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This is the screamer Reference Manual, version 4.0.0, generated automatically by Declt version 4.0 beta 2 "William Riker" on Thu Sep 15 06:06:47 2022 GMT+0.
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* mode: text; mode: autofill; fillcolumn: 78 * Screamer is an extension of Common Lisp that adds support for nondeterministic programming. Screamer consists of two levels. The basic nondeterministic level adds support for backtracking and undoable side effects. On top of this nondeterministic substrate, Screamer provides a comprehensive constraint programming language in which one can formulate and solve mixed systems of numeric and symbolic constraints. Together, these two levels augment Common Lisp with practically all of the functionality of both Prolog and constraint logic programming languages such as CHiP and CLP(R). Furthermore, Screamer is fully integrated with Common Lisp. Screamer programs can coexist and interoperate with other extensions to as CLIM and Iterate. In several ways Screamer is more efficient than other implementations of backtracking languages. First, Screamer code is transformed into Common Lisp which can be compiled by the underlying Common Lisp system. Many competing implementations of nondeterministic Lisp are interpreters and thus are far less efficient than Screamer. Second, the backtracking primitives require fairly low overhead in Screamer. Finally, this overhead to support backtracking is only paid for by those portions of the program which use the backtracking primitives. Deterministic portions of user programs pass through the ScreamertoCommonLisp transformation unchanged. Since in practise, only small portions of typical programs utilize the backtracking primitives, Screamer can produce more efficient code than compilers for languages in which backtracking is more pervasive. Screamer was written by Jeffrey Mark Siskind and David Allen McAllester, see file LICENSE for licensing information. This version of Screamer is based on released version 3.20, and is being dragged kicking  and screaming  into the 21st century: * Support for Symbolics, AKCL, etc. has been stripped. * It has been modified to run in ANSI Common Lisp, as opposed to CLtL1/CLtL2. * Ongoing maintenance work: original screamer.lisp has been split into package.lisp and screamer.lisp, ChangeLog.old, and some information has been moved over to TODO. * Ongoing development and documentation work: a new manual is in the making, and add support for missing Common Lisp special forms in nondeterministic context is planned. ...the progress is rather glacial, however. Don't hold your breath. See TODO for the current task list. Source files part of the distribution not currently referenced in the screamer.asd: screams.lisp  A file containing all of the examples from the Screamer manual and the two papers ircs9303 and aaai93. To use, first compile and load Screamer and Iterate, compile and load this file, and then type (INPACKAGE :SCREAMS). equations.lisp  A file containing some equations for testing Screamer's numeric constraint satisfaction procedures. To use, first compile and load Screamer, compile and load this file, and then type (INPACKAGE :SCREAMS). iscream.el  If you run Lisp on Unix under GNUEmacs using ILisp you can load this Emacs Lisp file (preferably byte compiled first). You must also then set the variable SCREAMER:*ISCREAM?* to T. This will enable the Screamer macro LOCALOUTPUT and improve the behavior of YORNP and PRINTVALUES under ILisp. Subdirectory papers/ contains the original Screamer manual and papers: screamer.pdf screamer.dvi screamer.ps  PDF, DVI, and Postscript versions of an outdated manual for Screamer. The code in this manual has some bugs but corrected versions are included in screams.lisp. ircs9303.pdf ircs9303.dvi ircs9303.ps  PDF, DVI, and Postscript versions of a paper describing the fundamentals of nondeterministic CommonLisp. This paper is available at Technical Report 9303 of the University of Pennsylvania Institute for Research in Cognitive Science. The appropriate BibTeX entry is: \newcommand{\Screamer}{{\mbox{\sc Screamer}}} \newcommand{\CommonLisp}{{\mbox{\sc Common Lisp}}} @string{IRCS = {University of Pennsylvania Institute for Research in Cognitive Science}} @techreport{SiskindM93, author = {Jeffrey Mark Siskind and David Allen McAllester}, title = {{\Screamer:} A