2 noticers attached to X1 and
X2 restrict V to equal T. Likewise if it later becomes known that X1 is not
equal to X2 noticers attached to X1 and X2 restrict V to equal NIL.
* If V ever becomes known to equal T then a noticer attached to V restricts X1
to be equal to X2. Likewise if V ever becomes known to equal NIL then a
noticer attached to V restricts X1 not to be equal to X2.
* If X1 is known to be real then the noticer attached to X2 continually
restrict the upper bound of X1 to be no higher than the upper bound of X2
and the lower bound of X1 to be no lower than the lower bound of X2.
Likewise for bounds of X1 if X2 is known to be real.
Restricting two values x1 and x2 to be equal is performed by attaching
noticers to x1 and x2. These noticers continually restrict the domains of x1
and x2 to be equivalent sets (using the Common Lisp function = as a test
function) as their domains are restricted.
Restricting two values X1 and X2 to not be equal is also performed by
attaching noticers to X1 and X2. These noticers however do not restrict the
domains or ranges of X1 or X2. They simply monitor their continually
restrictions and fail when any assertion causes X1 to be known to be equal to
X2.

# >=V (X &REST XS)

All arguments are constrained to be real. Returns T when called
with one argument. A call such as (>=V X1 X2 ... Xn) with more than two
arguments behaves like a conjunction of two argument calls:
(ANDV (>=V X1 X2) ... (>=V Xi Xi+1) ... (>=V Xn-1 Xn))
When called with two arguments, returns T if X1 is know to be greater than or
equal to X2 at the time of the call, NIL if X1 is known to be less than X2,
and otherwise a new boolean variable V.
Values of V, X1, and X2 are mutually constrained:
* V is equal to T iff X1 is known to be greater than or equal to X2.
* V is equal to NIL iff X2 is know to be less than X2.
* If V is known to be T, X1 is constrained to be greater than or equal to X2.
* If V is known to be NIL, X1 is constrained to be less than X2.

# >V (X &REST XS)

All arguments are constrained to be real. Returns T when called with one
argument. A call such as (>V X1 X2 ... Xn) with more than two arguments
behaves like a conjunction of two argument calls:
(ANDV (> X1 X2) ... (> Xi Xi+1) ... (> Xn-1 Xn))
When called with two arguments, returns T if X1 is know to be greater than X2
at the time of the call, NIL if X1 is known to be less than or equal to X2,
and otherwise a new boolean variable V.
Values of V, X1, and X2 are mutually constrained:
* V is equal to T iff X1 is known to be greater than X2.
* V is equal to NIL iff X2 is known to be less than or equal to X2.
* If V is known to be T, X1 is constrained to be greater than X2.
* If V is known to be NIL, X1 is constrained to be less than or equal to X2.

# A-BOOLEAN

Equivalent to (EITHER T NIL).

# A-BOOLEANV (&OPTIONAL (NAME NIL NAME?))

Returns a boolean variable.

# A-MEMBER-OF (SEQUENCE)

Nondeterministically returns an element of SEQUENCE. The elements are
returned in the order that they appear in SEQUENCE. The SEQUENCE must be
either a list or a vector.

# A-MEMBER-OFV (VALUES &OPTIONAL (NAME NIL NAME?))

Returns a variable whose value is constrained to be one of VALUES.
VALUES can be either a vector or a list designator.

# A-NUMBERV (&OPTIONAL (NAME NIL NAME?))

Returns a variable whose value is constained to be a number.

# A-REAL-ABOVEV (LOW &OPTIONAL (NAME NIL NAME?))

Returns a real variable whose value is constrained to be greater than or equal to LOW.

# A-REAL-BELOWV (HIGH &OPTIONAL (NAME NIL NAME?))

Returns a real variable whose value is constrained to be less than or equal to HIGH.

# A-REAL-BETWEENV (LOW HIGH &OPTIONAL (NAME NIL NAME?))

Returns a real variable whose value is constrained to be greater than or
equal to low and less than or equal to high. If the resulting real variable is
bound, its value is returned instead. Fails if it is known that low is greater
than high at the time of call.
The expression (A-REAL-BETWEENV LOW HIGH) is an abbreviation for:
(LET ((V (MAKE-VARIABLE)))
(ASSERT! (REALPV V))
(ASSERT! (>=V V LOW))
(ASSERT! (<=V V HIGH))
(VALUE-OF V))

# A-REALV (&OPTIONAL (NAME NIL NAME?))

Returns a real variable.

# AN-INTEGER

Generator yielding integers in sequence 0, 1, -1, 2, -2, ...

# AN-INTEGER-ABOVE (LOW)

Generator yielding integers starting from LOW and continuing sequentially
in increasing direction.

# AN-INTEGER-ABOVEV (LOW &OPTIONAL (NAME NIL NAME?))

Returns an integer variable whose value is constrained to be greater than
or equal to LOW.

# AN-INTEGER-BELOW (HIGH)

Generator yielding integers starting from HIGH and continuing sequentially
in decreasing direction.

# AN-INTEGER-BELOWV (HIGH &OPTIONAL (NAME NIL NAME?))

Returns an integer variable whose value is constrained to be less than or
equal to HIGH.

# AN-INTEGER-BETWEEN (LOW HIGH)

Nondeterministically returns an integer in the closed interval [LOW, HIGH].
The results are returned in ascending order. Both LOW and HIGH must be
integers. Fails if the interval does not contain any integers.

# AN-INTEGER-BETWEENV (LOW HIGH &OPTIONAL (NAME NIL NAME?))

Returns an integer variable whose value is constrained to be greater than
or equal to LOW and less than or equal to HIGH. If the resulting integer
variable is bound, its value is returned instead. Fails if it is known that
there is no integer between LOW and HIGH at the time of call.
The expression (AN-INTEGER-BETWEENV LOW HIGH) is an abbreviation for:
(LET ((V (MAKE-VARIABLE)))
(ASSERT! (INTEGERPV V))
(ASSERT! (>=V V LOW))
(ASSERT! (<=V V HIGH))
(VALUE-OF v))

# AN-INTEGERV (&OPTIONAL (NAME NIL NAME?))

Returns an integer variable.

# ANDV (&REST XS)

Restricts each argument to be boolean.
Returns T if called with no arguments, or if all arguments are known to equal
T after being restricted to be boolean, and returns NIL if any argument is
known to equal NIL after this restriction.
Otherwise returns a boolean variable V. The values of the arguments and V are
mutually constrained:
* If any argument is later known to equal NIL value of V becomes NIL.
* If all arguments are later known to equal T, value of V becomes T.
* If value of V is later known to equal T, all arguments become T.
* If value of V is later known to equal NIL, and all but one argument is
known to be T, the remaining argument becomes NIL.
Note that unlike CL:AND, ANDV is a function and always evaluates all its
arguments. Secondly, any non-boolean argument causes it to fail.

# APPLY-NONDETERMINISTIC (FUNCTION &REST ARGUMENTS)

Analogous to the CL:APPLY, except FUNCTION can be either a nondeterministic
function, or an ordinary deterministic function.
You must use APPLY-NONDETERMINISTIC to apply a nondeterministic function. An
error is signalled if a nondeterministic function object is used with
CL:APPLY.
You can use APPLY-NONDETERMINISTIC to apply either a deterministic or
nondeterministic function, though even if all of the ARGUMENTS are
deterministic and FUNCTION is a deterministic function object, the call
expression will still be nondeterministic (with presumably a single value),
since it is impossible to determine at compile time that a given call to
APPLY-NONDETERMINISTIC will be passed only deterministic function objects for
function.

# APPLY-SUBSTITUTION (X)

If X is a CONS, or a variable whose value is a CONS, returns
a freshly consed copy of the tree with all variables dereferenced.
Otherwise returns the value of X.

# APPLYV (F X &REST XS)

F must be a deterministic function. If all arguments X are bound, returns
the result of calling F on the dereferenced values of spread arguments.
Otherwise returns a fresh variable V, constrained to be equal to the result
of calling F on the dereferenced values of arguments.
Additionally, if all but one of V and the argument variables become known, and
the remaining variable has a finite domain, then that domain is further
restricted to be consistent with other arguments.

# BOOLEANP (X)

Returns true iff X is T or NIL.

# BOOLEANPV (X)

The expression (BOOLEANPV X) is an abbreviation for (MEMBERV X '(T NIL)).

# BOUND? (X)

Returns T if X is not a variable or if X is a bound variable. Otherwise
returns NIL. BOUND? is analogous to the extra-logical predicates `var' and
`nonvar' typically available in Prolog.

# COUNT-TRUES (&REST XS)

Returns the number of time a non-NIL value occurs in its arguments.

# COUNT-TRUESV (&REST XS)

Constrains all its arguments to be boolean. If each argument is known, returns
the number of T arguments. Otherwise returns a fresh constraint variable V.
V and arguments are mutually constrained:
* Lower bound of V is the number arguments known to be T.
* Upper bound of V is the number arguments minus the number of arguments known to be NIL.
* If lower bound of V is constrained to be equal to number of arguments known
to be NIL, all arguments not known to be NIL are constrained to be T.
* If Upper bound of V is constrained to be equal to number of arguments known
to be T, all arguments not known to be T are constrained to be NIL.

