5th

5th was a typed concatenative programing language in development by John Nowak.

The type system was basically just a mildly augmented Hindley-Milner. Functions were all unary from stacks to stacks. Stacks were represented as nested pairs with a kind restriction such that pairs were always left-nested and functions were always from stacks to stacks.

 kind  = *
       | stack
 *     = integer           -- types of values
       | boolean
       | [stack -> stack]  -- quotations
 stack = 0                 -- the empty stack
       | stack *           -- juxtaposition denotes "cons"

Example types:

 swap   : forall (s : stack) (a b : *), s a b -> s b a
 apply  : forall (s t : stack), s [s -> t] -> t
 apply1 : forall (s : stack) (a b : *), s a [0 a -> 0 b] -> s b
 map    : forall (s : stack) (a b : *), s (list a) [0 a -> 0 b] -> s (list b)
 each   : forall (s : stack) (a : *), s (list a) [s a -> s] -> s

For algebraic data types, I generated eliminators. For example, declaring the usual 'list' data type would get you the following constructors and eliminator:

 null   : forall (s : stack) (a : *), s -> s (list a)
 cons   : forall (s : stack) (a : *), s a (list a) -> s (list a)
 unlist : forall (s t : stack) (a : *),
   s (list a) [s -> t] [s a (list a) -> t] -> t

You could use these to write familiar functions:

 sum : forall (s : stack) (a : *), s (list a) -> s integer
 sum = [0] [nip sum 1 +] unlist

I should note that, because you're often recursing on a stack of a different size, you probably want to support polymorphic recursion. Without it, the type system will force you to stick to strictly iterative functions. A conservative rule would just be to require a type signature on all recursive functions (as inference for polymorphic recursion is an undecidable problem).