Metaprogramming

1
Meta-programming

• Vocabulary
• Meta-language manipulating language
• Object language manipulated language
• can be the same!
• In LP
• use LP to reason about LP
• meta-programs programs manipulating programs
• compilers, debuggers, editors,
• here interpreters

2
Interpreters

• Functional description
• Input program written in some language
• Output result of executing the program
• Representation of object program
• important decision
• program structure, data structures
• ground representation
• non-ground representation
• meta- object languages integrated (dangerous?)

3
Ground representation

• Model the universe of formulas
• formulas ? terms of the meta-language
• One possible coding obj ? meta
• notation ltAgt coding of A
• define a mapping F(A) ? T(ltAgt)
• constants, variables ? constants
• functors, predicate symbols ? functors
• logical connectives ? functors

4
A possible coding

• Alphabet
• predicates, functors, constants ? themselves
• variable ? constant v_n (n unique for each var)
• Formulas
• lt?Agt not(ltAgt)
• ltL1 ? ? Lmgt ltL1gt,,ltLmgt
• ltH ? Bgt if(ltHgt,ltBgt)
• lt ? G gt if(, ltGgt)
• Programs
• ltC1,,Cngt ltC1gt, , ltCngt
• or stored in facts clause/1

5
Some sidenotes

• Meta- object-level should not get mixed
• Prolog no automatic tools to prevent this
• typed languages types for coded programs
• Static dynamic representations
• dynamic coded program given in some argument
• static coded program stored in clauses

6
Interpreting a program

• We have a search problem!
• initial state query
• final state empty clause
• operations resolution
• selection of goal
• selection of unifying clauses
• Notes
• example implementations return the chain of
  clauses used as solution path (not answer
  substitution)
• solution using a static program dfs is simpler

7
Whats the use?

• Direct execution surely more efficient
• Own execution surely more flexible!
• alternative search strategies
• debugging (tracing, statistics)
• dynamic object programs (database updates)
• collect proof tree (or even SLD-tree)
• other logics (fuzzy, nonmonotonic, modal)
• other languages (CF DCG grammars)
• applications transformation, verification,
  synthesis

8
Ground non-ground

• Ground interpreters are slow
• main reason variables represented as constants
• renaming, unification, application, answer
  extraction
• Non-ground
• use variable manipulation capabilities of the
  meta-language
• represent object-level vars with meta-level vars
• semantics changes!
• same variables for obj. formulas individuals
• typing helps
• more pragmatic, less logical and surprisingly
  simple

9
Meta-interpreting full Prolog

• Negation
• use negation as failure
• System predicates
• handle separately as special cases
• Cuts
• obvious way does not work
• needs ancestor cut or programmed backtracking

10
Advanced debugging

• Tracing just add output/input commands
• Error types
• ? G does not terminate (stack overflow)
• program returns wrong answers
• program does not return some correct answer
• Reasons
• M(P) is not correct / complete in relation to the
  intended model IM of the programmer

11
Debugging nontermination

• Add a depth bound D to computations
• When D is exceeded
• return call stack to the current goal
• Reasons for nontermination
• loops (,Gi,,Gj,), Gi is an instance of Gj
• non-inductive definitions
• How to find good D?

12
Wrong answers

• P is incorrect (with respect to IM)
• ? P must contain an incorrect clause C
• When is C H ? B1,,Bn incorrect?
• There exists an instance C? such that
• (B1 Bm)? is in IM but H? is not
• C? counter-example of C
• Idea
• find counter-examples from incorrect computations
• How?

13
Wrong answers method 1

• Algorithm
• Construct the proof tree of the wrong answer
• Traverse the tree bottom-up (postorder)
• Ask oracle for each node (atom) whether it is
  true or not (yes/no)
• Interpretation of oracles answer
• No current node is the head of the
  counter-example
• Yes continue right or upwards
• Answers can also be provided by another (correct)
  program!

14
Better method for wrong answers

• Method 1 asks (in worst case) about every node
• Query complexity of oracle queries
• very important if oracle is a human
• Method 1 size of the proof tree
• Method 2 depth of the proof tree
• Idea
• advance top-down, search for wrong descendants
• if none then the current node is a
  counter-example
• otherwise advance to the wrong node

15
Missing solutions

• P should compute A but ?A fails
• A is not covered by P
• When does P cover some A?
• C H ? B1, , Bn
• B1,,Bm? ? M(P)
• H? is an instance of A
• if P can compute H? then P can also compute A
• Idea for debugging
• Find lowest-level uncovered goal MG
• Clauses defining MG are suspects (for the missing
  solution)

16
Debugging the missing solution

• Idea try to solve A anyway
• If (when) A fails
• for each C H ? B1,,Bn s.t. H? A? (mgu)
• ask if theres a ground instance of (B1,,Bn)? in
  IM
• no A is uncovered (and C is a suspect)
• yes we continue from a failing (uncovered) Bi?
• If A succeeds, it is clearly covered

17
Requirements for the instance-oracle

• oracle(C, Answer)
• Answer is either
• a ground instance of C that is true in IM
• no, if none
• human oracle
• some user-friendliness?
• ask only for the variables of C
• computer
• compute all goals H, B1, , Bm
• bind remaining variables (to what? any constants?)

18
Expert systems

• Definition of an ES
• guide for humans in problems that require some
  kind of expertise
• Typical tasks
• diagnosis find reasons to symptoms
• control prevent a system from entering abnormal
  states
• planning find a sequence of actions (e.g.
  assembly)

19
Characteristics of ESs

• Inference engine knowledge base
• KB knowledge about the domain (rules)
• IE infers new knowledge from the KB
• Uncertainty incompleteness possible in KB
• Commercial ES GUI dialogue
• Explanation capabilities
• How the result was achieved
• Why something was shown true
• Why something was asked about
• Support for knowledge acquisition

20
ES LP

• KB IE clauses, SLD-resolution
• some systems (OPL5) use forward chaining
• ES must assume that KB is incomplete
• KB in general terms
• user gives the missing details
• symptom F, program P find cause A such that
• P ? A - F (abductive reasoning)

21
Acquiring knowledge

• Enhance meta-interpreter
• ask for missing knowledge
• e.g. symptoms in a diagnosis case
• Things to note
• decide how to store acquired knowledge
• do not ask same thing twice
• do not ask blindly anything

22
Justifying and explaining

• Answer with questions
• Why?
• Why does the ES ask me this (fact F)?
• Answer rule A ? B1,,F,Bm is to be used in the
  reasoning and F is not known
• How?
• How did the ES come up with conclusion G?
• Answer interpret the proof tree of G to the user

23
Telling how

• Construct the proof tree PG of G
• Explain the structure of PG to the user
• tell what was asked for and what was deduced
• filter out trivia
• Enhancements
• show tree level by level
• ask user which parts of the tree should be
  explained

24
Reasoning with uncertainty

• Here a simplistic Mycin-like implementation
• Add certainty factors to rules
• clause(if(H,B), CF)
• CF our amount of trust in rule H ? B
• Modify solver to compute with these
• p(B1,,Bm) minp(Bi) i1..n
• p(A) p(B?)CF, where
• clause(if(H,B), CF) is in P and
• ? mgu(A,H)
• Threshold cutoff p lt 0.0001 fail