-- use smap and if-then machines to identify and predict next digits from an integer sequence fragment: -- see: -- updated to the version 3.1.1 language -- 2021/11/26 fixed a bug that caused a crash when trying to create if then machines. -- min and max ngram lenghts for the prediction if-then machines: min |ngram len> => |3> max |ngram len> => |9> -- min and max fragment lengths for id-sequence operator: min |fragment len> => |3> max |fragment len> => |3> -- Fibonacci: fib |0> => |0> fib |1> => |1> -- fib |*> !=> arithmetic(fib minus[1] |_self>, |+>, fib minus[2] |_self>) |> fib |*> !=> fib minus[1] |_self> ++ fib minus[2] |_self> -- factorial: fact |0> => |1> -- fact |*> !=> arithmetic(|_self>, |*>, fact minus[1] |_self>) |> fact |*> !=> |_self> ** fact minus[1] |_self> -- now learn our four sequences, counting, Fibonacci, factorial, primes: print (| > . |Learning our sequences ... >) int-seq |count> => srange(|1>, |100>) |> int-seq |fib> => fib srange(|1>, |30>) |> int-seq |fact> => fact srange(|1>, |15>) |> int-seq |primes> => such-that[is-prime] srange(|1>, |200>) |> -- learn what is a digit: list-of |digits> => |0> + |1> + |2> + |3> + |4> + |5> + |6> + |7> + |8> + |9> is-digit |*> #=> is-mbr(|_self>) list-of |digits> is-integer |*> #=> is-subset(clean split |_self>) list-of |digits> -- define a digit encoder: -- digit-encoder |*> #=> op-if(is-digit |_self>, |op: Gaussian-0.6>, |op: identity>) |_self> -- -- define an integer encoder: -- integer-encoder |*> #=> op-if(is-integer |_self>, |op: Gaussian-1>, |op: identity>) |_self> -- -- define our helper operators: -- Gaussian-0.6 |*> #=> Gaussian[0.6] |_self> -- Gaussian-1 |*> #=> Gaussian[1] |_self> -- identity |*> #=> |_self> -- define a digit encoder: digit-encoder |*> #=> if( is-digit |__self> ): Gaussian[0.6] |__self> else: |__self> end: -- define an integer encoder: integer-encoder |*> #=> if( is-integer |__self> ): Gaussian[1] |__self> else: |__self> end: -- define the if-then machine create-rule for the id-sequence code: create-single-rule (*) #=> node |label> => |node:> __ node |number> _ |:> __ node |idx> int-seq-pattern node |label> => |__self> node |idx> => plus[1] node |idx> -- define the if-then machine create-rule for the predict-next and fuzzy-predict-next code: create-next-rules (*) #=> node |label> => |node:> __ node |number> _ |:> __ node |idx> pattern node |label> => sselect[1,-2] |__self> fuzzy-pattern node |label> => integer-encoder sselect[1,-2] |__self> next-1 node |label> => sselect[-1,-1] |__self> node |idx> => plus[1] node |idx> -- node |label> => |node:> __ node |number> _ |:> __ node |idx> pattern node |label> => sselect[1,-3] |__self> fuzzy-pattern node |label> => integer-encoder sselect[1,-3] |__self> next-2 node |label> => sselect[-2,-1] |__self> node |idx> => plus[1] node |idx> -- node |label> => |node:> __ node |number> _ |:> __ node |idx> pattern node |label> => sselect[1,-4] |__self> fuzzy-pattern node |label> => integer-encoder sselect[1,-4] |__self> next-3 node |label> => sselect[-3,-1] |__self> node |idx> => plus[1] node |idx> -- node |label> => |node:> __ node |number> _ |:> __ node |idx> pattern node |label> => sselect[1,-5] |__self> fuzzy-pattern node |label> => integer-encoder sselect[1,-5] |__self> next-4 node |label> => sselect[-4,-1] |__self> node |idx> => plus[1] node |idx> -- a helper operator: -- extract-node-number |*> #=> sselect[2,2] ssplit[": "] |_self> extract-node-number |*> #=> extract-value extract-category |_self> not |no> => |yes> not |yes> => |no> -- define our if-then machine creation operator: create-if-then-machine (*,*) #=> node |number> => plus[1] clean select[-1,-1] ket-sort extract-node-number rel-kets[then] |> if( not do-you-know node |number> ): node |number> => |1> end: node |idx> => |1> smap(min |ngram len>, max |ngram len>, |__self1>) |__self0> node |label> => |node:> __ node |number> _ |: *> then node |label> => |__self2> -- print out start learning message: print (| > . |Starting to learn our sequences ... >) -- now use it to create the next-k if-then machines: create-if-then-machine(|op: create-next-rules>, |integer sequence: counting>) int-seq |count> create-if-then-machine(|op: create-next-rules>, |integer sequence: fibonacci>) int-seq |fib> create-if-then-machine(|op: create-next-rules>, |integer sequence: factorial>) int-seq |fact> create-if-then-machine(|op: