Secure diffuse computing: class #6

Teacher: Serpette

Hop semantics

$\beta$-equations

(1)
\begin{align} \lambda x. M\;N\rightarrow M \{x/N\} \end{align}
(2)
\begin{equation} M[x:=N] \end{equation}

Recursion

(3)
\begin{align} (\lambda x.x\;x) = \Delta \end{align}

What means apply x to itself. This introduces a funny concept of x:

(4)
\begin{align} x \equiv x \rightarrow x \end{align}

(x is a set, marked as E on whiteboard by the teacher)

Reductions

  • Strong - reduction in compile time (ASAP)
  • Weak
    • Lazy/by need - (only Haskell?) passing unreduced results, reducing them only when needed
    • ?/by value- (Lisp, Scheme) reduction when computing the function

In strong the strings are reduced before we know that we ever need them.

Unclear, need to ask the teachers, since most is obviously derived works.