Object Oriented Rules and Inheritance

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Object Oriented Rules and Inheritance

• Fabrício Teles Marcos Aurélio, August 2006

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Outline

• Purely Relational Rule Languages x Purely Object
  Oriented Languages
• Hybrid Object Oriented Rule Languages
• Inheritance Taxonomy
• Yangs Inheritance Postulates
• CHORD Extending CHR? with High-Order Object
  Oriented Constraints
• Case Study Triangram

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Knowledge Representation and Rule Based Languages

• Strong points
• provides built-in FOL deduction with negation as
  failure
• the most powerful and versatile inference
  mechanism
• with formal semantics
• provides bases for implementation of other
  mechanisms like abduction, induction, planning,
  non-monotonic reasoning
• uses rules that
• are intuitive and modular
• preserve the truth (detachment)
• can be acquired by machine learning

• Weak points
• non-intuitive codification of the terminological
  and procedural knowledge
• poor facility to structure complex entities
• limitations of the tools and methodologies of
  distributed development on a large scale
• poor standardization
• few non-AI computational services, libraries
  available for reuse
• limited interoperability with other languages

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Knowledge Representation and Rule Based Languages

• Rules often represent expert knowledge in a
  natural way (If...Then)
• Rules represent modular knowledge

X
Y (? ? X) ? Y ? Y (? ? X) ? Y X
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Knowledge Representation and Object Oriented
Languages

• Strong points
• intuitive codification of the terminological and
  procedural knowledge
• facilities to structure complex entities
• tools and methodologies of distributed
  development on a large scale consolidated and
  very spread out
• API for the most varied computational services
  and languages
• emphasis in the standardization, interoperability
  and reuse

• Weak points
• no built-in general purpose inference machine
• any mechanism of inference beyond inheritance
  must be implemented from scratch
• codifies behaviors procedurally
• no techniques to learn objects from data
• neither complete nor standard declarative formal
  semantics

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Hybrid Object OrientedRule Languages

• OO Requirements
• Object identity
• Complex Objects
• Classes
• Encapsulation
• Inheritance
• Overriding and Overloading

• Reasoning Requirements
• Declarative Language
• Predicates with logical variables
• Automatic deduction
• Formal semantics
• Computational completeness

Hybrid Rules Objects
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Rules and objects how integrate?
Object Oriented Systems
Rule Based Systems
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Integrating rules with objectssyntactic
alternatives

• Hybrid system object oriented system in which
• procedural methods of the classes are substituted
  by encapsulated rules bases, or
• Hybrid system rule based system in which
• instances of logical terms in the facts base are
  substituted by
• objects instances of a hierarchy of classes
• logical terms in the premises and conclusions of
  the rules are substituted by
• object patterns with logical variables in the
  place of
• object names and attribute values
• possibly also name of classes and attributes

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Substitute procedural methodsby encapsulated
rule bases
Classes Hierarchy
Object Base
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Substitutefact base byobject base
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F-Logic

• Frame Logic is a deductive object oriented
  database language
• Syntactical integration between Object Oriented
  Paradigm and Rules
• Combines rules expressivity and declarative
  semantics with object oriented concepts.
• Implements Structural and Behavioral Inheritance
  with support for Single-source Multiple
  Inheritance
• Flora is an implementation for F-logic over XSB
  Prolog

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Flora Metamodel
Sequential Transaction Frame Logic Programming
Frame Logic Programming
Sequential Transaction Logic Programming
General Logic Programming
Hilog Logic Programming
Definite Logic Programming
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HiLog Metamodel
closure(R)(X,Y) - R(X,Y). closure(R)(X,Y) -
R(X,Z), closure(R)(Z,Y).
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F-Logic Metamodel
john person, johnage -gt 31, johnchildren -gtgt
bob,mary
john personage -gt 31, children -gtgt bob,mary
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F-Logic Metamodel
john.age 31, john..children bob,
john..children mary
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F-Logic Metamodel
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F-Logic Metamodel
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F-Logic Metamodel
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F-Logic Metamodel
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F-Logic Metamodel
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F-Logic Metamodel
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F-Logic OO Concepts
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F-Logic Program Example with Rules
Triangram Rules - Poligon Regularity
XirregularPolygon - Xtriangleside-gtgtS1,S2
and tnot(S1 S2) and S1.length \
S2.length. Xhypotenuse-gtHypotenuse -
Xtriangle and X..triangleSideposition-gtb
ase, side-gtBase and X..triangleSideposit
ion-gtleft, side-gtLeft and
X..triangleSideposition-gtright, side-gtRight
and if (Base.length gt Left.length and
Base.length gt Right.length) then
Hypotenuse Base else if Left.length
gt Right.length then Hypotenuse
Left else Hypotenuse
Right.
Triangram Rule Segment Adjacency
Sadjacent-gtgtX - XsegmentLine, Xadjacent-gtgtS.
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Inheritance Taxonomy (1/4)
Inheritance
Structural
Behavioral
engineersalary(2009)?5000 ? johnengineer ? joh
nsalary(2009)?5000
flowerpetalColor?color ? mary
flower ? marypetalColor?color
code engineersalary(X)?V-VX2 ?
johnengineer ? johnsalary(X)?V-VX2
Values
Code
Signatures
Non-monotonic reasoning in FLORA-2, Kifer, 2005
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Code Inheritance Example

