/// <param name="prectoparen">parenthesize stuff w prec ≤ prectoparen</param>
private bool Needs_paren(Expr e, int prectoparen)
{
CompositeExpr ce = e as CompositeExpr;
int prec;
if (ce != null)
{
prec = Syntax.Fixes.Find(ce.Head).Precedence;
if (prec == -1)
{
prec = int.MaxValue; // function calls, power, subscript, and root have highest precedence
}
}
else
{
prec = (e is ComplexNumber) ? Syntax.Fixes.Find(WellKnownSym.plus).Precedence
: (e is IntegerNumber) && ((IntegerNumber)e).Num < 0 ? Syntax.Fixes.Find(WellKnownSym.minus).Precedence
: (e is DoubleNumber) && ((DoubleNumber)e).Num < 0 ? Syntax.Fixes.Find(WellKnownSym.minus).Precedence
: (e is DoubleNumber) && ((DoubleNumber)e).Num.ToString("R").IndexOfAny(new char[] { 'e', 'E' }) >= 0 ? Syntax.Fixes.Find(WellKnownSym.plus).Precedence
: int.MaxValue; // assuming everything else is an atom of one sort or another. Possibly wrong, for user-defined Exprs
}
if (prec <= prectoparen)
{
return(true);
}
if (ce != null)
{
Syntax.OpRelPos orp = Syntax.Fixes.Find(ce.Head);
if (orp.Precedence != -1 && ce.Args.Length > 0)
{
Syntax.K k = Syntax.Fixes.Table[orp.Precedence].Kind;
if (k == Syntax.K.Prefix || k == Syntax.K.PrefixOpt)
{
return(false);
}
if (k == Syntax.K.BinPrimaryAndSecondary2)
{
// might be an operator at the start
if (ce.Args[0].Annotations["initial op"] != null)
{
return(false);
}
CompositeExpr ce2 = ce.Args[0] as CompositeExpr;
if (ce2 != null && Syntax.Fixes.Find(ce2.Head).Precedence == orp.Precedence)
{
return(false);
}
}
return(Needs_paren(ce.Args[0], prectoparen));
}
}
return(false);
}
private T _Translate(WellKnownSym s)
{
switch (s.ID)
{
case WKSID.del:
return(__TranslateOperator(s, Unicode.N.NABLA, Syntax.TType.Ord));
case WKSID.differentiald:
return(__TranslateOperator(s, Unicode.D.DOUBLE_STRUCK_ITALIC_SMALL_D, Syntax.TType.Ord));
case WKSID.partiald:
return(__TranslateOperator(s, Unicode.P.PARTIAL_DIFFERENTIAL, Syntax.TType.Ord));
case WKSID.integral:
return(__TranslateOperator(s, Unicode.I.INTEGRAL, Syntax.TType.LargeOp));
case WKSID.i:
return(__TranslateOperator(s, Unicode.D.DOUBLE_STRUCK_ITALIC_SMALL_I, Syntax.TType.Ord));
case WKSID.e:
return(__TranslateOperator(s, Unicode.D.DOUBLE_STRUCK_ITALIC_SMALL_E, Syntax.TType.Ord));
default:
KeyValuePair <Syntax.WOrC, Syntax.TType>?val;
val = Syntax.CharWKSMap[s];
if (val == null)
{
Syntax.OpRelPos orp = Syntax.Fixes.Find(s);
if (orp.Precedence == -1)
{
return(__TranslateWord(s, s.ID.ToString(), Syntax.TType.LargeOp));
}
else
{
Syntax.OpRel or = Syntax.Fixes.Table[orp.Precedence];
Syntax.WOrC op = or.Ops[orp.Position];
Syntax.TType tt = or.Types[orp.Position];
return(__TranslateOperator(s, op, tt));
}
}
else
{
return(__TranslateOperator(s, val.Value.Key, val.Value.Value));
}
}
}
private T _Translate(CompositeExpr e)
{
List <T> lt; // for local use because, sigh, c# doesn't handle this case of definitions used or duplicated across switch cases well
T t; // this too, sigh
Syntax.OpRelPos orp = Syntax.Fixes.Find(e.Head);
if (orp.Precedence != -1)
{
Syntax.OpRel or = Syntax.Fixes.Table[orp.Precedence];
Syntax.WOrC op = or.Ops[orp.Position];
Syntax.TType tt = or.Types[orp.Position];
switch (or.Kind)
{
case Syntax.K.BinLeft:
case Syntax.K.BinRight:
case Syntax.K.BinAlone:
Trace.Assert(e.Args.Length == 2);
return(__WrapTranslatedExpr(e, Translate_thing(e.Head, e.Args, op, tt, orp.Precedence, or.Kind)));
case Syntax.K.BinAllOfLike:
Trace.Assert(e.Args.Length >= 2);
return(__WrapTranslatedExpr(e, Translate_multithing(e, e.Args, op, tt, orp.Precedence)));
case Syntax.K.BinPrimaryAndSecondary:
if (e.Head != or.Heads[0])
{
Trace.Assert(e.Args.Length == 1);
// Division is a special case because it can be represented as the vertical fraction representation, which is not dealt with
// in our syntax table.
