Catala is not at all about "proving the law" formally (I'm not even sure what it would mean?). It's about having a formal language to translate law into that both matches the way law is usually written ("default logic") and allows to make numerical computations on. This can typically be used to implement tax or benefits law so that it is way easier to check that the algorithm computing taxes/benefits is correct compared to the actual state of the art of using general purpose programming languages.
definition qualified_employee_discount
under condition is_property consequence
equals
if employee_discount >=
customer_price \* gross_profit_percentage
then customer_price \* gross_profit_percentage
else employee_discount
Dang, I wish all law was written like this instead of the purposefully obfuscated legalise of (lobbied) legislative lawyers meant to mislead people and slip in loopholes for their interest groups to profit of.
Clear legislature is definitely something every person in the world would benefit of - if the the country's administration would want that.
For me, a great advantage is that this system makes it far simpler to understand the impact of a change, say a multi-pronged bill incl millionaire taxes, energy subsidy changes etc.
I don’t know if they do it, but it allows proving properties of the law. For example, that the tax increases with income or that an exception doesn’t accidentally increase the tax paid.