[Haskell-cafe] haskell prop. logic
patrickm7860 at yahoo.co.uk
Wed Feb 9 17:57:34 CET 2011
Hello all I'm working on a project and I'm down to my last 3 functions.I need
some help(in any form) with them as I'm a beginner in haskell.I tried to create
a description on how the functions should behave below ,if you still have some
questions don't hesitate to ask.
Also here is the code for the function I've written so far(some with help).
propagateUnits :: Formula->Formula
If a clause in a propositional formula contains only one literal, then that
literal must be true (so that the particular clause can be satisfied). When this
happens,we can remove the unit clauses (the ones that contain only one literal),
all the clauses where the literal appears and also, from the remaining clauses,
we can delete the negation of the literal (because if P is true, -P will be
false).For example, in the formula (P v Q v R) ^ (-P v Q v -R) ^ (P) we have one
unit clause (the third clause(P) ). Because this one has to be true for the
whole formula to be true we assign True to P and try to find
a satisfying assignment for the remaining formula. Finally because -P cannot be
true (given the assigned value of P) then the second clause is reduced by
eliminating the symbol -P . This simplification results in the revised formula
(Q v -R).
The resulting simplification can create other unit clauses. For example in the
formula (-P v Q) ^ (P) is simplified to (Q) when the unit clause (P) is
propagated. This makes (Q) a unit clause which can now also be simplified to
give a satisfying assignment to the formula. The function should apply unit
propagation until it can no longer make any further simplifications.
Note that if both P and -P are unit clauses then the formula is unsatisfiable.
In this case the function should return a formula with an empty clause in it to
indicate that the formula could not be satisfied.
update :: Node -> [Node]
The update function should take in a Node and return a list of the Nodes that
result from assigning True to an unassigned atom in one case and False in the
other (ie. a case
split). So the list returned should have two nodes as elements. One node should
contain the formula with an atom assigned True and the model updated with this
assignment, and the other should contain the formula with the atom assigned
False and the model updated to show this. The lists of unassigned atoms of each
node should also be updated accordingly. This function should use your
implemented assign function to make the assignments. It should also use the
chooseAtom function provided to select the literal to assign.
search :: (Node -> [Node]) -> [Node] -> Int -> (Bool, Int)
The search function should perform a backtracking search. The function takes the
update function as input and uses it to generate nodes in the search space. The
search function also takes in a list which has one element, the initial node
consisting of the formula along with an initial model. It should generate nodes
using the update function and check nodes using the given check function. If a
node is unsatisfiable then it should
abandon that branch of the search. If a node is satisfiable then a satisfying
assignment has been found and so it should return True. If a node is neither
satisfiable or unsatisfiable then it should generate new nodes from this node.
If all possible branches of the search space have been tried, i.e. the list of
nodes to try has become the empty list, then it should return False since all
possible assignments have been tried. The search function also has an Int
argument which should be an integer that tracks how many
calls to the update function have been made. The search function should return a
pair consisting of the truth value of the formula and the number of calls to
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