(Print this page as a cover sheet for your printouts)

CSCE 420 HOMEWORK 2
Dr. Daugherity
Due: 11:59 P.M. Monday, October 30, 2017

"On my honor, as an Aggie, I have neither given nor received any unauthorized 
aid on any portion of the academic work included in this assignment."


________________________________	________________________________
Typed or printed name of student	           Signature of student

NOTE:  Please follow your lab instructor's directions for submitting your 
assignment through CSNET.  ONLY ASSIGNMENTS SUBMITTED TO CSNET WILL BE GRADED!
Make a printout of each source file and staple it behind this cover sheet.
Sign it and turn it in in class Tuesday.  IF YOU DO NOT TURN IN A SIGNED COVER 
SHEET YOUR WORK WILL NOT BE GRADED!

NOTE:  Homework will be graded on build.tamu.edu, using g++ 7.2.0 with 
-std=c++17, or javac and java, or python3.

You are free to develop your programs on any other platform, but it is your 
responsibility to make sure your programs also compile and execute correctly on
build.tamu.edu as specified.

NOTE:  Each file submitted (hw2pr1.cpp, etc.--see below) must begin as follows:
//Your name and UIN
//CSCE 420
//Due: Ocotber 2, 2017
//hw2pr1.cpp (or whatever this file name is)

NOTE:  Also write a README.txt file with whatever information is needed to
compile and run your programs.  Zip the README.txt and the homework files into
a single file named hw2.zip and submit to CSNET.

The grade for this lab will be based on style (formatting, variable names, 
comments, etc.), syntax (no compilation or link errors), and correctness 
(passes all test cases).  Your grade for this lab is:
Problem #	 1       2       3       4 
Style             /2      /4      /4      /2 
Syntax            /3      /6      /6      /3 
Correctness       /5      /10     /10     /5
-------------------------------------------------------------------
Total             /10     /20     /20     /10
Grand total _____/50

1. (10 points) Code the mutually-recursive max_value and min_value functions
specified in Figure 5.3 and use them to find the max (root's value) 
of a tree read in from the keyboard as a nested list.  For example, the tree in Figure 5.2 would be input as
	((3,12,8),(2,4,6),(14,5,2))
Name your program hw2pr1.cpp, etc.

2. (20 points) Modify problem 1 to do both alpha and beta pruning according to
Figure 5.7 and print a message "alpha pruning" or "beta pruning" each time that
occurs (in addition to the max of the tree).  For example, the tree
	((3,8,(7,(3,0,7),(8,8,2))),
	 (4,(7,9,8),8),
	 (((3,6,4),2,6),((9,2,9),4,7,(6,4,5) ),4,(6,4,5))
	)
would print "alpha pruning" 3 times and "beta pruning" 3 times.
Name your program hw2pr2.cpp, etc.

3. (20 points) Write a Horn clause inference engine which accepts a filename
from the user, reads Horn clauses from that file, and then makes all possible 
deductions using forward chaining.  The format of the input file will be one 
Horn clause per line in PROLOG notation (see section 9.4.2).  For example, if
the data file contains

	B:-A.
	D:-B,C.
	A.
	C.

then the program will deduce B and D are true.  For another test file use
Fig. 7.15.  

Name your program hw2pr3.cpp etc.  Hint: Fig. 7.14 gives the pseudocode.

OPTIONAL EXTRA CREDIT 
=====================
4. (10 points) Write a backtracking prover based on the DPLL_satisfiable
function in Fig. 7.17 which first reads Horn clauses as in the example from
problem 3, then a query preceded by a question mark (that is, what you are
asking to be proven).

	B:-A.
	D:-B,C.
	A.
	C.
	?D

To prove D is equivalent to saying the Horn clauses entail (imply) D.  Since an
implication is only false if the "if" side is true and the "then" side is false,
we add "not D" to the list of Horn clauses and call DPLL_satisfiable.  If it
returns false, that means "not not D" must be true, which is D, which is what
we were trying to prove, so output "Proven!"  If the query had been E then
adding "not E" and calling DPLL_satisfiable would result in true, so output
"Cannot prove."

Hint: In PROLOG notation "not D" can be written
	:-D.
Since the "then" side can always be or'ed with false, this is equivalent to
	D --> false
which is equivalent to "not D."  Another way of thinking about it is that the
"then" side of a Horn clause is false or'ed with whatever terms are there (in
this case none).

Name your program hw2pr4.cpp etc.