September Morn Update
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Ingy döt Net
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6856 changed files with 141342 additions and 21127 deletions
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". noun define -. CRLF NB. Fixed tacit universal Turing machine code...
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utm=.
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(((":@:(]&:>)@:(6&({::)) ,: (":@] 9&({::))) ,. ':'"_) ,. 2&({::) >@:(((
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48 + ]) { a."_)@[ ; (] $ ' '"_) , '^'"_) 3&({::))@:([ (0 0 $ 1!:2&2)@:(
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'A changeless cycle was detected!'"_)^:(-.@:(_1"_ = 1&({::))))@:((((3&(
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{::) + 8&({::)) ; 1 + 9&({::)) 3 9} ])@:(<@:((0: 0&({::)@]`(<@(1&({::))
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@])`(2&({::)@])} ])@:(7 3 2&{)) 2} ])@:(<"0@:(6&({::) (<@[ { ]) 0&({::)
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) 7 8 1} ])@:([ (0 0 $ 1!:2&2)@:(((":@:(]&:>)@:(6&({::)) ,: (":@] 9&({:
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:))) ,. ':'"_) ,. 2&({::) >@:(((48 + ]) { a."_)@[ ; (] $ ' '"_) , '^'"_
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) 3&({::))^:(0 = 4&({::) | 9&({::)))@:(<@:(1&({::) ; 3&({::) { 2&({::))
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6} ])@:(<@:(3&({::) + _1 = 3&({::)) 3} ])@:(<@:(((_1 = 3&({::)) {:: 5&
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({::)) , 2&({::) , (3&({::) = #@:(2&({::))) {:: 5&({::)) 2} ])^:(-.@:(_
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1"_ = 1&({::)))^:_)@:((0 ; (({. , ({: % 3:) , 3:)@:$ $ ,)@:(}."1)@:(".;
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._2)@:(0&({::))) 9 0} ])@:(<@:('' ; 0"_) 5} ])@:(5&(] , a: $~ [))@:(,~)
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(((":@:(]&:>)@:(6&({::)) ,: (":@] 9&({::))) ,. ':'"_) ,. 2&({::) >@:(((48 + ]
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) { a."_)@[ ; (] $ ' '"_) , '^'"_) 3&({::))@:([ (0 0 $ 1!:2&2)@:('A changeles
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s cycle was detected!'"_)^:(-.@:(_1"_ = 1&({::))))@:((((3&({::) + 8&({::)) ;
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1 + 9&({::)) 3 9} ])@:(<@:((0 (0 {:: ])`(<@:(1 {:: ]))`(2 {:: ])} ])@:(7 3 2&
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{)) 2} ])@:(<"0@:(6&({::) (<@[ { ]) 0&({::)) 7 8 1} ])@:([ (0 0 $ 1!:2&2)@:((
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(":@:(]&:>)@:(6&({::)) ,: (":@] 9&({::))) ,. ':'"_) ,. 2&({::) >@:(((48 + ])
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{ a."_)@[ ; (] $ ' '"_) , '^'"_) 3&({::))^:(0 = 4&({::) | 9&({::)))@:(<@:(1&(
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{::) ; 3&({::) { 2&({::)) 6} ])@:(<@:(3&({::) + _1 = 3&({::)) 3} ])@:(<@:(((_
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1 = 3&({::)) {:: 5&({::)) , 2&({::) , (3&({::) = #@:(2&({::))) {:: 5&({::)) 2
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} ])^:(-.@:(_1"_ = 1&({::)))^:_)@:((0 ; (({. , ({: % 3:) , 3:)@:$ $ ,)@:(}."1
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)@:(".;._2)@:(0&({::))) 9 0} ])@:(<@:('' ; 0"_) 5} ])@:(,&(;:',,,,,'))@:(,~)
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)
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NB. Structured derivation of the universal Turing machine...
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NB. Structured derivation of the universal Turing machine...
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o=. @: NB. Composition of verbs (functions)
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c=. "_ NB. Constant verb (function)
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f=. &{:: NB. fetch
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e=. <@: NB. enclose
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NB.--------------------------------------------------------------------------------------
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NB. Quick and dirty tacit toolkit...
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NB. utm (dyadic verb)...