Portable Efficient Implementation of Nondeterministic {\CommonLisp}}, institution = IRCS, year = 1993, number = {IRCS9303}} The code in this paper is included in screams.lisp. aaai93.pdf aaai93.dvi aaai93.ps  PDF, DVI, and Postscript versions of a paper describing the constraint package included with Screamer. This paper will appear in the Proceedings of AAAI93. The appropriate BibTeX entry is: The code in this paper is also included in screams.lisp. \newcommand{\Lisp}{{\mbox{\sc Lisp}}} @string{AAAI93 = {Proceedings of the Eleventh National Conference on Artifical Intelligence}} @inproceedings{SiskindM93a, author = {Jeffrey Mark Siskind and David Allen McAllester}, title = {Nondeterministic {\Lisp} as a Substrate for Constraint Logic Programming}, booktitle = AAAI93, year = 1993, month = jul} Following are old notes regarding incompatibilities between Screamer 3.20 and Screamer 2.4 (as eg. described in papers/screamer.ps): Screamer 3.20 contains numerous bug fixes, performance enhancements and novel features over Screamer 2.4, the prior widely released version. I do not have the time to describe all such improvements. Until the completion of a new Screamer manual you must resort to looking at the source code. At the beginning of the file there is a fairly extensive change log. A small number of incompatibilities have been introduced in the transition from Screamer 2.4 to Screamer 3.20. These are summarized below. Those already familiar with Screamer should have no difficulty modifying their code modulo these changes. 1. All Screamer code must be recompiled. The Screamer 3.20 runtime is incompatibile with the Screamer 2.4 compiler. 2. The function MAPVALUES has been removed. An expression such as: (MAPVALUES function expression) can be rewritten using the new FOREFFECTS macro as follows: (FOREFFECTS (FUNCALL function expression)) The new syntax is every bit as powerful as the old syntax. In fact it is more powerfull. MAPVALUES used to require that the function argument be a deterministic expression while the new syntax makes no such requirement. (Note that FUNCALL still requires that its first argument evaluate to a deterministic function.) 3. You no longer need to reload Screamer after doing an UNWEDGESCREAMER since Screamer keeps track of which functions are intrinsic and UNWEDGESCREAMER does not purge those functions. 4. The following functions have been renamed: NUMBERV > NUMBERPV REALV > REALPV INTEGERV > INTEGERPV BOOLEANV > BOOLEANPV The original names were inconsistent with the naming convention that every function ending in V names a lifted version of the function name without the V. I.e. NUMBERV would have been a lifted version of a function NUMBER but there is no ground function. NUMBERV was really a lifted version of NUMBERP and thus should have been named NUMBERPV. 5. A new naming convention has been introduced. All nondeterministic `generators' now begin with the prefix A or AN. This results in the following name changes: INTEGERBETWEEN > ANINTEGERBETWEEN MEMBEROF > AMEMBEROF FLIP > ABOOLEAN Furthermore, `lifted generators' both begin with A or AN and end with V. This results in the following name changes: REALABOVEV > AREALABOVEV REALBELOWV > AREALBELOWV REALBETWEENV > AREALBETWEENV INTEGERABOVEV > ANINTEGERABOVEV INTEGERBELOWV > ANINTEGERBELOWV INTEGERBETWEENV > ANINTEGERBETWEENV 6. The variable *FUZZ* has been eliminated. The functionality of this variable has been replaced by additional arguments to the REORDER function. 7. REORDER now takes four arguments: (COSTFUNCTION TERMINATE? ORDER FORCEFUNCTION) instead of one. The FORCEFUNCTION is the same as the prior lone argument. The COSTFUNCTION is a function to be applied to each VARIABLE at each reordering step to return its cost. Typical values for COSTFUNCTION are #'DOMAINSIZE or #'RANGESIZE. The COSTFUNCTION can return NIL which causes REORDER to not consider that variable for further forcing. ORDER is a two argument predicate applied to the nonNIL cost functions computed for the variables at each reordering step. Typical values are #'<, to choose the least cost, and #'>, to choose the greatest cost variable to force next. TERMINATE? is a one argument predicate applied to the (nonNIL) cost function computed for the variable chosen to force next. If TERMINATE? returns T then the variable reordering and forcing terminates. The following is a typical call to REORDER used to solve numerical