Research proof index

Rice's theorem: no SKI term is a non-trivial predicate. More specifically, say a term P is a predicate if, for every term x, P · x reduces to either TT or FF. A predicate P is trivial if either it always reduces to true, or always to false. This version of Rice's theorem derives a contradiction from the existence of a predicate P and...

Sqrt correctly computes Nat.sqrt.

Registers preservation: both reach states with the same registers.

A program halts with result a iff evaluation returns Part.some a.

A state is halted iff it is normal (has no successor) in the reduction system.

Reverse step correspondence: if p.toStandardForm steps from s to s', then either: (1) p steps from s to s' (same step), or (2) s' is halted in p.toStandardForm, and p steps to a state that is also halted with the same registers (this only happens for jumps with unbounded targets).