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test_prover.js
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test_prover.js
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tests = {
// Recall that Prover takes the /negated/ sentence that is to be proved
// as input; i.e. Prover is really a Refuter.
noRuleApplication: function() {
var parser = new Parser();
var f = parser.parseFormula('p');
var prover = new Prover([f, f.negate()], parser);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.closedBranches.length, 1);
},
addDuplicateInitNodes: function() {
var input = '(a∨b),(¬a∨¬n1),(¬b∨¬n2),¬(a∧n2),¬(b∧n2),a↔¬n2|=a';
var parser = new Parser();
var parsedInput = parser.parseInput(input);
var premises = parsedInput[0];
var conclusion = parsedInput[1];
var initFormulas = premises.concat([conclusion.negate()]);
var prover = new Prover(initFormulas, parser);
prover.pauseLength = 0;
prover.start();
var sentree = new SenTree(prover.tree, parser);
assertEqual(sentree.nodes.length, 16);
},
pruneBranch: function() {
var parser = new Parser();
var f = parser.parseFormula('(¬R∧¬S∧((R∧¬S)∨(¬R∧S))∧(Q∨P))').nnf();
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.closedBranches.length, 2);
},
carefulWithDuplicateBranchesWhenPruningAlternatives: function() {
var input = '(¬∃x(Rx∧¬Fx)→∃x(Rx∧¬Fx))→∃x(Rx∧¬Fx)';
var parser = new Parser();
var f = parser.parseFormula(input).negate();
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.closedBranches.length, 4);
},
refutepandnotp: function() {
var parser = new Parser();
var f = parser.parseFormula('p∧¬p');
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assert(prover.tree.openBranches.length == 0);
},
prooftest2: function() {
var parser = new Parser();
var f = parser.parseFormula('∀x(Fx→Fx)').negate();
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assert(prover.tree.openBranches.length == 0);
},
prooftest4: function() {
var parser = new Parser();
var f = parser.parseFormula('¬∃y∀x(Fy→Fx)');
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
},
dontMarkUsedNodesUnused: function() {
// see commit fd1eaff: When the tree for the below input is found to
// close, some closed branches are removed by pruneBranch. One of these
// branches was originally closed by expanding an earlier beta node.
// Before this fix, that beta node was marked unused (and therefore
// removed from the sentence tree) even though it is also used to close
// another branch that is not removed. Now I check that a node is
// really not used anywhere else before marking it as unused in
// pruneBranch.
var input = 'Ac, ∀x(Ax→Tx), ∀x(Mx→¬Tx), Mb, ∀xIxx, ∀x∀y(Ixy→Iyx), ∀x∀y(Ixy→(Ax→Ay)), ∀x∀y(Ixy→(Mx→My)), ∀x∀y(Ixy→(Tx→Ty)) |= ¬Ibc';
var parser = new Parser();
var parsedInput = parser.parseInput(input);
var premises = parsedInput[0];
var conclusion = parsedInput[1];
var initFormulas = premises.concat([conclusion.negate()]);
var prover = new Prover(initFormulas, parser);
prover.pauseLength = 0;
prover.start();
var nodes = prover.tree.closedBranches[0].nodes;
for (var i=0; i<nodes.length; i++) {
if (nodes[i].formula.string == '(¬Ac ∨ Tc)') {
assert(nodes[i].used != '');
return;
}
}
assert(false)
},
equality1: function() {
// checks that termsNode properties in equality problems are
// adjusted when trees are copied for backtracking
var parser = new Parser();
var f = parser.parseFormula('∀x(g(x)=f(x) ∨ ¬(x=a)) ∧ ∀x(g(f(x))=x) ∧ b=c ∧ Pg(g(a))b → Pac').negate();
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
var numUsed = 0;
var nodes = prover.tree.closedBranches[0].nodes;
for (var i=0; i<nodes.length; i++) {
if (nodes[i].used) numUsed++;
}
assert(numUsed > 10);
},
modalT: function() {
var parser = new Parser();
var f = parser.parseFormula('□p→p').negate();
['universality', 'reflexivity'].forEach(function(c) {
var prover = new Prover([f], parser, [c]);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
var numNodes = c == 'universality' ? 4 : 5;
assertEqual(prover.tree.closedBranches[0].nodes.length, numNodes);
});
var prover = new Prover([f], parser, ['seriality']);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 1);
},
modalEuclidean: function() {
var parser = new Parser();
var f = parser.parseFormula('□p→□□p').negate();
var prover = new Prover([f], parser, ['reflexivity', 'euclidity']);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
},
modalG1: function() {
var parser = new Parser();
var f = parser.parseFormula('◇□p→□◇p').negate();
['universality', 'euclidity'].forEach(function(c) {
var prover = new Prover([f], parser, [c]);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
var numNodes = c == 'universality' ? 7 : 11;
assertEqual(prover.tree.closedBranches[0].nodes.length, numNodes);
});
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 1);
},
// emil: function() {
// var parser = new Parser();
// var f = parser.parseFormula('◇□A→(◇□B→◇□(A∧B))').negate();
// var prover = new Prover([f], parser, ['reflexivity', 'symmetry', 'transitivity']);
// prover.pauseLength = 0;
// prover.start();
// assertEqual(prover.tree.openBranches.length, 0);
// },
transitivityTwice: function() {
var parser = new Parser();
var f = parser.parseFormula('◇□(P∨Q)→□(¬P→◇Q)').negate();
var prover = new Prover([f], parser, ['symmetry', 'transitivity']);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
},
noSerialityLoop: function() {
var parser = new Parser();
var f = parser.parseFormula('◇(p∧□q)→◇(p∧◇q)').negate();
var prover = new Prover([f], parser, ['seriality']);
prover.pauseLength = 0;
prover.start();
assertEqual(prover.tree.openBranches.length, 0);
},
invalidtest1: function() {
var parser = new Parser();
var f = parser.parseFormula('∀x¬Ff(ab)').negate(); // old prover says invalid and stops at the double negation!
var prover = new Prover([f], parser);
prover.pauseLength = 0;
prover.start();
assert(prover.tree.openBranches.length > 0);
},
s5_Fails_should_be_able_to_detect_infinite_tree: function() {
var parser = new Parser();
var f = parser.parseFormula('◇p').negate();
var prover = new Prover([f], parser, ['universality']);
prover.pauseLength = 0;
prover.modelfinder.nextStep = function() { return false; };
prover.onfinished = function(res) {
assertEqual(res, 0);
return true;
}
for (var i=0; i<100; i++) {
prover.stopTimeout = true;
if (prover.nextStep()) break;
}
assert(i<100);
},
}