• Rules

R1 _at_ softDeptbonus()-gtB -
softDepttotal-gtT, B T 100. R2 _at_ code
softDeptbonus1()-gtB - softDepttotal-gtT, B
T 100.
?- johnbonus()-gtB.B 1000.
?- johnbonus1()-gtB.B 3000.
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Inheritance Taxonomy (2/4)
class1att1?color ? class2att1?tree
? class2class1 ? objclass2att1?value ? value
color ? value tree
Inheritance
class1att1?color ? class2att1?integer
? class2class1 ? objclass2 ? objatt1?integer
Monotonic
Non-monotonic
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Inheritance Taxonomy (3/4)
Inheritance

• humanlegs?2 ? policehasGun?true ?
  shaftpolice ? shafthuman
• ?
• shaftlegs?2 ? shafthasGun?true

flowerpetalColor?color ? mary
flower ? marypetalColor?color
Simple
Multiple
quakerpolicy?pacifist ? republicanpolicy?paci
fist ? nixon quaker ? nixon republican
? nixonpolicy-gtpacifist
quakerpolicy?pacifist ? republicanpolicy?hawk
? nixon quaker ? nixon republican
? nixon.policy unknown
Single Source
Multiple Source
Source Based
Value Based
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Inheritance Taxonomy (4/4)
Inheritance
elephantcolor?gray ? royalElephantcolor?whit
e ? royalElephant elephant ? clyde
royalElephant ? clydecolor?white
elephantcolor?gray ? royalElephantcolor?white
? royalElephant elephant ? clyde
royalElephant ? clydecolor?white ?
clydecolor?gray ? white gray
elephantcolor?gray ? royalElephantcolor?white
? royalElephant elephant ? clyde
royalElephant ? false
w/ Overriding
wo/ Overriding
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Source x Value Based Multiple Inheritance
c1

• Source-based c2..m and c3..m cancel each other
  regardless of the set of values
• Value-based c2..m and c3..m do not cancel each
  other when they return the same set of values
  (since there is no real conflict)

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Inheritance and Negation

• Non-Monotonic Inheritance (NMI) is a form of
  default reasoning,
• Thus, in order to provide semantics and implement
  inheritance we can reuse another form of default
  reasoning Negation As Failure (NAF)
• F-Logic programs inheritance semantics reuses
  General Logic Programs' Well-Founded Semantics
  for NAF
• Flora implements F-logic inheritance by reusing
  SLG resolution of XSB Prolog

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Yangs Postulates

• Embodies the common intuition behind
  non-monotonic multiple inheritance
• An object model for some F-logic program is an
  interpretation for every F-atom under a
  three-valued semantics

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Main Concepts

• Inheritance Contexts
• cm is an inheritance context for o if o is a
  member of class cand m?v is locally defined at c
  for some value v
• Local context
• sm is a local context if is a fact or if it is
  derived through some rule
• Overriding
• the inheritance context sm overrides cm for o
  if c?s and sc
• Inheritance Candidates
• cm is an inheritance candidate for o if it is
  an inheritance context which is not overriden by
  any other inheritance context
• Inheritance Conflict
• An inheritance conflict occurs when there is more
  than one inheritance candidate for inheriting
  some field m to o

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Main Concepts

• Each concept previously defined can be
• Strong
• Some concept is strong if all of its
  preconditions are true.
• Weak
• Some concept is weak if some of its
  preconditions is undefined.

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Example

• quakerpolicy?pacifist ? republicanpolicy?hawk
  ?
• partypolicy-gtpacifist
• quaker party ? republican party
• nixon quaker ? nixon republican
• __________________________________________________
  ______

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Translation Schema

• Transforms every FLP F into a GLP G such that
• WFS(G) ? OptimisticObjectModel (F)
• Two parts
• Transformation rules, each one rewriting an FLP
  fragment into a corresponding GLP fragment
• Trailer GLP rules, concatenated at the end of the
  transformation result

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Translation Schema
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Translation Schema Trailer Rules
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XirregularPolygon - Xtriangleside-gtgtS1
length-gtL1, side-gtgtS2length-gtL12,
S1\S2, L1 \ L2.
isa(X,irregularPolygon) - isa(X,triangle),
mvd(X,side,S1), mvd(X,side,S2), fd(S1,length,
L1), fd(S2, length, L2), S1\S2, L1\L2.
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CHORDExtending CHR? with High-Order Object
Oriented Constraints
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CHORD Metamodel
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Reusing Yangs Approach on CHORD

