Answer to “what reduction is this?”

In lambda calculus, the predecessor function is surprisingly difficult, of course when compared with the successor, addition or multiplication.

In the post What reduction is this? I used chemlambda with the stupid sequential reduction strategy stated in Y again: conflict!, namely:

  •  we start with a g-pattern and we reduce it sequentially
  • at each step we identify first all the LEFT patterns from the following moves: beta, DIST, FAN-IN, LOC PR
  • we do the moves only from LEFT to RIGHT
  • repeat until no move available OR until conflict.

… And there is no conflict in the predecessor reduction.

In the post “What reduction is this?” I asked some questions, let me answer:

  • what kind of evaluation strategy is this?  NO EVALUATION STRATEGY, BECAUSE THERE ARE NO VALUES
  • are there reduction steps and self-multiplication steps? NO, THEY MIX  WITH NO EXTERNAL CONTROL
  • is this in lambda calculus? NO, IS INSPIRED FROM, BUT BETTER
  • what can we learn from this particular example? THAT IT WORKS WITHOUT EVALUATION STRATEGY, WITHOUT EXTERNAL CONTROL AND WITHOUT SIGNALS-THROUGH-WIRES-AND GATES.

This is a streamlined version of the reduction hidden in

PRED(3) –> 2

where numbers appear as stacks of pair FO and A nodes. They are “bare” numbers, in the sense that all the currying has been eliminated.

Admire the mechanical, or should I say chemical precision of the process of reduction (in chemlambda, stupid sequential strategy). In the following figure I eliminated all the unnecessary nodes and arrows and we are left now with the pure phenomenon.

 

pred_2

I find amazing that it works even with this stupidest strategy. Shows that chemlambda is much better than anything on the market.

Let me tell again: this is outside IT fundamental assumption that everything  is reduced at signals send through wires, then processed by gates. 

It is how nature works.

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