Preventing avalanche of runtime errors in Mathematica

Question

A typical situation I run into when notebook grows beyond a couple of functions -- I evaluate an expression, but instead of correct answer I get Beep followed by dozens of useless warnings followed by "further Output of ... will be suppressed"

One thing I found useful -- use Python-like "assert" inside functions to enforce internal consistency. Any other tips?

Assert[expr_, msg_] := If[Not[expr], Print[msg]; Abort[], None]

edit 11/14 A general cause of a warning avalanche is when a subexpression evaluates to "bad" value. This causes the parent expression to evaluate to a "bad" value and this "badness" propagates all the way to the root. Built-ins evaluated along the way notice the badness and produce warnings. "Bad" could mean an expression with wrong Head, list with wrong number of elements, negative definite matrix instead of positive definite, etc. Generally it's something that doesn't fit in with the semantics of the parent expression.

One way do deal with this is to redefine all your functions to return unevaluated on "bad input." This will take care of most messages produced by built-ins. Built-ins that do structural operations like "Part" will still attempt to evaluate your value and may produce warnings.

Having the debugger set to "break on Messages" prevents an avalanche of errors, although it seems like an overkill to have it turned on all the time

Answer 1

As others have pointed out, there are three ways to deal with errors in a consistent manner:

1. correctly typing parameters and setting up conditions under which your functions will run,
2. dealing correctly and consistently with errors generated, and
3. simplifying your methodology to apply these steps.

As Samsdram pointed out, correctly typing your functions will help a great deal. Don't forget about the : form of Pattern as it is sometimes easier to express some patterns in this form, e.g. x:{{_, _} ..}. Obviously, when that isn't sufficient PatternTests (?) and Conditions (/;) are the way to go. Samdram covers that pretty well, but I'd like to add that you can create your own pattern test via pure functions, e.g. f[x_?(Head[#]===List&)] is equivalent to f[x_List]. Note, the parentheses are necessary when using the ampersand form of pure functions.

The simplest way to deal with errors generated is obviously Off, or more locally Quiet. For the most part, we can all agree that it is a bad idea to completely shut off the messages we don't want, but Quiet can be extremely useful when you know you are doing something that will generate complaints, but is otherwise correct.

Throw and Catch have their place, but I feel they should only be used internally, and your code should communicate errors via the Message facilities. Messages can be created in the same manner as setting up a usage message. I believe the key to a coherent error strategy can be built using the functions Check, CheckAbort, AbortProtect.

Example

An example from my code is OpenAndRead which protects against leaving open streams when aborting a read operation, as follows:

OpenAndRead[file_String, fcn_]:=
Module[{strm, res},
  strm = OpenRead[file];
  res = CheckAbort[ fcn[strm], $Aborted ];
  Close[strm];
  If[res === $Aborted, Abort[], res] (* Edited to allow Abort to propagate *)
]

which, Until recently, has the usage

fcn[ file_String, <otherparams> ] := OpenAndRead[file, fcn[#, <otherparams>]&]
fcn[ file_InputStream, <otherparams> ] := <fcn body>

However, this is annoying to do every time.

This is where belisarius solution comes into play, by creating a method that you can use consistently. Unfortunately, his solution has a fatal flaw: you lose support of the syntax highlighting facilities. So, here's an alternative that I came up with for hooking into OpenAndRead from above

MakeCheckedReader /: 
    SetDelayed[MakeCheckedReader[fcn_Symbol, symbols___], a_] :=
    Quiet[(fcn[file_String, symbols] := OpenAndRead[file, fcn[#, symbols] &];
           fcn[file_Symbol, symbols] := a), {RuleDelayed::"rhs"}]

which has usage

MakeCheckedReader[ myReader, a_, b_ ] := {file$, a, b} (*as an example*)

Now, checking the definition of myReader gives two definitions, like we want. In the function body, though, file must be referred to as file$. (I have not yet figured out how to name the file var as I'd wish.)

Edit: MakeCheckedReader works by not actually doing anything itself. Instead, the TagSet (/:) specification tells Mathematica that when MakeCheckedReader is found on the LHS of a SetDelayed then replace it with the desired function definitions. Also, note the use of Quiet; otherwise, it would complain about the patterns a_ and b_ appearing on the right side of the equation.

