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I'm a) an academic b) familiar with CT c) involved in high-performance compiler research d) sympathetic to your software/compiler approach. CT is extremely useful and should not be dismissed, but I'd agree that in "normal" software its usefulness is limited.
Proving theorems which are impossible to prove without compression by CT, because the technical details exceed human mental ability.
If I may to attempt a summary, the main point of CT is to find the formally simplest languages which can be interpreted in the practically widest mathematical settings, to get a large number of specific theorems from a small number of general ones.
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