Standard ML formal-semantic Projects

cakeml

3 911 9.8 Standard ML

CakeML: A Verified Implementation of ML

Project mention: The Deep Link Equating Math Proofs and Computer Programs | news.ycombinator.com | 2023-10-11

If I understand what you are asking about correctly, then I do think you are mistaken.
As a sibling comment observed, you would be proving something about a program, but proving things about programs is both possible and done.
This ranges from things like CakeML (https://cakeml.org/) and CompCert (compilers with verified correctness proofs of their optimizations) to something simple like absence of runtime type errors in statically strongly soundly-typed languages.
Of note is that you are proving properties of your program, not proving them perfect in every way. The properties of your program that you prove can vary wildly in both difficulty and usefulness. A sufficiently advanced formally verified compiler like CakeML can transfer a high-level proof about your source code to a corresponding proof about the behavior of the generated machine-executable code.
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NOTE: The open source projects on this list are ordered by number of github stars. The number of mentions indicates repo mentiontions in the last 12 Months or since we started tracking (Dec 2020). The latest post mention was on 2023-10-11.