constraints: (REORDER #'RANGESIZE #'(LAMBDA (X) (< X 1E6)) #'> #'DIVIDEANDCONQUERFORCE) The following is a typical call to REORDER used to solve symbolic constraints: (REORDER #'DOMAINSIZE #'(LAMBDA (X) (DECLARE (IGNORE X)) NIL) #'< #'LINEARFORCE) 8. Instead of the standard Screamer file preamble which used to be: (INPACKAGE :) (USEPACKAGE '(:LISP :SCREAMER)) (SHADOWINGIMPORT '(SCREAMER::DEFUN)) there is now a different standard preamble. Loading Screamer creates a predefined package SCREAMERUSER which is useful for small student and demonstration programs. If you wish your file to be in the SCREAMERUSER package the single line: (INPACKAGE :SCREAMERUSER) should be placed at the top of the file. In addition: (INPACKAGE :SCREAMERUSER) should be typed to the Listener after loading Screamer. More complex programs typically reside in their own package. You can place a program in its own package by using the following preamble to your file: (INPACKAGE :CLUSER) (SCREAMER:DEFINESCREAMERPACKAGE : ) (INPACKAGE :MYPACKAGE)
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The main system appears first, followed by any subsystem dependency.
Nondeterministic programming and constraint propagation.
Nikodemus Siivola <nikodemus@randomstate.net>
Jeffrey Mark Siskind & David Allen McAllester
MIT
4.0.0
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Files are sorted by type and then listed depthfirst from the systems components trees.
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screamer (system).
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screamer (system).
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package.lisp (file).
screamer (system).
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Packages are listed by definition order.
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commonlisp.
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Definitions are sorted by export status, category, package, and then by lexicographic order.
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Set to T to enable the dynamic extent optimization, NIL to disable it. Default is platform dependent.
T if Screamer is running under ILisp/GNUEmacs with iscream.el loaded.
Discretize integer variables whose range is not greater than this number. Discretize all integer variables if NIL. Must be an integer or NIL.
Ignore propagations which reduce the range of a variable by less than this ratio.
The version of Screamer which is loaded.
Strategy to use for FUNCALLV and APPLYV. Either :GFC for Generalized Forward Checking, or :AC for Arc Consistency. Default is :GFC.
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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 ALLVALUES.
Returns a list containing NIL if BODY is empty.
An ALLVALUES expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the ALLVALUES appears in, the BODY is
always in a nondeterministic context. An ALLVALUES expression itself is
always deterministic.
ALLVALUES is analogous to the ‘bagof’ primitive in Prolog.
Restricts X to T. No meaningful result is returned. The argument X can be
either a variable or a nonvariable.
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.
First evaluates OBJECTIVEFORM, which should evaluate to constraint variable V.
Then repeatedly evaluates FORM1 in nondeterministic 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 reverseengineered. Lacking information on just how BESTVALUE 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 BESTVALUE, please send email to nikodemus@randomstate.net.
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 *STANDARDOUTPUT* before returning values from BODY.
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 nonvariable.
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 nonboolean 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.
Convenience wrapper around DEFPACKAGE. Passes its argument directly
to DEFPACKAGE, and automatically injects two additional options:
(:shadowingimportfrom :screamer :defun :multiplevaluebind :yornp) (:use :cl :screamer)
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 choicepoint and evaluates the first ALTERNATIVE returning its values. When backtracking follows to this choicepoint, the next ALTERNATIVE is evaluated and its values are returned. When no more ALTERNATIVES remain, the current choicepoint is removed and backtracking continues to the next most recent choicepoint.
