Meta-Programming

1
Meta-Programming

• t.k.prasad_at_wright.edu
• http//www.knoesis.org/tkprasad/

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

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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.

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).

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Tracing Basic Meta-Interpreter

• tracep( Goal ) -
• tracep(Goal, 0).
• tracep( true, Dpth ) - !.
• tracep((G1, G2),Dpth )-!,
• tracep(G1, Dpth), tracep(G2, Dpth).

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(contd)

• tracep( G, D ) -
• display(Call, G, D),
• clause(G,B),
• D1 is D1,
• tracep(B, D1),
• display(Exit, G, D),
• display_redo(G, D).
• tracep( G, D ) -
• display(Fail, G, D), fail.

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(contd)

• display( Msg, G, D ) -
• tab(D), write(Msg),
• write(G), nl.
• display_redo( G, D ) -
• true
• display(Redo, G, D), fail.

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(Trace Output)

• 4 ?- tracep(member(5,1,5,3)).
• Callmember(5, 1, 5, 3)
• Callmember(5, 5, 3)
• Exitmember(5, 5, 3)
• Exitmember(5, 1, 5, 3)
• true
• Redomember(5, 1, 5, 3)
• Redomember(5, 5, 3)
• Callmember(5, 3)
• Callmember(5, )
• Failmember(5, )
• Failmember(5, 3)
• Failmember(5, 5, 3)
• Failmember(5, 1, 5, 3)
• false.

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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

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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.

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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,AQ-Q) -
• var(A).

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(contd)

• collect_var(A,Q) -
• A .. PAs,
• collect_vars(As,Q).
• collect_vars(,Q-Q) - !.
• collect_vars(AAs, 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

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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

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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)

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(contd)

• 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)

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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.

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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

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Application

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

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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
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(contd)

• 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)).

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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

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(contd)

• process( Msg, Msg _).
• Use a fact
• process( Msg, (Msg - Body) _) - call(
  Body).
• Use a rule
• process( Msg, _ Methods) -
• process( Msg, Methods).

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• ?- 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 44)) ? creep
• Exit (9) get_methods(rectangle(4, 4),
  (area(_G555)-_G555 is 44)) ? creep
• Exit (8) get_methods(square(4),
  (area(_G555)-_G555 is 44)) ? creep
• Call (8) process(area(_G414),
  (area(_G555)-_G555 is 44)) ? creep
• Call (9) _G414 is 44 ? creep
• Exit (9) 16 is 44 ? creep
• Exit (8) process(area(16), (area(16)-16 is
  44)) ? creep
• Exit (7) send(square(4), area(16)) ? creep
• A 16 .