🚀 go-pugleaf

In article <602@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
>are dynamically typed languages.  Mathematical notation is generally
>closer to dynamically typed languages than to statically typed
>languages.
>
>In fact, I'd go so far as to claim that it is static type checking
>that is the peculiar notion, not dynamic typing.  Static typing
>originated, as near as I can determine, with low-level languages like
>Fortran an Algol that were little more than glorified assemblers.
>They had to give type declarations so that they could generate code
>that an assembly language programmer expected to be generated for
>expressions.  Much later, static typing took on religious significance
>as an element of the great god Structured Programming, and became a
>living force.  Now people have actually come to believe, against all
>evidence, that static typing is important for program reliability.
>


When I write:
             let S be a set
             let f:S -> X
             let Y = f(S) and let Z = {g(s): for s IN Y}
             for each  s in S let k_s = f(S)

a human being could figure out that:
           X, Y and Z are also sets
          that by f(S) I mean to apply f to each element of S
and that the last line makes more sense if we interpret f(S) as a typo
that should really be f(s)

How is a dynamically typed programming language going to figure this
out?