Lambda the Ultimate

Greetings,

I am having trouble wrapping my head around by-value substitution in lambda calculus. To try to warm up to lambda calculus I wrote a reducer, which works for leftmost outermost evaluation. However, when I tried to implement by-value it seemed to work fine, accept in a situation where by-value should have failed. Instead I get the same reduction as if I were using the left-outermost substitution (which in this case should succeed). I am using the definition given in Sestoft, Peter's "Demonstrating Lambda Calculus Reduction." Given this occurrence of an error, I am led to the conclusion that either (1) I got lucky on left-outermost reduction or (2) I am missing something on by-value reduction.

I would greatly appreciate any feedback or advice that this community can give.

Sincerely,

Jon