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coq
Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
Have a look at the WHATWG specs then - this might be a lot like what you want. E.g. Fecth [1].
Effectively, most of the spec could be written in pseudocode, except they expanded each pseudocode line into a complete sentence and annotated the whole thing with markers, links and commentary. The result is the afromentioned "cookbook style".
I'm not sure if this is actually easier to read than pseudocode though.
[1] https://fetch.spec.whatwg.org/#main-fetch
Systems I've used for this include https://agda.readthedocs.io/en/v2.6.0.1/getting-started/what... https://coq.inria.fr https://www.idris-lang.org and https://isabelle.in.tum.de
An easier alternative is to try disproving the statement, by executing it on thousands of examples and seeing if any fail. That gives us less confidence than a full proof, but can still be better than traditional "there exists" tests. This is called property checking or property-based testing. Systems I've used for this include https://hypothesis.works https://hackage.haskell.org/package/QuickCheck https://scalacheck.org and https://jsverify.github.io
Systems I've used for this include https://agda.readthedocs.io/en/v2.6.0.1/getting-started/what... https://coq.inria.fr https://www.idris-lang.org and https://isabelle.in.tum.de
An easier alternative is to try disproving the statement, by executing it on thousands of examples and seeing if any fail. That gives us less confidence than a full proof, but can still be better than traditional "there exists" tests. This is called property checking or property-based testing. Systems I've used for this include https://hypothesis.works https://hackage.haskell.org/package/QuickCheck https://scalacheck.org and https://jsverify.github.io
Systems I've used for this include https://agda.readthedocs.io/en/v2.6.0.1/getting-started/what... https://coq.inria.fr https://www.idris-lang.org and https://isabelle.in.tum.de
An easier alternative is to try disproving the statement, by executing it on thousands of examples and seeing if any fail. That gives us less confidence than a full proof, but can still be better than traditional "there exists" tests. This is called property checking or property-based testing. Systems I've used for this include https://hypothesis.works https://hackage.haskell.org/package/QuickCheck https://scalacheck.org and https://jsverify.github.io