short-hand for equality-based guards. â» one-way unification. â» only instantiates head. â» does not instantiate cons
Constraint Handling Rules A Tutorial for (Prolog) Programmers
Tom Schrijvers Katholieke Universiteit Leuven, Belgium
[email protected]
ICLP 2008 – December 9-13, 2008
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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About This Tutorial
Expected background: I know & like programming
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About This Tutorial
Expected background: I know & like programming I know Prolog, . . .
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About This Tutorial
Expected background: I know & like programming I know Prolog, . . . I but have an itch that Prolog doesn’t scratch
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About This Tutorial
Expected background: I know & like programming I know Prolog, . . . I but have an itch that Prolog doesn’t scratch I . . . or you will have at the end of this tutorial
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About This Tutorial
Expected mindset: I forget about Prolog for now
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About This Tutorial
Expected mindset: I forget about Prolog for now I do not assume things to work as in Prolog
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About This Tutorial
Expected mindset: I forget about Prolog for now I do not assume things to work as in Prolog I really, they won’t be the same!!!
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About This Tutorial
Expected mindset: I forget about Prolog for now I do not assume things to work as in Prolog I really, they won’t be the same!!! You’ve been warned!
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About This Tutorial
Expected mindset: I forget about Prolog for now I do not assume things to work as in Prolog I really, they won’t be the same!!! You’ve been warned! Also: I do not expect anything from the word “constraint”
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About This Tutorial
Expected mindset: I forget about Prolog for now I do not assume things to work as in Prolog I really, they won’t be the same!!! You’ve been warned! Also: I do not expect anything from the word “constraint” I CHR constraints aren’t
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About this tutorial
What you’ll learn:
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About this tutorial
What you’ll learn: 1 how CHR works (operationally)
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About this tutorial
What you’ll learn: 1 how CHR works (operationally) 2 how to program in CHR
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About this tutorial
What you’ll learn: 1 how CHR works (operationally) 2 how to program in CHR 3 just maybe, what CHR is good for
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
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Art 101: Mixing Paint
As novice, you have to start at the bottom of the ladder:
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Art 101: Mixing Paint
As novice, you have to start at the bottom of the ladder: I Learning how to obtain different colors
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Art 101: Mixing Paint
As novice, you have to start at the bottom of the ladder: I Learning how to obtain different colors I by mixing paint
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Art 101: Mixing Paint
As novice, you have to start at the bottom of the ladder: I Learning how to obtain different colors I by mixing paint I Made easy by the Paint Mixing Rules (PMR) language
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The Paint
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Fewer Paint
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The Rules
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The Rules
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The Rules
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PMR as CHR Under the hood, PMR is of course CHR: PMR
CHR
paints
constraints
rules
simplification rules (textual)
mixing bucket
constraint store
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Paint as Constraints
Declaring our paint colors, in textual form: :- chr_constraint red.
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%
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Paint as Constraints
Declaring our paint colors, in textual form: :- chr_constraint red. :- chr_constraint blue.
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% %
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Paint as Constraints
Declaring our paint colors, in textual form: :- chr_constraint :- chr_constraint :- chr_constraint :- chr_constraint ...
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red. blue. yellow. orange.
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% % % %
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Paint as Constraints?
Are paint colors really “constraints”?
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Paint as Constraints?
Are paint colors really “constraints”? No: not in the Constraint Programming sense
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Paint as Constraints?
Are paint colors really “constraints”? No: not in the Constraint Programming sense Yes: in the CHR sense I 1st-class entities in CHR I rewritten by rules
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Paint as Constraints?
Are paint colors really “constraints”? No: not in the Constraint Programming sense Yes: in the CHR sense I 1st-class entities in CHR I rewritten by rules (Are Prolog predicates really “predicates”?)
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The Paint Rules in CHR
Simplification Rule: head body .
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The Paint Rules in CHR
Simplification Rule: head body . “head may be replaced with body ”
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The Paint Rules in CHR
Simplification Rule: head body . “head may be replaced with body ” % red, blue
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purple.
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The Paint Rules in CHR
Simplification Rule: head body . “head may be replaced with body ” % red, blue
purple.
% red, yellow
orange.
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The Paint Rules in CHR
Simplification Rule: head body . “head may be replaced with body ” % red, blue
purple.
% red, yellow
orange.
% blue, yellow green. Tom Schrijvers (K.U.Leuven)
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Time For. . .
. . . a cocktail break! Tom Schrijvers (K.U.Leuven)
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Cocktail Break
You can have as many heads as you like: vodka, martini vodka_martini.
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Cocktail Break
You can have as many heads as you like: vodka, martini vodka_martini. tequila, cointreau, lime margarita.
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Cocktail Break
You can have as many heads as you like: vodka, martini vodka_martini. tequila, cointreau, lime margarita. gin, cherry_brandy, cointreau, grenadine, pineapple, lemon, angostura_bitters singapore_sling. but at least one! Tom Schrijvers (K.U.Leuven)
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Cocktail Break
Warning: too many heads may cause a headache!
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Cocktail Break
Warning: too many heads may cause a headache! vodka_martini, margarita, singapore_sling hangover, blackout.
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Cocktail Break
Warning: too many heads may cause a headache! vodka_martini, margarita, singapore_sling hangover, blackout. You can have many constraints in the body too.
