/// <summary>
/// Converts to a HOL term
/// </summary>
/// <param name="precision"></param>
/// <returns></returns>
public string ToHOLExplicit(int precision, VariableCollection vars)
{
StringBuilder str = new StringBuilder();
switch (type)
{
case IneqType.Eq:
// Eq becomes Le
str.Append("mk_le_ineq ");
break;
case IneqType.Le:
str.Append("mk_le_ineq ");
break;
case IneqType.Ge:
str.Append("mk_ge_ineq ");
break;
}
str.Append(lhs.ToHOLExplicit(precision, vars));
str.Append(rhs.ToHOLExplicit(precision));
return(str.ToString());
}
/// <summary>
/// Converts to a HOL term
/// </summary>
/// <param name="precision"></param>
/// <returns></returns>
public string ToHOLExplicit(int precision, VariableCollection vars)
{
StringBuilder str = new StringBuilder();
if (c.value == 0)
{
return("");
}
str.Append("(mk_term ");
str.Append(c.ToHOLExplicit(precision));
str.Append('"' + vars[varName].ToString() + '"');
str.Append(')');
return(str.ToString());
}
/// <summary>
/// Generates a test for arithmetic
/// </summary>
static void GenerateArithTest()
{
FileStream fs = new FileStream("arith_test_data.hl", FileMode.Create);
StreamWriter w = new StreamWriter(fs);
Random rnd = new Random(0);
w.WriteLine("let data = [");
for (int i = 0; i < 1000; i++)
{
decimal n1 = rnd.Next(1000000000, 2000000000);
decimal n2 = rnd.Next(1000000000, 2000000000);
// n1 *= rnd.Next(1000000000, 2000000000);
// n2 *= rnd.Next(1000000000, 2000000000);
n1 *= rnd.Next(100000, 500000);
n2 *= rnd.Next(100000, 500000);
int x1 = (int)Math.Log10((double)n1);
int x2 = (int)Math.Log10((double)n2);
LpNumber m1 = new LpNumber(n1);
LpNumber m2 = new LpNumber(n2);
w.Write(m1.ToHOLExplicit(0));
w.Write(",");
w.Write(m2.ToHOLExplicit(0));
if (i < 999)
{
w.Write(";");
}
w.Write("(* {0}, {1} *)", x1, x2);
w.WriteLine();
}
w.WriteLine("];;");
w.Flush();
fs.Close();
}
/// <summary>
/// Converts the LP into HOL data
/// </summary>
/// <param name="writer"></param>
public void ConvertToHOL(StreamWriter writer, int precision)
{
// Find target variables
foreach (var term in objective.Terms)
{
vars[term.varName].TargetVariable = true;
}
// Compute the precision constant
decimal mul = 1;
for (int i = 0; i < precision; i++)
{
mul *= 10;
}
// Dependencies
writer.WriteLine("module Lp = struct");
// writer.WriteLine("needs \"arith/prove_lp.hl\";;");
// writer.WriteLine("open Prove_lp;;");
// Target
writer.WriteLine("let target = `" + objective.ToHOLString(precision, vars) + "`;;");
// Target bound
writer.WriteLine("let target_bound = `" + upperBound.ToHOLString(100) + "`;;");
// Precision
// LpNumber precision_constant = new LpNumber(mul * mul * mul);
writer.Write("let precision_constant = ");
writer.Write("Int " + mul);
// writer.Write(precision_constant.ToHOLExplicit(0));
writer.WriteLine(";;");
// Constraints
int counter = 0;
writer.WriteLine("let ineqs = [");
vars.MakeSimpleNames();
for (int i = 0; i < ineqs.Count; i++)
{
Inequality ineq = ineqs[i];
LpNumber m = ineq.Marginal; //ineqMarginals[i];
if (ineq.Id.name == "lnsum_def")
{
throw new Exception("lnsum_def cannot be active");
}
// Ignore zero values
if (m.IsZero(precision))
{
continue;
}
// m *= mul * mul;
m *= mul;
ineq = ineq * mul;
writer.Write("ASSUME (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write("), ");
writer.Write(m.ToHOLExplicit(precision));
writer.WriteLine(";");
counter++;
}
writer.WriteLine("];;");
int constraintIneqs = counter;
// Variables
// Sort variables
varIneqs.Sort(new VarsComparer(vars));
// Save target variables first
writer.WriteLine("let target_vars = [");
counter = 0;
for (; counter < varIneqs.Count; counter++)
{
Inequality ineq = varIneqs[counter];
if (!vars[ineq.lhs.Terms.First().varName].TargetVariable)
{
break;
}
LpNumber m = ineq.Marginal; //varIneqMarginals[i];
m *= mul * mul;
ineq = ineq * mul;
writer.Write("ASSUME (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write("), ");
writer.Write(m.ToHOLExplicit(precision));
writer.WriteLine(";");
}
writer.WriteLine("];;\n\n");
writer.WriteLine("let var_ineqs = [");
// writer.WriteLine("let vars = [");
// counter = 0;
for (int i = counter; i < varIneqs.Count; i++)
{
Inequality ineq = varIneqs[i];
LpNumber m = ineq.Marginal; //varIneqMarginals[i];
if (m.IsZero(precision))
{
throw new Exception("Unexpected zero");
}
if (i < varIneqs.Count - 1)
{
Inequality ineq2 = varIneqs[i + 1];
LpNumber m2 = ineq2.Marginal;
if (m2.IsZero(precision))
{
throw new Exception("Unexpected zero");
}
if (ineq.lhs.Terms.First().varName == ineq2.lhs.Terms.First().varName)
{
m *= mul * mul;
m2 *= mul * mul;
ineq = ineq * mul;
ineq2 = ineq2 * mul;
writer.Write("var2_le_transform (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write(", ");
writer.Write(m.ToHOLExplicit(precision));
writer.Write(") ");
writer.Write("(");
writer.Write(ineq2.ToHOLExplicit(precision, vars));
writer.Write(", ");
writer.Write(m2.ToHOLExplicit(precision));
writer.WriteLine(");");
i++;
continue;
}
}
m *= mul * mul;
ineq = ineq * mul;
writer.Write("var1_le_transform (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write(", ");
writer.Write(m.ToHOLExplicit(precision));
writer.WriteLine(");");
// writer.WriteLine(";");
}
writer.WriteLine("];;");
Console.WriteLine("Inequalities for constraints: {0}", constraintIneqs);
Console.WriteLine("Inequalities for variables: {0}", varIneqs.Count);
Console.WriteLine("Number of variables: {0}", vars.Number);
Console.WriteLine("Total constraints: {0}", constraintIneqs + varIneqs.Count);
writer.WriteLine("let start = Sys.time();;");
writer.WriteLine("let result = prove_lp ineqs var_ineqs target_vars target_bound precision_constant;;");
// writer.WriteLine("let result = Prove_lp.prove_lp ineqs vars target_bound precision_constant;;");
writer.WriteLine("end;;");
writer.WriteLine("Sys.time() -. Lp.start;;");
// writer.WriteLine("let done_message = \"{0} done\";;", fname);
writer.WriteLine("concl (Lp.result);;");
writer.Flush();
}
