Download presentation

Presentation is loading. Please wait.

Published byChasity Tindle Modified over 3 years ago

1
1 Chapter 4:Constraint Logic Programs Where we learn about the only programming concept rules, and how programs execute

2
2 Constraint Logic Programs u User-Defined Constraints u Programming with Rules u Evaluation u Derivation Trees and Finite Failure u Goal Evaluation u Simplified Derivation Trees u The CLP Scheme

3
3 User-Defined Constraints u Many examples of modelling can be partitioned into two parts u a general description of the object or process u and specific information about the situation at hand u The programmer should be able to define their own problem specific constraints u Rules enable this

4
4 Rules A user defined constraint to define the model of the simple circuit: parallel_resistors(V,I,R1,R2) parallel_resistors(V,I,R1,R2) :- V = I1 * R1, V = I2 * R2, I1 + I2 = I. And the rule defining it

5
5 Using Rules parallel_resistors(V,I,R1,R2) :- V = I1 * R1, V = I2 * R2, I1 + I2 = I. Behaviour with resistors of 10 and 5 Ohms Behaviour with 10V battery where resistors are the same It represents the constraint (macro replacement)

6
6 User-Defined Constraints u user-defined constraint: p(t1,...,tn) where p is an n-ary predicate and t1,...,tn are expressions u literal: a prim. or user-defined constraint u goal: a sequence of literals L1,...,Lm u rule: A :- B where A is a user-defined constraint and B a goal u program: a sequence of rules

7
7 Its not macro replacement! parallel_resistors(VA,IA,10,5), parallel_resistors(VB,IB,8,3), VA + VB = V, I = IB, I = IA Imagine two uses of parallel resistors After macro replacement (converting comma to conj) Confused the two sets of local variables I1, I2

8
8 Renamings u A renaming r is a bijective (invertable) mapping of variables to variables u A syntactic object is a constraint, user- defined constraint, goal or rule u Applying a renaming to a syntactic object gives the object with each variable x replaced by r(x) u variant o’ of object o has renaming r(o’)=o

9
9 Rewriting User-Defined Cons. u goal G of the form (or empty m=0 []) u L 1,..., L i-1, L i, L i+1,..., L m u L i is of the form p(t 1,...,t n ) u R is of the form p(s 1,...,s n ) :- B u r is a renaming s.t. vars in r(R) not in G u The rewriting of G at Li by R using renaming r is u L 1,...,L i-1,t 1 =r(s 1 ),...,t n =r(s n ),r(B),L i+1,...,L m

10
10 Rewriting Example parallel_resistors(VA,IA,10,5), parallel_resistors(VB,IB,8,3), VA + VB = V, I = IB, I = IA Rewrite the first literal with rule parallel_resistors(V,I,R1,R2) :- V = I1 * R1, V = I2 * R2, I1 + I2 = I. Renaming: parallel_resistors(V’,I’,R1’,R2’) :- V’ = I1’*R1’, V’ = I2’*R2’, I1’+I2’ = I’. VA=V’, IA=I’, 10=R1’, 5=R2’, V’ = I1’*R1’, V’ = I2’*R2’, I1’+I2’ = I’, parallel_resistors(VB,IB,8,3), VA + VB = V, I = IB, I = IA Rewrite the 8th literal Renaming: parallel_resistors(V’’,I’’,R1’’,R2’’) :- V’’=I1’’*R1’’, V’’=I2’’*R2’’, I1’’+I2’’=I’’. VA=V’, IA=I’, 10=R1’, 5=R2’, V’ = I1’*R1’, V’ = I2’*R2’, I1’+I2’ = I’, VB=V’’, IB=I’’, 8=R1’’, 3=R2’’, V’’=I1’’*R1’’, V’’=I2’’*R2’’, I1’’+I2’’=I’’ VA + VB = V, I = IB, I = IA Simplifying onto the variables of interest V and I

11
11 Programming with Rules A voltage divider circuit, where cell must be 9 or 12V resistors 5,9 or 14 voltage_divider(V,I,R1,R2,VD,ID) :- V1 = I*R1, VD= I2*R2, V = V1+VD, I = I2+ID. cell(9). (shorthand for cell(9) :- [].) cell(12). resistor(5). resistor(9). resistor(14).