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Running the Rules Paint-Mixing Engine: I Prolog (SWI-Prolog, . . . ) I Leuven CHR system
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Running the Rules Paint-Mixing Engine: I Prolog (SWI-Prolog, . . . ) I Leuven CHR system Everything in a file: paint.pl :- use_module(library(chr)). :- chr_constraint red. ... red, blue purple. ...
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Running the Rules Paint-Mixing Engine: I Prolog (SWI-Prolog, . . . ) I Leuven CHR system Everything in a file: paint.pl :- use_module(library(chr)). :- chr_constraint red. ... ?- [paint]. red, blue purple. ...
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Running the Rules
red, blue purple. red, yellow orange. blue, yellow green. ?- red, blue.
I I
queries answers
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Running the Rules
red, blue purple. red, yellow orange. blue, yellow green. ?- red, blue. purple I I
queries answers
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?- red, yellow.
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Running the Rules
red, blue purple. red, yellow orange. blue, yellow green. ?- red, blue. purple I I
queries answers
?- red, yellow. orange ?- blue, yellow.
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Running the Rules
red, blue purple. red, yellow orange. blue, yellow green. ?- red, blue. purple I I
queries answers
?- red, yellow. orange ?- blue, yellow. green
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
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,
. I
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query: left-to-right
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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query: left-to-right
I
active constraint: blue
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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query: left-to-right
I
active constraint: blue
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put in constraint store
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
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I
active constraint: blue
I
fire first rule?
I
no partner red in constraint store
.
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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I
active constraint: blue
I
fire second rule?
I
no blue in head
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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I
active constraint: blue
I
fire third rule?
I
no partner yellow in constraint store
.
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
,
. I
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deactivate constraint blue
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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active constraint: yellow
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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I
active constraint: yellow
I
put in constraint store
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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I
active constraint: yellow
I
fire first rule?
I
no yellow in head
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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I
active constraint: yellow
I
fire second rule?
I
no partner red in constraint store
.
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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,
.
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I
active constraint: yellow
I
fire third rule?
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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,
I
active constraint: yellow
I
fire third rule!
I
with partner blue in constraint store
.
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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,
.
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I
fire third rule!
I
delete the matched head constraints
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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,
.
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I
fire third rule!
I
add the body to (front of) query
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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,
.
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I
active constraint: green
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In Slow Motion red, blue purple. red, yellow orange. blue, yellow green.
?-
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.
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to make a long story short: I
...
I
final constraint store
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red, yellow. orange
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red, yellow. orange ?- yellow, red. orange
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red.
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red. red
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red, yellow, blue.
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red, yellow, blue. orange blue
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red, blue, yellow.
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What Happens?
red, blue purple. red, yellow orange. blue, yellow green. ?- red, blue, yellow. purple yellow
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Summary
Simplification Rule: I head body . I replace head with body
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Summary
Simplification Rule: I head body . I replace head with body Queries: I processed left-to-right I incrementally I active constraint looks for partners
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
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Brown
Brown stays brown. brown, orange brown. brown, green brown. brown, purple brown. ...
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Short Hand Simpagation rule: headk \head r body . brown \ orange true. brown \ green true. brown \ purple true. ...
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Short Hand Simpagation rule: headk \head r body . brown \ orange true. brown \ green true. brown \ purple true. ... I
headk : kept head
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(1 or more)
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Short Hand Simpagation rule: headk \head r body . brown \ orange true. brown \ green true. brown \ purple true. ... I I
headk : kept head headr : removed head
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(1 or more) (1 or more)
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Short Hand Simpagation rule: headk \head r body . brown \ orange true. brown \ green true. brown \ purple true. ... I I I
headk : kept head headr : removed head true : Prolog’s no-op
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(1 or more) (1 or more)
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Lead to Gold philosophers_stone \ lead gold. ?- philosophers_stone, lead.
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Lead to Gold philosophers_stone \ lead gold. ?- philosophers_stone, lead. philosophers_stone gold
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Lead to Gold philosophers_stone \ lead gold. ?- philosophers_stone, lead. philosophers_stone gold ?- philosophers_stone, lead, lead.
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Lead to Gold philosophers_stone \ lead gold. ?- philosophers_stone, lead. philosophers_stone gold ?- philosophers_stone, lead, lead. philosophers_stone gold gold Tom Schrijvers (K.U.Leuven)
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All Combinations philosophers_stone \ lead gold. ?- lead, lead.
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All Combinations philosophers_stone \ lead gold. ?- lead, lead. lead lead
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All Combinations philosophers_stone \ lead gold. ?- lead, lead. lead lead ?- lead, lead, philosophers_stone.
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All Combinations philosophers_stone \ lead gold. ?- lead, lead. lead lead ?- lead, lead, philosophers_stone. philosophers_stone gold gold Tom Schrijvers (K.U.Leuven)
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All Combinations philosophers_stone \ lead gold. ?- lead, lead. lead lead ?- lead, lead, philosophers_stone. philosophers_stone gold gold Rule fires with all combinations! Tom Schrijvers (K.U.Leuven)
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Summary
Simplification Rule: I head body . I replace head with body
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Summary
Simplification Rule: I head body . I replace head with body Simpagation Rule: I headk \headr body . I replace headr with body I in the presence of headk I fires all possible combinations
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
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Piggy Bank Merger
:- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K). I
constraints can have arguments
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Piggy Bank Merger
:- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K). I I
constraints can have arguments arity must be declared
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Piggy Bank Merger
:- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K). I I I
constraints can have arguments arity must be declared Prolog terms as arguments
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
?- piggy(5),piggy(1),piggy(4),piggy(2).
