Hi, I am looking for someone who are good at SML programming. This is
the question I meet http://www.geocities.com/dwt06182002/tautology_checker.htm
please contact me via dwt06182002@yahoo.com
Tkx...
Thank you for your answer, but I need a brand new one. This one is
been used for others. Would you write a totally different SML code for
me? That will be great for me...Would you?
Great job....it helps me a lot...thank you
I have rewritten the file as requested.
I have changed the names to follow exactly the definition in the
problem specification; I have removed the distribute function; I have
removed the inter function and replaced it with an intersects
function; and have made several other simplifying changes.
I have placed the revised file at:
http://www.rbnn.com/google/ml/checker2.sml .
Here is a log file:
checker (
Disj (
Atom "A",
Neg (
Disj (
Conj (Atom "A", Neg (Atom "B")),
Conj (Neg (Atom "C"), Atom "C"))
)
)
)
Here is the actual code:
(*version 3*)
datatype form =
Atom of string Neg of form Conj of form * form Disj of
form * form;
fun NNF (Neg(Neg p))= NNF p
NNF (Neg (Conj(p,q))) = NNF (Disj (Neg p, Neg q))
NNF (Neg (Disj(p,q))) = NNF (Conj (Neg p, Neg q))
NNF (Conj(p,q)) = Conj(NNF p, NNF q)
NNF (Disj(p,q)) = Disj(NNF p, NNF q)
NNF (Neg p) = Neg (NNF p)
NNF (p) = p;
fun CNF (Conj(p,q)) = Conj (CNF p, CNF q)
CNF (Disj(p,Conj(q,r))) = Conj(CNF(Disj(p,q)), CNF(Disj(p,r)))
CNF (Disj(Conj(q,r),p)) = Conj (CNF (Disj (q,p)), CNF (Disj
(r,p)))
CNF p = p;
fun atoms (Atom a) = [a]
atoms (Disj(p,q)) = atoms p @ atoms q
atoms _ = ;
fun negations (Neg(Atom a)) = [a]
negations (Disj(p,q)) = negations p @ negations q
negations _ = ;
fun intersects(_,)= false
intersects(,_)=false
intersects(p,q)=((hd p)=(hd q)) orelse intersects (p,tl q) orelse
intersects (tl p, q);
fun tautology (Conj(p,q)) = tautology p andalso tautology q
tautology p = intersects(atoms p, negations p);
fun checker(p)= tautology (CNF (NNF p)); ISO TC 37/SC 4 N105 2003-10-28 Language Resource Management::
File Format: PDF/Adobe Acrobat - View as HTML<DE id=8 section=3 type=ed> The Word checker is marking some errors, instance using XML schema types. The role and usefulness of special values
http://www.tc37sc4.org/new_doc/ISO_TC_37-4_N105_Allocated_comments_for_CD_24610-1.pdfHOME |
Sure.
I have uploaded a commented version of checker2.sml to:
http://www.rbnn.com/google/ml/checker2.sml
and I have pasted it below (although sometimes code does not paste
very clearly) .
Because ML is interpretive, I recommend also just trying out different
examples to see what happens. For example, try
intersects (["a"], ["b" , "a"])
and similarly with the other functions
(*follows the description here:
http://www.geocities.com/dwt06182002/tautology_checker.htm*)
(* A propositional formula*)
datatype form =
Atom of string Neg of form Conj of form * form Disj of
form * form;
(*NNF takes a propositional formula as input and
converts it into an equivalent formula in negation normal form that
has only literals negated
*)
fun NNF (Neg(Neg p))= NNF p
NNF (Neg (Conj(p,q))) = NNF (Disj (Neg p, Neg q))
NNF (Neg (Disj(p,q))) = NNF (Conj (Neg p, Neg q))
NNF (Conj(p,q)) = Conj(NNF p, NNF q)
NNF (Disj(p,q)) = Disj(NNF p, NNF q)
NNF (Neg p) = Neg (NNF p)
NNF (p) = p;
(*CNF takes a propositional formula in negation normal form as input
and converts it recursively
using the distributive law into a propositional formula in conjunction
normal form. The algorithm follows the
description.*)
fun CNF (Conj(p,q)) = Conj (CNF p, CNF q)
CNF (Disj(p,Conj(q,r))) = Conj(CNF(Disj(p,q)), CNF(Disj(p,r)))
CNF (Disj(Conj(q,r),p)) = Conj (CNF (Disj (q,p)), CNF (Disj
(r,p)))
CNF p = p;
(* The function Atom takes as input a propositional form that is a
disjunct of literals and returns
a list of the atoms that appear as un-negated literals in that
form. *)
fun atoms (Atom a) = [a]
atoms (Disj(p,q)) = atoms p @ atoms q
atoms _ = ;
(* The function negations takes as input a propositional form that is
a disjunct of literals and returns a list of the
atoms that appear as negated literals in the form*)
fun negations (Neg(Atom a)) = [a]
negations (Disj(p,q)) = negations p @ negations q
negations _ = ;
(* The function intersects takes two lists and returns true if they
have non-empty intersection*)
fun intersects(_,)= false
intersects(,_)=false
intersects(p,q)=((hd p)=(hd q)) orelse intersects (p,tl q) orelse
intersects (tl p, q);
(*The function tautology takes as input a form that is in conjunction
normal form and determines if it is a tautology.