# DIVIDE-AND-CONQUER-FORCE (VARIABLE)

Returns X if X is not a variable. If X is a bound variable then returns its
value. Otherwise implements a single binary-branching step of a
divide-and-conquer search algorithm. There are always two alternatives, the
second of which is tried upon backtracking.
If it is known to have a finite domain D then this domain is split into two
halves and the value of X is nondeterministically restricted to be a member
one of the halves. If X becomes bound by this restriction then its value is
returned. Otherwise, X itself is returned.
If X is not known to have a finite domain but is known to be real and to have
both lower and upper bounds then nondeterministically either the lower or
upper bound is restricted to the midpoint between the lower and upper bound.
If X becomes bound by this restriction then its dereferenced value is
returned. Otherwise, X itself is returned.
An error is signalled if X is not known to be restricted to a finite domain
and either is not known to be real or is not known to have both a lower and
upper bound.
When the set of potential values may be infinite, users of
DIVIDE-AND-CONQUER-FORCE may need to take care to fail when the range size of
the variable becomes too small, unless other constraints on it are sufficient
to guarentee failure.
The method of splitting the domain into two halves is left unspecified to give
future implementations leeway in incorporating heuristics in the process of
determining a good search order. All that is specified is that if the domain
size is even prior to splitting, the halves are of equal size, while if the
domain size is odd, the halves differ in size by at most one.

# DOMAIN-SIZE (X)

Returns the domain size of X.
If X is an integer variable with an upper and lower bound, its domain size
is the one greater than the difference of its bounds. Eg. [integer 1:2] has
domain size 2.
If X is a variable with an enumerated domain, its domain size is the size of
that domain.
If X is a CONS, or a variable whose value is a CONS, its domain size is the
product of the domain sizes of its CAR and CDR.
Other types of unbound variables have domain size NIL, whereas non-variables
have domain size of 1.

# EQUALV (X Y)

Returns T if the aggregate object X is known to equal the aggregate object
Y, NIL if the aggregate object X is known not to equal the aggregate object Y,
and a new boolean variable V if it is not known whether or not X equals Y when
EQUALV is called.
The values of X, Y and V are mutually constraints via noticers so that V
equals T if and only if X is known to equal Y and V equals NIL if and only if
X is known not to equal Y.
Noticers are attached to V as well as to all variables nested in both in X and
Y. When the noticers attached to variables nested in X and Y detect that X is
known to equal Y they restrict V to equal T. Likewise, when the noticers
attached to variables nested in X and Y detect that X is known not to equal Y
they restrict V to equal NIL.
Furthermore, if V later becomes known to equal T then X and Y are unified.
Likewise, if V later becomes known to equal NIL then X and Y are restricted to
not be equal. This is accomplished by attaching noticers to the variables
nested in X and Y which detect when X becomes equal to Y and fail.
The expression (KNOWN? (EQUALV X Y)) is analogous to the extra-logical predicate
`==' typically available in Prolog.
The expression (KNOWN? (NOTV (EQUALV X Y))) is analogous to the extra-logical
predicate `\=' typically available in Prolog.
The expression (ASSERT! (EQUALV X Y)) is analogous to Prolog unification.
The expression (ASSERT! (NOTV (EQUALV X Y))) is analogous to the
disunification operator available in Prolog-II.

# FAIL

Backtracks to the most recent choice-point.
FAIL is deterministic function and thus it is permissible to reference #'FAIL,
and write (FUNCALL #'FAIL) or (APPLY #'FAIL).
Calling FAIL when there is no choice-point to backtrack to signals an error.

# FUNCALL-NONDETERMINISTIC (FUNCTION &REST ARGUMENTS)

Analogous to CL:FUNCALL, except FUNCTION can be either a nondeterministic
function, or an ordinary determinisitic function.
You must use FUNCALL-NONDETERMINISTIC to funcall a nondeterministic function.
An error is signalled if you attempt to funcall a nondeterministic
function object with CL:FUNCALL.
You can use FUNCALL-NONDETERMINISTIC to funcall either a deterministic or
nondeterministic function, though even if all of the ARGUMENTS are
deterministic and FUNCTION is a deterministic function object, the call
expression will still be nondeterministic (with presumably a single value),
since it is impossible to determine at compile time that a given call to
FUNCALL-NONDETERMINISTIC will be passed only deterministic function objects
for function.

# FUNCALLV (F &REST X)

F must be a deterministic function. If all arguments X are bound, returns
the result of calling F on the dereferenced values of arguments.
Otherwise returns a fresh variable V, constrained to be equal to the result
of calling F on the dereferenced values of arguments.
Additionally, if all but one of V and the argument variables become known, and
the remaining variable has a finite domain, then that domain is further
restricted to be consistent with other arguments.

# GROUND? (X)

The primitive GROUND? is an extension of the primitive BOUND? which
can recursively determine whether an entire aggregate object is
bound. Returns T if X is bound and either the value of X is atomic or
a CONS tree where all atoms are bound.
Otherwise returns nil.

# INTEGERPV (X)

Returns T if X is known to be integer valued, and NIL if X is known be
non-integer value.
If it is not known whether or not X is integer valued when INTEGERPV is called
then INTEGERPV creates and returns a new boolean variable V.
The values of X and V are mutually constrained via noticers so that V is equal
to T if and only if X is known to be integer valued, and V is equal to NIL if
and only if X is known to be non-integer valued.
If X later becomes known to be integer valued, a noticer attached to X
restricts V to equal T. Likewise, if X later becomes known to be non-integer
valued, a noticer attached to X restricts V to equal NIL.
Furthermore, if V ever becomes known to equal T then a noticer attached to V
restricts X to be integer valued. Likewise, if V ever becomes known to equal
NIL then a noticer attached to V restricts X to be non-integer valued.

# LINEAR-FORCE (X)

Returns X if it is not a variable. If X is a bound variable then returns
its value.
If X is an unbound variable then it must be known to have a countable set of
potential values. In this case X is nondeterministically restricted to be
equal to one of the values in this countable set, thus forcing X to be bound.
The dereferenced value of X is then returned.
An unbound variable is known to have a countable set of potential values
either if it is known to have a finite domain or if it is known to be integer
valued.
An error is signalled if X is not known to have a finite domain and is not
known to be integer valued.
Upon backtracking X will be bound to each potential value in turn, failing
when there remain no untried alternatives.
Since the set of potential values is required only to be countable, not
finite, the set of untried alternatives may never be exhausted and
backtracking need not terminate. This can happen, for instance, when X is
known to be an integer but lacks either an upper of lower bound.
The order in which the nondeterministic alternatives are tried is left
unspecified to give future implementations leeway in incorporating heuristics
in the process of determining a good search order.

# MAKE-VARIABLE (&OPTIONAL (NAME NIL NAME?))

Creates and returns a new variable. Variables are assigned a name
which is only used to identify the variable when it is printed. If the
parameter NAME is given then it is assigned as the name of the
variable. Otherwise, a unique name is assigned. The parameter NAME can
be any Lisp object.

# MAXV (X &REST XS)

Constrains its arguments to be real. If called with a single argument,
returns its value. If called with multiple arguments, behaves as if a
combination of two argument calls:
(MAXV X1 X2 ... Xn) == (MAXV (MAXV X1 X2) ... Xn)
If called with two arguments, and either is known to be greater than or equal
to the other, returns the value of that argument. Otherwise returns a real
variable V, mutually constrained with the arguments:
* Maximum of the values of X1 and X2 is constrained to equal V. This
includes constraining their bounds appropriately. If it becomes know that
cannot be true. FAIL is called.
* If both arguments are integers, V is constrained to be an integer.

# MEMBERV (X SEQUENCE)

Returns T if X is known to be a member of SEQUENCE (using the Common Lisp
function EQL as a test function), NIL if X is known not to be a member of
SEQUENCE, and otherwise returns a new boolean variable V.
When a new variable is created, the values of X and V are mutually constrained
via noticers so that V is equal to T if and only if X is known to be a member
of SEQUENCE and V is equal to NIL if and only if X is known not to be a member
of SEQUENCE.
* If X later becomes known to be a member of SEQUENCE, a noticer attached to X
restricts v to equal T. Likewise, if X later becomes known not to be a
member of SEQUENCE, a noticer attached to X restricts V to equal NIL.
* If V ever becomes known to equal T then a noticer attached to V restricts X
to be a member of SEQUENCE. Likewise, if V ever becomes known to equal NIL
then a noticer attached to V restricts X not to be a member of SEQUENCE.
The current implementation imposes two constraints on the parameter SEQUENCE.
First, SEQUENCE must be bound when MEMBERV is called. Second, SEQUENCE must
not contain any unbound variables when MEMBERV is called.
The value of parameter SEQUENCE must be a sequence, i.e. either a list or a
vector.

