private BranchingRule <TERM> EvalB(ConsList <TERM> inputs, int qA, TERM regA, TERM pathCond, int qB, TERM regB, Func <int, int, int> stateComposer, Sequence <TERM> outputFromB, bool isFinal)
{
if (inputs == null)
{
int qAB = stateComposer(qA, qB);
if (isFinal)
{
var fr = B.GetFinalRuleFrom(qB);
if (fr.IsNotUndef)
{
return(this.CreateFinalComposedRule(pathCond, qAB, outputFromB, fr, regB));
}
else
{
return(UndefRule <TERM> .Default);
}
}
else
{
TERM regAB = (regA.Equals(regVar_1) && regB.Equals(regVar_2) ? regVar : JoinRegs(regA, regB));
var res = new BaseRule <TERM>(outputFromB, regAB, qAB);
return(res);
}
}
else
{
return(EvalB_Rule(B.GetRuleFrom(qB), qA, regA, pathCond, inputs, regB, stateComposer, outputFromB, isFinal));
}
}
int TotalIteRules(STb <FuncDecl, Expr, Sort> stb)
{
int count = 0;
foreach (var state in stb.States)
{
var rule = stb.GetRuleFrom(state);
count += IteRules(rule);
}
return(count);
}
public STb <FUNC, TERM, SORT> Minimize()
{
var s = stb.Solver;
var alphaSort = s.MkOptionSort(stb.InputSort);
var autoSort = s.MkTupleSort(alphaSort, stb.OutputListSort, stb.RegisterSort, stb.RegisterSort);
var autoVar = s.MkVar(3, autoSort);
var autoInput = s.MkProj(0, autoVar);
var autoSomeInput = s.MkGetSomeValue(autoInput);
var autoOutputList = s.MkProj(1, autoVar);
var autoOldReg = s.MkProj(2, autoVar);
var autoNewReg = s.MkProj(3, autoVar);
Func <TERM, TERM> finalSubstitute = (t) => s.ApplySubstitution(t, stb.RegVar, autoOldReg);
Func <TERM, TERM> nonFinalSubstitute = (t) => finalSubstitute(s.ApplySubstitution(t, stb.InputVar, autoSomeInput));
int acceptingState = stb.States.Max() + 1;
int errorState = stb.States.Max() + 2;
var moves = new List <Move <TERM> >();
foreach (var state in stb.States)
{
var nonFinalConds = new List <TERM>();
foreach (var nonFinal in st.GetNonFinalMovesFrom(state))
{
var rule = nonFinal.Label;
var conds = new List <TERM>();
conds.Add(s.MkIsSome(autoInput));
conds.Add(nonFinalSubstitute(rule.Guard));
var outputList = autoOutputList;
foreach (var yield in rule.Output)
{
conds.Add(s.MkIsCons(outputList));
conds.Add(s.MkEq(s.MkFirstOfList(outputList), nonFinalSubstitute(yield)));
outputList = s.MkRestOfList(outputList);
}
conds.Add(s.MkIsNil(outputList));
conds.Add(s.MkEq(autoNewReg, nonFinalSubstitute(rule.Update)));
var cond = s.MkAnd(conds);
moves.Add(Move <TERM> .Create(state, nonFinal.TargetState, cond));
nonFinalConds.Add(cond);
}
var finalConds = new List <TERM>();
foreach (var rule in st.GetFinalRules(state))
{
var conds = new List <TERM>();
conds.Add(s.MkIsNone(autoInput));
conds.Add(finalSubstitute(rule.Guard));
var outputList = autoOutputList;
foreach (var yield in rule.Output)
{
conds.Add(s.MkIsCons(outputList));
conds.Add(s.MkEq(s.MkFirstOfList(outputList), finalSubstitute(yield)));
outputList = s.MkRestOfList(outputList);
}
conds.Add(s.MkIsNil(outputList));
var cond = s.MkAnd(conds);
moves.Add(Move <TERM> .Create(state, acceptingState, cond));
finalConds.Add(cond);
}
}
//moves.Add(Move<TERM>.Create(errorState, errorState, s.True));
var auto = Automaton <TERM> .Create(stb.Solver, stb.InitialState, new int[] { acceptingState }, moves);
auto.CheckDeterminism(stb.Solver);
var blocks = auto.BookkeepingMinimize(stb.Solver);
Func <STbRule <TERM>, STbRule <TERM> > redirect = null;
redirect = r =>
{
switch (r.RuleKind)
{
case STbRuleKind.Undef:
return(r);
case STbRuleKind.Base:
return(new BaseRule <TERM>(r.Yields, r.Register, blocks[r.State].GetRepresentative()));
case STbRuleKind.Ite:
var t = redirect(r.TrueCase);
var f = redirect(r.FalseCase);
return(new IteRule <TERM>(r.Condition, t, f));
default:
throw new NotImplementedException();
}
};
var minimized = new STb <FUNC, TERM, SORT>(stb.Solver, stb.Name + "_min", stb.InputSort, stb.OutputSort, stb.RegisterSort, stb.InitialRegister,
blocks[stb.InitialState].GetRepresentative());
var representatives = new HashSet <int>();
foreach (var state in stb.States)
{
representatives.Add(blocks[state].GetRepresentative());
}
foreach (var state in representatives)
{
minimized.AssignRule(state, redirect(stb.GetRuleFrom(state)).CollapseRedundantITEs(s));
minimized.AssignFinalRule(state, redirect(stb.GetFinalRuleFrom(state)).CollapseRedundantITEs(s));
}
return(minimized);
}
public STb <FUNC, TERM, SORT> Compose()
{
