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code for the fourth article
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‎README.md

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@@ -3,13 +3,16 @@ This git repository contains code presented in a series of articles
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introducing functional programming via Nix's language:
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1. [On Nix's Language: Introduction][tales-nix-1];
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2. [On Nix's Language: Recursive Functions][tales-nix-2].
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2. [On Nix's Language: Closures][tales-nix-3].
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2. [On Nix's Language: Recursive Functions][tales-nix-2];
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3. [On Nix's Language: Closures][tales-nix-3];
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4. [On Nix's Language: Pragmatism, laziness][tales-nix-4].
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**<u>Note</u>**: Some of the code doesn't compile, on purpose (e.g. [hw1][gh-mb-nix-hw1])
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**<u>Note</u>**: Some of the code doesn't compile, on purpose (e.g.
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[hw1][gh-mb-nix-hw1]).
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[gh-mb-nix-hw1]: https://github.com/mbivert/nix-series-code/blob/master/hw/hw1.nix
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[tales-nix-1]: https://tales.mbivert.com/on-nix-language/
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[tales-nix-2]: https://tales.mbivert.com/on-nix-language-recursive-functions/
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[tales-nix-3]: https://tales.mbivert.com/on-nix-language-closures/
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[tales-nix-4]: https://tales.mbivert.com/on-nix-language-pragmatism-laziness/

‎lazy/list.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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nil = null;
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cons = h: t: [h t];
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car = xs: elemAt xs 0;
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cdr = xs: elemAt xs 1;
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# And that's exactly the code we have for the
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# previous version: just the list implementation
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# has changed.
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zeroes = cons 0 (zeroes);
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take = n: xs: let aux = acc: xs: i:
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if i == n then
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acc
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else
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aux (cons (car xs) acc) (cdr xs) (i + 1)
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; in aux nil xs 0;
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xs = take 5 zeroes;
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in
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deepSeq xs xs

‎lazy/lists.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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nil = null;
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isEmpty = xs: xs == nil;
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cons = x: xs: {
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car = x;
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cdr = xs;
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};
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car = xs: xs.car;
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cdr = xs: xs.cdr;
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zeroes = cons 0 (zeroes);
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# Actually we would need to reverse the output, or to use
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# append instead of cons (more expensive), but it's good
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# enough to demonstrate our point.
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take = n: xs: let aux = acc: xs: i:
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if i == n then
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acc
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else
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aux (cons (car xs) acc) (cdr xs) (i + 1)
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; in aux nil xs 0;
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xs = take 5 zeroes;
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in
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deepSeq xs xs
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‎lazy/set.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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nil = null;
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isEmpty = xs: xs == nil;
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cons = x: xs: {
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car = x;
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cdr = xs;
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};
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car = xs: xs.car;
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cdr = xs: xs.cdr;
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zeroes = cons 0 (zeroes);
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# Actually we would need to reverse the output, or to use
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# append instead of cons (more expensive), but it's good
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# enough to demonstrate our point.
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take = n: xs: let aux = acc: xs: i:
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if i == n then
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acc
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else
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aux (cons (car xs) acc) (cdr xs) (i + 1)
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; in aux nil xs 0;
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xs = take 5 zeroes;
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in
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deepSeq xs xs
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‎lazy/sieve.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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# Any lazy list implementation would do, as
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# long as it respect our "API".
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nil = null;
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isEmpty = xs: xs == nil;
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cons = h: t: [h t];
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car = xs: elemAt xs 0;
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cdr = xs: elemAt xs 1;
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take = n: xs: let aux = acc: xs: i:
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if i == n then
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acc
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else
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aux (cons (car xs) acc) (cdr xs) (i + 1)
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; in aux nil xs 0;
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reverse = xs: let aux = acc: xs:
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if isEmpty xs then acc
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else aux (cons (car xs) acc) (cdr xs)
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; in aux nil xs
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;
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toFloat = n: n + 0.1 - 0.1;
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isDiv = i: j: ceil(toFloat(i) / j) * j == i;
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sieve = let aux = p: i:
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if i != 1 && p i then
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# This is the most "correct" variant for the accumulated
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# closure; but both would work OK in this context.
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cons i (aux (j : (j <= i || !(isDiv j i)) && (p j)) (i + 1))
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else
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aux p (i + 1)
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; in aux (i: i != 1) 1;
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xs = reverse (take 10 sieve);
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in
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deepSeq xs xs
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‎list/iterate.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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iterate = f: n: [f n]++(iterate f (f n));
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take = n: xs:
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if n == 0 then
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[]
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else
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[(head xs)]++(take (n - 1) (tail xs))
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;
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xs = take 5 (iterate (x: 2*x) 1);
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in
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deepSeq xs xs