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
?-
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5€
,
1€
,
4€
Constraint Handling Rules
,
2€
.
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
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1€
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,
2€
.
5€
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
?-
, 5€
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4€
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2€
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1€
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
?-
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4€
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2€
.
6€
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
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,
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,
2€
.
10€
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
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, 10€
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Piggy Bank Merger :- chr_constraint piggy/1. piggy(I), piggy(J) K is I + J, piggy(K).
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,
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.
12€
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CHR(X )
CHR is an embedded language I embedded in host language X
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CHR(X )
CHR is an embedded language I embedded in host language X I here X = Prolog
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CHR(X )
CHR is an embedded language I embedded in host language X I here X = Prolog 2-way communication:
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CHR(X )
CHR is an embedded language I embedded in host language X I here X = Prolog 2-way communication: I Prolog calls CHR constraints e.g. all along from toplevel
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CHR(X )
CHR is an embedded language I embedded in host language X I here X = Prolog 2-way communication: I Prolog calls CHR constraints e.g. all along from toplevel I CHR calls Prolog e.g. K is I + J
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Not Just Numbers
:- chr_constraint value/1. value(I), value(J) append(I,J,K), value(K).
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Not Just Numbers
:- chr_constraint value/1. value(I), value(J) append(I,J,K), value(K).
?- value([a]), value([b]).
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Not Just Numbers
:- chr_constraint value/1. value(I), value(J) append(I,J,K), value(K).
?- value([a]), value([b]). value([b,a]).
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Not Just Numbers
:- chr_constraint value/1. value(I), value(J) append(I,J,K), value(K).
?- value([a]), value([b]). value([b,a]). ?- value([f(a),g(b)]), value([h(i,j)]).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Not Just Numbers
:- chr_constraint value/1. value(I), value(J) append(I,J,K), value(K).
?- value([a]), value([b]). value([b,a]). ?- value([f(a),g(b)]), value([h(i,j)]). value([h(i,j),f(a),g(b)]).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Not Just Numbers
:- chr_constraint value/1. value(I), value(J) append(I,J,K), value(K).
?- value([a]), value([b]). value([b,a]). ?- value([f(a),g(b)]), value([h(i,j)]). value([h(i,j),f(a),g(b)]). Any Prolog terms!
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary
CHR constraints I zero or more arguments I Prolog terms
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary
CHR constraints I zero or more arguments I Prolog terms Bodies I CHR constraints and I Prolog predicate calls
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Overview
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Tom Schrijvers (K.U.Leuven)
Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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Count Down
Problem: write a program to enumerate values: ?- generate(5).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Count Down
Problem: write a program to enumerate values: ?- generate(5). value(5) value(4) value(3) value(2) value(1)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Count Down
Solution: :- chr_constraint generate/1.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Count Down
Solution: :- chr_constraint generate/1. :- chr_constraint value/1.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Count Down
Solution: :- chr_constraint generate/1. :- chr_constraint value/1. generate(N) value(N), M is N - 1, generate(M).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Running the Program
:- chr_constraint generate/1. :- chr_constraint value/1. generate(N) value(N), M is N - 1, generate(M).
?- generate(5).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Running the Program
:- chr_constraint generate/1. :- chr_constraint value/1. generate(N) value(N), M is N - 1, generate(M).
?- generate(5). % waiting
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Running the Program
:- chr_constraint generate/1. :- chr_constraint value/1. generate(N) value(N), M is N - 1, generate(M).
?- generate(5). % waiting % still waiting
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Running the Program
:- chr_constraint generate/1. :- chr_constraint value/1. generate(N) value(N), M is N - 1, generate(M).
?- generate(5). % waiting % still waiting ERROR: Out of local stack
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Running the Program
:- chr_constraint generate/1. :- chr_constraint value/1. generate(N) value(N), M is N - 1, generate(M).
?- generate(5). % waiting % still waiting ERROR: Out of local stack Recursion without a base case!
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Guarded Rules :- chr_constraint generate/1. :- chr_constraint value/1. generate(N) N == 0 | true. generate(N) N > 0 | value(N), M is N - 1, generate(M).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Guarded Rules :- chr_constraint generate/1. :- chr_constraint value/1. generate(N) N == 0 | true. generate(N) N > 0 | value(N), M is N - 1, generate(M).
Guarded rule: I apply rule if guard succeeds
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Guarded Rules :- chr_constraint generate/1. :- chr_constraint value/1. generate(N) N == 0 | true. generate(N) N > 0 | value(N), M is N - 1, generate(M).
Guarded rule: I apply rule if guard succeeds I guard is optional
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Guarded Rules :- chr_constraint generate/1. :- chr_constraint value/1. generate(N) N == 0 | true. generate(N) N > 0 | value(N), M is N - 1, generate(M).