var stack = new SimpleStack <Tuple <int, int> >();
int stateId = 1;
var stateIdMap = new Dictionary <Tuple <int, int>, int>();
var revStateIdMap = new Dictionary <int, Tuple <int, int> >();
var q0A_x_q0B = new Tuple <int, int>(A.InitialState, B.InitialState);
stack.Push(q0A_x_q0B);
stateIdMap[q0A_x_q0B] = 0;
revStateIdMap[0] = q0A_x_q0B;
Func <int, int, int> ComposeStates = (x, y) =>
{
var xy = new Tuple <int, int>(x, y);
int q;
if (stateIdMap.TryGetValue(xy, out q))
{
return(q);
}
else
{
q = stateId;
stateId += 1;
stateIdMap[xy] = q;
revStateIdMap[q] = xy;
stack.Push(xy);
return(q);
}
};
var A2B = new STb <FUNC, TERM, SORT>(solver, A.Name + "2" + B.Name, A.InputSort, B.OutputSort, regSort, JoinRegs(A.InitialRegister, B.InitialRegister), 0);
//create normal composed rules
while (stack.IsNonempty)
{
var qA_x_qB = stack.Pop();
var qA = qA_x_qB.Item1;
var qB = qA_x_qB.Item2;
var ruleA = A.GetRuleFrom(qA);
if (ruleA.IsNotUndef)
{
var qAB_rule = Comp(solver.True, ruleA, qB, ComposeStates, false);
A2B.AssignRule(stateIdMap[qA_x_qB], qAB_rule);
}
else
{
A2B.AssignRule(stateIdMap[qA_x_qB], UndefRule <TERM> .Default);
}
}
foreach (var qAB in A2B.States)
{
var qA_x_qB = revStateIdMap[qAB];
var qA = qA_x_qB.Item1;
var qB = qA_x_qB.Item2;
var ruleA = A.GetFinalRuleFrom(qA);
if (ruleA.IsNotUndef)
{
var qAB_Frule = Comp(solver.True, ruleA, qB, (p, q) => qAB, true);
A2B.AssignFinalRule(qAB, qAB_Frule);
}
}
A2B.EliminateDeadends();
//Func<Rule<TERM>, Rule<TERM>> ReplaceWithEpsilon = (r) =>
// {
// };
//var aut = A2B.ToST(true).automaton.RelpaceAllGuards(ReplaceWithEpsilon);
return(A2B);
}
static public ComputationTree ToComputationTrees(STb <FuncDecl, Expr, Sort> stb, bool includeOutput)
{
var ctx = ((Z3Provider)stb.Solver).Z3;
var states = stb.States.Select((State, Index) => new { State, Index, Name = "S" + State });
var csEnumSort = ctx.IntSort;
var outputListSort = stb.OutputListSort as ListSort;
var resultSort = ctx.MkTupleSort(ctx.MkSymbol(stb.Name + "#STATE"),
new[] { ctx.MkSymbol("#CS"), ctx.MkSymbol("#OUT"), ctx.MkSymbol("#VARS") },
new[] { csEnumSort, outputListSort, stb.RegisterSort });
var csField = resultSort.FieldDecls[0];
var outputField = resultSort.FieldDecls[1];
var registerField = resultSort.FieldDecls[2];
var inputVar = stb.Solver.MkVar(0, stb.InputSort);
var registerVar = stb.Solver.MkVar(1, stb.RegisterSort);
var computationVar = stb.Solver.MkVar(2, resultSort);
var csProjection = csField.Apply(computationVar);
var outputProjection = outputField.Apply(computationVar);
var registerProjection = registerField.Apply(computationVar);
Func <int, Expr[], Expr, Expr> createResult = (state, yields, register) =>
{
Expr output;
if (includeOutput)
{
output = yields.Length == 0 ? outputProjection : ctx.MkFuncDecl("Append", new Sort[] { outputListSort, outputListSort }, outputListSort).Apply(
outputProjection, ctx.MkFuncDecl("List", yields.Select(x => x.Sort).ToArray(), outputListSort).Apply(yields));
}
else
{
output = outputProjection;
}
var result = resultSort.MkDecl.Apply(
ctx.MkInt(state),
output,
register != null ? register : registerProjection);
return(result.Substitute(registerVar, registerProjection));
};
ComputationNode ruleNode;
var stateComps = stb.States.Select(State => new { State, Computation = ToComputationTree(ctx, stb.GetRuleFrom(State), registerVar, registerProjection, createResult) }).ToList();
if (stateComps.Count == 0)
{
ruleNode = new UndefinedNode();
}
else
{
ruleNode = new SwitchNode(stateComps.Select(x => ctx.MkEq(csProjection, ctx.MkInt(x.State))).ToArray(), stateComps.Select(x => x.Computation).ToArray());
}
ComputationNode finalNode;
var finalComps = stb.States.Where(s => stb.IsFinalState(s))
.Select(State => new { State, Computation = ToComputationTree(ctx, stb.GetFinalRuleFrom(State), registerVar, registerProjection, createResult) }).ToList();
if (finalComps.Count == 0)
{
finalNode = new UndefinedNode();
}
else
{
finalNode = new SwitchNode(finalComps.Select(x => ctx.MkEq(csProjection, ctx.MkInt(x.State))).ToArray(), finalComps.Select(x => x.Computation).ToArray());
}
var initialState = resultSort.MkDecl.Apply(
ctx.MkInt(stb.InitialState),
outputListSort.Nil,
stb.InitialRegister);
return(new ComputationTree
{
Move = ruleNode,
Finish = finalNode,
InitialState = initialState,
EnumSorts = new EnumSort[] { },
});
}
