Setting up diagnostic error messages in large Mathematica projects - error-handling

Question

Whenever I create a large Mathematica project I run into this problem: Preventing avalanche of runtime errors in Mathematica, i.e., Mathematica's error message are opaque, archaic, and legion.
The idea then is to disable all of Mathematica's own error messages and implement type checking and error messages of your own in every Function and Module. However I have not found a simple and efficient way of doing this and end up with, e.g., some function generating an error 20 function calls deep and then get a whole cascade of error messages all the way back up to the main routine.
How would you set up a simple mechanism for this that only generates one error message at the function that experiences the error and a simple list of the chain of function calls?
EDIT: Since it has come up in a couple of answers; I am specifically looking for something lightweight regarding the output it produces (otherwise I could just stick with Mathematica's error messages) and obviously also lightweight in computational overhead. So while Stack and Trace are definitely light on the overhead, their output in complex projects is not quick to parse and some work needs to be done simplifying it.

Answer 1

YAsI - Yet Another (silly?) Idea ...
Re-reading your question ...
The idea then is to disable all of Mathematica's own error messages and implement type checking and error messages of your own in every Function and Module.
Found this:
$MessagePrePrint = ( #; Print[Stack[_][[;; -5]]]; Abort[]) &
v[x_, y_] := w[x, y];
w[x_, y_] := x/y;
StackComplete#v[1, 0];
During evaluation of In[267]:= {StackComplete[v[1,0]];,
StackComplete[v[1,0]], v[1,0], w[1,0], 1/0, 1/0, Message[Power::infy,1/0]}
Out[267]= $Aborted
conclusion ... Aborts at first message and leaves a "reasonable" stack trace. "Reasonable" means "Should be improved".
But it is completely non-intrusive!

Answer 2

To get the ball rolling here is one idea that I've been toying with; the creation of a pseudo stack.
First make a global variable theStack={} and then in every Function or Module start with AppendTo[theStack,"thisFuncName"] and end with theStack=Most#theStack. Assuming moderate (~a few tens) depth of function calls, this should not add any significant overhead.
Then implement your own typing/error checking and use Print#theStack;Abort[]; on errors.
Refinements of this method could include:
Figuring out a way to dynamically get "thisFuncionName" so that the AppendTo[] can be made into an identical function call for all Functions and Module.
Using Message[] Instead of Print[].
Pushing other important variables / stateful information on theStack.

Answer 3

One attempt to implement #Timo's idea (theStack)
Incomplete and perhaps flawed, but just to keep thinking about it:
Clear["Global`*"];
funcDef = t_[args___] \[CircleMinus] a_ :>
{t["nude", args] := a,
ReleaseHold[Hold[t[args] :=
(If[! ValueQ[theStack], theStack = {}];
AppendTo[theStack, ToString[t]];
Check[ss = a, Print[{"-TheStack->", Evaluate#theStack}];
Print#Hold[a]; Abort[]];
theStack = Most#theStack;
Return[ss])
]]};
v[x_, y_]\[CircleMinus] (Sin# g[x, y]) /. funcDef;
g[x_, y_]\[CircleMinus] x/y /. funcDef;
v[2, 3]
v[2, 0]
Output:
Out[299]= Sin[2/3]
During evaluation of In[295]:= Power::infy: Infinite expression 1/0 encountered. >>
During evaluation of In[295]:= {-TheStack->,{v,g}}
During evaluation of In[295]:= Hold[2/0]
Out[300]= $Aborted