12
12 Programming with Rules Aim: find component values such that the divider voltage VD is between 5.4 and 5.5 V when the divider current ID is 0.1A voltage_divider(V,I,R1,R2,VD,ID), 5.4 <= VD, VD <= 5.5, ID = 0.1, cell(V), resistor(R1), resistor(R2). Note: when rewriting cell and resistor literals there is a choice of which rule to use (V=9,R1=5,R2=5) unsatisfiable constraint (V=9,R1=5,R2=9) satisfiable constraint

13
13 Programming with Rules Consider the factorial function, how do we write rules for a predicate fac(N,F) where F = N! (R1) fac(0,1). (R2) fac(N,N*F) :- N >= 1, fac(N-1, F). Note how the definition is recursive (in terms of itself) and mimics the mathematical definition

14
14 Programming with Rules (R1) fac(0,1). (R2) fac(N,N*F) :- N >= 1, fac(N-1, F). Rewriting the goal fac(2,X) (i.e. what is 2!) Simplified onto variable X, then answer X = 2 Different rewriting: the constraints are unsatisfiable

15
15 Evaluation u In each rewriting step we should check that the conjunction of primitive constraints is satisfiable u derivation does this u in each step a literal is handled u primitive constraints: added to constraint store u user-defined constraints: rewritten

16
16 Evaluation u derivation for : u where each to is a derivation step u derivation for G is a derivation for the state

17
17 Evaluation u state: where G 1 is a goal and C 1 is a constraint u derivation step: G 1 is L 1, L 2,..., L m u L 1 is a primitive constraint, C 2 is C 1 /\ L 1 u if solv(C /\ L 1 ) = false then G 2 = [] u else G 2 = L 2,..., L m u L 1 is a user-defined constraint, C 2 is C 1 and G 2 is the rewriting of G 1 at L 1 using some rule and renaming

18
18 Derivation for Derivation for fac(1,Y) Corresponding answer simplified to Y is Y = 1

19
19 Derivation for Derivation for fac(1,Y) A failed derivation for fac(1,Y)

20
20 Derivations u For derivation beginning at u success state: where solv(C) != false u successful derivation: last state is success u answer: simpl(C, vars( )) u fail state: where solv(C) = false u failed derivation: last state is fail state

21
21 Derivation Trees u derivation tree for goal G u root is u the children of each state are the states reachable in one derivation step u Encodes all possible derivations u when leftmost literal is prim. constraint only one child u otherwise children ordered like rule order

22
22 Derivation Tree Example failed derivation answer: Y = 1

23
23 Derivation Trees u The previous example shows three derivations, 2 failed and one successful u finitely failed: if a derivation tree is finite and all derivations are failed u next slide a finitely failed derivation tree u infinite derivation tree: some derivations are infinite

24
24 Finitely Failed Example

25
25 Infinite Derivation Tree (S1) stupid(X) :- stupid(X). (S2) stupid(1). Answer: X=1 Infinite derivation

26
26 Goal Evaluation u Evaluation of a goal performs an in-order depth-first search of the derivation tree u when a success state is encountered the system returns an answer u the user can ask for more answers in which case the search continues u execution halts when the users requests no more answers or the entire tree is explored

27
27 Goal Evaluation Example Return answer: Y = 1 more? Return no more

28
28 Goal Evaluation Example 2 The evaluation never finds an answer, even though infinitely many exist

29
29 Simplified Derivation Trees u Derivation trees are very large u A simplified form which has the most useful information u constraints in simplified form (variables in the initial goal and goal part of state) u uninteresting states removed

30
30 Simplified State u simplified state: in derivation for G u replace C 0 with C 1 =simpl(C 0, vars(G,G 0 )) u if x=t in C 1 replace x by t in G 0 giving G 1 u replace C 1 with C 2 =simpl(C 1, vars(G,G 1 )) u Example

31
31 Simplified Derivation u A state is critical if it is the first or last state of a derivation or the first literal is a user- defined constraint u A simplified derivation for goal G contains all the critical states in simplified form u similarly for a simplified derivation tree

32
32 Example Simplified Tree Note: fail states are and success states contain answers

33
33 The CLP Scheme u The scheme defines a family of programming languages u A language CLP(X) is defined by u constraint domain X u solver for the constraint domain X u simplifier for the constraint domain X u Example we have used CLP(Real) u Another example CLP(Tree)

34
34 CLP(R) u Example domain for chapters 5,6,7 u Elements are trees containing real constants u Constraints are for trees u and for arithmetic

35
35 Constraint Logic Programs Summary u rules: for user-defined constraints u multiple rules for one predicate u can be recursive u derivation: evaluates a goal u successful: gives an answer (constraint) u failed: can go no further u infinite u scheme: defines a CLP language

Similar presentations

OK

An Effective SPARQL Support over Relational Database Jing Lu, Feng Cao, Li Ma, Yong Yu, Yue Pan SWDB-ODBIS 2007 SNU IDB Lab. Hyewon Lim July 30 th, 2009.

An Effective SPARQL Support over Relational Database Jing Lu, Feng Cao, Li Ma, Yong Yu, Yue Pan SWDB-ODBIS 2007 SNU IDB Lab. Hyewon Lim July 30 th, 2009.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on maggi product Ppt on cse related topics about information Ppt on edge detection python Ppt on stock market in india Ppt on artificial intelligence for speech recognition Ppt on principles of object-oriented programming php Ppt on american vs british accents Ppt on rise of buddhism and jainism Ppt on model view controller python Ppt on regional trade agreements japan