Evaluates BODY as an implicit PROGN in a nondeterministic context and
returns NIL.
The body is repeatedly backtracked to its first choicepoint until the body
fails.
Local side effects performed by BODY are undone when FOREFFECTS returns.
A FOREFFECTS expression can appear in both deterministic and nondeterministic contexts. Irrespective of what context the FOREFFECTS appears in, BODY are always in a nondeterministic context. A FOREFFECTS expression is is always deterministic.
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.
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 ITHVALUE returns, but
local side effects performed by DEFAULT and by I are not undone when ITHVALUE
returns.
An ITHVALUE expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the ITHVALUE appears in, FORM is
always in a nondeterministic context, while DEFAULT and I are in whatever
context the ITHVALUE appears in.
An ITHVALUE 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 ITHVALUE expression to
nondeterministically return multiple times.
If I is nondeterministic then the ITHVALUE 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.
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 nonvariable.
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 nonboolean 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.
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 macroexpansions such as INCF depends
on the exact macroexpansion. If (INCF (FOO)) expands using eg. SETFOO, LOCAL
is unable to undo the sideeffect.
LOCAL cannot distinguish between initially uninitialized and intialized
places, such as unbound variables or hashtable 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.
Currently unsupported.
When running under ILisp with iscream.el loaded, does nondeterminism aware output to Emacs, which will be deleted when the current choice is unwound.
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.
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 ONEVALUE returns, but local side effects performed by DEFAULT are not undone when ONEVALUE returns.
A ONEVALUE expression can appear in both deterministic and nondeterministic
contexts. Irrespective of what context the ONEVALUE appears in, FORM is
always in a nondeterministic context, while DEFAULT is in whatever context the
ONEVALUE form appears.
A ONEVALUE 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 ONEVALUE form to nondeterministically return multiple times. ONEVALUE is analogous to the cut primitive (‘!’) in Prolog.
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.
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 PRINTVALUES, either because there are no further values or
because the user declines to produce further values.
A PRINTVALUES expression can appear in both deterministic and
nondeterministic contexts. Irrespective of what context the PRINTVALUES
appears in, the BODY are always in a nondeterministic context. A
PRINTVALUES expression itself is always deterministic.
PRINTVALUES is analogous to the standard toplevel user interface in Prolog.
Whenever FAIL is called during execution of BODY, executes FAILINGFORMS before unwinding.
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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 twoargument 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.
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 twoargument 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 noninteger, and the other is known to
be a real, V is constrained to be a noninteger.
* If one argument is known to be a nonreal, and the other is known
to be a real, V is constrained to be nonreal.
Note: Numeric contagion rules of Common Lisp are not applied if either argument equals zero.
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
twoargument 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 noninteger, and the other is known to
be a real, V is constrained to be a noninteger.
* If one argument is known to be a nonreal, and the other is known
to be a real, V is constrained to be nonreal.
Note: Numeric contagion rules of Common Lisp are not applied if X2 equals zero.
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 Xn1 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.
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
twoargument 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.
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 Xn1 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.
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 Xn1 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.
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 Xn1 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.
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 Xn1 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.
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) ... (> Xn1 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.
Equivalent to (EITHER T NIL).
Returns a boolean variable.
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.
Returns a variable whose value is constrained to be one of VALUES. VALUES can be either a vector or a list designator.
Returns a variable whose value is constained to be a number.
Returns a real variable whose value is constrained to be greater than or equal to LOW.
Returns a real variable whose value is constrained to be less than or equal to HIGH.
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 (AREALBETWEENV LOW HIGH) is an abbreviation for:
(LET ((V (MAKEVARIABLE)))
(ASSERT! (REALPV V))
(ASSERT! (>=V V LOW))
(ASSERT! (<=V V HIGH))
(VALUEOF V))
Returns a real variable.
Generator yielding integers in sequence 0, 1, 1, 2, 2, ...
Generator yielding integers starting from LOW and continuing sequentially in increasing direction.