Edit 2: Leonid pointed out how to be able to use file not file$ when defining a checked reader. The updated solution is as follows:

MakeCheckedReader /: 
    SetDelayed[MakeCheckedReader[fcn_Symbol, symbols___], a_] :=
    Quiet[(fcn[file_String, symbols] := OpenAndRead[file, fcn[#, symbols] &];
           SetDelayed @@ Hold[fcn[file_Symbol, symbols], a]), 
           {RuleDelayed::"rhs"}]

The reasoning for the change is explained in this answer of his. Defining myReader, as above, and checking its definition, we get

myReader[file$_String,a_,b_]:=OpenAndRead[file$,myReader[#1,a_,b_]&]
myReader[file_Symbol,a_,b_]:={file,a,b}

Answer 2

I'm coming late to the party, with an accepted answer and all, but I want to point out that definitions of the form:

f[...] := Module[... /; ...]

are very useful in this context. Definitions of this kind can perform complex calculations before finally bailing out and deciding that the definition was not applicable after all.

I will illustrate how this can be used to implement various error-handling strategies in the context of a specific case from another SO question. The problem is to search a fixed list of pairs:

data = {{0, 1}, {1, 2}, {2, 4}, {3, 8}, {4, 15}, {5, 29}, {6, 50}, {7,
     88}, {8, 130}, {9, 157}, {10, 180}, {11, 191}, {12, 196}, {13, 
    199}, {14, 200}};

to find the first pair whose second component is greater than or equal to a specified value. Once that pair is found, its first component is to be returned. There are lots of ways to write this in Mathematica, but here is one:

f0[x_] := First @ Cases[data, {t_, p_} /; p >= x :> t, {1}, 1]

f0[100] (* returns 8 *)

The question, now, is what happens if the function is called with a value that cannot be found?

f0[1000]
error: First::first: {} has a length of zero and no first element.

The error message is cryptic, at best, offering no clues as to what the problem is. If this function was called deep in a call chain, then a cascade of similarly opaque errors is likely to occur.

There are various strategies to deal with such exceptional cases. One is to change the return value so that a success case can be distinguished from a failure case:

f1[x_] := Cases[data, {t_, p_} /; p >= x :> t, {1}, 1]

f1[100] (* returns {8} *)
f1[1000] (* returns {} *)

However, there is a strong Mathematica tradition to leave the original expression unmodified whenever a function is evaluated with arguments outside of its domain. This is where the Module[... /; ...] pattern can help out:

f2[x_] :=
  Module[{m},
    m = Cases[data, {t_, p_} /; p >= x :> t, {1}, 1];
    First[m] /; m =!= {}
  ]

f2[100] (* returns 8 *)
f2[1000] (* returns f2[1000] *)

Note that the f2 bails out completely if the final result is the empty list and the original expression is returned unevaluated -- achieved by the simple expedient of adding a /; condition to the final expression.

One might decide to issue a meaningful warning if the "not found" case occurs:

f2[x_] := Null /; Message[f2::err, x] 
f2::err = "Could not find a value for ``.";

With this change the same values will be returned, but a warning message will be issued in the "not found" case. The Null return value in the new definition can be anything -- it is not used.

One might further decide that the "not found" case just cannot occur at all except in the case of buggy client code. In that case, one should cause the computation to abort:

f2[x_] := (Message[f2::err, x]; Abort[])

In conclusion, these patterns are easy enough to apply so that one can deal with function arguments that are outside the defined domain. When defining functions, it pays to take a few moments to decide how to handle domain errors. It pays in reduced debugging time. After all, virtually all functions are partial functions in Mathematica. Consider: a function might be called with a string, an image, a song or roving swarms of nanobots (in Mathematica 9, maybe).

A final cautionary note... I should point out that when defining and redefining functions using multiple definitions, it is very easy to get unexpected results due to "left over" definitions. As a general principle, I highly recommend preceding multiply-defined functions with Clear:

Clear[f]
f[x_] := ...
f[x_] := Module[... /; ...]
f[x_] := ... /; ...

Answer 3

The problem here is essentially one of types. One function produces a bad output (incorrect type) which is then fed into many subsequent functions producing lots of errors. While Mathematica doesn't have user defined types like in other languages, you can do pattern matching on function arguments without too much work. If the match fails the function doesn't evaluate and thus doesn't beep with errors. The key piece of syntax is "/;" which goes at the end of some code and is followed by the test. Some example code (and output is below).

Input:
Average[x_] := Mean[x] /; VectorQ[x, NumericQ]
Average[{1, 2, 3}]
Average[$Failed]

Output:
2
Average[$Failed]

If the test is simpler, there is another symbol that does similar pattern testing "?" and goes right after an argument in a pattern/function declaration. Another example is below.

Input:
square[x_?NumericQ] := x*x
square[{1, 2, 3}]
square[3]

Output:
square[{1, 2, 3}]
9