[bwfan123]

This is a nice explanation of language, and the world-model that the language is intended to depict. If I understand you correctly, formalism is a kind of language where the world-model (ie, items and actions in the world depicted by the language) leaves no room for doubt.

[skydhash]

Pretty much and if we take programming languages, where inputs and RNG are not specified by the formal grammar of that language, the programmer needs to split them between good values and bad values. And ideally, halt the program when it detects the latter as the result would be nonsense.

So a program is a more restrictive version of the programming languages, which itself is a more restrictive version of a computer. But the tools to specify those restrictions are not perfect as speed and intuitiveness would suffer greatly (haskell vs python).