Returns an integer variable whose value is constrained to be greater than or equal to LOW.
Generator yielding integers starting from HIGH and continuing sequentially in decreasing direction.
Returns an integer variable whose value is constrained to be less than or equal to 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.
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 (ANINTEGERBETWEENV LOW HIGH) is an abbreviation for:
(LET ((V (MAKEVARIABLE)))
(ASSERT! (INTEGERPV V))
(ASSERT! (>=V V LOW))
(ASSERT! (<=V V HIGH))
(VALUEOF v))
Returns an integer variable.
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 nonboolean argument causes it to fail.
Analogous to the CL:APPLY, except FUNCTION can be either a nondeterministic
function, or an ordinary deterministic function.
You must use APPLYNONDETERMINISTIC to apply a nondeterministic function. An
error is signalled if a nondeterministic function object is used with
CL:APPLY.
You can use APPLYNONDETERMINISTIC 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 APPLYNONDETERMINISTIC will be passed only deterministic function objects for function.
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.
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.
Returns true iff X is T or NIL.
The expression (BOOLEANPV X) is an abbreviation for (MEMBERV X ’(T NIL)).
Returns T if X is not a variable or if X is a bound variable. Otherwise returns NIL. BOUND? is analogous to the extralogical predicates ‘var’ and ‘nonvar’ typically available in Prolog.
Returns the number of time a nonNIL value occurs in its arguments.
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.
Returns X if X is not a variable. If X is a bound variable then returns its
value. Otherwise implements a single binarybranching step of a
divideandconquer 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
DIVIDEANDCONQUERFORCE 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.
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 nonvariables have domain size of 1.
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 extralogical predicate
‘==’ typically available in Prolog.
The expression (KNOWN? (NOTV (EQUALV X Y))) is analogous to the extralogical
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 PrologII.
Backtracks to the most recent choicepoint.
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 choicepoint to backtrack to signals an error.
Analogous to CL:FUNCALL, except FUNCTION can be either a nondeterministic
function, or an ordinary determinisitic function.
You must use FUNCALLNONDETERMINISTIC to funcall a nondeterministic function.
An error is signalled if you attempt to funcall a nondeterministic
function object with CL:FUNCALL.
You can use FUNCALLNONDETERMINISTIC 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 FUNCALLNONDETERMINISTIC will be passed only deterministic function objects for function.
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.
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.
Returns T if X is known to be integer valued, and NIL if X is known be
noninteger 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 noninteger 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 noninteger
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 noninteger valued.
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.
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.
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.
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.
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.
Analogous to the CL:MULTIPLEVALUECALL, except FUNCTIONFORM can evaluate to either a nondeterministic function, or an ordinary deterministic function.
You must use MULTIPLEVALUECALLNONDETERMINISTIC to multiplevaluecall a
nondeterministic function. An error is signalled if a nondeterministic function
object is used with CL:MULTIPLEVALUECALL.
You can use MULTIPLEVALUECALLNONDETERMINISTIC to call either a
deterministic or nondeterministic function, though even if all of the
VALUESFORMS are deterministic and FUNCTIONFORM 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 MULTIPLEVALUECALLNONDETERMINISTIC will be passed
only deterministic function objects for function.
While MULTIPLEVALUECALLNONDETERMINISTIC appears to be a function, it
is really a specialoperator implemented by the codewalkers processing
nondeterministic source contexts.
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 (SYMBOLFUNCTION ’FOO) in deterministic context
will return an ordinary deterministic Common Lisp function, which will signal
an error at runtime.
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.
Returns T if X is known to be numeric, NIL if X is known to be
nonnumeric, 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 nonnumeric.
* 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 nonnumeric, 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 nonnumeric.
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 nonboolean argument causes it to fail.
Removes any information about FUNCTIONNAME from Screamer’s whocalls database.
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.
Returns T if X is known to be real, NIL if X is known to be nonreal,
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 nonreal.
* 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 nonreal, 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 nonreal.
