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Meta-Programming

Meta-Programming. t.k.prasad@wright.edu http://www.knoesis.org/tkprasad/. Meta-Programs : Program manipulating Programs. Extend Prolog introduce new search strategy or modify existing search strategy add expressive logical connective extend/modify syntax/semantics Enable Debugger

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Meta-Programming

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  1. Meta-Programming t.k.prasad@wright.edu http://www.knoesis.org/tkprasad/ L11MetaPgm

  2. Meta-Programs : Program manipulating Programs • Extend Prolog • introduce new search strategy or modify existing search strategy • add expressive logical connective • extend/modify syntax/semantics • Enable Debugger • Support Theorem Provers and Rule-based Systems L11MetaPgm

  3. Basic Meta-Interpreter prove( true ) :- !. prove( (G1, G2) ) :- !, prove(G1), prove(G2). prove( G ) :- system(G), G. prove( G ) :- clause(G,B), prove(B). • System-predicate holds of built-ins. L11MetaPgm

  4. Upgrading the Meta-Interpreter • Adding an or-operator prove( (G1 ; G2) ) :- prove(G1). prove( (G1 ; G2) ) :- prove(G2). • Changing the order of evaluation from right to left prove( (G1, G2) ) :- !, prove(G2), prove(G1). L11MetaPgm

  5. Tracing Basic Meta-Interpreter tracep( Goal ) :- tracep(Goal, 0). tracep( true, Dpth ) :- !. tracep((G1, G2),Dpth ):-!, tracep(G1, Dpth), tracep(G2, Dpth). L11MetaPgm

  6. (cont’d) tracep( G, D ) :- display(’Call:’, G,D), clause(G,B), D1isD+1, tracep(B, D1), display(’Exit:’, G,D), display_redo(G,D). tracep( G, D ) :- display(’Fail:’, G,D), fail. L11MetaPgm

  7. (cont’d) display( Msg,G, D ) :- tab(D), write(Msg), write(G), nl. display_redo( G, D ) :- true ; display(’Redo:’, G, D), fail. L11MetaPgm

  8. (Trace Output) 4 ?- tracep(member(5,[1,5,3])). Call:member(5, [1, 5, 3]) Call:member(5, [5, 3]) Exit:member(5, [5, 3]) Exit:member(5, [1, 5, 3]) true ; Redo:member(5, [1, 5, 3]) Redo:member(5, [5, 3]) Call:member(5, [3]) Call:member(5, []) Fail:member(5, []) Fail:member(5, [3]) Fail:member(5, [5, 3]) Fail:member(5, [1, 5, 3]) false. L11MetaPgm

  9. Other AI Applications • Forward chaining or Bottom-up computation • From facts to all conclusions • Heuristic search (incl. breadth-first search) • Diagnosis; Explanation generation • Determine the set of facts, which when assumed, proves the goal • Abductive reasoning L11MetaPgm

  10. Meta-level Definition not(A) :- call(A), !, fail. not(A). • Meta-variables range over terms encoding a goal. ?-setof(X, G, L). • X and L are object variables, while G is meta-variable. L11MetaPgm

  11. Program Manipulation Example • Write a meta-program to collect all variables in a formula A. constant(A) :- atom(A); integer(A) ; float(A). collect_var(A,Q-Q) :- constant(A). collect_var(A,[A|Q]-Q) :- var(A). L11MetaPgm

  12. (cont’d) collect_var(A,Q) :- A =.. [P|As], collect_vars(As,Q). collect_vars([],Q-Q) :- !. collect_vars([A|As], Q-Qt) :- collect_var(A, Q-Qs), collect_vars(As, Qs-Qt). ?-collect_var(p(X,Y), L). L= [X,Y| _1]-_1 • Difference lists for efficient append L11MetaPgm

  13. Theorem Proving Applications and others • Proving equivalence of boolean expressions, arithmetic expressions, etc • Normalization of expressions • Refutation theorem proving • Goal reordering based on binding information for efficient execution of query • Pretty Printing L11MetaPgm

  14. Equational Reasoning: Example • Prove two terms are equivalent given that the operators satisfy certain equality constraints. • Associativity: (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) • Commutativity: (a + b) =(b + a) (a * b) =(b * a) L11MetaPgm

  15. (cont’d) • Identity: (a + 0) = a = (0 + a) (a * 1) = a = (1 * a) • Zero: (a * 0) = 0 = (0 * a) • Distributive Law: (a + b) * c =(a * c + b * c) L11MetaPgm

  16. Digression : Normal Form • Equality constraints induce an equivalence relation on terms (e.g., arithmetic expressions) • An equivalence relation partitions the set of terms into equivalence classes • A normal form of a term is the representative of the equivalence class to which the term belongs. L11MetaPgm

  17. Normalization Procedure • Associative operation : Ignore nestings • collapse term trees to lists • Commutative operation : Ignore order • sort • Zeros and Identities • simplify + delete elements • Distributivity • sum of products form or product of sums form L11MetaPgm

  18. Application • Evaluation of a variable-free/constant arithmetic expression is normalization. 2 + 3 => 5 (1 + (1 + 2) + 1) => 5 • Equality constraints given by axioms are used as rewrite rules for normalization. • Definition of primitive operations • Relationship among operations L11MetaPgm

  19. An Interpreter for Object-Oriented Programs • Class Definition object(Object, Methods) E.g., object(rectangle(Len,Wid),[(area(A) :- A is Len * Wid)] ). class-name + instance variables message method L11MetaPgm

  20. (cont’d) • object/instance rectangle(5,10) • passing a message send(Object-instance, Message) E.g., send(rectangle(5,10),area(A)). • specifying class-subclass hierarchy E.g., isa(square(sd),rectangle(sd,sd)). L11MetaPgm

  21. Interpreter Code send( Object, Message) :- get_methods( Object, Methods), process( Message, Methods). % Find Object's methods % Execute corresponding method get_methods( Object, Methods) :- object( Object, Methods). % Private methods get_methods( Object, Methods) :- isa( Object, Super), get_methods( Super, Methods). % Inherited methods L11MetaPgm

  22. (cont’d) process( Msg, [Msg | _]). % Use a fact process( Msg, [ (Msg :- Body) | _]) :- call( Body). % Use a rule process( Msg, [_ | Methods]) :- process( Msg, Methods). L11MetaPgm

  23. ?- trace, send(square(4), area(A)). Call: (7) send(square(4), area(_G414)) ? creep Call: (8) get_methods(square(4), _G551) ? creep Call: (9) object(square(4), _G551) ? creep Fail: (9) object(square(4), _G551) ? creep Redo: (8) get_methods(square(4), _G551) ? creep Call: (9) isa(square(4), _G551) ? creep Exit: (9) isa(square(4), rectangle(4, 4)) ? creep Call: (9) get_methods(rectangle(4, 4), _G554) ? creep Call: (10) object(rectangle(4, 4), _G554) ? creep Exit: (10) object(rectangle(4, 4), [ (area(_G555):-_G555 is 4*4)]) ? creep Exit: (9) get_methods(rectangle(4, 4), [ (area(_G555):-_G555 is 4*4)]) ? creep Exit: (8) get_methods(square(4), [ (area(_G555):-_G555 is 4*4)]) ? creep Call: (8) process(area(_G414), [ (area(_G555):-_G555 is 4*4)]) ? creep Call: (9) _G414 is 4*4 ? creep Exit: (9) 16 is 4*4 ? creep Exit: (8) process(area(16), [ (area(16):-16 is 4*4)]) ? creep Exit: (7) send(square(4), area(16)) ? creep A = 16 . L11MetaPgm

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