private Dictionary <SingleType, IType> ContextSubstitution(Dictionary <SingleType, IType> origin, Dictionary <SingleType, IType> substs)
{
var _origin = CopyContext(origin);
foreach (var key in origin.Keys)
{
_origin[key] = LambdaTypeEvaluator.Subst(_origin[key], substs);
}
return(_origin);
}
///HACK: context is singleType too, but really it's variable
private IType _GetLambdaType(LambdaExpression expr, Dictionary <SingleType, IType> context, out Dictionary <SingleType, IType> substs)
{
if (expr is Variable)
{
substs = new Dictionary <SingleType, IType>();
var variable = new SingleType((expr as Variable).Name);
if (context.ContainsKey(variable))
{
var cv = new List <SingleType>();
var type = RemoveQuantifiers(context[variable], out cv);
var d = new Dictionary <SingleType, IType>();
cv.ForEach(v => d[v] = GetNewType());
type = LambdaTypeEvaluator.Subst(type, d);
return(type);
}
else
{
//create context
var v = new SingleType((expr as Variable).Name);
if (globalContext.ContainsKey(v))
{
return(globalContext[v]);
}
var type = GetNewType();
globalContext[v] = new Universal(type, type);
FreeVariables.Add(new SingleType((expr as Variable).Name));
return(_GetLambdaType(expr, new Dictionary <SingleType, IType>()
{
{ v, globalContext[v] }
}, out substs));
}
}
if (expr is Application)
{
var appl = expr as Application;
var substs1 = new Dictionary <SingleType, IType>();
var type1 = _GetLambdaType(appl.Left, context, out substs1);
var newContext = Merge(context, substs1);
var substs2 = new Dictionary <SingleType, IType>();
var type2 = _GetLambdaType(appl.Right, newContext, out substs2);
var type3 = LambdaTypeEvaluator.Subst(type1, substs2);
var beta = GetNewType();
var v = new Unificator(new Equation[] { new Equation(type3, new Implication(type2, beta)) }).Solve();
substs = Merge(Merge(substs2, substs1), v);
return(LambdaTypeEvaluator.Subst(beta, substs));
}
if (expr is Abstraction)
{
var abstr = expr as Abstraction;
var newContext = CopyContext(context);
var variable = new SingleType(abstr.Variable.Name);
var beta = GetNewType();
newContext[variable] = beta;
var type1 = _GetLambdaType(abstr.Expression, newContext, out substs);
return(new Implication(LambdaTypeEvaluator.Subst(beta, substs), type1));
}
if (expr is LetExpression)
{
var let = expr as LetExpression;
var substs1 = new Dictionary <SingleType, IType>();
var type = _GetLambdaType(let.Left, context, out substs1);
var newContext = CopyContext(context);
var variableType = ConnectAllFreeVariables(type, Merge(context, substs1));
var variable = new SingleType(let.Variable.Name);
if (newContext.ContainsKey(variable))
{
newContext.Remove(variable);
}
newContext = Merge(newContext, substs1);
newContext[variable] = variableType;
var substs2 = new Dictionary <SingleType, IType>();
var type2 = _GetLambdaType(let.Right, newContext, out substs2);
substs = Merge(substs1, substs2);
return(type2);
}
throw new NotImplementedException("Type of expr is not supported");
}