Guarded rule: I apply rule if guard succeeds I guard is optional I guard may contain any Prolog, but may not bind any variables from the head (pure check) Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Even Shorter
generate(N) N > 0 | value(N), M is N - 1, generate(M).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Even Shorter
generate(N) N > 0 | value(N), M is N - 1, generate(M).
?- generate(5).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Even Shorter
generate(N) N > 0 | value(N), M is N - 1, generate(M).
?- generate(5). value(5) value(4) value(3) value(2) value(1) generate(0)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary Simplification Rule: I head guard | body . I replace head with body I if guard succeeds
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary Simplification Rule: I head guard | body . I replace head with body I if guard succeeds Simpagation Rule: I headk \headr guard | body . I replace headr with body I in the presence of headk I if guard succeeds Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Overview
62/112 1 2 3 4 5 6 7 8 9 10 11 12 13
Tom Schrijvers (K.U.Leuven)
Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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CHR Style: Matching
:- chr_constraint generate/1. :- chr_constraint value/1. generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M).
Matching: I “inline” notation for guard I same meaning as explicit guard
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Constraint Handling Rules
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Meaning of Matching Maching
Guard
c(X) true.
c(X) true | true.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Meaning of Matching Maching
Guard
c(X) true.
c(X) true | true.
c(a) true.
c(X) X == a | true.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Meaning of Matching Maching
Guard
c(X) true.
c(X) true | true.
c(a) true.
c(X) X == a | true.
c(f(A)) true.
c(X) nonvar(X), X = f(A) | true.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Meaning of Matching Maching
Guard
c(X) true.
c(X) true | true.
c(a) true.
c(X) X == a | true.
c(f(A)) true.
c(X) nonvar(X), X = f(A) | true.
c(X,X) true.
c(X,Y) X == Y | true.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Meaning of Matching Maching
Guard
c(X) true.
c(X) true | true.
c(a) true.
c(X) X == a | true.
c(f(A)) true.
c(X) nonvar(X), X = f(A) | true.
c(X,X) true.
c(X,Y) X == Y | true.
c(X), d(X) true.
c(X), d(Y) X == Y | true.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World! ?- p(Free).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World! ?- p(Free). Hello, World! Free = world
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World! ?- p(Free). Hello, World! Free = world ?- p(hello).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World! ?- p(Free). Hello, World! Free = world ?- p(hello). No Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
?- c(world).
?- p(Free). Hello, World! Free = world ?- p(hello). No Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
?- c(world). Hello, World!
?- p(Free). Hello, World! Free = world ?- p(hello). No Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
?- c(world). Hello, World!
?- p(Free). Hello, World! Free = world
?- c(Free).
?- p(hello). No Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
?- c(world). Hello, World!
?- p(Free). Hello, World! Free = world
?- c(Free). c(Free)
?- p(hello). No Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
?- c(world). Hello, World!
?- p(Free). Hello, World! Free = world
?- c(Free). c(Free)
?- p(hello). No
?- c(hello).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Matching: CHR vs. Prolog p(world) :- writeln(’Hello, World!’). :- chr_constraint c/1. c(world) writeln(’Hello, World!’). ?- p(world). Hello, World!
?- c(world). Hello, World!
?- p(Free). Hello, World! Free = world
?- c(Free). c(Free)
?- p(hello). No
?- c(hello). c(hello)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary
Matching I short-hand for equality-based guards I one-way unification I only instantiates head I does not instantiate constraints
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Overview
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Tom Schrijvers (K.U.Leuven)
Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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Combining Rules
generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K). What’s the outcome? ?- generate(4).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Combining Rules
generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K). What’s the outcome? ?- generate(4). value(10)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Combining Rules
generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K). What’s the outcome? ?- generate(4). value(10) ?- generate(5).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Combining Rules
generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K). What’s the outcome? ?- generate(4). value(10) ?- generate(5). value(15)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
Tom Schrijvers (K.U.Leuven)
2
5
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
5
2 Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
Tom Schrijvers (K.U.Leuven)
2
M is 2 - 1
Constraint Handling Rules
M 5
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
M is 2 - 1
M
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2 Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
1
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2 Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
5
2 Tom Schrijvers (K.U.Leuven)
1 Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
1
M is 1 - 1
M 5
2 Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
M is 1 - 1
2 Tom Schrijvers (K.U.Leuven)
M 5
1 Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
M is 1 - 1
M 5
3 Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
0
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3 Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
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0 Tom Schrijvers (K.U.Leuven)
3 Constraint Handling Rules
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In Slow Motion generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). value(I), value(J) K is I + J, value(K).
?-
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Constraint Handling Rules
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Combining Rules generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true. What’s the outcome? ?- generate(4).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Combining Rules generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true. What’s the outcome? ?- generate(4). value(2) value(3)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Combining Rules generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true. What’s the outcome? ?- generate(4). value(2) value(3) ?- generate(10).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Combining Rules generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true. What’s the outcome? ?- generate(4). value(2) value(3) ?- generate(10). value(2) value(3) value(5) value(7) Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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How Does It Work? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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Alternatives? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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Tom Schrijvers (K.U.Leuven)
Just added value(3). What now?
Constraint Handling Rules
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Alternatives? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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Tom Schrijvers (K.U.Leuven)
Just added value(3). What now? I remove value(6) ?