A conjunct in the conjunction normal form is a tautology if and only
if its atoms and negated atoms intersect nontrivially, that
is, if there both A and ~A occur in the same conjuct for some atom
A.*)
fun tautology (Conj(p,q)) = tautology p andalso tautology q
tautology p = intersects(atoms p, negations p);
(*The function checker takes a propositional form as input, converts
it into conjunction normal form, and then determines using
tautology whether or not the form is a tautology*)
fun checker(p)= tautology (CNF (NNF p)); Changes from V8.0pl3 to V8.0pl4 ::
Concerning Ocaml, extracted code is now ensured to always type-check, .. Sophia-Antipolis) - Correctness proof of Stalmarck tautology checker algorithm
http://coq.inria.fr/V8.0pl4/CHANGESHOME |
Thanks for your code, Would you give me some comments in the
code to explain what is happening. That will be helped me a lot...appreciate it.
Thank you for your question. I enjoy ML coding, as it is a very
beautiful language.
Coincidentally I just solved exactly this problem, and have the
solution ready for you, from:
https://answers.google.com/answers/main?cmd=threadview&id=117574.
A solution is at:
http://www.rbnn.com/google/ml/checker.sml
based on the URLs:
http://www.cl.cam.ac.uk/users/lcp/MLbook/programs/sample3.sml.gz
http://www.cl.cam.ac.uk/users/lcp/MLbook/programs/sample4.sml.gz
from:
Sample programs for ML for the Working Programmer:
http://www.cl.cam.ac.uk/users/lcp/MLbook/programs/
These URLs are in gzipped format, if you cannot read them they have
been unzipped, respectively, here:
http://www.rbnn.com/google/ml/sample3.sml
http://www.rbnn.com/google/ml/sample4.sml
Here is a script illustrating that code:
Here is a sample run:
% sml.bat
Standard ML of New Jersey, Version 110.0.7, September 28, 2000
[CM&CMB]
- use "checker.sml";
[opening checker.sml]
infix mem
val mem = fn : ''a * ''a list -> Visa vs. the Z-Axis::
Sep 18, 2007 Have lunch with Donald Knuth, paid for with the $327.68 check he . perl, python, ruby, smarty, sql, vb, vbnet, xml, code (Generic).
http://marknelson.us/2007/09/18/visa/HOME |
Using Proof in Transformation Synthesis for Automatic Parallelisation::
File Format: Adobe PostScriptHamdan’s thesis [Ham00] SML is then passed to the transformer where changes in the. code are made to increase the eciency. The possible changes to the code
http://www.macs.hw.ac.uk/~greg/publications/ajc.phd.psHOME |
bool
GC #0.0.0.0.1.15: (0 ms)
val inter = fn : ''a list * ''a list -> ''a list
datatype prop
= Atom of string Conj of prop * prop Disj of prop * prop Neg
of prop
val nnf = fn : prop -> prop
val distrib = fn : prop * prop -> prop
val cnf = fn : prop -> prop
exception NonCNF
val positives = fn : prop -> string list
val negatives = fn : prop -> string list
GC #0.0.0.0.2.59: (0 ms)
val taut = fn : prop -> bool
val checker = fn : prop -> bool
val it = () : unit
- checker (
Disj (
Atom "A",
Neg (
Disj (
Conj (Atom "A", Neg (Atom "B")),
Conj (Neg (Atom "C"), Atom "C"))
)
)
)
;
val it = true : bool
- checker(Atom "A");
val it = false : bool
-------
Should you like any more information or explanation, please do use the
"Request Clarification" button before rating this answer.
 How much does getting a small tattoo on your hip/stomach hurt?
 Do anyone else have an itchy anus? ?
|
Using SML to code Tautology checker...