{ lib }:

let
  inherit (lib)
    all
    concatStringsSep
    findFirst
    flip
    getAttr
    head
    isFunction
    length
    recursiveUpdate
    splitVersion
    tail
    take
    versionAtLeast
    versionOlder
    zipListsWith
    ;
in
recursiveUpdate lib (rec {

  versions =
    let
      truncate = n: v: concatStringsSep "." (take n (splitVersion v));
      opTruncate =
        op: v0: v:
        let
          n = length (splitVersion v0);
        in
        op (truncate n v) (truncate n v0);
    in
    rec {

      /*
        Get string of the first n parts of a version string.

        Example:
        - truncate 2 "1.2.3-stuff"
          => "1.2"

        - truncate 4 "1.2.3-stuff"
          => "1.2.3.stuff"
      */

      inherit truncate;

      /*
        Get string of the first three parts (major, minor and patch)
        of a version string.

        Example:
          majorMinorPatch "1.2.3-stuff"
          => "1.2.3"
      */
      majorMinorPatch = truncate 3;

      /*
        Version comparison predicates,
          - isGe v0 v <-> v is greater or equal than v0   [*]
          - isLe v0 v <-> v is lesser  or equal than v0   [*]
          - isGt v0 v <-> v is strictly greater than v0   [*]
          - isLt v0 v <-> v is strictly lesser  than v0   [*]
          - isEq v0 v <-> v is equal to v0                [*]
          - range low high v <-> v is between low and high [**]

        [*]  truncating v to the same number of digits as v0
        [**] truncating v to low for the lower bound and high for the upper bound

          Examples:
          - isGe "8.10" "8.10.1"
            => true
          - isLe "8.10" "8.10.1"
            => true
          - isGt "8.10" "8.10.1"
            => false
          - isGt "8.10.0" "8.10.1"
            => true
          - isEq "8.10" "8.10.1"
            => true
          - range "8.10" "8.11" "8.11.1"
            => true
          - range "8.10" "8.11+" "8.11.0"
            => false
          - range "8.10" "8.11+" "8.11+beta1"
            => false
      */
      isGe = opTruncate versionAtLeast;
      isGt = opTruncate (flip versionOlder);
      isLe = opTruncate (flip versionAtLeast);
      isLt = opTruncate versionOlder;
      isEq = opTruncate pred.equal;
      range = low: high: pred.inter (versions.isGe low) (versions.isLe high);
    };

  /*
    Returns a list of list, splitting it using a predicate.
     This is analoguous to builtins.split sep list,
     with a predicate as a separator and a list instead of a string.

    Type: splitList :: (a -> bool) -> [a] -> [[a]]

    Example:
      splitList (x: x == "x") [ "y" "x" "z" "t" ]
      => [ [ "y" ] "x" [ "z" "t" ] ]
  */
  splitList =
    pred: l: # put in file lists
    let
      loop = (
        vv: v: l:
        if l == [ ] then
          vv ++ [ v ]
        else
          let
            hd = head l;
            tl = tail l;
          in
          if pred hd then
            loop (
              vv
              ++ [
                v
                hd
              ]
            ) [ ] tl
          else
            loop vv (v ++ [ hd ]) tl
      );
    in
    loop [ ] [ ] l;

  pred = {
    # Predicate intersection, union, and complement
    inter =
      p: q: x:
      p x && q x;
    union =
      p: q: x:
      p x || q x;
    compl = p: x: !p x;
    true = p: true;
    false = p: false;

    # predicate "being equal to y"
    equal = y: x: x == y;
  };

  /*
    Emulate a "switch - case" construct,
    instead of relying on `if then else if ...`
  */
  /*
    Usage:
    ```nix
    switch-if [
      if-clause-1
      ..
      if-clause-k
    ] default-out
    ```
    where a if-clause has the form `{ cond = b; out = r; }`
    the first branch such as `b` is true
  */

  switch-if = c: d: (findFirst (getAttr "cond") { } c).out or d;

  /*
    Usage:
    ```nix
    switch x [
      simple-clause-1
      ..
      simple-clause-k
    ] default-out
    ```
    where a simple-clause has the form `{ case = p; out = r; }`
    the first branch such as `p x` is true
    or
    ```nix
    switch [ x1 .. xn ] [
      complex-clause-1
      ..
      complex-clause-k
    ] default-out
    ```
    where a complex-clause is either a simple-clause
    or has the form { cases = [ p1 .. pn ]; out = r; }
    in which case the first branch such as all `pi x` are true

    if the variables p are not functions,
    they are converted to a equal p
    if out is missing the default-out is taken
  */

  switch =
    var: clauses: default:
    with pred;
    let
      compare = f: if isFunction f then f else equal f;
      combine =
        cl: var:
        if cl ? case then compare cl.case var else all (equal true) (zipListsWith compare cl.cases var);
    in
    switch-if (map (cl: {
      cond = combine cl var;
      inherit (cl) out;
    }) clauses) default;

  /*
    Override arguments to mkCoqDerivation for a Coq library.

    This function allows you to easily override arguments to mkCoqDerivation,
    even when they are not exposed by the Coq library directly.

    Type: overrideCoqDerivation :: AttrSet -> CoqLibraryDerivation -> CoqLibraryDerivation

    Example:

    ```nix
    coqPackages.lib.overrideCoqDerivation
      {
        defaultVersion = "9999";
        release."9999".sha256 = "1lq8x86vd3vqqh2yq6hvyagpnhfq5wmk5pg2z0xq7b7dbbbhyfkw";
      }
      coqPackages.QuickChick;
    ```

    This example overrides the `defaultVersion` and `release` arguments that
    are passed to `mkCoqDerivation` in the QuickChick derivation.

    Note that there is a difference between using `.override` on a Coq
    library vs this `overrideCoqDerivation` function. `.override` allows you
    to modify arguments to the derivation itself, for instance by passing
    different versions of dependencies:

    ```nix
    coqPackages.QuickChick.override { ssreflect = my-cool-ssreflect; }
    ```

    whereas `overrideCoqDerivation` allows you to override arguments to the
    call to `mkCoqDerivation` in the Coq library.

    Note that all Coq libraries in Nixpkgs have a `version` argument for
    easily using a different version.  So if all you want to do is use a
    different version, and the derivation for the Coq library already has
    support for the version you want, you likely only need to update the
    `version` argument on the library derivation.  This is done with
    `.override`:

    ```nix
    coqPackages.QuickChick.override { version = "1.4.0"; }
    ```
  */
  overrideCoqDerivation =
    f: drv:
    (drv.override (args: {
      mkCoqDerivation = drv_: (args.mkCoqDerivation drv_).override f;
    }));
})