# MINV (X &REST XS)

Constrains its arguments to be real. If called with a single argument,
returns its value. If called with multiple arguments, behaves as if a
combination of two argument calls:
(MINV X1 X2 ... Xn) == (MINV (MINV X1 X2) ... Xn)
If called with two arguments, and either is known to be less than or equal to
the other, returns the value of that argument. Otherwise returns a real variable
V, mutually constrained with the arguments:
* Minimum of the values of X1 and X2 is constrained to equal V. This
includes constraining their bounds appropriately. If it becomes know that
cannot be true. FAIL is called.
* If both arguments are integers, V is constrained to be an integer.

# MULTIPLE-VALUE-CALL-NONDETERMINISTIC (FUNCTION-FORM &REST VALUES-FORMS)

Analogous to the CL:MULTIPLE-VALUE-CALL, except FUNCTION-FORM can evaluate
to either a nondeterministic function, or an ordinary deterministic function.
You must use MULTIPLE-VALUE-CALL-NONDETERMINISTIC to multiple-value-call a
nondeterministic function. An error is signalled if a nondeterministic function
object is used with CL:MULTIPLE-VALUE-CALL.
You can use MULTIPLE-VALUE-CALL-NONDETERMINISTIC to call either a
deterministic or nondeterministic function, though even if all of the
VALUES-FORMS are deterministic and FUNCTION-FORM evaluates to a deterministic
function object, the call expression will still be nondeterministic (with
presumably a single value), since it is impossible to determine at compile
time that a given call to MULTIPLE-VALUE-CALL-NONDETERMINISTIC will be passed
only deterministic function objects for function.
While MULTIPLE-VALUE-CALL-NONDETERMINISTIC appears to be a function, it
is really a special-operator implemented by the code-walkers processing
nondeterministic source contexts.

# NONDETERMINISTIC-FUNCTION? (X)

Returns T if X is a nondeterministic function and NIL otherwise.
#'FOO returns a nondeterministic function object iff it is used in nondeterminisitc
context and FOO is either a nondeterministic LAMBDA form, or the name of a
nondeterministic function defined using SCREAMER::DEFUN.
Currently, if FOO is a nondeterministic function defined using
SCREAMER::DEFUN, #'FOO and (SYMBOL-FUNCTION 'FOO) in deterministic context
will return an ordinary deterministic Common Lisp function, which will signal
an error at runtime.

# NOTV (X)

Restricts X to be a boolean.
Returns T if this restricts X to NIL, and T if this restricts X to NIL.
Otherwise returns a new boolean variable V. V and X are mutually constrained
via noticers, so that if either is later known to equal T, the other is
restricted to equal NIL and vice versa.
Note that unlike CL:NOT NOTV does not accept arbitrary values as arguments: it
fails if its argument is not T, NIL, or variable that can be restricted to a
boolean.

# NUMBERPV (X)

Returns T if X is known to be numeric, NIL if X is known to be
non-numeric, and otherwise returns a new boolean variable V.
The values of X and V are mutually constrained via noticers so that V is equal
to T if and only if X is known to be numeric and V is equal to NIL if and only
if X is known to be non-numeric.
* If X later becomes known to be numeric, a noticer attached to X restricts V
to equal T. Likewise, if X later becomes known to be non-numeric, a noticer
attached to X restricts V to equal NIL.
* If V ever becomes known
to equal T then a noticer attached to V restricts X to be numeric. Likewise,
if V ever becomes known to equal NIL then a noticer attached to V restricts X
to be non-numeric.

# ORV (&REST XS)

Restricts each argument to be boolean.
Returns NIL if called with no arguments, or if all arguments are known to
equal NIL after being restructed to be boolean, and returns T if any argument
is known to equal T after this restriction.
Otherwise returns a boolean variable V. The values of arguments and V are
mutually constrained:
* If any argument is later known to equal T, value of V becomes T.
* If all arguments are later known to equal NIL, value of V becomes NIL.
* If value of V is later known to equal NIL, all arguments become NIL.
* If value of V is later known to equal T, and all but one argument is
known to be NIL, the remaining argument becomes T.
Note that unlike CL:OR, ORV is a function and always evaluates all its
arguments. Secondly, any non-boolean argument causes it to fail.

# PURGE (FUNCTION-NAME)

Removes any information about FUNCTION-NAME from Screamer's
who-calls database.

# RANGE-SIZE (X)

Returns the range size of X. Range size is the size of the range values
of X may take.
If X is an integer or a bound variable whose value is an integer, it has the
range size 0. Reals and bound variables whose values are reals have range size
0.0.
Unbound variables known to be reals with an upper and lower bound have a range
size the difference of their upper and lower bounds.
Other types of objects and variables have range size NIL.

# REALPV (X)

Returns T if X is known to be real, NIL if X is known to be non-real,
and otherwise returns a new boolean variable V.
The values of X and V are mutually constrained via noticers so that V is equal
to T if and only if X is known to be real and V is equal to NIL if and only if
X is known to be non-real.
* If X later becomes known to be real, a noticer attached to X restricts V to
equal T. Likewise, if X later becomes known to be non-real, a noticer
attached to X restricts V to equal NIL.
* If V ever becomes known to equal T then a noticer attached to V restricts X
to be real. Likewise, if V ever becomes known to equal NIL then a noticer
attached to V restricts X to be non-real.

# REORDER (COST-FUNCTION TERMINATE? ORDER FORCE-FUNCTION)

Returns an ordering force function based on arguments.
The FORCE-FUNCTION is any (potentially nondeterministic) function
which can be applied to a variable as its single argument with the
stipulation that a finite number of repeated applications will force
the variable to be bound. The FORCE-FUNCTION need not return any useful value.
The ordering force function which is returned is a nondeterministic function
which takes a single argument X. This argument X can be a list of values where
each value may be either a variable or a non-variable.
The ordering force function repeatedly selects a "best" variable using using
COST-FUNCTION and ORDER. Eg. using #'DOMAIN-SIZE and #'< as the COST-FUNCTION
and ORDER, then the variable with the smallest domain will be forced first.
Function TERMINATE? is then called with the determined cost of that variable,
and unless it returns true, FORCE-FUNCTION is applied to that variable to
force constrain it.
Process then iterates until all variables become bound or TERMINATE? returns
true.
The ordering force function does not return any meaningful result.
Screamer currently provides two convenient force-functions, namely
#'linear-force and #'divide-and-conquer-force though future implementations
may provide additional ones. (The defined Screamer protocol does not provide
sufficient hooks for the user to define her own force functions.)

# SOLUTION (ARGUMENTS ORDERING-FORCE-FUNCTION)

ARGUMENTS is a list of values. Typically it is a list of
variables but it may also contain nonvariables.
The specified ORDERING-FORCE-FUNCTION is used to force each of the variables
in list to be bound.
Returns a list of the values of the elements of list in the same order that
they appear in list, irrespective of the forcing order imposed by the
ORDERING-FORCE-FUNCTION.
The ORDERING-FORCE-FUNCTION can be any function which takes a list of values
as its single argument that is guaranteed to force all variables in that list
to be bound upon its return. The returned value of the ORDERING-FORCE-FUNCTION
is ignored.
The user can construct her own ORDERING-FORCE-FUNCTION or use one of the
following alternatives provided with Screamer:
(STATIC-ORDERING #'LINEAR-FORCE),
(STATIC-ORDERING #'DIVIDE-AND-CONQUER-FORCE),
(REORDER COST-FUN TERMINATE-TEST ORDER #'LINEAR-FORCE) and
(REORDER COST-FUN TERMINATE-TEST ORDER #'DIVIDE-AND-CONQUER-FORCE).
Future implementation of Screamer may provide additional forcing and ordering
functions.

# STATIC-ORDERING (FORCE-FUNCTION)

Returns an ordering force function based on FORCE-FUNCTION.
The ordering force function which is returned is a nondeterministic function
which takes a single argument X. This argument X can be a list of values where
each value may be either a variable or a non-variable. The ordering force
function applies the FORCE-FUNCTION in turn to each of the variables in X, in
the order that they appear, repeatedly applying the FORCE-FUNCTION to a given
variable until it becomes bound before proceeding to the next variable. The
ordering force function does not return any meaningful result.
FORCE-FUNCTION is any (potentially nondeterministic) function which can be
applied to a variable as its single argument with the stipulation that a
finite number of repeated applications will force the variable to be bound.
The FORCE-FUNCTION need not return any useful value.
Screamer currently provides two convenient force-functions, namely
#'LINEAR-FORCE and #'DIVIDE-AND-CONQUER-FORCE though future implementations
may provide additional ones. (The defined Screamer protocol does not provide
sufficient hooks for the user to define her own force functions.)

# TEMPLATE (TEMPLATE)

Copies an aggregate object, replacing any symbol beginning with a question
mark with a newly created variable.
If the same symbol appears more than once in X, only one variable is created
for that symbol, the same variable replacing any occurrences of that symbol.
Thus (TEMPLATE '(A B (?C D ?E) ?E)) has the same effect as:
(LET ((?C (MAKE-VARIABLE))
(?E (MAKE-VARIABLE)))
(LIST 'A 'B (LIST C 'D E) E)).
This is useful for creating patterns to be unified with other structures.

