S, K, and I combinators with example from C# using MoreLINQ's pipe (K combinator). Implementations of S, K, and I combinators in F# and JavaScript. Ends with proof that SKK = I.

1. Combinators
Mike Harris

2. How to Add Data Without Stopping Flow?
CSV Filter
Add
File ID

3. How to Add Data Without Stopping Flow? (LINQ)
CSV Filter
Add
File ID
read Where ???
C#

4. How to Add Data Without Stopping Flow? (LINQ)
CSV Filter
Add
File ID
read Where ???
C#

5. How to Add Data Without Stopping Flow?
K combinator
CSV Filter
Add File
ID
read Where Pipe
C#

6. MoreLINQ’s Pipe
public static IEnumerable<T> Pipe<T>(
this IEnumerable<T> source,
Action<T> action
)
C#

7. MoreLINQ’s Pipe in Context
csv.GetRecords<TTarget>()
.Where(x => x.PricingDate != "")
.Pipe(x => { x.FileId = fileId; })
…
C#

8. Combinators

9. K combinator
let K x y = x
F#

10. K combinator
const tap =
f => x => {f(x); return x;};
const K = tap;
JS

11. I combinator
let I x = x
F#

12. I combinator
const identity =
x => x;
const I = identity;
JS

13. S combinator
let S x y z =
x z (y z)
F#

14. S combinator
const seq =
function(/*funcs*/) {
const funcs =
Array.prototype.slice.call(arguments);
return x =>
funcs.forEach(f => f(x));
};
const S = seq;
JS

15. Example

16. I = SKK
I = SKK
logic

17. I = SKK
I x = SKK x
definitions
• I x = x
• K xy = x
• S xyz = xz(yz) logic

18. I = SKK
I x = SKK x
= Kx (Kx)
definitions
• I x = x
• K xy = x
• S xyz = xz(yz) logic

19. I = SKK
I x = SKK x
= Kx (Kx)
= Kx x
definitions
• I x = x
• K xy = x
• S xyz = xz(yz) logic

20. I = SKK
I x = SKK x
= Kx (Kx)
= Kx x
= x
definitions
• I x = x
• K xy = x
• S xyz = xz(yz) logic

21. Lightning!

22. Extensional Equality
csv.GetRecords<TTarget>()
.Where(x => x.PricingDate != "")
.Pipe(x => { x.FileId = fileId; })
…
C#

23. Thank you!
Mike Harris
@MikeMKH
http://comp-phil.blogspot.com/