What's interesting about this view is that theorem provers ultimately boil down to sufficiently advanced type checking (the book Type Theory and Formal Proof is an excellent overview of this topic). Literally the heart of proof assistants like Lean is "if it compiles, you've proved it".
So more practical type systems can be viewed as "little" theorem provers in the sense the author is describing. "Thinking in types" so to speak, is mathematically equivalent to "writing little proofs in your head". I would also add that merely using types is not equivalent to "thinking in types" as one would be required to do writing a sufficiently advanced Haskell program.
So more practical type systems can be viewed as "little" theorem provers in the sense the author is describing. "Thinking in types" so to speak, is mathematically equivalent to "writing little proofs in your head". I would also add that merely using types is not equivalent to "thinking in types" as one would be required to do writing a sufficiently advanced Haskell program.