# TRAIL (FUNCTION)

When called in non-deterministic context, adds FUNCTION to the trail.
Outside non-deterministic context does nothing.
Functions on the trail are called when unwinding from a nondeterministic
selection (due to either a normal return, or calling FAIL.)

# UNWEDGE-SCREAMER

Removes any information about all user defined functions from
Screamer's who-calls database.

# UNWIND-TRAIL

DEPRECATED.
Calls all functions installed using TRAIL, and removes them from the trail.
Using UNWIND-TRAIL is dangerous, as TRAIL is used by Screamer internally to
eg. undo effects of local assignments -- hence users should never call it. It
is provided at the moment only for backwards compatibility with classic
Screamer.

# VALUE-OF (X)

Returns X if X is not a variable. If X is a variable then VALUE-OF
dereferences X and returns the dereferenced value. If X is bound then
the value returned will not be a variable. If X is unbound then the
value returned will be a variable which may be X itself or another
variable which is shared with X.

# Private

# DIVIDE-AND-CONQUER-FORCE-NONDETERMINISTIC (CONTINUATION-13637 VARIABLE)

Returns X if X is not a variable. If X is a bound variable then returns its
value. Otherwise implements a single binary-branching step of a
divide-and-conquer search algorithm. There are always two alternatives, the
second of which is tried upon backtracking.
If it is known to have a finite domain D then this domain is split into two
halves and the value of X is nondeterministically restricted to be a member
one of the halves. If X becomes bound by this restriction then its value is
returned. Otherwise, X itself is returned.
If X is not known to have a finite domain but is known to be real and to have
both lower and upper bounds then nondeterministically either the lower or
upper bound is restricted to the midpoint between the lower and upper bound.
If X becomes bound by this restriction then its dereferenced value is
returned. Otherwise, X itself is returned.
An error is signalled if X is not known to be restricted to a finite domain
and either is not known to be real or is not known to have both a lower and
upper bound.
When the set of potential values may be infinite, users of
DIVIDE-AND-CONQUER-FORCE may need to take care to fail when the range size of
the variable becomes too small, unless other constraints on it are sufficient
to guarentee failure.
The method of splitting the domain into two halves is left unspecified to give
future implementations leeway in incorporating heuristics in the process of
determining a good search order. All that is specified is that if the domain
size is even prior to splitting, the halves are of equal size, while if the
domain size is odd, the halves differ in size by at most one.

# FUNCTION-RECORD-BODY (INSTANCE)

@arg[extid]{A @class{extid}}
@return[sytemid]{puri:uri or nil}
Returns the System ID part of this External ID.

# FUNCTION-RECORD-CALLEES (INSTANCE)

@arg[extid]{A @class{extid}}
@return[sytemid]{puri:uri or nil}
Returns the System ID part of this External ID.

# FUNCTION-RECORD-DETERMINISTIC? (INSTANCE)

@arg[extid]{A @class{extid}}
@return[sytemid]{puri:uri or nil}
Returns the System ID part of this External ID.

# FUNCTION-RECORD-FUNCTION-NAME (INSTANCE)

# FUNCTION-RECORD-LAMBDA-LIST (INSTANCE)

# FUNCTION-RECORD-OLD-DETERMINISTIC? (INSTANCE)

# FUNCTION-RECORD-SCREAMER? (INSTANCE)

# LINEAR-FORCE-NONDETERMINISTIC (CONTINUATION-11587 X)

Returns X if it is not a variable. If X is a bound variable then returns
its value.
If X is an unbound variable then it must be known to have a countable set of
potential values. In this case X is nondeterministically restricted to be
equal to one of the values in this countable set, thus forcing X to be bound.
The dereferenced value of X is then returned.
An unbound variable is known to have a countable set of potential values
either if it is known to have a finite domain or if it is known to be integer
valued.
An error is signalled if X is not known to have a finite domain and is not
known to be integer valued.
Upon backtracking X will be bound to each potential value in turn, failing
when there remain no untried alternatives.
Since the set of potential values is required only to be countable, not
finite, the set of untried alternatives may never be exhausted and
backtracking need not terminate. This can happen, for instance, when X is
known to be an integer but lacks either an upper of lower bound.
The order in which the nondeterministic alternatives are tried is left
unspecified to give future implementations leeway in incorporating heuristics
in the process of determining a good search order.

# NONDETERMINISTIC-FUNCTION-FUNCTION (INSTANCE)

# SOLUTION-NONDETERMINISTIC (CONTINUATION-11565 ARGUMENTS ORDERING-FORCE-FUNCTION)

ARGUMENTS is a list of values. Typically it is a list of
variables but it may also contain nonvariables.
The specified ORDERING-FORCE-FUNCTION is used to force each of the variables
in list to be bound.
Returns a list of the values of the elements of list in the same order that
they appear in list, irrespective of the forcing order imposed by the
ORDERING-FORCE-FUNCTION.
The ORDERING-FORCE-FUNCTION can be any function which takes a list of values
as its single argument that is guaranteed to force all variables in that list
to be bound upon its return. The returned value of the ORDERING-FORCE-FUNCTION
is ignored.
The user can construct her own ORDERING-FORCE-FUNCTION or use one of the
following alternatives provided with Screamer:
(STATIC-ORDERING #'LINEAR-FORCE),
(STATIC-ORDERING #'DIVIDE-AND-CONQUER-FORCE),
(REORDER COST-FUN TERMINATE-TEST ORDER #'LINEAR-FORCE) and
(REORDER COST-FUN TERMINATE-TEST ORDER #'DIVIDE-AND-CONQUER-FORCE).
Future implementation of Screamer may provide additional forcing and ordering
functions.