Answer 4

A suggestion for extracting stack, maybe something that relies on Trace?
An example of using Trace below, from Chris Chiasson. This code saves evaluation tree of 1 + Sin[x + y] + Tan[x + y] into ~/temp/msgStream.m
Developer`ClearCache[];
SetAttributes[recordSteps, HoldAll];
recordSteps[expr_] :=
Block[{$Output = List#OpenWrite["~/temp/msgStream.m"]},
TracePrint[Unevaluated[expr], _?(FreeQ[#, Off] &),
TraceInternal -> True];
Close /# $Output;
Thread[
Union#Cases[
ReadList["~/temp/msgStream.m", HoldComplete[Expression]],
symb_Symbol /;
AtomQ#Unevaluated#symb &&
Context#Unevaluated#symb === "System`" :>
HoldComplete#symb, {0, Infinity}, Heads -> True],
HoldComplete]
];
recordSteps[1 + Tan[x + y] + Sin[x + y]]
To answer Samsdram's question, the code below (also from Chris) gives evaluation tree of a Mathematica expression. Here is the post from MathGroup with source code and examples.
(Attributes## = {HoldAllComplete}) & /# {traceToTreeAux, toVertex,
HoldFormComplete, getAtoms, getAtomsAux}
MakeBoxes[HoldFormComplete[args___], form_] :=
MakeBoxes[HoldForm[args], form]
edge[{head1_, pos1_, xpr1_}, {head2_, pos2_, xpr2_}] :=
Quiet[Rule[{head1, vertexNumberFunction#pos1, xpr1}, {head2,
vertexNumberFunction#pos2, xpr2}], {Rule::"rhs"}]
getAtomsAux[atom_ /; AtomQ#Unevaluated#atom] :=
Sow[HoldFormComplete#atom, getAtomsAux]
getAtomsAux[xpr_] := Map[getAtomsAux, Unevaluated#xpr, Heads -> True]
getAtoms[xpr_] := Flatten#Reap[getAtomsAux#xpr][[2]]
toVertex[traceToTreeAux[HoldForm[heldXpr_], pos_]] := toVertex[heldXpr]
toVertex[traceToTreeAux[HoldForm[heldXprs___], pos_]] :=
toVertex#traceToTreeAux[Sequence[], pos]
(*this code is strong enough to not need the ToString commands,but \
some of the resulting graph vertices give trouble to the graphing \
routines*)
toVertex[
traceToTreeAux[xpr_, pos_]] := {ToString[
Short#Extract[Unevaluated#xpr, 0, HoldFormComplete], StandardForm],
pos, ToString[Short#First#originalTraceExtract#{pos}, StandardForm]}
traceToTreeAux[xpr_ /; AtomQ#Unevaluated#xpr, ___] := Sequence[]
traceToTreeAux[_HoldForm, ___] := Sequence[]
traceToTreeAux[xpr_, pos_] :=
With[{lhs = toVertex#traceToTreeAux[xpr, pos],
args = HoldComplete ## Unevaluated#xpr},
Identity[Sequence][
ReleaseHold[
Function[Null, edge[lhs, toVertex##], HoldAllComplete] /# args],
ReleaseHold#args]]
traceToTree[xpr_] :=
Block[{vertexNumber = -1, vertexNumberFunction,
originalTraceExtract},
vertexNumberFunction[arg_] :=
vertexNumberFunction[arg] = ++vertexNumber;
originalTraceExtract[pos_] :=
Extract[Unevaluated#xpr, pos, HoldFormComplete]; {MapIndexed[
traceToTreeAux, Unevaluated#xpr, {0, Infinity}]}]
TraceTreeFormPlot[trace_, opts___] :=
Block[{$traceExpressionToTree = True},
Through#{Unprotect, Update}#SparseArray`ExpressionToTree;
SparseArray`ExpressionToTree[trace, Infinity] = traceToTree#trace;
With[{result = ToExpression#ToBoxes#TreeForm[trace, opts]},
Through#{Unprotect, Update}#SparseArray`ExpressionToTree;
SparseArray`ExpressionToTree[trace, Infinity] =.;
Through#{Update, Protect, Update}#SparseArray`ExpressionToTree;
result]];
TraceTreeFormPlot[Trace[Tan[x] + Sin[x] - 2*3 - 55]]

Answer 5

Perhaps we have been over thinking this. What if we just tweaked the pattern matching on the arguments a little. For instance, if we modified the function to check for a numeric quantity and added some code to print an error if it fails. For instance,
TypeNumeric[x_] := If[! NumericQ[Evaluate[x]],
Print["error at "]; Print[Stack[]]; Print["Expression "]; Print[x]; Print["Did
not return a numeric value"];Return[False],
(*Else*)
Return[True];]
SetAttributes[TypeNumeric, HoldAll];
Step 2: If you have a function, f[x_] that requires a numeric quantity, just write it with the standard pattern test and all should be well
Input:
f[x_?TypeNumeric] := Sqrt[x]
f[Log[y]]
f[Log[5]]
Output:
error at
{f}
Expression
Log[y]
Did not return a numeric value
f[Log[y]]
Sqrt[Log[5]]
I believe this will work and, it makes robust type checking as simple as a writing a function or two. The problem is that this could be hugely inefficient because this code evaluates the expression x twice, once for the type checking and once for real. This could be bad if an expensive function call is involved.
I haven't figured out the way around this second problem and would welcome suggestions on that front. Are continuations the way out of this problem?
Hope this helps.