if (e.Head == WellKnownSym.divide && !e.Annotations.ContainsKey("inline"))
{
return(__TranslateVerticalFraction(e, Translate(IntegerNumber.One), Translate(e.Args[0])));
}
else
{
lt = new List <T>();
if (or.Kind == Syntax.K.BinPrimaryAndSecondary)
{
lt.Add(Translate_maybe_paren(or.Identity, orp.Precedence));
}
lt.Add(__TranslateOperator(e.Head, op, tt));
lt.Add(Translate_maybe_paren(e.Args[0], orp.Precedence));
return(__WrapTranslatedExpr(e, lt));
}
}
else
{
// FIXME!!!! currently this only works for times and divide; ignores Syntax! Ideally ought to be merged w BinPriAndSec2
Trace.Assert(e.Args.Length > 0);
if (e.Args.Length == 1)
{
return(Translate(e.Args[0]));
}
else
{
List <Expr> num = new List <Expr>();
List <CompositeExpr> denom = new List <CompositeExpr>();
List <CompositeExpr> denominline = new List <CompositeExpr>();
foreach (Expr ee in e.Args)
{
CompositeExpr ce = ee as CompositeExpr;
if (ce != null && ce.Head == WellKnownSym.divide)
{
Trace.Assert(ce.Args.Length == 1);
if (ce.Annotations.ContainsKey("inline"))
{
denominline.Add(ce);
}
else
{
denom.Add(ce);
}
}
else
{
num.Add(ee);
}
}
lt = new List <T>();
if (num.Count > 1 || (denom.Count == 0 && denominline.Count > 0))
{
AddTimes(lt, num);
}
else
{
lt.Add(Translate(num[0]));
}
if (denom.Count != 0)
{
if (num.Count == 0)
{
lt.Add(Translate(IntegerNumber.One));
}
T nt = __WrapTranslatedExpr(null, lt);
lt = new List <T>();
if (denom.Count > 1)
{
List <Expr> denomraw = new List <Expr>();
foreach (CompositeExpr ce in denom)
{
denomraw.Add(ce.Args[0]);
}
AddTimes(lt, denomraw);
}
else
{
lt.Add(Translate(denom[0].Args[0]));
}
T dt = __WrapTranslatedExpr(null, lt);
t = __TranslateVerticalFraction(e, denom[0].Head, nt, dt);
}
else
{
if (num.Count == 0)
{
t = Translate(IntegerNumber.One);
}
else
{
t = __WrapTranslatedExpr(e, lt);
}
}
if (denominline.Count > 0)
{
lt = new List <T>();
lt.Add(t);
foreach (CompositeExpr division in denominline)
{
lt.Add(__TranslateOperator(division.Head, '/', Syntax.TType.Ord));
lt.Add(Translate(division.Args[0]));
}
return(__WrapTranslatedExpr(e, lt));
}
else
{
return(t);
}
}
}
case Syntax.K.BinPrimaryAndSecondary2:
if (e.Head != or.Heads[0])
{
Trace.Assert(e.Args.Length == 1);
return(__TranslateOperatorApplication(e, __TranslateOperator(e.Head, op, tt), Translate_maybe_paren(e.Args[0], orp.Precedence)));
}
else
{
Trace.Assert(e.Args.Length > 0);
lt = new List <T>();
if (e.Annotations["initial op"] != null)
{
lt.Add(__TranslateOperator(e, 0, (char)e.Annotations["initial op"], tt));
}
lt.Add(Translate_maybe_paren(e.Args[0], orp.Precedence - 1));
bool checkminus = (Syntax.Fixes.Find(WellKnownSym.minus).Precedence == orp.Precedence);
for (int i = 1; i < e.Args.Length; i++)
{
CompositeExpr ce = e.Args[i] as CompositeExpr;
Syntax.OpRelPos orp2 = new Syntax.OpRelPos(-1, -1);
if (ce != null)
{
orp2 = Syntax.Fixes.Find(ce.Head);
}
if (checkminus && NumberStartsWithMinus(e.Args[i]))
{