# VARIABLE-ENUMERATED-ANTIDOMAIN (INSTANCE)

# VARIABLE-ENUMERATED-DOMAIN (INSTANCE)

# VARIABLE-LOWER-BOUND (INSTANCE)

# VARIABLE-NAME (INSTANCE)

# VARIABLE-NOTICERS (INSTANCE)

# VARIABLE-POSSIBLY-BOOLEAN? (INSTANCE)

# VARIABLE-POSSIBLY-INTEGER? (INSTANCE)

# VARIABLE-POSSIBLY-NONBOOLEAN-NONNUMBER? (INSTANCE)

# VARIABLE-POSSIBLY-NONINTEGER-REAL? (INSTANCE)

# VARIABLE-POSSIBLY-NONREAL-NUMBER? (INSTANCE)

# VARIABLE-UPPER-BOUND (INSTANCE)

# VARIABLE-VALUE (INSTANCE)

# Undocumented

# *-RULE-DOWN (Z X Y)

# *-RULE-UP (Z X Y)

# *V-INTERNAL (XS)

# *V2 (X Y)

# +-RULE-DOWN (Z X Y)

# +-RULE-UP (Z X Y)

# +V-INTERNAL (XS)

# +V2 (X Y)

# -V-INTERNAL (X XS)

# -V2 (X Y)

# /-RULE (Z X Y)

# /=-RULE (X Y)

# /=V-INTERNAL (X XS)

# /=V2 (X Y)

# /V-INTERNAL (X XS)

# /V2 (X Y)

# <-RULE (X Y)

# <=-RULE (X Y)

# <=V-INTERNAL (X XS)

# <=V2 (X Y)

# <V-INTERNAL (X XS)

# <V2 (X Y)

# =-RULE (X Y)

# =V-INTERNAL (X XS)

# =V2 (X Y)

# >=V-INTERNAL (X XS)

# >V-INTERNAL (X XS)

# A-BOOLEAN-NONDETERMINISTIC (CONTINUATION)

# A-MEMBER-OF-NONDETERMINISTIC (CONTINUATION SEQUENCE)

# A-TUPLE (VARIABLES VARIABLE VALUE)

# A-TUPLE-NONDETERMINISTIC (CONTINUATION-11862 VARIABLES VARIABLE VALUE)

# AN-INTEGER-ABOVE-NONDETERMINISTIC (CONTINUATION LOW)

# AN-INTEGER-BELOW-NONDETERMINISTIC (CONTINUATION HIGH)

# AN-INTEGER-BETWEEN-NONDETERMINISTIC (CONTINUATION LOW HIGH)

# AN-INTEGER-NONDETERMINISTIC (CONTINUATION)

# ANDV-INTERNAL (XS)

# APPLY-NONDETERMINISTIC-NONDETERMINISTIC (CONTINUATION FUNCTION ARGUMENT &REST ARGUMENTS)

# ARGUMENTS-FOR-APPLYV (X XS)

# ASSERT!-/=V (X &REST XS)

# ASSERT!-/=V-INTERNAL (X XS)

# ASSERT!-/=V2 (X Y)

# ASSERT!-<=V (X &REST XS)

# ASSERT!-<=V-INTERNAL (X XS)

# ASSERT!-<=V2 (X Y)

# ASSERT!-<V (X &REST XS)

# ASSERT!-<V-INTERNAL (X XS)

# ASSERT!-<V2 (X Y)

# ASSERT!-=V (X &REST XS)

# ASSERT!-=V-INTERNAL (X XS)

# ASSERT!-=V2 (X Y)

# ASSERT!->=V (X &REST XS)

# ASSERT!->=V-INTERNAL (X XS)

# ASSERT!->V (X &REST XS)

# ASSERT!->V-INTERNAL (X XS)

# ASSERT!-APPLYV (F X &REST XS)

# ASSERT!-BOOLEANPV (X)

# ASSERT!-CLAUSE (XS PS)

# ASSERT!-CONSTRAINT (PREDICATE POLARITY? VARIABLES)

# ASSERT!-CONSTRAINT-AC (PREDICATE POLARITY? VARIABLES)

# ASSERT!-CONSTRAINT-GFC (PREDICATE POLARITY? VARIABLES)

# ASSERT!-EQUALV (X Y)

# ASSERT!-FALSE (X)

# ASSERT!-FUNCALLV (F &REST X)

# ASSERT!-INTEGERPV (X)

# ASSERT!-MEMBERV (X Y)

# ASSERT!-MEMBERV-INTERNAL (X Y)

# ASSERT!-NOTV-ANDV (&REST XS)

# ASSERT!-NOTV-ANDV-INTERNAL (XS)

# ASSERT!-NOTV-APPLYV (F X &REST XS)

# ASSERT!-NOTV-BOOLEANPV (X)

# ASSERT!-NOTV-EQUALV (X Y)

# ASSERT!-NOTV-FUNCALLV (F &REST X)

# ASSERT!-NOTV-INTEGERPV (X)

# ASSERT!-NOTV-MEMBERV (X Y)

# ASSERT!-NOTV-MEMBERV-INTERNAL (X Y)

# ASSERT!-NOTV-NUMBERPV (X)

# ASSERT!-NOTV-REALPV (X)

# ASSERT!-NUMBERPV (X)

# ASSERT!-ORV (&REST XS)

# ASSERT!-ORV-INTERNAL (XS)

# ASSERT!-REALPV (X)

# ASSERT!-TRUE (X)

# ATTACH-NOTICER! (NOTICER X)

# ATTACH-NOTICER!-INTERNAL (NOTICER X)

# CACHE-DEFINITION (FUNCTION-NAME LAMBDA-LIST BODY CALLEES)

# CALLEES (FUNCTION-NAME)

# CALLERS (FUNCTION-NAME)

# CHECK-FUNCTION-NAME (FUNCTION-NAME)

# CHECK-LAMBDA-LIST (LAMBDA-LIST)

# CHECK-LAMBDA-LIST-INTERNAL (LAMBDA-LIST &OPTIONAL MODE)

# COMPUTE-CALLEES (BODY ENVIRONMENT)

# CONTAINS-LOCAL-SETF/SETQ? (FORM ENVIRONMENT)

# CONTAINS-VARIABLES? (X)

# COPY-FUNCTION-RECORD (INSTANCE)

# COPY-NONDETERMINISTIC-FUNCTION (INSTANCE)

# COPY-VARIABLE (INSTANCE)

# CORRUPTED? (VARIABLE)

# COUNT-TRUES-INTERNAL (XS)

# COUNT-TRUESV-INTERNAL (XS)

# CPS-CONVERT (FORM CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-BLOCK (NAME BODY CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-CALL (FUNCTION-NAME ARGUMENTS CONTINUATION TYPES VALUE? ENVIRONMENT &OPTIONAL DUMMY-ARGUMENTS)

# CPS-CONVERT-FUNCTION-NAME (FUNCTION-NAME)

# CPS-CONVERT-IF (ANTECEDENT CONSEQUENT ALTERNATE CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-LET (BINDINGS BODY DECLARATIONS CONTINUATION TYPES VALUE? ENVIRONMENT &OPTIONAL NEW-BINDINGS)

# CPS-CONVERT-LET* (BINDINGS BODY DECLARATIONS CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-LOCAL-SETF/SETQ (ARGUMENTS CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-MULTIPLE-VALUE-CALL (NONDETERMINISTIC? FUNCTION FORMS CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-MULTIPLE-VALUE-CALL-INTERNAL (NONDETERMINISTIC? FUNCTION FORMS CONTINUATION TYPES VALUE? ENVIRONMENT &OPTIONAL ARGUMENTS)

# CPS-CONVERT-MULTIPLE-VALUE-PROG1 (FORM FORMS CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-PROGN (BODY CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-RETURN-FROM (NAME RESULT ENVIRONMENT)

# CPS-CONVERT-SETQ (ARGUMENTS CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-CONVERT-TAGBODY (BODY CONTINUATION TYPES VALUE? ENVIRONMENT)

