```Chapel
record Pair {
type fst; /* : A */
type snd; /* : B */
}
```
```Haskell
data Pair = MkPair
{ fst :: A
, snd :: B
}
```
* So, we can't enforce that the user doesn't pass `int` to our `length` function defined on lists.
* We also can't enforce that `InL` is instantiated with the right type.
* So, we lose some safety compare to Haskell...
* ...but we're getting the compiler to do arbitrary computations for us at compile-time.
---
# Worked Example: Binary Search Tree
In Haskell, binary search trees can be defined as follows:
```Haskell
data BSTree = Empty
| Node Int BSTree BSTree
balancedOneTwoThree = Node 2 (Node 1 Empty Empty) (Node 3 Empty Empty)
```
Written using Algebraic Data Types, this is:
$$
\text{BSTree} = \text{Unit} + (\text{Int} \times \text{BSTree} \times \text{BSTree})
$$
In Haskell (using sums and products):
```Haskell
type BSTree' = Unit `Sum` (Int `Pair` (BSTree' `Pair` BSTree'))
balancedOneTwoThree' = InR (2 `MkPair` (InR (1 `MkPair` (InL MkUnit `MkPair` InL Unit)) `MkPair`
InR (3 `MkPair` (InL MkUnit `MkPair` InL Unit))))
```
---
# Worked Example: Binary Search Tree
* Recalling the Haskell version:
```Haskell
type BSTree' = Unit `Sum` (Int `Pair` (BSTree' `Pair` BSTree'))
balancedOneTwoThree' = InR (2 `MkPair` (InR (1 `MkPair` (InL MkUnit `MkPair` InL Unit)) `MkPair`
InR (3 `MkPair` (InL MkUnit `MkPair` InL Unit))))
```
* We can't define `BSTree'` in Chapel (no type-of-types), but we can define `balancedOneTwoThree'`:
```Chapel
type balancedOneTwoThree =
InR(Pair(2, Pair(InR(Pair(1, Pair(InL(), InL()))),
InR(Pair(3, Pair(InL(), InL()))))));
```
* :white_check_mark: We can use algebraic data types to build arbitrarily complex data structures ◼.
---
# Returning to Pragmatism
* We could've defined our list type in terms of `InL`, `InR`, and `Pair`.
* However, it was cleaner to make it look more like the non-ADT Haskell version.
* Recall that it looked like this:
```Chapel
record Nil {}
record Cons { param head: int; type tail; }
type myList = Cons(1, Cons(2, Cons(3, Nil)));
```
```Haskell
data ListOfInts = Nil
| Cons Int ListOfInts
myList = Cons 1 (Cons 2 (Cons 3 Nil))
```
* We can do the same thing for our binary search tree:
```Chapel
record Empty {}
record Node { param value: int; type left; type right; }
type balancedOneTwoThree = Node(2, Node(1, Empty, Empty),
Node(3, Empty, Empty));
```
```Haskell
data BSTree = Empty
| Node Int BSTree BSTree
balancedOneTwoThree = Node 2 (Node 1 Empty Empty)
(Node 3 Empty Empty)
```
---
# A General Recipe
To translate a Haskell data type definition to Chapel:
* For each constructor, define a `record` with that constructor's name
* The fields of that record are `type` fields for each argument of the constructor
- If the argument is a value (like `Int`), you can make it a `param` field instead
* A visual example, again:
```Chapel
record C1 { type arg1; /* ... */ type argi; }
// ...
record Cn { type arg1; /* ... */ type argj; }
```
```Haskell
data T = C1 arg1 ... argi
| ...
| Cn arg1 ... argj
```
---
# Inserting and Looking Up in a BST
```Chapel
proc insert(type t: Empty, param x: int) type do return Node(x, Empty, Empty);
proc insert(type t: Node(?v, ?left, ?right), param x: int) type do
select true {
when x < v do return Node(v, insert(left, x), right);
otherwise do return Node(v, left, insert(right, x));
}
type test = insert(insert(insert(Empty, 2), 1), 3);
proc lookup(type t: Empty, param x: int) param do return false;
proc lookup(type t: Node(?v, ?left, ?right), param x: int) param do
select true {
when x == v do return true;
when x < v do return lookup(left, x);
otherwise do return lookup(right, x);
}
```
```Haskell
insert :: Int -> BSTree -> BSTree
insert x Empty = Node x Empty Empty
insert x (Node v left right)
| x < v = Node v (insert x left) right
| otherwise = Node v left (insert x right)
test = insert 3 (insert 1 (insert 2 Empty))
lookup :: Int -> BSTree -> Bool
lookup x Empty = False
lookup x (Node v left right)
| x == v = True
| x < v = lookup x left
| otherwise = lookup x right
```
It really works!
```Chapel
writeln(test : string);
// prints Node(2,Node(1,Empty,Empty),Node(3,Empty,Empty))
writeln(lookup(test, 1));
// prints true for this one, but false for '4'
```
---
# A Key-Value Map
```Chapel
record Empty {}
record Node { param key: int; param value; type left; type right; }
proc insert(type t: Empty, param k: int, param v) type do return Node(k, v, Empty, Empty);
proc insert(type t: Node(?k, ?v, ?left, ?right), param nk: int, param nv) type do
select true {
when nk < k do return Node(k, v, insert(left, nk, nv), right);
otherwise do return Node(k, v, left, insert(right, nk, nv));
}
proc lookup(type t: Empty, param k: int) param do return "not found";
proc lookup(type t: Node(?k, ?v, ?left, ?right), param x: int) param do
select true {
when x == k do return v;
when x < k do return lookup(left, x);
otherwise do return lookup(right, x);
}
type test = insert(insert(insert(Empty, 2, "two"), 1, "one"), 3, "three");
writeln(lookup(test, 1)); // prints "one"
writeln(lookup(test, 3)); // prints "three"
writeln(lookup(test, 4)); // prints "not found"
```
---
# Conclusion
* Chapel's type-level programming is surprisingly powerful.
* We can write compile-time programs that are very similar to Haskell programs.
* This allows us to write highly parameterized code without paying runtime overhead.
* This also allows us to devise powerful compile-time checks and constraints on our code.
* This approach allows for general-purpose programming, which can be applied to `your use-case`