lt.Add(Translate(e.Args[i]));
}
else if (ce != null && orp2.Precedence == orp.Precedence &&
or.Heads[orp.Position] != or.Heads[orp2.Position])
{
Trace.Assert(ce.Args.Length == 1);
lt.Add(__TranslateOperator(e, i, or.Ops[orp2.Position], tt));
lt.Add(Translate_maybe_paren(ce.Args[0], orp.Precedence));
}
else
{
lt.Add(__TranslateOperator(e, i, op, tt));
lt.Add(Translate_maybe_paren(e.Args[i], orp.Precedence - 1));
}
}
return(__WrapTranslatedExpr(e, lt));
}
case Syntax.K.PrefixOpt:
case Syntax.K.Prefix:
if (tt == Syntax.TType.LargeOp && op.Word == null) // Only summation? This seems oddly hard-coded.
{
Trace.Assert(0 < e.Args.Length && e.Args.Length < 4);
return(__TranslateBigOp(e, e.Head, op.Character, e.Args.Length > 1 ? Translate(e.Args[0]) : null, e.Args.Length > 2 ? Translate(e.Args[1]) : null,
Translate_maybe_paren(e.Args[e.Args.Length - 1], orp.Precedence - 1)));
}
else if (or.Kind == Syntax.K.PrefixOpt && e.Args.Length == 0)
{
return(__TranslateOperator(e.Head, op, tt));
}
else
{
//Trace.Assert(e.Args.Length == 1);//CJ disabled temporarily for site visit demo
return(__WrapTranslatedExpr(e, Translate_prepostfix(e.Head, e.Args[0], op, tt, orp.Precedence, or.Kind)));
}
case Syntax.K.Postfix:
Trace.Assert(e.Args.Length == 1);
return(__WrapTranslatedExpr(e, Translate_prepostfix(e.Head, e.Args[0], op, tt, orp.Precedence, or.Kind)));
}
}
if (e.Head is WellKnownSym)
{
WellKnownSym wks = (WellKnownSym)e.Head;
WKSID id = wks.ID;
switch (id)
{
case WKSID.im:
Trace.Assert(e.Args.Length == 1);
return(__TranslateFunctionApplication(e, __TranslateOperator(e.Head, Unicode.B.BLACK_LETTER_CAPITAL_I, Syntax.TType.Ord),
Translate_maybe_parenfn(e.Args[0], _showInvisibles)));
#if false
case WKSID.magnitude:
Trace.Assert(e.Args.Length == 1);
return(__TranslateDelims(e, false, 0, '|', Translate(e.Args[0]), 1, '|'));
#endif
case WKSID.magnitude:
if (e.Args.Length == 1)
{
return(__TranslateDelims(e, false, "|l", '|',
__WrapTranslatedExpr(null, Translate(e.Args[0])),
"|r", '|'));
}
break;
case WKSID.power:
Trace.Assert(e.Args.Length == 2);
if (e.Args[0] is CompositeExpr && ((CompositeExpr)e.Args[0]).Head == WellKnownSym.power)
{
t = Translate_definite_paren(e.Args[0]);
}
else
{
t = Translate_maybe_parenfn(e.Args[0]);
}
return(__AddSuperscript(e, t, Translate(e.Args[1])));
case WKSID.subscript:
Trace.Assert(e.Args.Length == 2);
if (e.Args[0] is CompositeExpr && (((CompositeExpr)e.Args[0]).Head == WellKnownSym.power ||
((CompositeExpr)e.Args[0]).Head == WellKnownSym.subscript))
{
t = Translate_definite_paren(e.Args[0]);
}
else
{
t = Translate_maybe_parenfn(e.Args[0]);
}
return(__AddSubscript(e, t, Translate(e.Args[1])));
case WKSID.re:
Trace.Assert(e.Args.Length == 1);
return(__TranslateFunctionApplication(e, __TranslateOperator(e.Head, Unicode.B.BLACK_LETTER_CAPITAL_R, Syntax.TType.Ord),
Translate_maybe_parenfn(e.Args[0], _showInvisibles)));
case WKSID.root:
if (e.Args[0] is IntegerNumber && (e.Args[0] as IntegerNumber).Num == 2)