# CPS-NON-CONVERT-CALL (FUNCTION-NAME ARGUMENTS CONTINUATION TYPES VALUE? ENVIRONMENT &OPTIONAL DUMMY-ARGUMENTS)

# DECLARE-DETERMINISTIC (FUNCTION-NAME)

# DECLARE-NONDETERMINISTIC (FUNCTION-NAME)

# DETERMINE-WHETHER-CALLERS-ARE-DETERMINISTIC (FUNCTION-NAME FUNCTION-NAMES ENVIRONMENT)

# DETERMINE-WHETHER-DETERMINISTIC (FUNCTION-NAME ENVIRONMENT)

# DETERMINISTIC-LAMBDA-LIST? (LAMBDA-LIST ENVIRONMENT)

# DETERMINISTIC? (FORM ENVIRONMENT)

# ELIMINATE-VARIABLES (X)

# EMACS-EVAL (EXPRESSION)

# EVERY-OTHER (LIST)

# EXPAND-LOCAL-SETF (PAIRS ENVIRONMENT)

# EXPAND-LOCAL-SETQ (PAIRS ENVIRONMENT)

# FIND-BEST (COST ORDER LIST)

# FINITE-DOMAIN? (VARIABLE)

# FORM-CALLEES (FORM ENVIRONMENT)

# FUNCALL-NONDETERMINISTIC-NONDETERMINISTIC (CONTINUATION FUNCTION &REST ARGUMENTS)

# FUNCTION-DEFINITION (FUNCTION-NAME ENVIRONMENT)

# SETFFUNCTION-RECORD-BODY (NEW-VALUE INSTANCE)

# SETFFUNCTION-RECORD-CALLEES (NEW-VALUE INSTANCE)

# SETFFUNCTION-RECORD-DETERMINISTIC? (NEW-VALUE INSTANCE)

# SETFFUNCTION-RECORD-FUNCTION-NAME (NEW-VALUE INSTANCE)

# SETFFUNCTION-RECORD-LAMBDA-LIST (NEW-VALUE INSTANCE)

# SETFFUNCTION-RECORD-OLD-DETERMINISTIC? (NEW-VALUE INSTANCE)

# FUNCTION-RECORD-P (OBJECT)

# SETFFUNCTION-RECORD-SCREAMER? (NEW-VALUE INSTANCE)

# GET-FUNCTION-RECORD (FUNCTION-NAME)

# INDIRECT-CALLEES (FUNCTION-NAME)

# INDIRECT-CALLEES-INTERNAL (FUNCTION-NAMES CALLEES)

# INDIRECT-CALLERS (FUNCTION-NAME)

# INDIRECT-CALLERS-INTERNAL (FUNCTION-NAMES CALLERS)

# INFINITY-* (X Y)

# INFINITY-+ (X Y)

# INFINITY-- (X Y)

# INFINITY-MAX (X Y)

# INFINITY-MIN (X Y)

# INTEGERS-BETWEEN (LOW HIGH)

# IS-MAGIC-CONTINUATION? (CONTINUATION)

# IS-MAGIC-DECLARATION? (FORM)

# KNOWN?-/=V (X &REST XS)

# KNOWN?-/=V-INTERNAL (X XS)

# KNOWN?-/=V2 (X Y)

# KNOWN?-/=V2-INTERNAL (X Y)

# KNOWN?-/=V2-VARIABLE (X Y)

# KNOWN?-<=V (X &REST XS)

# KNOWN?-<=V-INTERNAL (X XS)

# KNOWN?-<=V2 (X Y)

# KNOWN?-<=V2-INTERNAL (X Y)

# KNOWN?-<=V2-VARIABLE (X Y)

# KNOWN?-<V (X &REST XS)

# KNOWN?-<V-INTERNAL (X XS)

# KNOWN?-<V2 (X Y)

# KNOWN?-<V2-INTERNAL (X Y)

# KNOWN?-<V2-VARIABLE (X Y)

# KNOWN?-=V (X &REST XS)

# KNOWN?-=V-INTERNAL (X XS)

# KNOWN?-=V2 (X Y)

# KNOWN?-=V2-INTERNAL (X Y)

# KNOWN?-=V2-VARIABLE (X Y)

# KNOWN?->=V (X &REST XS)

# KNOWN?->=V-INTERNAL (X XS)

# KNOWN?->V (X &REST XS)

# KNOWN?->V-INTERNAL (X XS)

# KNOWN?-APPLYV (F X &REST XS)

# KNOWN?-BOOLEANPV (X)

# KNOWN?-CONSTRAINT (F POLARITY? X)

# KNOWN?-EQUALV (X Y)

# KNOWN?-FALSE (X)

# KNOWN?-FUNCALLV (F &REST X)

# KNOWN?-INTEGERPV (X)

# KNOWN?-MEMBERV (X Y)

# KNOWN?-MEMBERV-INTERNAL (X Y)

# KNOWN?-MEMBERV-LIST (X Y)

# KNOWN?-MEMBERV-LIST-INTERNAL (X Y)

# KNOWN?-NOTV-APPLYV (F X &REST XS)

# KNOWN?-NOTV-BOOLEANPV (X)

# KNOWN?-NOTV-EQUALV (X Y)

# KNOWN?-NOTV-FUNCALLV (F &REST X)

# KNOWN?-NOTV-INTEGERPV (X)

# KNOWN?-NOTV-MEMBERV (X Y)

# KNOWN?-NOTV-MEMBERV-INTERNAL (X Y)

# KNOWN?-NOTV-MEMBERV-LIST (X Y)

# KNOWN?-NOTV-MEMBERV-LIST-INTERNAL (X Y)

# KNOWN?-NOTV-NUMBERPV (X)

# KNOWN?-NOTV-REALPV (X)

# KNOWN?-NUMBERPV (X)

# KNOWN?-REALPV (X)

# KNOWN?-TRUE (X)

# LAMBDA-EXPRESSION? (FORM)

# MAGIC-CONTINUATION-ARGUMENT (CONTINUATION)

# MAKE-FUNCTION-RECORD (&KEY ((FUNCTION-NAME DUM55) NIL) ((LAMBDA-LIST DUM56) NIL) ((BODY DUM57) NIL) ((CALLEES DUM58) NIL) ((DETERMINISTIC? DUM59) T) ((OLD-DETERMINISTIC? DUM60) NIL) ((SCREAMER? DUM61) *SCREAMER?*))

# MAKE-NONDETERMINISTIC-FUNCTION (&KEY ((FUNCTION DUM105) NIL))

# MAKE-VARIABLE-INTERNAL (&KEY ((NAME DUM3157) NIL) ((NOTICERS DUM3158) NIL) ((ENUMERATED-DOMAIN DUM3159) T) ((ENUMERATED-ANTIDOMAIN DUM3160) NIL) ((VALUE DUM3161) NIL) ((POSSIBLY-INTEGER? DUM3162) T) ((POSSIBLY-NONINTEGER-REAL? DUM3163) T) ((POSSIBLY-NONREAL-NUMBER? DUM3164) T) ((POSSIBLY-BOOLEAN? DUM3165) T) ((POSSIBLY-NONBOOLEAN-NONNUMBER? DUM3166) T) ((LOWER-BOUND DUM3167) NIL) ((UPPER-BOUND DUM3168) NIL))

# MAX-RULE-DOWN (Z X Y)

# MAX-RULE-UP (Z X Y)

# MAXV-INTERNAL (X XS)

# MAXV2 (X Y)

# MIN-RULE-DOWN (Z X Y)

# MIN-RULE-UP (Z X Y)

# MINV-INTERNAL (X XS)

# MINV2 (X Y)

# MODIFIED-FUNCTION-DEFINITIONS (FUNCTION-NAME ENVIRONMENT)

# NEEDS-SUBSTITUTION? (FORM ENVIRONMENT)

# SETFNONDETERMINISTIC-FUNCTION-FUNCTION (NEW-VALUE INSTANCE)

# NONDETERMINISTIC-FUNCTION?-INTERNAL (OBJECT)

# OCCURS-IN? (X VALUE)

# ORV-INTERNAL (XS)

# PEAL-OFF-DOCUMENTATION-STRING-AND-DECLARATIONS (BODY &OPTIONAL DOCUMENTATION-STRING?)

# PERFORM-SUBSTITUTIONS (FORM ENVIRONMENT)

# POSSIBLY-BETA-REDUCE-FUNCALL (CONTINUATION TYPES FORM VALUE?)

# PRINT-NONDETERMINISTIC-FUNCTION (NONDETERMINISTIC-FUNCTION STREAM PRINT-LEVEL)

# PRINT-VARIABLE (X STREAM PRINT-LEVEL)

# PROCESS-SUBFORMS (FUNCTION FORM FORM-TYPE ENVIRONMENT)

# PROPAGATE-AC (PREDICATE POLARITY? VARIABLES)

# PROPAGATE-GFC (PREDICATE POLARITY? VARIABLES UNASSIGNED-VARIABLE)

# PRUNE-ENUMERATED-DOMAIN (X &OPTIONAL (ENUMERATED-DOMAIN (VARIABLE-ENUMERATED-DOMAIN X)))

# QUOTIFY (THING)

# REORDER-INTERNAL (VARIABLES COST-FUNCTION TERMINATE? ORDER FORCE-FUNCTION)

# REORDER-INTERNAL-NONDETERMINISTIC (CONTINUATION-13815 VARIABLES COST-FUNCTION TERMINATE? ORDER FORCE-FUNCTION)

# RESTRICT-BOOLEAN! (X)

# RESTRICT-BOUNDS! (X LOWER-BOUND UPPER-BOUND)

# RESTRICT-ENUMERATED-ANTIDOMAIN! (X ENUMERATED-ANTIDOMAIN)

# RESTRICT-ENUMERATED-DOMAIN! (X ENUMERATED-DOMAIN)

# RESTRICT-FALSE! (X)

# RESTRICT-INTEGER! (X)

# RESTRICT-LOWER-BOUND! (X LOWER-BOUND)

# RESTRICT-NONBOOLEAN! (X)

# RESTRICT-NONINTEGER! (X)

# RESTRICT-NONNUMBER! (X)

# RESTRICT-NONREAL! (X)

# RESTRICT-NUMBER! (X)

# RESTRICT-REAL! (X)

# RESTRICT-TRUE! (X)

# RESTRICT-UPPER-BOUND! (X UPPER-BOUND)

# RESTRICT-VALUE! (X VALUE)

# RUN-NOTICERS (X)

# SCREAMER-ERROR (HEADER &REST ARGS)

# SELF-EVALUATING? (THING)

# SET-ENUMERATED-DOMAIN! (X ENUMERATED-DOMAIN)

# STATIC-ORDERING-INTERNAL (VARIABLES FORCE-FUNCTION)

# STATIC-ORDERING-INTERNAL-NONDETERMINISTIC (CONTINUATION-11643 VARIABLES FORCE-FUNCTION)

# TEMPLATE-INTERNAL (TEMPLATE VARIABLES)

# TRANSFORM-ASSERT! (FORM POLARITY?)

# TRANSFORM-DECIDE (FORM POLARITY?)

# TRANSFORM-KNOWN? (FORM POLARITY?)

# UNWIND-TRAIL-TO (TRAIL-POINTER)

# VALID-FUNCTION-NAME? (FUNCTION-NAME)

# VARIABLE-BOOLEAN? (X)

# SETFVARIABLE-ENUMERATED-ANTIDOMAIN (NEW-VALUE INSTANCE)

# SETFVARIABLE-ENUMERATED-DOMAIN (NEW-VALUE INSTANCE)

# VARIABLE-FALSE? (X)

# VARIABLE-INTEGER? (X)

# SETFVARIABLE-LOWER-BOUND (NEW-VALUE INSTANCE)

# SETFVARIABLE-NAME (NEW-VALUE INSTANCE)

# VARIABLE-NONBOOLEAN? (X)

# VARIABLE-NONINTEGER? (X)

# VARIABLE-NONNUMBER? (X)

# VARIABLE-NONREAL? (X)

# SETFVARIABLE-NOTICERS (NEW-VALUE INSTANCE)

# VARIABLE-NUMBER? (X)

# SETFVARIABLE-POSSIBLY-BOOLEAN? (NEW-VALUE INSTANCE)

# SETFVARIABLE-POSSIBLY-INTEGER? (NEW-VALUE INSTANCE)

# SETFVARIABLE-POSSIBLY-NONBOOLEAN-NONNUMBER? (NEW-VALUE INSTANCE)

# SETFVARIABLE-POSSIBLY-NONINTEGER-REAL? (NEW-VALUE INSTANCE)

# SETFVARIABLE-POSSIBLY-NONREAL-NUMBER? (NEW-VALUE INSTANCE)

# VARIABLE-REAL? (X)

# VARIABLE-TRUE? (X)

# SETFVARIABLE-UPPER-BOUND (NEW-VALUE INSTANCE)

# SETFVARIABLE-VALUE (NEW-VALUE INSTANCE)

# VARIABLE? (OBJECT)

# VARIABLES-IN (X)

# VARIABLIZE (X)

# VOID-CONTINUATION (CONTINUATION)

# WALK (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-BLOCK (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-CATCH (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-EVAL-WHEN (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-FLET/LABELS (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT FORM-TYPE)

# WALK-FOR-EFFECTS (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-FULL (MAP-FUNCTION FORM)

# WALK-FUNCTION (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-FUNCTION-CALL (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-GO (MAP-FUNCTION FORM)

# WALK-IF (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-LAMBDA-LIST (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? LAMBDA-LIST ENVIRONMENT)

