I think that all programming languages contain some constructs that have undefined behavior.
The C Standard explicitly lists various constructs as having undefined behavior. It also specifies that: Undefined behavior is otherwise indicated in this International Standard by the words “undefined behavior” or by the omission of any explicit definition of behavior.; the second half of the sentence refers to what might be called implicit undefined behavior. Implicit undefined behavior can be subdivided into intentional and unintentional. Intentional undefined behavior applies to constructs that the committee considered and decided (and continues to decide) to say nothing about (e.g., question 19), while unintentional undefined behavior applies to constructs that the committee did not explicitly consider (when discovered, these often end up as defect reports, which are sometimes resolved as intentionally undefined behavior).
Fans of some languages claim that ‘their’ language does not contain any undefined behaviors.
Ada does not explicitly specify any construct as having undefined behavior, but it does specify that some constructs generate a bounded error; a rose by any other name…
I sometimes bump into language inventors claiming that ‘their’ language is fully specified, i.e., does not contain any undefined behaviors. My first question to them, about the behavior of division involving negative values, invariable requires me to explain that there are two possible ways of doing it (ignorance is bliss when fully specifying a language). The invariable answer is that the behavior is whatever the underlying implementation does (which is often written in C). In other words, they have imported all the undefined behaviors of the implementation language.
Follow-up question include: what is the order of expression evaluation (e.g., left-to-right, right-to-left, inside out…), what is the order of function argument evaluation (often driven by the direction of stack growth), what is the order of initialization and other order related questions that comes to mind. Their fully specified language quickly turns out to be a sham.
A recent post by John Regehr talks about Gödel’s incompleteness Theorem as a source of undefined behavior. My understanding is that the underlying argument is built on non-termination. How is it possible to tell the difference between non-termination and lasting longer than the age of the universe? In itself I don’t think this theorem is a source of undefined behavior; more enlightenment welcome.