Constraint Handling Rules
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Alternatives? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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Tom Schrijvers (K.U.Leuven)
Just added value(3). What now? I remove value(6) ? I remove value(9) ?
Constraint Handling Rules
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Alternatives? generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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Tom Schrijvers (K.U.Leuven)
Just added value(3). What now? I remove value(6) ? I remove value(9) ? I unspecified in CHR!
Constraint Handling Rules
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Alternate Ending generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
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Alternate Ending generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
Tom Schrijvers (K.U.Leuven)
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Alternate Ending generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
Tom Schrijvers (K.U.Leuven)
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Alternate Ending generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
Tom Schrijvers (K.U.Leuven)
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Alternate Ending generate(1) true. generate(N) N > 1 | value(N), M is N - 1, generate(M). value(I) \ value(J) J mod I =:= 0 | true.
Tom Schrijvers (K.U.Leuven)
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Summary
CHR Programs I
Programs consist of a sequence of rules
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary
CHR Programs I I
Programs consist of a sequence of rules Active constraint traverses the rules top-to-bottom to find any that fire
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary
CHR Programs I I
I
Programs consist of a sequence of rules Active constraint traverses the rules top-to-bottom to find any that fire Rest of query/body waits
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
74 / 112
Summary
CHR Programs I I
I I
Programs consist of a sequence of rules Active constraint traverses the rules top-to-bottom to find any that fire Rest of query/body waits Unspecified which partner is found
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Overview
75/112 1 2 3 4 5 6 7 8 9 10 11 12 13
Tom Schrijvers (K.U.Leuven)
Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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Simpagation with Hk = ∅
Simpagation rule
headk \headr guard | body .
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Simpagation with Hk = ∅
Simpagation rule
headk \headr guard | body . What if head k = ∅?
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
76 / 112
Simpagation with Hk = ∅
Simpagation rule
headk \headr guard | body . What if head k = ∅? Simplification rule
head r guard | body .
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
76 / 112
Simpagation with Hr = ∅ Simpagation rule
headk \headr guard | body .
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Simpagation with Hr = ∅ Simpagation rule
headk \headr guard | body . What if head r = ∅?
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
77 / 112
Simpagation with Hr = ∅ Simpagation rule
headk \headr guard | body . What if head r = ∅? Propagation rule
head k ==> guard | body . I add body I in the presence of head k I if guard holds Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
77 / 112
Propagation
a, b ==> c. ?- a, b.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Propagation
a, b ==> c. ?- a, b. a b c
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
78 / 112
Propagation
a, b ==> c. ?- a, b. a b c ?- a, b, b.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
78 / 112
Propagation
a, b ==> c. ?- a, b. a b c ?- a, b, b. a b b c c
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
78 / 112
Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2 Constraint Handling Rules
5 80 / 112
Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2 Constraint Handling Rules
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Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2 Constraint Handling Rules
5 80 / 112
Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2 Constraint Handling Rules
5 80 / 112
Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
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Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2
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Constraint Handling Rules
4
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Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2
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Constraint Handling Rules
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5 80 / 112
Cellular Automaton Writing Wolfram’s celluar automaton Rule 110 in CHR.
d c b a 1 Tom Schrijvers (K.U.Leuven)
2
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Cellular Automaton CHR cells % black(Name,Below,Above,Generation). :- chr_constraint black/4. % white(Name,Below,Above,Generation). :- chr_constraint white/4.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Cellular Automaton CHR cells % black(Name,Below,Above,Generation). :- chr_constraint black/4. % white(Name,Below,Above,Generation). :- chr_constraint white/4. d
?- white(d,c,a,1), black(c,b,d,1), white(b,a,c,1), white(a,d,b,1).
c b a 1
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
81 / 112
Automaton Rule white(C,_,_.G) , black(B,A,C,G) , white(A,_,_,G) ==> G < 10 | NG is G + 1, black(B,A,C,NG).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Automaton Rule white(C,_,_.G) , black(B,A,C,G) , white(A,_,_,G) ==> G < 10 | NG is G + 1, black(B,A,C,NG). ?- white(d,c,a,1), black(c,b,d,1), white(b,a,c,1), white(a,d,b,1).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
82 / 112
Automaton Rule white(C,_,_.G) , black(B,A,C,G) , white(A,_,_,G) ==> G < 10 | NG is G + 1, black(B,A,C,NG). ?- white(d,c,a,1), black(c,b,d,1), white(b,a,c,1), white(a,d,b,1).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Another Example of Propagation generate(N) ==> value(2).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Another Example of Propagation generate(N) ==> value(2). generate(N), value(I) ==> I < N | J is I + 1, value(J).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Another Example of Propagation generate(N) ==> value(2). generate(N), value(I) ==> I < N | J is I + 1, value(J). value(I) \ value(J) J mod I =:= 0 | true. ?- generate(10).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
83 / 112
Another Example of Propagation generate(N) ==> value(2). generate(N), value(I) ==> I < N | J is I + 1, value(J). value(I) \ value(J) J mod I =:= 0 | true. ?- generate(10). value(2) value(3) value(5) value(7) generate(10)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary Simplification Rule: head guard | body . I
replace head with body
Simpagation Rule: headk \headr guard | body . I
replace headr with body
I
in the presence of headk
Propagation Rule: head ==> guard | body . I add body I in the presence of head I fires once for each combination (propagation history) Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Overview
85/112 1 2 3 4 5 6 7 8 9 10 11 12 13
Tom Schrijvers (K.U.Leuven)
Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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Biased Coin?
coin heads. coin tails. What’s the outcome? ?- coin.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
86 / 112
Biased Coin?
coin heads. coin tails. What’s the outcome? ?- coin. heads
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
86 / 112
Biased Coin?
coin heads. coin tails. What’s the outcome? ?- coin. heads Rules are tried in order!