# WALK-LAMBDA-LIST-REDUCING (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? LAMBDA-LIST ENVIRONMENT &OPTIONAL MODE)

# WALK-LET/LET* (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT FORM-TYPE)

# WALK-MACRO-CALL (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-MULTIPLE-VALUE-CALL (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-MULTIPLE-VALUE-CALL-NONDETERMINISTIC (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-MULTIPLE-VALUE-PROG1 (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-PROGN (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-PROGV (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-QUOTE (MAP-FUNCTION FORM)

# WALK-RETURN-FROM (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-SETF (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-SETQ (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-TAGBODY (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-THE (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-THROW (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# WALK-UNWIND-PROTECT (MAP-FUNCTION REDUCE-FUNCTION SCREAMER? PARTIAL? NESTED? FORM ENVIRONMENT)

# Y-OR-N-P (&OPTIONAL (FORMAT-STRING NIL FORMAT-STRING?) &REST FORMAT-ARGS)

# MACRO

# Public

# ALL-VALUES (&BODY BODY)

Evaluates BODY as an implicit PROGN and returns a list of all of the
nondeterministic values yielded by the it.
These values are produced by repeatedly evaluating the body and backtracking
to produce the next value, until the body fails and yields no further values.
Accordingly, local side effects performed by the body while producing each
value are undone before attempting to produce subsequent values, and all local
side effects performed by the body are undone upon exit from ALL-VALUES.
Returns a list containing NIL if BODY is empty.
An ALL-VALUES expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the ALL-VALUES appears in, the BODY is
always in a nondeterministic context. An ALL-VALUES expression itself is
always deterministic.
ALL-VALUES is analogous to the `bagof' primitive in Prolog.

# ASSERT! (X)

Restricts X to T. No meaningful result is returned. The argument X can be
either a variable or a non-variable.
This assertion may cause other assertions to be made due to noticers attached
to X.
A call to ASSERT! fails if X is known not to equal T prior to the assertion or
if any of the assertions performed by the noticers result in failure.
Except for the fact that one cannot write #'ASSERT!, ASSERT! behaves like a
function, even though it is implemented as a macro.
The reason it is implemented as a macro is to allow a number of compile time
optimizations. Expressions like (ASSERT! (NOTV X)), (ASSERT! (NUMBERPV X))
and (ASSERT! (NOTV (NUMBERV X))) are transformed into calls to functions
internal to Screamer which eliminate the need to create the boolean
variable(s) normally returned by functions like NOTV and NUMBERPV. Calls to
the functions NUMBERPV, REALPV, INTEGERPV, MEMBERV, BOOLEANPV, =V, <V, <=V,
>V, >=V, /=V, NOTV, FUNCALLV, APPLYV and EQUALV which appear directly nested
in a call to ASSERT!, or directly nested in a call to NOTV which is in turn
directly nested in a call to ASSERT!, are similarly transformed.

# BEST-VALUE (FORM1 OBJECTIVE-FORM &OPTIONAL (FORM2 NIL FORM2?))

First evaluates OBJECTIVE-FORM, which should evaluate to constraint variable V.
Then repeatedly evaluates FORM1 in non-deterministic context till it fails. If
previous round of evaluation produced an upper bound B for V, the during the
next round any change to V must provide an upper bound higher than B, or that
that change fails.
If the last successful evaluation of FORM produced an upper bound for V,
returns a list of two elements: the the primary value of FORM1 from that
round, and the upper bound of V.
Otherwise if FORM2 is provided, returns the result of evaluating it, or else
calls fails.
Note: this documentation string is entirely reverse-engineered. Lacking
information on just how BEST-VALUE was intended to work, it is hard to tell
what is a bug, an accident of implementation, and what is a feature. If you
have any insight into BEST-VALUE, please send email to
nikodemus@random-state.net.

# COUNT-FAILURES (&BODY BODY)

Executes BODY keeping track of the number of times FAIL has been called
without unwinding from BODY. After BODY completes, reports the number of
failures to *STANDARD-OUTPUT* before returning values from BODY.

# DECIDE (X)

Restricts X to a be boolean. After X is restricted a nondeterministic
choice is made. For one branch, X is restricted to equal T and (DECIDE X)
returns T as a result. For the other branch, X is restricted to equal NIL and
(DECIDE X) returns NIL as a result. The argument X can be either a variable
or a non-variable.
The initial restriction to boolean may cause other assertions to be made due
to noticers attached to X. A call to DECIDE immediately fails if X is known
not to be boolean prior to the assertion or if any of the assertions performed
by the noticers result in failure.
Restricting X to be boolean attaches a noticer on X so that any subsequent
assertion which restricts X to be non-boolean will fail.
Except for implementation optimizations (DECIDE X) is equivalent to:
(EITHER (PROGN (ASSERT! X) T) (PROGN (ASSERT! (NOTV X)) NIL))
Except for the fact that one cannot write #'DECIDE, DECIDE behaves like a
function, even though it is implemented as a macro.
The reason it is implemented as a macro is to allow a number of compile time
optimizations. Expressions like (DECIDE (NOTV X)), (DECIDE (NUMBERPV X))
and (DECIDE (NOTV (NUMBERPV X))) are transformed into calls to functions
internal to Screamer which eliminate the need to create the boolean
variable(s) normally returned by functions like notv and numberv. Calls to
the functions NUMBERPV, REALPV, INTEGERPV, MEMBERPV, BOOLEANPV, =V, <V, <=V,
>V, >=V, /=V, NOTV, FUNCALLV, APPLYV and EQUALV which appear directly nested
in a call to decide, or directly nested in a call to NOTV which is in turn
directly nested in a call to decide, are similarly transformed.

# DEFINE-SCREAMER-PACKAGE (DEFINED-PACKAGE-NAME &BODY OPTIONS)

Convenience wrapper around DEFPACKAGE. Passes its argument directly
to DEFPACKAGE, and automatically injects two additional options:
(:shadowing-import-from :screamer :defun :multiple-value-bind :y-or-n-p)
(:use :cl :screamer)

# EITHER (&BODY ALTERNATIVES)

Nondeterministically evaluates and returns the value of one of its
ALTERNATIVES.
EITHER takes any number of arguments. With no arguments, (EITHER) is
equivalent to (FAIL) and is thus deterministic. With one argument, (EITHER
X) is equivalent to X itself and is thus deterministic only when X is
deterministic. With two or more argument it is nondeterministic and can only
appear in a nondeterministic context.
It sets up a choice-point and evaluates the first ALTERNATIVE returning its
values. When backtracking follows to this choice-point, the next ALTERNATIVE
is evaluated and its values are returned. When no more ALTERNATIVES remain,
the current choice-point is removed and backtracking continues to the next
most recent choice-point.

# FOR-EFFECTS (&BODY BODY &ENVIRONMENT ENVIRONMENT)

Evaluates BODY as an implicit PROGN in a nondeterministic context and
returns NIL.
The body is repeatedly backtracked to its first choice-point until the body
fails.
Local side effects performed by BODY are undone when FOR-EFFECTS returns.
A FOR-EFFECTS expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the FOR-EFFECTS appears in, BODY are
always in a nondeterministic context. A FOR-EFFECTS expression is is always
deterministic.

# GLOBAL (&BODY BODY &ENVIRONMENT ENVIRONMENT)

Evaluates BODY in the same fashion as PROGN except that all SETF and SETQ
forms lexically nested in its body result in global side effects which are not
undone upon backtracking.
Note that this affects only side effects introduced explicitly via SETF and
SETQ. Side effects introduced by Common Lisp builtin functions such as RPLACA
are always global anyway.
LOCAL and GLOBAL may be nested inside one another. The nearest lexically
surrounding one determines whether or not a given SETF or SETQ results in a
local or global side effect.
Side effects default to be global when there is no surrounding LOCAL or GLOBAL
expression. Global side effects can appear both in deterministic as well as
nondeterministic contexts. In nondeterministic contexts, GLOBAL as well as
SETF are treated as special forms rather than macros. This should be
completely transparent to the user.

# ITH-VALUE (I FORM &OPTIONAL (DEFAULT '(FAIL)))

Returns the Ith nondeterministic value yielded by FORM.
I must be an integer. The first nondeterministic value yielded by FORM is
numbered zero, the second one, etc. The Ith value is produced by repeatedly
evaluating FORM, backtracking through and discarding the first I values and
deterministically returning the next value produced.
No further execution of FORM is attempted after it successfully yields the
desired value.
If FORM fails before yielding both the I values to be discarded, as well as
the desired Ith value, then DEFAULT is evaluated and its value returned
instead. DEFAULT defaults to (FAIL) if not present.
Local side effects performed by FORM are undone when ITH-VALUE returns, but
local side effects performed by DEFAULT and by I are not undone when ITH-VALUE
returns.
An ITH-VALUE expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the ITH-VALUE appears in, FORM is
always in a nondeterministic context, while DEFAULT and I are in whatever
context the ITH-VALUE appears in.
An ITH-VALUE expression is nondeterministic if DEFAULT is present and is
nondeterministic, or if I is nondeterministic. Otherwise it is deterministic.
If DEFAULT is present and nondeterministic, and if FORM fails, then it is
possible to backtrack into the DEFAULT and for the ITH-VALUE expression to
nondeterministically return multiple times.
If I is nondeterministic then the ITH-VALUE expression operates
nondeterministically on each value of I. In this case, backtracking for each
value of FORM and DEFAULT is nested in, and restarted for, each backtrack of
I.

