Prolog a declarative language A program in a

Prolog a declarative language • A program in a declarative programming language consists of assertions rather than assignments and control flow statements. • These declarations are actually statements or propositions in symbolic logic. • Program doesn’t state how a result is to be computed but what the result is.

Prolog program composition • Collections of statements • Kinds of statements – Facts – Rules • Statements are constructed from terms – A term is a constant, a variable, or a structure

Prolog program elements • Constants are – Atoms or integers • Atoms are – Symbolic values of Prolog – String of letters, digits, and underscores that begins with a lowercase letter OR – String of any printable ASCII characters delimited by apostrophes

Prolog program elements • Variables are – any string of letters, digits, and underscores that begins with an upper case letter – not bound to types by declarations – bound to values and types by instantiations • Instantiation occurs only in resolution process – not like variables in imperative languages

Prolog program elements • Structures – have the general form functor(parameter_list) – functor is any atom & it identifies the structure – parameter_list can be any list of atoms variables or other structures. – are the way to specify facts in Prolog – can be thought of as objects – are relations – are predicates

Prolog facts • Facts – state relations explicitly • man(paul). • rich(joan). – SWI-Prolog doesn’t like spaces between the name of the relation and the left parenthesis. PDProlog doesn’t care. – are propositions that are assumed to be true – are the statements from which new information can be inferred – are headless Horn clauses – have no intrinsic semantics

Prolog rules • Rules – – – are headed Horn clauses right side is the antecedent or if part left side is the consequent or then part consequent must be a single term, antecedent may be either a single term or a conjunction • • • rich(joan) : - has_money(joan). rich(joan) : - has_health(joan), has_job(joan). Conjunctions contain multiple terms separated by logical and : - is read as if , means and

Example parent(X, Y) : - mother(X, Y). parent(X, Y) : - father(X, Y). grandparent(X, Z) : - parent(X, Y), parent(Y, Z). sibling(X, Y) : mother(M, X), mother(M, Y), father (F, X), father(F, Y).

Prolog as a theorem proving model • proposition – is the form of theorem that we want to prove or disprove – is called a goal – is called a query – syntactic form is that of a headless Horn clause • man(fred). – returns yes OR returns no – yes means that system proved goal was true under given database of facts and relationships – no means either the goal was proved false OR system was simply unable to prove it.

Sidebar 1 • The process of determining useful values for variables is called unification. • The temporary assigning of values to variables to allow unification is called instantiation. • Resolution is an inference rule that allows inferred propositions to be computed from given propositions.

Sidebar 2 • Horn clauses come in two forms – Single atomic proposition on the left side OR – Empty left side – Left side is called the head – Horn clauses with left sides are called headed Horn clauses – Horn clauses with empty left sides are called headless Horn clauses.

Example Database: p(X) : - q(X), not (r(X)). r(X) : - w(X), not (s(X)). q(a). q(b). q(c). s(a). w(a). w(b). Queries p(a). p(b). p(c).

Example Database: bachelor(P) : - male(P), not (married(P)). male(henry). male(tom). married(tom). Queries: bachelor(henry). bachelor(tom). bachelor(Who). married(Who). not(married(Who)).

Prolog operators • relational operators = = >= <= > < • Assignment operator is is peculiar - not like ordinary assignment operator

Behavior of Prolog “is” • takes an arithmetic expression as its right operand • takes a variable as its left operand • all variables in the arithmetic expression must already be instantiated • left-side variable cannot be previously instantiated • Discussion Examples: A is B / 17 + C X is X + 1

Prolog Arithmetic Example • • • speed(ford, 100). speed(chevy, 105). speed(dodge, 95). speed(volvo, 80). time(ford, 20). time(chevy, 21). time(dodge, 24). time(volvo, 24). distance (X, Y) : - speed(X, Speed), time(X, Time), Y is Speed * Time.

Short Prolog backtracking example /* facts */ likes(jake, chocolate). likes(jake, apricots). likes(darcie, licorice). likes(darcie, apricots). /* query or goal */ likes(jake, What), likes(darcie, What).

Miscellanea • parameters , arguments • arity – number of parameters/arguments in a parameter list • anonymous variable – used when don’t care mother (X, _). likes (_, What). • logical operators , means and ; means or + means not in SWI - Prolog not means not in PD Prolog

Miscellania • retract( ). - can be used to delete a single fact or relation • forget( ). – can be used to remove a file you have consulted • halt. – exits gracefully from SWI-Prolog • differences between – listing. – dir p. – dir.

Prolog lists • Lists – are written in square brackets with commas between the list’s element [condor, whooping_crane, dusky_seaside_sparrow] – can be used as the argument of a relation rarebird([condor, whooping_crane, dusky_seaside_sparrow]). – – can be queried can take advantage of anonymous variables have a head and a tail can be processed recursively

List Example Database: rarebird([condor, whooping_crane, dusky_seaside_sparrow]). Queries: rarebird(condor). rarebird(What).

List Example - continued Database: rarebird([condor, whooping_crane, dusky_seaside_sparrow]). noteworthy(Bird) : - rarebird([Bird, __]). noteworthy(Bird) : - rarebird([__, Bird]). Queries: rarebird(condor). rarebird(What). noteworthy(condor). noteworthy(Who).

List Example - continued Database: rarebird([condor, whooping_crane, dusky_seaside_sparrow]). noteworthy(Bird) : - rarebird([Bird, __]). noteworthy(Bird) : - rarebird([__, Bird]). rarebird(Bird) : - noteworthy(Bird). Queries: rarebird(condor). rarebird(What). noteworthy(condor). noteworthy(Who).

Head | Tail examples • Database rarebird([condor, whooping_crane, dusky_seaside_sparrow]). • Query rarebird([H | T]).

P 638. pro append ([], List). append([Head | List_1], List_2, [Head | List_3]) : append (List_1, List_2, List_3).

P 6382. pro list_op_2( [], []). list_op_2( [Head | Tail], List) : list_op_2 (Tail, Result), append (Result, [Head], List).

P 639. pro member (Element, [Element | _ ] ). member (Element, [_ | List]) : - member (Element, List

Matching a goal to a fact • Start with facts and rules and attempt to find a sequence of matches that lead to the goal. – Called bottom-up resolution – Also called forward chaining • Start with the goal and attempt to find a sequence of matching propositions that lead to a set of original facts in the database. – Called top-down resolution – Also called backward chaining • Prolog implementations use backward chaining.

How is solution found? • A depth-first search finds a complete sequence of proposition - a proof- for the first subgoal before working on the others. • A breadth-first search works on all subgoals of a given goal in parallel. • Prolog’s designers chose depth-first approach – uses fewer resources

Backtracking • When a goal with multiple subgoals is being processed and the system fails to show the truth of one of the subgoals, the system abandons the subgoal it could not prove. • It then reconsiders the previous subgoal, if there is one, and attempts to find an alternative solution to it. • A new solution is found by beginning the search where the previous search for that subgoal stopped. • Multiple solutions to a subgoal result from different instantiations of its variables.