create-next-rules>, |integer sequence: primes>) int-seq |primes> -- now create the id-sequence if-then machines: min |ngram len> => |3> max |ngram len> => |3> create-if-then-machine(|op: create-single-rule>, |integer sequence: counting>) int-seq |count> create-if-then-machine(|op: create-single-rule>, |integer sequence: fibonacci>) int-seq |fib> create-if-then-machine(|op: create-single-rule>, |integer sequence: factorial>) int-seq |fact> create-if-then-machine(|op: create-single-rule>, |integer sequence: primes>) int-seq |primes> -- print out finished learning message: print (|Finished learning> __ extract-value to-comma-number how-many rel-kets[*] |> __ |rules.> . | >) -- define the id-sequence operator: simm-pattern (*) #=> then drop-below[0.8] similar-input[int-seq-pattern] |__self> id-sequence |*> #=> smap(min |fragment len>, max |fragment len>, |op: simm-pattern>) ssplit[" "] |_self> -- define the predict-next operator: predict-nodes |*> #=> natural-sort drop-below[0.97] similar-input[pattern] ssplit[" "] |_self> do-you-know-prediction |*> #=> do-you-know predict-nodes |_self> predict-next |*> #=> unlearn[the] |result> the |result> => predict-nodes |__self> -- print-result the |result> if( do-you-know the |result> ): print-next the |result> else: |Anomaly, no sequence detected ... > end: print-result |#EMPTY#> => |Anomaly, no sequence detected ... > print-result |*> #=> print-next |_self> -- define the print-next operators: print-next-1 |yes> #=> print (extract-value round[1] push-float 100 tmp |var> _ | % > __ then tmp |var> __ | pattern: > _ smerge[" "] pattern tmp |var> _ | next-1: > _ smerge[" "] next-1 tmp |var>) print-next-2 |yes> #=> print (extract-value round[1] push-float 100 tmp |var> _ | % > __ then tmp |var> __ | pattern: > _ smerge[" "] pattern tmp |var> _ | next-2: > _ smerge[" "] next-2 tmp |var>) print-next-3 |yes> #=> print (extract-value round[1] push-float 100 tmp |var> _ | % > __ then tmp |var> __ | pattern: > _ smerge[" "] pattern tmp |var> _ | next-3: > _ smerge[" "] next-3 tmp |var>) print-next-4 |yes> #=> print (extract-value round[1] push-float 100 tmp |var> _ | % > __ then tmp |var> __ | pattern: > _ smerge[" "] pattern tmp |var> _ | next-4: > _ smerge[" "] next-4 tmp |var>) print-next |*> #=> tmp |var> => |__self> print-next-1 do-you-know next-1 |__self> print-next-2 do-you-know next-2 |__self> print-next-3 do-you-know next-3 |__self> print-next-4 do-you-know next-4 |__self> |results> -- define the fuzzy-predict-next operator: -- fuzzy-predict version that matches sequences even if they are different lengths: -- fuzzy-predict-nodes |*> #=> drop-below[0.5] similar-input[fuzzy-pattern] integer-encoder ssplit[" "] |_self> -- fuzzy-predict version that only matches sequences of exactly the same length: fuzzy-predict-nodes |*> #=> drop-below[0.5] strict-similar-input[fuzzy-pattern] integer-encoder ssplit[" "] |_self> do-you-know-fuzzy-prediction |*> #=> do-you-know fuzzy-predict-nodes |_self> fuzzy-predict-next |*> #=> unlearn[the] |result> the |result> => fuzzy-predict-nodes |__self> -- print-result the |result> if( do-you-know the |result> ): print-next the |result> else: |Anomaly, no sequence detected ... > end: print-usage |*> #=> print | > print |Usage:> print | Split the input sequence on the space char, and identify which sequence it belongs to:> print | id-sequence ket(1 2 3 4)> print | id-sequence ket(2 3 5 8)> print | > print | Given a sequence, return matching nodes:> print | predict-nodes ket(2 3 5 8)> print | > print | Given a sequence, predict the next elements:> print | predict-next ket(1 2 3)> print | predict-next ket(1 2 3 4 5)> print | predict-next ket(2 3 5 8)> print | predict-next ket(2 6 24)> print | predict-next ket(2 3 5 7)> print | predict-next ket(9 9 9)> print | > print | Given a sequence, test if it is recognized:> print | do-you-know-prediction ket(2 6 24)> print | do-you-know-prediction ket(9 9 9)> print | > print | > print | Given a sequence, return fuzzy matching nodes:> print | fuzzy-predict-nodes ket(11 12 13 14)> print | > print | Given a sequence, fuzzy-predict the next elements:> print | fuzzy-predict-next ket(2 3 5 7 11)> print | fuzzy-predict-next ket(9 9 9)> print | > print | Given a sequence, test if it is fuzzy-recognized:> print | do-you-know-fuzzy-prediction ket(9 9 9)> print | > print-usage