‎list/list0.nix

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#!/bin/nix-instantiate
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["hello" "world"]

‎list/list1.nix

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#!/bin/nix-instantiate
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[("hel" + "lo") "world"]

‎list/list2.nix

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#!/bin/nix-instantiate
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[1 ("hello") (x: 3)]

‎list/list3.nix

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#!/bin/nix-instantiate
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[(1+3) "hi" ("hello"+" "+"world") 3 (x: 3)]

‎list/list4.nix

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#!/bin/nix-instantiate
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let
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# toString can't coerce a function (e.g. (x: 3)) to a
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# string, hence why we're applying it here
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xs = [(1+3) "hi" ("hello"+" "+"world") 3 ((x: 3) 2)];
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in
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"${toString xs}"

‎list/list5.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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xs = []++[1 2]++[]++[3 4]++[5];
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in
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"${toString xs}"

‎list/list6.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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xs = [(1+3) "hi" ("hello"+" "+"world") 3 (x: 3)];
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in
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deepSeq xs xs

‎list/list7.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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# concatLists' parameter *must* be a list of lists, no
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# scalars allowed down there
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xs = concatLists (map (x: if !isList x then [x] else x) [[1 2] 3]);
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# This is a more efficient and more general "variant" of
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# concatLists (equivalent to concatLists (map f xs))
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ys = concatMap (x: if !isList x then [x] else x) [[1 2] 3 [4]];
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# the ' indicates that foldl is *strict* here, meaning, it
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# will systematically evaluate the list entries before processing
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# them (like deepSeq does).
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n = foldl' add 0 (map (x: 2*x) [1 2 3]);
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in
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trace(xs)
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trace(ys)
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trace(n)
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"ok"
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‎list/list8.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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map = f: xs: let n = length xs; aux = acc: i:
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if i >= n then
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acc
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else
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aux (acc++[(f (elemAt xs i))]) (i + 1)
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; in aux [] 0;
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map2 = f: xs: if xs == [] then xs
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else [(f (head xs))] ++ (map2 f (tail xs));
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xs = map (x: 2*x) [1 2 3];
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ys = map2 (y: 2*y) [1 2 3];
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in
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trace(deepSeq xs xs)
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trace(deepSeq ys ys)
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"ok"

‎list/take.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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# with head/tail
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take = n: xs:
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if xs == [] || n == 0 then
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[]
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else
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[(head xs)]++(take (n - 1) (tail xs))
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;
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# with elemAt and an auxiliary function
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take2 = n: xs: let m = length xs; aux = acc: i:
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if i >= m then
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acc
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else
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aux (acc++[(elemAt xs i)]) (i + 1)
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; in aux [] 0;
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# and with foldl'
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take3 = n: xs: elemAt (foldl' (acc: x:
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let
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m = elemAt acc 0;
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ys = elemAt acc 1;
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in
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if m >= n then acc
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else [(m + 1) (ys++[x])]
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) [0 []] xs) 1;
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xs = take 5 [1 2];
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ys = take2 2 [1 2 3 4 5];
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zs = take 0 [];
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ts = take3 3 [1 2 3 4 5];
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us = take3 9 [1 2 3 4 5];
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in
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trace(deepSeq xs xs)
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trace(deepSeq ys ys)
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trace(deepSeq zs zs)
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trace(deepSeq ts ts)
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trace(deepSeq us us)
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"ok"