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Coin Flipping in Prolog CHR coin heads. coin tails.
Prolog p_coin :- heads. p_coin :- tails.
What’s the outcome?
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
87 / 112
Coin Flipping in Prolog CHR coin heads. coin tails.
Prolog p_coin :- heads. p_coin :- tails.
What’s the outcome? ?- coin. heads
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
87 / 112
Coin Flipping in Prolog CHR coin heads. coin tails.
Prolog p_coin :- heads. p_coin :- tails.
What’s the outcome? ?- coin. heads
Tom Schrijvers (K.U.Leuven)
?- p_coin. heads
Constraint Handling Rules
87 / 112
Coin Flipping in Prolog CHR coin heads. coin tails.
Prolog p_coin :- heads. p_coin :- tails.
What’s the outcome? ?- coin. heads
Tom Schrijvers (K.U.Leuven)
?- p_coin. heads ; y
Constraint Handling Rules
87 / 112
Coin Flipping in Prolog CHR coin heads. coin tails.
Prolog p_coin :- heads. p_coin :- tails.
What’s the outcome? ?- coin. heads
?- p_coin. heads ; y tails
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
87 / 112
Coin Flipping in Prolog CHR coin heads. coin tails.
Prolog p_coin :- heads. p_coin :- tails.
What’s the outcome? ?- coin. heads
?- p_coin. heads ; y tails
I
Prolog: backtracking
I
CHR: committed choice for simplification rules
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
87 / 112
Propagation Coin Flipping
coin ==> heads. coin ==> tails. What’s the outcome? ?- coin. heads tails coin
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
88 / 112
Propagation Coin Flipping
coin ==> heads. coin ==> tails. What’s the outcome? ?- coin. heads tails coin Rules are applied in sequence.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
88 / 112
Propagation Coin Flipping
coin ==> heads. coin tails. coin ==> side. What’s the outcome? ?- coin. heads tails
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
89 / 112
Propagation Coin Flipping
coin ==> heads. coin tails. coin ==> side. What’s the outcome? ?- coin. heads tails Rules are applied in sequence, until the active constraint is removed.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
89 / 112
Exploiting Rule Order generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Exploiting Rule Order generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). vs. generate(0) true. generate(N) value(N), M is N - 1, generate(M).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
90 / 112
Exploiting Rule Order generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). vs. generate(0) true. generate(N) value(N), M is N - 1, generate(M). for queries ?- generate(N). with N ≥ 0
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
90 / 112
Exploiting Rule Order generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). vs. generate(0) true. generate(N) value(N), M is N - 1, generate(M). for queries ?- generate(N). with N ≥ 0 Better Style?
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
90 / 112
Exploiting Rule Order generate(0) true. generate(N) N > 0 | value(N), M is N - 1, generate(M). vs. generate(0) true. generate(N) value(N), M is N - 1, generate(M). for queries ?- generate(N). with N ≥ 0 Better Style? Compare to: generate(0) :- !. generate(N) :- value(N), M is N - 1, generate(M). Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Summary
Rule Order I rules are tried from top to bottom I applied in sequence I until the active constraint is removed I committed choice: no alternatives explored for simplification rules
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
91 / 112
Overview
92/112 1 2 3 4 5 6 7 8 9 10 11 12 13
Tom Schrijvers (K.U.Leuven)
Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
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Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
93 / 112
Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world ?- c(X).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
93 / 112
Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world ?- c(X). c(X)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
93 / 112
Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world ?- c(X). c(X) ?- c(X), X = hello.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
93 / 112
Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world ?- c(X). c(X) ?- c(X), X = hello. hello
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
93 / 112
Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world ?- c(X). c(X) ?- c(X), X = hello. hello ?- c(X), c(world), X = hello.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
93 / 112
Hello, World! c(hello) writeln(hello). c(world) writeln(world). ?- c(hello), c(world). hello world ?- c(X). c(X) ?- c(X), X = hello. hello ?- c(X), c(world), X = hello. world hello X = hello Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
Reactivation I
constraints suspend in the constraint store
I
unification reactivates suspended constraints
93 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes ?- neq(A,B).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true. ?- neq(A,B), A = B. ?- neq(a,a). No ?- neq(a,b). Yes ?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No
?- neq(A,B), A = B. No
?- neq(a,b). Yes ?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No
?- neq(A,B), A = B. No ?- neq(A,B), A = a, B = a.
?- neq(a,b). Yes ?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes
?- neq(A,B), A = B. No ?- neq(A,B), A = a, B = a. No
?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes
?- neq(A,B), A = B. No ?- neq(A,B), A = a, B = a. No ?- neq(A,B), A = a, B = b.
