L4-ListsAndListOperations

7/27/2019 L4-ListsAndListOperations

1/33

MB: 5 March 2001 CS360 Lecture 4 1

Programming in Logic: Prolog

Lists and List Operations

Readings: Sections 3.1 & 3.2


2/33


Review

Declarative semantics of pure Prolog programdefines when a goal is true and for what

instantiation of variables.

Commas between goals mean and, semicolonsmean or.

Procedural semantics are determined by clauseand goal ordering.

Goal failure causes backtracking and unbindingof affected variables.


3/33


Programming Patterns

Today we start actually looking at programs

We will look at a lot of them!!

You should look for some underlying patternsof how to program in Prolog


4/33


Prolog Lists

The elements of a list can be anything includingother lists.

Remember that atoms could be made from asequence of special characters, the empty list is

the special atom [ ].


5/33


Lists

A non-empty list always contains two things, aheadand the tail. It is a structured data object.

The functor name is . and its arity is 2.

The list consisting of the item 3 is: .(3,[ ])


6/33


Lists contd

The list consisting of the two items 3 and xis: .(3,.(x,[ ]))

Lists are one of the most pervasive datastructures in Prolog, so there is a special

notation for them: [3, x]


7/33


Lists contd

Often want to describe beginning of list withoutspecifying the rest of it. For example,.(3,.(x,

T)) describes a list whose first two items are 3

andx, and whose remaining items could beanything (including empty).

Prolog provides a special notation for doingthis, |, e.g., [3,x |T]


8/33


Lists

[3, x | T] matches : [3,x], [3,x,y(5)], and [3,x,56, U, name(mike, barley)] (among others)

with T = [ ], [y(5)], and [56,U,name(mike, barley)]


9/33


Definition of List

List definition: list([ ]). list([I|L1]) :- list(L1).


10/33


List Operations

Since lists are an inductively defined datastructure, expect operations to be inductively

defined.

One common list operation is checking whethersomething is a member of the list.

member(Item, List)


11/33


List Membership

If defining list membership inductively, need to figureout base case for list variable.

Base case for defn of list is [ ], but not appropriate forbase case of membership. Why?

Need to look elsewhere. Whats the simplest case fordeciding membership?


12/33


List Membership

Its the first item in the list. Maybe this can beour base case.

member(Item, List) :- List = [Item | _ ].

Prolog is pattern-directed, i.e., does patternmatching, can use this to simplify base case:

member( I, [ I | _ ]).


13/33


List Membership

What if item is not the first one in list, thenwhat? Then need to check if its in the tail.

member(I, [ _ | T ]) :- member(I, T).

Dont we have to check for empty list case?No, because if we hit the empty list, thenIis not in

the list, so we should fail.


14/33


List Membership

KB:1. member(I, [ I | _ ]). 2. member(I, [_| T] :- member(I, T).Query

:

member(x, [ ]).

Response: noExecution Trace:[member(x,[ ])]


15/33


List Membership


:

member(x, [ w, x]).

Response:

Partial Execution Trace:[member(x,[ w, x ])] 2. I=x, T=[x][member(x, [x])]

continue trace


16/33


List Membership


:

member(X, [ w, x]).

Response:X=w ? ;

Partial Execution Trace:[member(X,[ w, x ])] 1. X=I, I=w

[ ] continue trace


17/33


List Concatenation

Define relation conc(L1, L2, L3) whereL3 is theresult of concatenatingL1 onto front ofL2.

What is the base case?

Go back to defn of list, what is base case?


18/33


List Concatenation

List defn base case is [ ], should this be ourbase case for defining concatenation?

conc([ ], ?, ?) - what is the result ofconcatenating [ ] onto anything? Are there

special cases?

conc([ ], L2, L2).


19/33


List Concatenation

What should the inductive step be? What was the inductive step for list defn?

What should the head look like? conc([ I | L1], L2, [ I | L3]) Whats the relation betweenL1, L2, andL3? conc(L1, L2, L3)


20/33


List Concatenation

Full definition: conc([ ], L, L). conc([ I | L1], L2, [I|L3]) :- conc(L1, L2, L3).

Try doing an execution trace for the query: conc(L1, L2, [1, 2, 3]).

What are the bindings forL1 andL2 if keepasking for alternatives?


21/33


Multi-Way Uses of Relations

We have seen that one nice feature of logicprogramming is its absence of control.

This means we can define one central relationand use it in a number of different ways. What

it means depends upon which arguments are

variables, partially variablized and/or constants.

conc/3 is an example of such a central relation.


22/33


Some Uses of Concatenation

member(I, L) :- conc(_, [ I | _ ], L).

last( Item, List) :- conc(_ , [Item], List).

sublist(SubList, List) :-conc(L1, L2, List),

conc(SubList, _, L2).


23/33


Clarity

We dont really need to write defns formember/2 and last/2, could just use conc/3.

What have we gained by writing thosedefinitions?

We write their definitions because we want it tobe obvious what were trying to do!


24/33


List Operations

Adds item to front of list: add(Item, List, [Item | List]).

Given the following code:add(1,[ ],L1), add(2, L1,L2),

add(3,L2,L3). What would be the binding for

L3?


25/33


List Operations

Deletes item from list: del(Item, [Item| Tail], Tail). del(Item, [Y | Tail], [Y | Tail1]) :-

del(Item, Tail, Tail1).

del/2 is non-deterministic, what woulddel(1,[1,2,1,3,1],L).

What would be the bindings forL if we

repeatedly asked for new alternatives?


26/33


Insert item into list: insert(I,List,NewList) :- del(I, NewList, List).

insert/3 also non-deterministic, what wouldinsert(x, [1,2,3], L)

bind toL if repeatedly ask for alternatives?


27/33


Permutation of a List

Lets define the permutation relation:perm(List, Permutation).

Are we clear about what is a permutation? Look at examples.

What type of definition will we look for?


28/33


Defining Permutation Relation

Where do we look for our cases?

What should be our base case?


29/33


Defining Permutation Relation

What should be our inductive case?

What should the head look like?

Whats the relationship between the differentparts?


30/33


Permutation Defined

permutation([ ],[ ]).permutation([X | L1], Perm) :-

permutation(L1, L2),

insert(X, L2, Perm).


31/33


Homework Quiz

Write definitions for the following relations: reverse(List, ReverseList)

subSet(Set, SubSet)

flatten(List, FlatList)


32/33


Summary

If data structure defined inductively thenusually operations are defined inductively.

However, sometimes the data structure basecase does not make sense for the operation,

then need to find new base case.

First part of coming up with inductive case isfinding what the head should be, often part ofhead is data structure inductive case.


33/33


Summary contd

Defining relations in pure Prolog allowsdefinitions to be used in many ways.

However, when some uses have common name(e.g., last) then should define new relation

from old using the common name.

Documents

L4-ListsAndListOperations