‎list/zipper.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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cons = h: t: [h t];
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car = xs: elemAt xs 0;
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cdr = xs: elemAt xs 1;
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zeroes = cons 0 (zeroes);
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tape = b: e: a: [b e a];
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prev = xs: elemAt xs 0;
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elem = xs: elemAt xs 1;
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next = xs: elemAt xs 2;
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right = t: tape (cons (elem t) (prev t)) (car (next t)) (cdr (next t));
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left = t: tape (cdr (prev t)) (car (prev t)) (cons (elem t) (next t));
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# Obviously, there are other ways of altering the current cell,
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# this is good enough for us
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alter = t: n: tape (prev t) ((elem t) + n) (next t);
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start = tape zeroes 0 zeroes;
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mem = alter (left (left (alter (right (alter start 5)) 3))) 1;
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in
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trace(deepSeq mem mem)
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"ok"

‎match.nix

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#!/bin/nix-instantiate
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with builtins;
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with (import ./string/strings.nix);
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let
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matchstar = y: xs: re: let x = charAt xs 0; in
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if x == "" then
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false
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else if matchhere xs re then
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true
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else if x == y || y == "." then
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matchstar y (eat1 xs) re
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else
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false;
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matchhere = xs: re:
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let
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x = charAt xs 0;
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r = charAt re 0;
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s = charAt re 1;
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in
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if r == "" then
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true
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else if s == "*" then
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matchstar r xs (eat1 (eat1 re))
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else if r == "$" && s == "" then
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x == ""
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else if x != "" && (r == "." || r == x) then
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matchhere (eat1 xs) (eat1 re)
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else
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false
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;
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match1 = xs: re:
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let
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# Note that charAt returns "" when there's not enough bytes
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x = charAt xs 0;
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r = charAt re 0;
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in
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if x == "" && r != "" then false
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else if matchhere xs re then true
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else match1 (eat1 xs) re
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;
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match = xs: re: let r = charAt re 0; in
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if r == "^" then matchhere xs (eat1 re)
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else match1 xs re;
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xmatch = s: re: if match s re then "true" else "false";
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in
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trace(''match("", ""): ${xmatch "" ""}'')
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trace(''match("foobar", ""): ${xmatch "foobar" ""}'')
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trace(''match("foobar", "foo"): ${xmatch "foobar" "foo"}'')
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trace(''match("foobar", "bar"): ${xmatch "foobar" "bar"}'')
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trace(''match("foobar", "baz"): ${xmatch "foobar" "baz"}'')
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trace(''match("barbaz", "baz"): ${xmatch "barbaz" "baz"}'')
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trace(''match("barbaz", ".ar"): ${xmatch "barbaz" ".ar"}'')
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trace(''match("barbaz", "ar."): ${xmatch "barbaz" "ar."}'')
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trace(''match("aaa", "b*"): ${xmatch "aaa" "b*"}'')
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trace(''match("aaa", "b.*"): ${xmatch "aaa" "b.*"}'')
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trace(''match("foobar", "b.*"): ${xmatch "foobar" "b.*"}'')
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trace(''match("foobar", "o.*a"): ${xmatch "foobar" "o.*a"}'')
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trace(''match("foobar", "^foo"): ${xmatch "foobar" "^foo"}'')
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trace(''match("foobar", "^bar"): ${xmatch "foobar" "^bar"}'')
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trace(''match("foobar", "oob$"): ${xmatch "foobar" "oob$"}'')
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trace(''match("foobar", "bar$"): ${xmatch "foobar" "bar$"}'')
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trace(''match("foobar", "o.*z*"): ${xmatch "foobar" "o.*z*"}'')
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trace(''match("foobar", "o.*z.*"): ${xmatch "foobar" "o.*z.*"}'')
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trace(''match("fo^bar", "o^b"): ${xmatch "fo^bar" "o^b"}'')
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trace(''match("foobar", "o^b"): ${xmatch "foobar" "o^b"}'')
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trace(''match("foobar", "o$b"): ${xmatch "foobar" "o$b"}'')
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"ok"

‎set/mod-fib.nix

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# Note that rec is mandatory here
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rec {
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fib = n:
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if n == 0 || n == 1 then
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n
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else
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fib(n - 1)+fib(n - 2)
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;
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}

‎set/mod.nix

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#!/bin/nix-instantiate
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with builtins;
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let
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m = (import ./mod-fib.nix);
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f = (import ./mod-fib.nix).fib;
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xs = [ (m.fib 10) (f 10) ];
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in
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deepSeq xs xs

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