[sun_machine]

Coq is essentially a verification system and functional programming language all in one. The functional programming language that the proofs are based on has similar (identical in some places) semantics to OCaml. Remaining faithful to these semantics, especially in a verifiable way, quickly becomes herculean. Even formalizing the semantics of a language is a process that takes months.

[allan_s]

I understand better, so basically before doing anything you will first need to define what each "part" of the language "means" in term of "logical operation" (like what does the dot operator '.' means in PHP, which type it accepts and it transforms them etc) Right ?

[clarus]

Coq itself is already a programming language, but pure in the sense there cannot be any side effects (like IOs). For this pure part there are already an interpreter and a compiler to OCaml, Haskell or Scheme.

To extend Coq with IOs you need to define each new external call. This is basically what is done in the files https://github.com/clarus/coq-chick-blog/blob/master/Computa... and https://github.com/clarus/coq-chick-blog/blob/master/Extract...