• Translate the initial set of CHORD rules into a
  set of CHR rules, transforming each F-atom in
  some special CHR predicate
• Attach some trailer rules implementing OO
  semantics

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Current Implementation

• Current implementation supports only
• F-Atoms and conjunctive F-molecules
• F-Atoms are only allowed as rule defined
  constraints

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Trailer Rules

• Alter normal CHR execution
• insert inheritance steps between constraint
  simplification steps

Normal CHR
Constraint Simplification!
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CHORD Runtime State Machine
Process Overriding
Constraint Simplification
Remove Candidates
Block Multiple-source Inheritance
Propagate Class Structure
Inherit Candidates
Propagate Inheritance Candidates
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Example

• GOAL
• quakerpolicy?pacifist, republicanpolicy?
  hawk, count?7,
• partypolicy-gtpacifist,
• quaker party, republican party, nixon
  quaker, nixon republican

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CHORD Runtime State Machine
CONSTRAINT STORE
quakerpolicy?pacifist, republicanpolicy?ha
wk, republicancount?7,
partypolicy-gtpacifist, quaker party,
republican party, nixon quaker, nixon
republican
Process Overriding
Constraint Simplification
Remove Candidates
Applies user rules, as in CHR? There are no rules
to fire
Block Multiple-source Inheritance
Propagate Class Structure
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine
CONSTRAINT STORE quakerpolicy?paci
fist, republicanpolicy?hawk,
republicancount?7, partypolicy-gtpacifist,
quaker party, republican party,
nixon quaker, nixon republican nixon
party
Process Overriding
Constraint Simplification
Remove Candidates
Block Multiple-source Inheritance
Propagate Class Structure
Propagates class structures, i.e. ab, bc ?
ac
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine
CONSTRAINT STORE quakerpolicy?paci
fist, republicanpolicy?hawk,
republicancount?7, partypolicy-gtpacifist,
quaker party, republican party,
nixon quaker, nixon republican nixon
party candidate_ifd(nixon,republican,count)
candidate_ifd(nixon,quaker,policy)
candidate_ifd(nixon,republican,policy)
candidate_ifd(nixon,party,policy)
candidate_ifd(republican,party,policy)
candidate_ifd(quaker,party,policy)
Process Overriding
Constraint Simplification
Remove Candidates
Block Multiple-source Inheritance
Propagate Class Structure
Calculate exhaustive list of inheritance
candidates, without taking overriding into
consideration
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine
Removes overriden inheritance candidates
Process Overriding
Constraint Simplification
Remove Candidates
CONSTRAINT STORE quakerpolicy?pacifi
st, republicanpolicy?hawk,
republicancount?7, partypolicy-gtpacifist,
quaker party, republican party, nixon
quaker, nixon republican nixon
party candidate_ifd(nixon,republican,count) candid
ate_ifd(nixon,quaker,policy) candidate_ifd(nixon,r
epublican,policy) candidate_ifd(nixon,party,policy
) candidate_ifd(republican,party,policy) candidate
_ifd(quaker,party,policy)
Block Multiple-source Inheritance
Propagate Class Structure
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine
Process Overriding
Constraint Simplification
Remove Candidates
CONSTRAINT STORE quakerpolicy?pacifist
, republicanpolicy?hawk, republicancount?7
, partypolicy-gtpacifist, quaker party,
republican party, nixon quaker, nixon
republican nixon party candidate_ifd(nixon,repu
blican,count) candidate_ifd(nixon,quaker,policy) c
andidate_ifd(nixon,republican,policy)
Block Multiple-source Inheritance
Propagate Class Structure
Removes inheritance Candidates causing multiple
inheritance conflicts
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine
Process Overriding
Constraint Simplification
Remove Candidates
Block Multiple-source Inheritance
CONSTRAINT STORE quakerpolicy?pacifist,
republicanpolicy?hawk, republicancount?7,
partypolicy-gtpacifist, quaker party,
republican party, nixon quaker, nixon
republican nixon party nixoncount?7
Propagate Class Structure
Define remaining candidates as local Definitions
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine
CONSTRAINT STORE quakerpolicy?pacifist,
republicanpolicy?hawk, republicancount?7,
partypolicy-gtpacifist, quaker party,
republican party, nixon quaker, nixon
republican nixon party nixoncount?7
Process Overriding
Constraint Simplification
Remove Candidates
Block Multiple-source Inheritance
Remove remaining intermediate helper constraints
Propagate Class Structure
Inherit Candidates
Propagate Inheritance Candidates
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CHORD Runtime State Machine

