CS 541 Lecture -*- Outline -*-

* Introduction to Logic Programming

** additional motivation for logic programming in particular

	immensely fruitful area of research
		(because of fundamental connections
			to both logic and computation)
	great tool for operational semantics and type theory,
                as it resembles their notation

** logic programming idea
------------------------------------------
         CREATING THE
     IDEA OF LOGIC PROGRAMMING

Recall motivation for declarative prog:
  1. write programs efficiently
  2. execute specifications
  3. separate directions about control
       and data structures

How would you specify a sort routine?





------------------------------------------

        sorted(List) = List'
                where ordered(List')
                  and permutation(List, List')

        Q: How can we then use this to sort some particular list L?
                exist L' . sort(L) = L'
        Q: How could such a theorem be proved?
                - give the sorted list L' (constructive)
                - prove that every list can be sorted (nonconstructive)
        
------------------------------------------
     ABSTRACTING FROM THE EXAMPLE

Model: programs are modeled as


Specification of a problem:
 a problem to be solved is







Answer to a problem:


------------------------------------------
        ... relations between input and output

        ... a decription of facts and relationships
        and an existential conjecture about the existence of a relationship.
        for example,
                sorted(List, List') if ordered(List')
                                         and permutation(List,List').
		exists O . L = [3,1,2] and sorted(L, O)?
        
        ... a constructive proof of the conjecture,
                which thus actually produces the output.
		e.g., the sorted list

	The problem (for the language designer/implementor) is:
		how to state such descriptions and conjectures
		how to instruct a system to do such constructive proofs
		how to do it fast

** History (omit)
        1930s Herbrand and others develop proof procedures for pred. calculus
        1960 Prawitz introduces unification as aid to theorem proving
        1965 Robinson's resolution algorithm
        1973 first FORTRAN version of Prolog (U. Marseille-Aix, Colmerauer)
        1977 first Prolog compiler (Edinburgh, due to Warren)
			as fast as LISP!
	1979 Kowalski's paper: Algorithm = Logic + Control
        1981 Japanese adopt Prolog for fifth-generation computing effort
		(This produces some interesting work, but not what was hoped)


** What to read in Dale Miller's notes
	"\Prolog: An Introduction to the Language and its Logic"

skimed parts would be helpful to read,
but don't have to be read very carefully.

essential               skim		topic
                        ch. 1		intro
ch. 2					kinds, types, and signatures
ch. 3					first-order Horn clauses
ch. 4					modules and the top level
			ch. 5		first-order Hereditary Harhop formulas
6.1-6.4					Simply-typed lambda terms and formulas
			6.5		higher-order logics
ch. 7					Computing with \-terms
ch. 8                                   Higher-order programming
                        ch. 9           higher-order hereditary Harrop formulas