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Gather together corresponding elements from multiple lists

Given several lists, gather together the first element from every list, the second element from every list, and so on for all corresponding index values in the lists. E.g. for these three lists, first = ['Bruce', 'Tommy Lee', 'Bruce'], last = ['Willis', 'Jones', 'Lee'], years = [1955, 1946, 1940] the result should produce 3 actors. The middle actor should be Tommy Lee Jones.
fsharp
let result = (List.zip3 first last years)

List Combinations

Given two source lists (or sets), generate a list (or set) of all the pairs derived by combining elements from the individual lists (sets). E.g. given suites = ['H', 'D', 'C', 'S'] and faces = ['2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K', 'A'], generate the deck of 52 cards, confirm the deck size and check it contains an expected card, say 'Ace of Hearts'.
fsharp
let cards = (List.fold_left (fun acc suite -> acc @ (List.map (fun face -> (suite, face)) faces)) [] suites)

printfn "Deck has %d cards" (List.length cards)
printfn "%s" (if (List.exists (fun e -> e = ("h", "A")) cards) then "Deck contains 'Ace of Hearts'" ; else "'Ace of Hearts' not in deck")
let product (set1 : List<'a>) (set2 : List<'a>) : List<'a * 'a> =
let p = new ResizeArray<'a * 'a>()
for e1 in set1 do for e2 in set2 do p.Add(e1, e2) done done
Array.to_list (p.ToArray())

// ------

let cards = product suites faces

printfn "Deck has %d cards" (List.length cards)
printfn "%s" (if (List.exists (fun e -> e = ("h", "A")) cards) then "Deck contains 'Ace of Hearts'" ; else "'Ace of Hearts' not in deck")
let deck =
suites
|> List.map (fun s -> faces |> List.map (fun f -> (s, f)))
|> List.concat

printfn "Deck has %d cards" (List.length deck)
match deck |> List.exists (fun e -> e = ("h", "A")) with
| true -> printfn "Deck contains 'Ace of Hearts'"
| _ -> printfn "'Ace of Hearts' not in deck"

Perform an operation on every item of a list

Perform an operation on every item of a list, e.g.
for the list ["ox", "cat", "deer", "whale"] calculate
the list of sizes of the strings, e.g. [2, 3, 4, 5]
fsharp
let lengths = List.map String.length ["ox"; "cat"; "deer"; "whale"]

Split a list of things into numbers and non-numbers

Given a list that might contain e.g. a string, an integer, a float and a date,
split the list into numbers and non-numbers.
fsharp
let (things:obj list) = [ "hello"; 25; 3.14; System.DateTime.Now ]

let isNumber (x:obj) =
match x with
| :? int | :? float | :? byte | :? decimal | :? int16 | :? int64 -> true
| _ -> false

let numbers, nonNumbers = things |> List.partition isNumber