?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes ?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
?- neq(A,B), A = B. No ?- neq(A,B), A = a, B = a. No ?- neq(A,B), A = a, B = b. Yes
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes ?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
?- neq(A,B), A = B. No ?- neq(A,B), A = a, B = a. No ?- neq(A,B), A = a, B = b. Yes ?- neq(A,B), A = f(C), B = f(D).
Constraint Handling Rules
94 / 112
A Constraint: Inequality neq(X,X) fail. neq(X,Y) X \= Y | true.
?- neq(a,a). No ?- neq(a,b). Yes ?- neq(A,B). neq(A,B)
Tom Schrijvers (K.U.Leuven)
?- neq(A,B), A = B. No ?- neq(A,B), A = a, B = a. No ?- neq(A,B), A = a, B = b. Yes ?- neq(A,B), A = f(C), B = f(D). neq(f(C),f(D)) Constraint Handling Rules
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Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ...
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra])
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra]) ?- domain(X,[d,f,h,s,z]), X = z.
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra]) ?- domain(X,[d,f,h,s,z]), X = z. X = z
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra]) ?- domain(X,[d,f,h,s,z]), X = z. X = z ?- domain(X,[d,f,h,s,z]), domain(X,[c,s,z]).
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra]) ?- domain(X,[d,f,h,s,z]), X = z. X = z ?- domain(X,[d,f,h,s,z]), domain(X,[c,s,z]). domain(X,[s,z])
Tom Schrijvers (K.U.Leuven)
Constraint Handling Rules
95 / 112
Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra]) ?- domain(X,[d,f,h,s,z]), X = z. X = z ?- domain(X,[d,f,h,s,z]), domain(X,[c,s,z]). domain(X,[s,z]) ?- domain(X,[d,f,h,s,z]), domain(X,[c,z]).
Tom Schrijvers (K.U.Leuven)
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Using Reactivation for Finite Domains domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). intersection(L1,L2,L3) :- ... ?- domain(X,[dog,fox,horse,snails,zebra]). domain(X,[dog,fox,horse,snail,zebra]) ?- domain(X,[d,f,h,s,z]), X = z. X = z ?- domain(X,[d,f,h,s,z]), domain(X,[c,s,z]). domain(X,[s,z]) ?- domain(X,[d,f,h,s,z]), domain(X,[c,z]). X = z Tom Schrijvers (K.U.Leuven)
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Summary
Reactivation I
rules may not fire because of lack of instantiation
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Summary
Reactivation I I
rules may not fire because of lack of instantiation upon instantiation, the rule may now fire
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Summary
Reactivation I I I
rules may not fire because of lack of instantiation upon instantiation, the rule may now fire useful for implementing constraint solvers
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
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Summary: CHR vs Prolog
Prolog
CHR
1
≥1
rule selection
unification
matching & guard
different rules
alternatives/backtracking
try all in sequence
failure
delay
heads
no rule
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CHR and Backtracking
p :- a. p :- b.
a c1. a c2.
b d1. b d2.
?- p. c1
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CHR and Backtracking
p :- a. p :- b.
a c1. a c2.
b d1. b d2.
?- p. c1 ; y d1
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CHR and Backtracking
p :- a. p :- b.
a c1. a c2.
b d1. b d2. I
?- p. c1 ; y d1
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I I
Constraint Handling Rules
Prolog creates choicepoints CHR does not Prolog backtracking undoes CHR changes 99 / 112
Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). split(X) ground(X) | true. split(X), domain(X,[V|Vs]) X = V ; domain(X,Vs). ?- domain(X,[d,z]), split(X).
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). split(X) ground(X) | true. split(X), domain(X,[V|Vs]) X = V ; domain(X,Vs). ?- domain(X,[d,z]), split(X). X = d ; y X = z
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). split(X) ground(X) | true. split(X), domain(X,[V|Vs]) X = V ; domain(X,Vs). ?- domain(X,[d,z]), split(X). X = d ; y X = z ?- domain(X,[d,f,z]), split(X).
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). split(X) ground(X) | true. split(X), domain(X,[V|Vs]) X = V ; domain(X,Vs). ?- domain(X,[d,z]), split(X). X = d ; y X = z ?- domain(X,[d,f,z]), split(X). X = d ; y domain(X,[f,z]) Tom Schrijvers (K.U.Leuven)
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). indomain(X) ground(X) | true. % indomain(X), domain(X,[V1,...,Vn]) X = V1;...;X = Vn.
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). indomain(X) ground(X) | true. % indomain(X), domain(X,[V1,...,Vn]) X = V1;...;X = Vn. indomain(X), domain(X,Vs) member(X,Vs).
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). indomain(X) ground(X) | true. % indomain(X), domain(X,[V1,...,Vn]) X = V1;...;X = Vn. indomain(X), domain(X,Vs) member(X,Vs). ?- domain(X,[d,f,z]), indomain(X).
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Backtracking for Labeling domain(X,L) ground(X) | memberchk(X,L). domain(X,[]) fail. domain(X,[V]) X = V. domain(X,L1), domain(X,L2) intersection(L1,L2,L), domain(X,L). indomain(X) ground(X) | true. % indomain(X), domain(X,[V1,...,Vn]) X = V1;...;X = Vn. indomain(X), domain(X,Vs) member(X,Vs). ?- domain(X,[d,f,z]), indomain(X). X = d ; y X = f ; y X = z
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Overview
102/112 1 2 3 4 5 6 7 8 9 10 11 12 13
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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Summary
You should now have an understanding of:
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Summary
You should now have an understanding of: I how CHR works.
