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The type definition of TermFn is more complex than what it actually does; but that is only because it automatically handles functions with an unspecified (potentially infinite) number of parameters;

All it does tough is just adding the "$" method that replaces the papp call.

to give an idea here how the case of a function from a single input to a single output looks like;

we'll call this type TermLam even if there's no type called so in plu-ts

type TermLam<PIn extends PType, POut extends PType> =
Term<PLam<PIn,POut>> & {
$: ( input: Term<PIn> ) => Term<POut>