Prolog for LinguistsSymbolic Systems 139P/239P

John Dowding

Week 2, October 15, 2001

jdowding@stanford.edu

Administrivia

Registration: Symbolic Systems or Linguistics

Bookstore will start returning C&M books at Oct. 22nd.

Course web page

http://www.stanford.edu/class/symbsys139p

programs used in class power point slides homework assignments, solutions

Office Hours

We have reserved 4 workstations in the Unix Cluster in Meyer library, fables 1-4

4:30-5:30 on Thursday

Course Schedule

1. Oct. 82. Oct. 153. Oct. 224. Oct. 29 (double up)5. Nov. 56. Nov. 127. Nov. 26 (double up)8. Dec. 3

No class on Nov. 19

Prolog program

A Prolog program is defined by a set of Predicates

Each Predicate has a unique Functor and Arityparent(Parent, Child)

a predicate whose functor is “parent” with arity 2.

Each Predicate is defined by a sequence of Clauses

A Clause is either a Fact or a Rule

fact(…).

head(…) :- goal1(…), … , goalN(…).

Each argument to a predicate is a Term

Terms

Each argument to a predicate is a Term

A Term is either: Atomic Variable Compound

Atoms are either constant symbols, or numbers

Compound terms have a functor and arity: functor(Arg1, Arg2, …, ArgN) Each Arg is itself a Term.

Homework solutions

exponential(+Base, +Exponent, ?Result) Base case: Base^0 = 1 Recursive case: Base ^ (N+1) = Base * (Base^N)

% exponential(+Base, +Exponent, ?Result)

exponential(Base, 0, s(0)):-

is_number(Base).

exponential(Base, s(Exponent), Result):-

exponential(Base, Exponent, PartialResult),

mult(PartialResult, Base, Result).

Factorial

factorial(+N, ?Factorial) fact(1) = 1 fact(N+1)= (N+1) * fact(N)

%factorial(+Number, ?Factorial)

factorial(s(0), s(0)).

factorial(s(Number), Factorial):-

factorial(Number, PartialFactorial),

mult(s(Number), PartialFactorial, Factorial).

Prolog Execution Model/Prolog Debugger

CALL EXIT

FAIL REDOparent(james, john).parent(james, alan).parent(florence, john).parent(florence, alan).parent(alan, elizabeth).parent(alan, emily).

Goal = parent(P, john) parent(james, john)parent(florence, john)

Execution Model (conjunctions)

parent(james, john).parent(james, alan).parent(florence, john).parent(florence, alan).parent(alan, elizabeth).parent(alan, emily).

female(emily).female(florence).female(elizabeth).

parent(Mother, john) female(Mother)parent(james, john) female(james)parent(florence, john) female(florence)

Execution Model – mult(s(s(s(0))), s(s(0)), Result)

mult(0, Term, 0):- is_number(Term).mult(s(Term1), Term2, Product):- mult(Term1, Term2, Partial), add(Term2, Partial, Product).

add(0, Sum, Sum):- is_number(Sum).add(s(Addend1), Addend2, s(Sum)):- add(Addend1, Addend2, Sum).

mult(s(s(0)),s(s(0)), Prod)

mult(s(0), s(s(0)), Partial) add(s(s(0)), Partial, Prod)

add(s(s(0)), Prod, Result)

mult(0, Term, 0):- is_number(Term).mult(s(Term1), Term2, Product):- mult(Term1, Term2, Partial), add(Term2, Partial, Product).

Prolog Debugger Demo

Built-In predicates: trace/0. notrace/0.

Debugger actions: ‘c’ or <cr> - creep ‘s’ – skip ‘l’ – leap ‘r’ – retry ‘f’ – fail ‘a’ - abort

And-Or Trees

or

andand and

ororor

ororor or

andandandandand and and

orororor

oror

or

And-Or Tree (cont.)

or

and and

mult(0, Term, 0):- is_number(Term).

mult(s(Term1), Term2, Product):- mult(Term1, Term2, Partial), add(Term2, Partial, Product).

or or or

is_number(Term)mult(Term1, Term2, Partial)

add(Term2,Partial,Product)

and and and and and and

Linked Lists

Prolog allows a special syntax for lists: [a,b,c] is a list of 3 elements [] is a special atom indicating a list with 0 elements

Internally, Prolog lists are regular Prolog terms with the functor ‘.’ (so called “dotted pairs”)[a,b,c] = ‘.’(a, ‘.’(b, ‘.’(c, []))).The symbol | in a list indicates “rest of list”, or the term that is the 2nd argument of a dotted pair.[a,b,c] = [a|[bc]].[Head|Tail] is a common expression for dividing a list into its first element (Head) and the rest of the list (Tail).

Example: list/1

% list(?List)

list([]).

list([_Head|Tail]):-

list(Tail).