{
return(__TranslateRadical(e, Translate(e.Args[1]), null));
}
else
{
return(__TranslateRadical(e, Translate(e.Args[1]), Translate(e.Args[0])));
}
case WKSID.differentiald:
case WKSID.partiald:
Trace.Assert(e.Args.Length == 1);
if (e.Args[0] is Sym)
{
return(__TranslateOperatorApplication(e, Translate(e.Head), Translate(e.Args[0])));
}
else
{
return(__TranslateOperatorApplication(e, Translate(e.Head), Translate_definite_paren(e.Args[0])));
}
case WKSID.integral:
Trace.Assert(e.Args.Length >= 2 && e.Args.Length <= 4);
return(__TranslateBigOp(e, e.Head, Unicode.I.INTEGRAL, e.Args.Length > 2 ? Translate(e.Args[2]) : null,
e.Args.Length > 3 ? Translate(e.Args[3]) : null,
__TranslateIntegralInternals(Translate(e.Args[0]), Translate(e.Args[1]))));
case WKSID.log:
if (e.Args.Length == 2)
{
T f = __TranslateWord(wks, wks.ID.ToString(), Syntax.TType.LargeOp);
f = __AddSubscript(null, f, Translate(e.Args[0]));
f = ParenAround(e.Head, false, f);
return(__TranslateFunctionApplication(e, f, Translate_maybe_parenfn(e.Args[1], _showInvisibles)));
}
break;
case WKSID.floor:
if (e.Args.Length == 1)
{
return(__TranslateDelims(e, false, Unicode.L.LEFT_FLOOR.ToString(), Unicode.L.LEFT_FLOOR,
__WrapTranslatedExpr(null, Translate(e.Args[0])),
Unicode.R.RIGHT_FLOOR.ToString(), Unicode.R.RIGHT_FLOOR));
}
break;
case WKSID.ceiling:
if (e.Args.Length == 1)
{
return(__TranslateDelims(e, false, Unicode.L.LEFT_CEILING.ToString(), Unicode.L.LEFT_CEILING,
__WrapTranslatedExpr(null, Translate(e.Args[0])),
Unicode.R.RIGHT_CEILING.ToString(), Unicode.R.RIGHT_CEILING));
}
break;
}
}
else if (e.Head == new LetterSym('→') || e.Head == new LetterSym(Unicode.R.RIGHTWARDS_DOUBLE_ARROW))
{
T arrow = __TranslateOperator(e.Head, ((LetterSym)e.Head).Letter, Syntax.TType.Rel);
if (e.Args.Length == 1)
{
return(__WrapTranslatedExpr(e, Translate(e.Args[0]), arrow));
}
else
{
Trace.Assert(e.Args.Length == 2);
return(__WrapTranslatedExpr(e, Translate(e.Args[0]), arrow, Translate(e.Args[1])));
}
}
else if (e.Head == new WordSym("brace"))
{
return(__TranslateDelims(e, false, "{", '{', __WrapTranslatedExpr(null, Translate_arglist(e, e.Args)), "}", '}'));
}
else if (e.Head == new WordSym("bracket"))
{
return(__TranslateDelims(e, false, "[", '[', __WrapTranslatedExpr(null, Translate_arglist(e, e.Args)), "]", ']'));
}
// FIXME: probably both branches here should use la and ra...
if (e.Args.Length == 1)
{
if (e.Head is WellKnownSym)
{
return(__TranslateFunctionApplication(e, Translate(e.Head), Translate_maybe_parenfn(e.Args[0], _showInvisibles)));
}
else
{
return(__TranslateFunctionApplication(e, Translate_maybe_parenfn(e.Head), Translate_definite_paren(e.Args[0], _showInvisibles)));
}
}
else
{
return(__TranslateFunctionApplication(e, Translate_maybe_parenfn(e.Head),
__TranslateDelims(e, _showInvisibles, "la", '(', __WrapTranslatedExpr(null, Translate_arglist(e, e.Args)), "ra", ')')));
}
}