Generating code from a natural language programming task is one of the most successful applications of Large Language Models (LLMs). Yet, the generated program may be buggy. Without an oracle, such as an existing, correct implementation or a formal specification, can we somehow estimate how likely the generated program is correct? In this paper, we propose a measure of incorrectness, called incoherence, that can be estimated efficiently in the absence of an oracle and allows us to establish a lower bound on the error, i.e., the probability that the LLM-generated program for that specification is incorrect. In our experiments, our incoherence-based methodology can automatically identify about two-thirds of incorrect programs without reports of false positives for the average task. In fact, an oracle-based evaluation of LLMs can be reliably replaced by an incoherence-based evaluation. In particular, we find a very strong agreement between the ranking of LLMs by the number of programs deemed correct via an oracle (pass@1) and the ranking of LLMs by the number of programs deemed correct via incoherence.

The presence of equivalent mutants has long been considered a major obstacle to the widespread adoption of mutation analysis and mutation testing. This paper presents a study on the types and prevalence of equivalent mutants in real-world Java programs. We conducted a ground-truth analysis of 1,992 mutants, sampled from 7 open source Java projects. Our analysis identified 215 equivalent mutants, which we grouped based on two criteria that describe why the mutants are equivalent and how challenging their detection is. From this analysis, we observed that (1) the median equivalent mutant rate across the 7 projects is 2.97%; (2) many equivalent mutants are caused by common programming patterns and their detection is not much more complex than structural pattern matching over an abstract syntax tree. Based on the findings of our ground-truth analysis, we developed Equivalent Mutant Suppression (EMS), a technique that comprises 10 efficient and targeted analyses. We evaluated EMS on 19 open- source Java projects, comparing the effectiveness and efficiency of EMS to two variants of Trivial Compiler Equivalence (TCE), the current state of the art in equivalent mutant detection. Additionally, we analyzed all 9,047 equivalent mutants reported by any tool to better understand the types and frequencies of equivalent mutants found. Overall, EMS detects 8,776 equivalent mutants within 325 seconds; TCE detects 2,124 equivalent mutants in 2,938 hours.

Learning the syntax and semantics of a new programming language is a challenge. It is common for learners to refer to language documentation many times and in many contexts as they build comfort and understanding. We review existing functional language documentation, finding that it tends to be organized according to the structure of the language. Each section interleaves narrative explanations, which introduce precise terminology that is then used consistently, with code examples. Sections often start with simpler special cases of a construct before considering it in full generality.