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Prolog for Linguists Symbolic Systems 139P/239P

Prolog for Linguists Symbolic 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. 22 nd. Course web page. http://www.stanford.edu/class/symbsys139p

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Prolog for Linguists Symbolic Systems 139P/239P

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  1. Prolog for Linguists Symbolic Systems 139P/239P John Dowding Week 2, October 15, 2001 jdowding@stanford.edu

  2. Administrivia • Registration: Symbolic Systems or Linguistics • Bookstore will start returning C&M books at Oct. 22nd.

  3. Course web page • http://www.stanford.edu/class/symbsys139p • programs used in class • power point slides • homework assignments, solutions

  4. Office Hours • We have reserved 4 workstations in the Unix Cluster in Meyer library, fables 1-4 • 4:30-5:30 on Thursday

  5. Course Schedule • Oct. 8 • Oct. 15 • Oct. 22 • Oct. 29 (double up) • Nov. 5 • Nov. 12 • Nov. 26 (double up) • Dec. 3 No class on Nov. 19

  6. Prolog program • A Prolog program is defined by a set of Predicates • Each Predicate has a unique Functor and Arity parent(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

  7. 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.

  8. 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).

  9. 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).

  10. Goal = parent(P, john) parent(james, john) parent(florence, john) parent(james, john). parent(james, alan). parent(florence, john). parent(florence, alan). parent(alan, elizabeth). parent(alan, emily). Prolog Execution Model/Prolog Debugger EXIT CALL FAIL REDO

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

  12. Execution Model – mult(s(s(s(0))), s(s(0)), Result) mult(s(s(0)),s(s(0)), 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). mult(s(0), s(s(0)), Partial) add(s(s(0)), Partial, Prod) 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).

  13. 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

  14. And-Or Trees or and and and or or or or or and and and and and and and or or or or or or or or or

  15. And-Or Tree (cont.) or mult(s(Term1), Term2, Product):- mult(Term1, Term2, Partial), add(Term2, Partial, Product). mult(0, Term, 0):- is_number(Term). and and is_number(Term) add(Term2,Partial,Product) mult(Term1, Term2, Partial) or or or and and and and and and

  16. 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).

  17. 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.

  18. Example: member/2 % member(?Element, ?List) member(Element, [Element|_Tail]). member(Element, [_Head|Tail]):- member(Element, Tail).

  19. 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).

  20. 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).

  21. 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

  22. Example: sublist/3 (cont) sublist1(SubList, List):- append(List1, _List2, List), append(_List3, SubList, List1).

  23. Example: “naïve” reverse % "naive reverse": nreverse(?List, ?ReversedList). nreverse([], []). nreverse([Head|Tail], ReversedList):- nreverse(Tail, ReversedTail), append(ReversedTail, [Head], ReversedList).

  24. 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).

  25. “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.

  26. 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.

  27. 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

  28. Arithmetic: Built-In is/2 • Arithmetic expressions are not normally evaluated in Prolog. • Built-In infix operatoris/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

  29. 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.

  30. Cut (cont.) Head1 :- Goal1, Goal2, …, GoalN, !, … Head2 :- … Head3 :- … … HeadN :- … • Removes the choice point that allows Head2 …HeadN • Removes any choice points that may have been introduced in Goal1 … GoalN. • We will discuss Cut in more detail later on.

  31. 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).

  32. 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).

  33. 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.

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