• Each state is associated to a sub-rule base
  associated with a part of the trailer
• Constraint Simplification state is associated to
  user rules and goal
• Since we can not control the order of the
  execution of the rules, we need some special
  strategy in order to implement state machines in
  CHR

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Implementing State Machines in CHRD

1. Associate each state to an unique constraint name

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Implementing State Machines in CHRD

• 2) Attach to each rule head of each state rule
  base the constraint associated to the state

Propagate Class Structure
XZ, ZY gt X ? Y XY. SC, OS gt
OC. OC, CMgtR gt OMgtR.
XZ, ZY, class_structure() gt X ? Y
XY. SC, OS, class_structure() gt
OC. OC, CMgtR, class_structure() gt
OMgtR.
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Implementing State Machines in CHRD

• 3) For each state rule base, add an
  simplification rule to simulate state
  transitions(this rule should be the last one in
  state rule base)

class_structure() ltgt propagate_candidates().
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Implementing State Machines in CHRD
XZ, ZY, class_structure() gt X ? Y
XY. SC, OS, class_structure() gt
OC. OC, CMgtR, class_structure() gt
OMgtR. class_structure() ltgt
propagate_candidates().
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Case Study Triangram
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Case Study - Triangram

• Simplification of the known Chinese game, the
  Tangram
• Tangram
• form complex figures using only 7 geometric 2D
  figures, without having overlapping between them
• It considers only the following types of
  different parts
• 5 isosceles triangles (2 small ones, 1 medium and
  2 great ones)
• 1 square
• 1 parallelogram

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Case Study - Triangram

• Exemplo Tangram

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Case Study - Triangram

• Triangram
• Basic parts are only of a type triangles
• Uses three types of triangles

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Case Study - Triangram

• Triangram
• The objective is to form geometric figures from
  the basic types of triangles
• It's only allowed to form a restricted number of
  types of figures the straight hexagons,
  pentagons and the quadrilaterals

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Case Study - Triangram

• UML/OCL
• Representation of the world convex polygons

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Case Study - Triangram

• UML/OCL
• Representation of the world triangle

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Case Study - Triangram

• Implementation
• 28 CHORD rules
• The largest one has 19 contraints on its head
• About 125 constraints on goal
• Average instances of the problem last about 1h to
  run

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Case Study - Triangram

• Implementation
• Goal
• Scenary being tested
• Class hierarchy
• Classes signatures
• Rules
• Invariants
• Methods
• Query ? propagation rules with the F-Atom of the
  method in the body of the rule and pre-conditions
  in the head
• Transactional ? simpagation rules with
  pre-conditions in the head, removals in
  simplificateHead and pos-conditions in the body

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Case Study - Triangram
CHORD Implementation - Goal
main() ltgt true ...
Class Hierarchy
scaleneTriangletriangle, isoscelesTriangletr
iangle, equilateralTriangleisoscelesTriangle,
...
Scenary being tested
tri1 equilateralTriangle side -gtgt s11
adjacent -gtgt s12, adjacent -gtgt s13,
length -gt 3 , ... , ...
Class signatures
triangleside gtgt segmentLine,
triangleSide gtgt triangleSide,
hypotenuse gt segmentLine, ...
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Case Study - Triangram
Invariants
... XsegmentLineadjacent-gtgtS gt true
SsegmentLineadjacent-gtgtX. Xtriangle,
Xside-gtgtS1, Xside-gtgtS2, S1length-gtL1,
S2length-gtL2 gt ne(S1,S2), L1 L2
XregularPolygon. ...
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Case Study - Triangram
Query Methods
... Pol1 rectangle side -gtgt SidePol1 length
-gt L, adjacent -gtgt A1 length -gt LA1
, parts -gtgt P1, parts -gtgt P2 , Pol2
isoscelesTriangle triangleSide -gtgt
TS1 side -gt SidePol2 length
-gt L, adjacent -gtgt A2
length -gt LA1 , position -gt base
gt ne(P1,Pol2), ne(P2,Pol2)
Pol1isCompatible(Pol2, SidePol1,
SidePol2)-gtvoid. ...
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Case Study - Triangram
Transactional Methods
... Pol11triangleisCompatible(Pol2, SidePol1,
SidePol2)-gtvoid, Pol2 triangle,
... \ A11adjacent -gtgt SidePol1, A12adjacent
-gtgt SidePol1, A21adjacent -gtgt SidePol2,
A22adjacent -gtgt SidePol2 gt A11 ! A12, A21
! A22 A11adjacent -gtgt A22, A12adjacent -gtgt
A21, A21adjacent -gtgt A12, A22adjacent -gtgt
A11, Pol3 rectangleside -gtgt
A11,A12,A21,A22, parts -gtgt
Pol1,Pol2, ...