Returns an ordering force function based on arguments.
The FORCEFUNCTION 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 FORCEFUNCTION 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 nonvariable.
The ordering force function repeatedly selects a "best" variable using using COSTFUNCTION and ORDER. Eg. using #’DOMAINSIZE and #’< as the COSTFUNCTION 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, FORCEFUNCTION 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 forcefunctions, namely #’linearforce and #’divideandconquerforce 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.)
ARGUMENTS is a list of values. Typically it is a list of
variables but it may also contain nonvariables.
The specified ORDERINGFORCEFUNCTION 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
ORDERINGFORCEFUNCTION.
The ORDERINGFORCEFUNCTION 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 ORDERINGFORCEFUNCTION
is ignored.
The user can construct her own ORDERINGFORCEFUNCTION or use one of the
following alternatives provided with Screamer:
(STATICORDERING #’LINEARFORCE),
(STATICORDERING #’DIVIDEANDCONQUERFORCE),
(REORDER COSTFUN TERMINATETEST ORDER #’LINEARFORCE) and
(REORDER COSTFUN TERMINATETEST ORDER #’DIVIDEANDCONQUERFORCE).
Future implementation of Screamer may provide additional forcing and ordering functions.
Returns an ordering force function based on FORCEFUNCTION.
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 nonvariable. The ordering force
function applies the FORCEFUNCTION in turn to each of the variables in X, in
the order that they appear, repeatedly applying the FORCEFUNCTION to a given
variable until it becomes bound before proceeding to the next variable. The
ordering force function does not return any meaningful result.
FORCEFUNCTION 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 FORCEFUNCTION need not return any useful value.
Screamer currently provides two convenient forcefunctions, namely #’LINEARFORCE and #’DIVIDEANDCONQUERFORCE 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.)
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 (MAKEVARIABLE))
(?E (MAKEVARIABLE)))
(LIST ’A ’B (LIST C ’D E) E)).
This is useful for creating patterns to be unified with other structures.
When called in nondeterministic context, adds FUNCTION to the trail.
Outside nondeterministic context does nothing.
Functions on the trail are called when unwinding from a nondeterministic selection (due to either a normal return, or calling FAIL.)
Removes any information about all user defined functions from Screamer’s whocalls database.
DEPRECATED.
Calls all functions installed using TRAIL, and removes them from the trail.
Using UNWINDTRAIL 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.
Returns X if X is not a variable. If X is a variable then VALUEOF 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.
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This must be globally NIL.
The function record table.
This must be globally NIL.
The counter for anonymous names.
This must be globally NIL.
This must be globally NIL.
The allowed lambda list keywords in order.
This must be NIL except when defining internal Screamer functions.
This must be globally NIL.
The trail.
Next: Ordinary functions, Previous: Special variables, Up: Internals [Contents][Index]
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Returns X if X is not a variable. If X is a bound variable then returns its
value. Otherwise implements a single binarybranching step of a
divideandconquer 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
DIVIDEANDCONQUERFORCE 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.
body.
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.
ARGUMENTS is a list of values. Typically it is a list of
variables but it may also contain nonvariables.
The specified ORDERINGFORCEFUNCTION 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
ORDERINGFORCEFUNCTION.
The ORDERINGFORCEFUNCTION 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 ORDERINGFORCEFUNCTION
is ignored.
The user can construct her own ORDERINGFORCEFUNCTION or use one of the
following alternatives provided with Screamer:
(STATICORDERING #’LINEARFORCE),
(STATICORDERING #’DIVIDEANDCONQUERFORCE),
(REORDER COSTFUN TERMINATETEST ORDER #’LINEARFORCE) and
(REORDER COSTFUN TERMINATETEST ORDER #’DIVIDEANDCONQUERFORCE).
Future implementation of Screamer may provide additional forcing and ordering functions.
name.
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structureobject.
t
screamer::*screamer?*
structureobject.
commonlisp.
structureobject.
t
t
t
t
t
t
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