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Summary
You should now have an understanding of: I how CHR works. I how CHR differs from Prolog.
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Summary
You should now have an understanding of: I how CHR works. I how CHR differs from Prolog. I that CHR is not exclusively about constraints .
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Overview
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Introduction The Art of CHR Simpagation For the Sake of Arguments En Guarde A Perfect Match Bigger Programs Propagation Order in the Rules Reactivation CHR vs. Prolog Tutorial Summary Facts about CHR
Constraint Handling Rules
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus)
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born 2002-2005 optimized compilation & program analysis (abstract interpretation), PhDs of Gregory Duck and Tom Schrijvers
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born 2002-2005 optimized compilation & program analysis (abstract interpretation), PhDs of Gregory Duck and Tom Schrijvers 2004 refined semantics, Gregory Duck et al.
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born 2002-2005 optimized compilation & program analysis (abstract interpretation), PhDs of Gregory Duck and Tom Schrijvers 2004 refined semantics, Gregory Duck et al. 2004 1st CHR workshop
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born 2002-2005 optimized compilation & program analysis (abstract interpretation), PhDs of Gregory Duck and Tom Schrijvers 2004 refined semantics, Gregory Duck et al. 2004 1st CHR workshop 2005-2008 computational complexity, PhD Jon Sneyers
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born 2002-2005 optimized compilation & program analysis (abstract interpretation), PhDs of Gregory Duck and Tom Schrijvers 2004 refined semantics, Gregory Duck et al. 2004 1st CHR workshop 2005-2008 computational complexity, PhD Jon Sneyers 2005- Leuven JCHR (Java), Peter Van Weert
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History: Programming Highlights
1991 CHR is born, Thom Fr¨ uhwirth 1995 Christian Holzbaur implements CHR(SICStus) 2002 Leuven CHR is born 2002-2005 optimized compilation & program analysis (abstract interpretation), PhDs of Gregory Duck and Tom Schrijvers 2004 refined semantics, Gregory Duck et al. 2004 1st CHR workshop 2005-2008 computational complexity, PhD Jon Sneyers 2005- Leuven JCHR (Java), Peter Van Weert 2007 first concurrent system, Sulzmann & Lam
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CHR Systems
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CHR Programs Thom Fr¨uhwirth, with his students: I
lots of example programs, constraint solvers and others
Thom Fr¨uhwirth & Tom Schrijvers, I
union-find
Jon Sneyers, I
Fibonacci heaps and Dijkstra’s shortest path
I
Hopcroft’s DFA minimization
I
Turing and RAM machine simulators
Henning Christiansen, I
meta-programming in CHR
... Tom Schrijvers (K.U.Leuven)
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CHR Theory & Applications Declarative Semantics I
classical first-order logic
I
linear logic
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(Fr¨ uhwirth) (Betz)
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CHR Theory & Applications Declarative Semantics I
classical first-order logic
I
linear logic
(Fr¨ uhwirth) (Betz)
Rewriting Properties I
confluence
(Fr¨ uhwirth;Duck;Haemmerle)
I
completion
(Fr¨ uhwirth&Abdennadher)
I
termination
(Fr¨ uhwirth;Voets&Pilozzi)
I
complexity
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(Fr¨ uhwirth;De Koninck)
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CHR Theory & Applications Declarative Semantics I
classical first-order logic
I
linear logic
(Fr¨ uhwirth) (Betz)
Rewriting Properties I
confluence
(Fr¨ uhwirth;Duck;Haemmerle)
I
completion
(Fr¨ uhwirth&Abdennadher)
I
termination
(Fr¨ uhwirth;Voets&Pilozzi)
I
complexity
(Fr¨ uhwirth;De Koninck)
Applications I
type systems
I
test case generation
(Schrijvers)
I
multi-agent systems
(Alberti)
I
...
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(Sulzmann & Stuckey)
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CHR Researchers around the World
Fig. 1. CHR research groups all over the world: 1. Ulm, Germany (Fr¨uhwirth, Meister, Betz, 2. Leuven, Belgium (Schrijvers, Demoen, Sneyers, De Koninck, Van Weert, . . . ); 3. Melbourne, Australia (Duck, Stuckey, Garc´ıa de la Banda, Wazny, Brand, . . . ); 4. Vi-
Djelloul, Raiser, . . . );
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CHR in Industry multi-headed business rules custom constraint solvers
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CHR in Industry multi-headed business rules custom constraint solvers I
Scientific Software & Systems Ltd. I
I
Cornerstone Technology Inc I
I
injection mould design tool
BSSE System and Software Engineering I
I
stock brokering software
test generation
MITRE Corporation I
optical network design
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Further Reading
I
CHR website (Google for) I I
I
programs papers
CHR Survey I
As Time Goes By: Constraint Handling Rules – A Survey of CHR Research from 1998 to 2007, J. Sneyers, P. Van Weert, T. Schrijvers, L. De Koninck.
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Thank You!
My Questions: Get the Quiz! Your Questions?
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