# KNOWN? (X)

Restricts X to be a boolean. If X is equal to T after being restricted to
be boolean, returns T. If X is equal to NIL or if the value of X is unknown
returns NIL. The argument X can be either a variable or a non-variable.
The initial restriction to boolean may cause other assertions to be made due
to noticers attached to X. A call to KNOWN? fails if X is known not to be
boolean prior to the assertion or if any of the assertions performed by the
noticers result in failure.
Restricting X to be boolean attaches a noticer on X so that any subsequent
assertion which restricts X to be non-boolean will fail.
Except for the fact that one cannot write #'KNOWN?, KNOWN? behaves like a
function, even though it is implemented as a macro.
The reason it is implemented as a macro is to allow a number of compile time
optimizations. Expressions like (KNOWN? (NOTV X)), (KNOWN? (NUMBERPV X))
and (KNOWN? (NOTV (NUMBERPV X))) are transformed into calls to functions
internal to Screamer which eliminate the need to create the boolean
variable(s) normally returned by functions like NOTV and NUMBERV. Calls to
the functions NUMBERPV, REALPV, INTEGERPV, MEMBERV, BOOLEANPV, =V, <V, <=V, V,
>=v, /=v, NOTV, FUNCALLV, APPLYV and EQUALV which appear directly nested in a
call to KNOWN?, or directly nested in a call to NOTV which is in turn directly
nested in a call to KNOWN?, are similarly transformed.

# LOCAL (&BODY BODY &ENVIRONMENT ENVIRONMENT)

Evaluates BODY in the same fashion as PROGN except that all SETF and SETQ
forms lexically nested in its body result in local side effects which are
undone upon backtracking.
This affects only side effects introduced explicitly via SETF and SETQ. Side
effects introduced by either user defined functions or builtin Common Lisp
functions such as RPLACA are always global.
Behaviour of side effects introduced by macro-expansions such as INCF depends
on the exact macro-expansion. If (INCF (FOO)) expands using eg. SET-FOO, LOCAL
is unable to undo the side-effect.
LOCAL cannot distinguish between initially uninitialized and intialized
places, such as unbound variables or hash-table keys with no prior values. As
a result, an attempt to assign an unbound variable inside LOCAL will signal an
error due to the system's attempt to first read the variable. Similarly,
undoing a (SETF GETHASH) when the key did not previously exist in the table
will insert a NIL into the table instead of doing a REMHASH. Easiest way
to work around this is by using TRAIL.
LOCAL and GLOBAL may be nested inside one another. The nearest lexically
surrounding one determines whether or not a given SETF or SETQ results in a
local or global side effect.
Side effects default to be global when there is no surrounding LOCAL or GLOBAL
expression. Local side effects can appear both in deterministic as well as
nondeterministic contexts though different techniques are used to implement
the trailing of prior values for restoration upon backtracking. In
nondeterministic contexts, LOCAL as well as SETF are treated as special forms
rather than macros. This should be completely transparent to the user.

# LOCAL-OUTPUT (&BODY FORMS)

Currently unsupported.
When running under ILisp with iscream.el loaded, does non-determinism aware
output to Emacs, which will be deleted when the current choice is unwound.

# NECESSARILY? (&BODY BODY)

Evaluates BODY as an implicit PROGN in nondeterministic context,
returning true if the body never yields false.
The body is repeatedly backtracked as long as it yields true. Returns the last
true value yielded by the body if it fails before yielding NIL, otherwise
returns NIL.
Local side effects performed by the body are undone when NECESSARILY? returns.
A NECESSARILY? expression can appear in both deterministic and
nondeterministic contexts. Irrespective of what context the NECESSARILY?
appears in, its body is always in a nondeterministic context. A NECESSARILY?
expression is always deterministic.

# ONE-VALUE (FORM &OPTIONAL (DEFAULT '(FAIL)))

Returns the first nondeterministic value yielded by FORM.
No further execution of FORM is attempted after it successfully returns one
value.
If FORM does not yield any nondeterministic values (i.e. it fails) then
DEFAULT is evaluated and its value returned instead. DEFAULT defaults to
(FAIL) if not present.
Local side effects performed by FORM are undone when ONE-VALUE returns, but
local side effects performed by DEFAULT are not undone when ONE-VALUE returns.
A ONE-VALUE expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the ONE-VALUE appears in, FORM is
always in a nondeterministic context, while DEFAULT is in whatever context the
ONE-VALUE form appears.
A ONE-VALUE expression is nondeterministic if DEFAULT is present and is
nondeterministic, otherwise it is deterministic.
If DEFAULT is present and nondeterministic, and if FORM fails, then it is
possible to backtrack into the DEFAULT and for the ONE-VALUE form to
nondeterministically return multiple times. ONE-VALUE is analogous to the cut
primitive (`!') in Prolog.

# POSSIBLY? (&BODY BODY)

Evaluates BODY as an implicit PROGN in nondeterministic context,
returning true if the body ever yields true.
The body is repeatedly backtracked as long as it yields NIL. Returns
the first true value yielded by the body, or NIL if body fails before
yielding true.
Local side effects performed by the body are undone when POSSIBLY? returns.
A POSSIBLY? expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the POSSIBLY? appears in, its body is
always in a nondeterministic context. A POSSIBLY? expression is always
deterministic.

# PRINT-VALUES (&BODY BODY)

Evaluates BODY as an implicit PROGN and prints each of the nondeterministic
values yielded by it using PRINT.
After each value is printed, the user is queried as to whether or not further
values are desired. These values are produced by repeatedly evaluating the
body and backtracking to produce the next value, until either the user
indicates that no further values are desired or until the body fails and
yields no further values.
Returns the last value printed.
Accordingly, local side effects performed by the body while producing each
value are undone after printing each value, before attempting to produce
subsequent values, and all local side effects performed by the body are undone
upon exit from PRINT-VALUES, either because there are no further values or
because the user declines to produce further values.
A PRINT-VALUES expression can appear in both deterministic and
nondeterministic contexts. Irrespective of what context the PRINT-VALUES
appears in, the BODY are always in a nondeterministic context. A
PRINT-VALUES expression itself is always deterministic.
PRINT-VALUES is analogous to the standard top-level user interface in Prolog.

# WHEN-FAILING ((&BODY FAILING-FORMS) &BODY BODY)

Whenever FAIL is called during execution of BODY, executes FAILING-FORMS
before unwinding.

# Private

# Undocumented

# CHOICE-POINT (FORM)

# CHOICE-POINT-EXTERNAL (&REST FORMS)

# CHOICE-POINT-INTERNAL (FORM)

# DEFMACRO-COMPILE-TIME (FUNCTION-NAME LAMBDA-LIST &BODY BODY)

# DEFSTRUCT-COMPILE-TIME (OPTIONS &BODY ITEMS)

# DEFUN (FUNCTION-NAME LAMBDA-LIST &BODY BODY &ENVIRONMENT ENVIRONMENT)

# DEFUN-COMPILE-TIME (FUNCTION-NAME LAMBDA-LIST &BODY BODY)

# DEFVAR-COMPILE-TIME (NAME &OPTIONAL INITIAL-VALUE DOCUMENTATION)

# MULTIPLE-VALUE-BIND (VARIABLES FORM &BODY BODY &ENVIRONMENT ENVIRONMENT)

# VARIABLE

# Public

# *DYNAMIC-EXTENT?*

Set to T to enable the dynamic extent optimization, NIL to
disable it. Default is platform dependent.

# *ISCREAM?*

T if Screamer is running under ILisp/GNUEmacs with iscream.el loaded.

# *MAXIMUM-DISCRETIZATION-RANGE*

Discretize integer variables whose range is not greater than this number.
Discretize all integer variables if NIL. Must be an integer or NIL.

# *MINIMUM-SHRINK-RATIO*

Ignore propagations which reduce the range of a variable by less than this
ratio.

# *SCREAMER-VERSION*

The version of Screamer which is loaded. This is currently still 3.20,
while we're considering how to express versions for this copy of Screamer in
the future.

# *STRATEGY*

Strategy to use for FUNCALLV and APPLYV. Either :GFC for Generalized
Forward Checking, or :AC for Arc Consistency. Default is :GFC.

# Private

# *FUNCTION-RECORD-TABLE*

The function record table.

# *LOCAL?*

This must be globally NIL.

# *NAME*

The counter for anonymous names.

# *NONDETERMINISTIC-CONTEXT?*

This must be globally NIL.

# *NONDETERMINISTIC?*

This must be globally NIL.

# *ORDERED-LAMBDA-LIST-KEYWORDS*

The allowed lambda list keywords in order.

# *SCREAMER?*

This must be NIL except when defining internal Screamer functions.

# *TRAIL*

The trail.