Since Prolog is untyped, we don’t have to know anything about Head except that it is a term.

Example: member/2

% member(?Element, ?List)

member(Element, [Element|_Tail]).

member(Element, [_Head|Tail]):-

member(Element, Tail).

Example: delete/3

% delete(+Element, +List, -NewList)

% delete/3 succeeds if NewList results from removing

% one occurrence of Element from List.

delete(Element, [Element|Tail], Tail).

delete(Element, [Head|Tail], [Head|NewTail]):-

delete(Element, Tail, NewTail).

Example: append/3

% append(?List1, ?List2, ?List3)

% append/3 succeds if List3 contains all the elements of

% List1, followed by all the elements of List2.

append([], List2, List2).

append([Head|List1], List2, [Head|List3]):-

append(List1, List2, List3).

Example: sublist/3

% sublist(?SubList, +List)

sublist(SubList, List):-

append(_List1, List2, List),

append(SubList, _List3, List2).

1st append finds a beginning point for the sublist

2nd append finds an end point

Example: sublist/3 (cont)

sublist1(SubList, List):-

append(List1, _List2, List),

append(_List3, SubList, List1).

Example: “naïve” reverse

% "naive reverse": nreverse(?List, ?ReversedList).

nreverse([], []).

nreverse([Head|Tail], ReversedList):-

nreverse(Tail, ReversedTail),

append(ReversedTail, [Head], ReversedList).

Example: efficient reverse/3

% reverse(+List, -ReversedList)

reverse(List, ReversedList):-

reverse_helper(List, [], ReversedList).

reverse_helper([], ReversedList, ReversedList).

reverse_helper([Head|Tail], PartialList, ReversedList):-

reverse_helper(Tail, [Head|PartialList], ReversedList).

“Pure Prolog” and non-logical built-ins

All the examples so far have been “pure Prolog” Contain no built-ins with non-logical side-effects

Prolog has many built-in predicates that have such side-effects: Type checking of terms Arithmetic Control execution Input and output Modify the program during execution Perform aggregation operations

Use of non-logical built-in predicates usually effects the reversability of your program.

Type-checking Built-in Predicates

var(X) – is true when X is an uninstantiated variable.

nonvar(X) – is true when X is not a variable.

atom(X) – is true when X is a symbolic constant.

number(X) – is true when X is a number

atomic(X) – is true when atom(X) or number(X).

compound(X) – is true when X is a compound term.

Term constructor/selectors: functor/3, arg/3

functor(+Term, ?Functor, ?Arity) Find the Functor and Arity of Term

functor(?Term, +Functor, +Arity) Constructs a new Term with Functor and Arity

arg(+N, +Term, ?SubTerm) Unifies SubTerm with the Nth argument of Term

Arithmetic: Built-In is/2

Arithmetic expressions are not normally evaluated in Prolog.Built-In infix operator is/2 evaluates it’s 2nd argument, and unifies the result with it’s 1st argument.| ?- X = 5 + 2.X = 5+2?yes| ?- X is 5 + 2.X = 7 ?yes

Any variables in the right-hand side of is/2 must be instantiated when it is evaluated.

Revisit operator and arithmetic at a later time

Cut (!)

The ! Symbol (pronounced “cut”) modifies the execution of your program by committing to certain choices. That is, it removes choice points.

Easy to describe what it does, more difficult to get used to using it properly.

Cut (cont.)

Head1 :- Goal1, Goal2, …, GoalN, !, …Head2 :- …Head3 :- ……HeadN :- …

Removes the choice point that allows Head2 …HeadNRemoves any choice points that may have been introduced in Goal1 … GoalN.We will discuss Cut in more detail later on.

Example: delete_first/3

% delete_first(+Element, +List, -NewList)

% removes the 1st occurrence of Element in List.

delete(Element, [Element|Tail], Tail):-

!.

delete(Element, [Head|Tail], [Head|NewTail]):-

delete(Element, Tail, NewTail).

Example: is_term/1

is_term(Atomic) :- atomic(Atomic).is_term(Variable):- var(Variable).is_term(CompoundTerm):-

compound(CompoundTerm), functor(CompoundTerm, _Functor, Arity).

is_term_helper(Arity, CompoundTerm).

is_term_helper(0, _CompoundTerm) :- !is_term_helper(Index, CompoundTerm):-

arg(Index, CompoundTerm, SubTerm),is_term(SubTerm),NextIndex is Index – 1,is_term_helper(NextIndex, CompoundTerm).

Homework

Read section in Sicstus Prolog manual on debugger.

Use debugger to trace through today’s example programs and understand how the work.

Implement: delete_all(+Element, +List, -NewList) that removes all

occurrences of Element from List to find NewList. replace_all(+Element, +List, +NewElement, -NewList) replaces

every occurrence of Element with NewElement in List to give NewList.