I'm writing a library in Coq that depends on user-supplied type parameters. One central part is a construction along the lines of
Require Import Ascii.
Require Import String.
Parameter UserType : Set. (* <<- placeholder for this example *)
Parameter UserToString : UserType -> string.
Inductive Tag : Set := TBool | TNat | TUser | TList : Tag -> Tag | TSum : Tag -> Tag -> Tag.
Fixpoint decodeT (t : Tag) : Set :=
match t with
| TBool => bool
| TNat => nat
| TUser => UserType (* <<- needed here *)
| TList t' => list (decodeT t')
| TSum l r => sum (decodeT l) (decodeT r)
end.
(* ...etc..., including: *)
Definition tostring (t : Tag) (v : decodeT t) : string := (* match t with ... end *) "dummy".
(* and other stuff *)
so I can't avoid those Parameters in some form. The whole library is split across multiple files, and because of the size it would be pretty uncomfortable to put everything in one file.
There's a top-level wrapper that exports all sub-modules. Ideally, I'd like to pass the parameters once when importing the library, and then this wrapper can do some magic to propagate them to all sub-modules, so that afterwards I don't have to worry about it anymore.
I've looked into various approaches, but nothing worked so far.
If I wrap the file contents in Sections, then the Parameters become extra arguments only on the definitions that use them, and then I have to manually splice them in everywhere when using the library's functions from outside.
If I don't wrap them in a Section, they are module parameters but I can't find a way to actually provide the value. (All forms of with Definition seem to require a module signature / Module Type? Duplicating all names & types to make an explicit signature would be prohibitively redundant, so maybe there is a way to make it work, but I couldn't find it. The documentation is also rather unhelpful...) Variations like using Context instead seem to have the same problem, as far as I tested things.
I'm happy to make a Module Type UserDefs (or typeclass, or whatever) that combines all the user definitions in a single value. I just don't know how to actually get it into the submodules.
So how do I do it? What needs to happen inside that sample file above, and what needs to happen on the outside, so that I can pass the definitions in once and then get a fully configured library to Import?
then I have to manually splice them in everywhere when using the library's functions from outside.
This is typically addressed by a mix of implicit parameters and type classes.
Declare a class for user-provided parameters.
Class UserParams : Type :=
{ UserType : Set
; UserToString : UserType -> string
}.
(* Make sure UserType and UserToString have UserParams as a maximally inserted implicit *)
Then in your library open sections parameterized by instances of that class:
Require Import Ascii.
Require Import String.
Section MyLib.
Context {userParams : UserParams}. (* Context generalizes Variable and allows you to set implicitness *)
Inductive Tag : Set := TBool | TNat | TUser | TList : Tag -> Tag | TSum : Tag -> Tag -> Tag.
Fixpoint decodeT (t : Tag) : Set :=
match t with
| TBool => bool
| TNat => nat
| TUser => UserType (* <<- needed here *)
| TList t' => list (decodeT t')
| TSum l r => sum (decodeT l) (decodeT r)
end.
(* ...etc..., including: *)
Definition tostring (t : Tag) (v : decodeT t) : string := (* match t with ... end *) "dummy".
(* and other stuff *)
End MyLib.
Then users instantiate the class
Require Import MyLib.
Instance myParams : UserParams :=
{| UserType := ...
; UserToString := ... |}.
And then your library functions will automatically be instantiated when you use them.