Understanding the Brain's Interpretation of Computer Languages: Semantics and Beyond

Computer languages and their interpretation have long been a subject of fascination and debate. When it comes to how the brain interprets these languages, opinions vary widely. Some, like Alan Kay, suggest that we don't yet fully understand how the brain works, while others, like Tom Crosley, provide thoughtful insights into program interpretation. Both perspectives offer valuable insights, but they form only part of a larger puzzle.

Program Interpretation: A Diverse Landscape

Crosley's approach emphasizes the importance of analyzing programs on their own terms, rather than relying solely on machine terms. This perspective suggests that programs should be considered independent entities, with their meanings derived from the context and not just the underlying hardware or compiler. However, this approach comes with its own set of challenges, particularly in the realm of semantics.

The Four Kinds of Semantics in Programming

Bertrand Meyer identified four key types of programming language semantics: translational, operational, denotational, and axiomatic. These categories represent a spectrum of interpretations, each with its own strengths and weaknesses.

Translational and Operational Semantics

Translational semantics are the weakest form, as they rely on an underlying machine or compiler. Operational semantics, while more robust, are still machine-dependent, focusing on the workings of a specific machine rather than a high-level language (HLL) that should ideally be independent of the machine. Both of these approaches can be limiting, especially when dealing with large semantic gaps between source code and machine targets.

Denotational and Axiomatic Semantics

Denotational and axiomatic semantics are more complex and challenging. These approaches seek to understand programs and languages in their own terms, much like grasping the concept of recursion or the symbolism of the Oroboros. While this path is more difficult, it often proves to be the most fruitful, making it worth persisting with.

Mental Models and Practical Challenges

Challenging as it may be, it's crucial to develop the ability to think denotationally and axiomatically about programs—without relying on operational semantics or specific machine implementations. When the semantic gap between the source code and the machine target is large, operational semantics can become too complex and practically unyielding.

Even with a deep understanding of operational semantics, it's important to recognize that a program, no matter how rigorously verified and proven, can still produce incorrect results if the system on which it runs is not correctly implemented. This is a significant concern, as verifying a system's correctness involves intricate tasks such as verifying the compiler, runtime system, operating system, and hardware.

Conclusion

While operational and translational semantics have their place, the pursuit of denotational and axiomatic semantics is a worthy endeavor. This approach not only aligns with the brain's natural interpretation of programmatic structures but also ensures that the system's correctness is maintained, regardless of the underlying implementation. As we continue to evolve our understanding, the divide between the brain and the digital realm will only grow, making this a topic of enduring interest.

Keywords: brain computer languages, semantics of programming, brain understanding of programming