{-# LANGUAGE OverloadedStrings #-}
module Plutarch.Docs.PlutarchLambdas (pid, pid') where 
import Plutarch.Prelude

Lambdas are the second form of Plutarch Terms. Lambda terms are represented at the type level by the infix type constructor :-->; a value of type Term s (a :--> b) evaluates to a function that takes a value of type a and produces a value of type b.

You can create Plutarch lambda Terms by applying the plam function to a Haskell-level function that works on Plutarch terms. The true type of plam itself is unimportant to end-users of Plutarch, but it should be thought of as

plam :: (Term s a -> Term s b) -> Term s (a :--> b)

To create the identity function as a Plutarch lambda, we would thus use:

-- | Haskell-level `id` function specialized to the `Term s a` type``
termId :: Term s a -> Term s a
termId x = x

-- | Plutarch-level `id` lambda
pid :: Term s (a :--> a)
pid = plam termId

-- | Equivalently:
pid' :: Term s (a :--> a)
pid' = plam $ \x -> x

Notice the type. A Plutarch lambda Term uses the :--> infix operator to encode a function type. So in the above case, pid is a Plutarch level function that takes a type a and returns the same type. As one would expect, :--> is right-associative, and things curry like a charm.

Guess what this Plutarch level function does:

f :: Term s (PInteger :--> PString :--> a :--> a)

It takes in an integer, a string, and a type a and returns the same type a. Notice that the types are all of kind PType. This means that when faced with filling out the gap:

f :: Term s (PInteger :--> PString :--> a :--> a)
f = plam $ \???

We know that the argument to plam here is a Haskell function g with type Term s PInteger -> Term s PString -> Term s a -> Term s a.

Function Application

Once we construct a Plutarch lambda Term using plam, it is rather useless unless we apply it to an argument. Plutarch provides two operators to do so

{- |
  High precedence infixl function application, to be used like
  function juxtaposition. e.g.:

  >>> f # x # y
  Conceptually: f x y
-}
(#) :: Term s (a :--> b) -> Term s a -> Term s b
infixl 8 #

{- |
  Low precedence infixr function application, to be used like
  `$`, in combination with `#`. e.g.:

  >>> f # x #$ g # y # z
  Conceptually: f x (g y z)
-}
(#$) :: Term s (a :--> b) -> Term s a -> Term s b
infixr 0 #$

The types of each operator match our intuition. Applying a lambda Term to a Term (tagged with the PType of the domain of the lambda) produces a Term (tagged with the PType of the codomain.).