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o=. @:
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c=."_
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'Q S T P F B M PRINT MOVE C'=. i.10 NB. Using 10 boxes
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NB. Left: Q - Instruction table, S - Turing machine state
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NB. Right: T - Data tape, P - Head position pointer, F - Display frequency
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NB. Local: B - Blank defaults, M - State and tape symbol read, PRINT - Printing symbol
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NB. MOVE - Tape head moving instruction, C - Step Counter
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ver=. (0:`)([:^:)
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DisplayTape=. > o (((48 + ]) { a.c)@[ ; ((] $ ' 'c) , '^'c))
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display=. ((((": o (]&:>) o (M f)) ,: (":@] C f)) ,. ':'c ) ,. (T f DisplayTape P f))
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NB. Displaying state, symbol, tape / step and pointer
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amend=. 0: (0 f)@]`(<@(1 f)@])`(2 f@])} ]
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d=. (fix=. (;:'f.')ver) (train=.(;:'`:')ver&6) (an=. <@:((,'0') (,&<) ]))
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ver=. (an f. o fix'ver')ver o an f.
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z=. ((an'')`($ ,)`) (`:6)
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d=. (a0=. `'') (a1=. (@:[) ((<'&')`) (`:6)) (a2=. (`(<(":0);_)) (`:6))
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av=. ((an o fix'a0')`) (`(an o fix'a1')) (`(an o fix'a2') ) (`:6)
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NB. execute (monadic verb)...
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Fetch=. (ver o train ;:'&{::')&.> o i. f.av
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tie=. ver o train ;:'`'
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FillLeft=. (_1 = P f ) {:: B f NB. Expanding and filling the tape
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FillRight=. ( P f = # o (T f)) {:: B f NB. with 0's (if necessary)
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ia=. <@[ { ] NB. Selecting by the indices of an array
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indices=. (, $~ 1 -.~ $) o (train"0 o ((1 -: L.)S:1 # <S:1) o (tie&'') o fix :: ] @:[)
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f=. ((ver o train ;:'&{')) o indices o train f.av
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e0=. (FillLeft , T f , FillRight)e T}] NB. Adjusting the tape
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e1=. (P f + _1 = P f)e P}] NB. and the pointer (if necessary)
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e2=. (S f ; P f { T f)e M}] NB. Updating the state and reading the tape symbol
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e3=. [(smoutput o display)^:(0 = F f | C f) NB. Displaying intermediate cycles
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e4=. (<"0 o (M f ia Q f)) (PRINT,MOVE,S)}] NB. Performing the printing, moving and state actions
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e5=. (amend o ((PRINT,P,T)&{))e T}] NB. Printing symbol on tape at the pointer position
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e6=. ((P f + MOVE f) ; 1 + C f) (P,C)}] NB. Updating the pointer (and the counter)
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'A B'=. 2 Fetch
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head=. (;:'<@:') {.~ 2 * 1 = # o [
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h=. train o (indices o train o (A f) (head , (B f) o ] , < o an o [ , (;:'}]')c) ]) f.av
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execute=. e6 o e5 o e4 o e3 o e2 o e1 o e0
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DropIfNB=. < o ('('"_ , ] , ')'"_) o ((}: ^: ('NB.' -: 3&{. o > o {:)) &. ;:)
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pipe=. ([ , ' o ' , ])&:>/ o |.
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al=. &(] , (a: $~ [)) NB. Appending local boxes
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cc=. 'A changeless cycle was detected!'c
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halt=. _1 c = S f NB. Halting when the current state is _1
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rt=. ((({. , ({: % 3:) , 3:) o $) $ ,) o (}."1) o (". ;. _2)
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NB. Reshaping the transition table as a 3D array (state,symbol,action)
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is=. ". o (, o ": o > , '=. ' , pipe o (DropIfNB;._2) o ". o ('0 ( : 0)'c)) f.av
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m0=. ,~ NB. Dyadic form (e.g., TPF f TuringMachine QS f )
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m1=. 5 al NB. Appending 5 local boxes (B,M,PRINT,MOVE,C)
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m2=. ('' ; 0 c)e B}] NB. Initializing local B (empty defaults as 0)
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m3=. (0 ; rt o (Q f)) (C,Q)}] NB. Setting (the counter and) the transition table
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m4=. execute^:(-. o halt)^:_ NB. Executing until a halt instruction is issued
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m5=. [smoutput o cc ^: (-. o halt) NB. or a changeless single cycle is detected
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m6=. display NB. Displaying (returning) the final status
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NB.--------------------------------------------------------------------------------------
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utm=. m6 o m5 o m4 o m3 o m2 o m1 o m0 f. NB. Fixing the universal Turing machine code
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NB. Producing the main (dyadic) verb utm...
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lr=. 5!:5@< NB. Linear representation
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Note 0
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NB. X (boxed list)...
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Q - Instruction table
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S - Turing machine initial state
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q: o $ o lr'utm' NB. The fixed tacit code length factors
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2 2 3 71
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NB. Y (boxed list)...
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T - Data tape
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P - Head position pointer
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F - Display frequency
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(12 71 $ ]) o lr'utm' NB. The fixed tacit code...
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(((":@:(]&:>)@:(6&({::)) ,: (":@] 9&({::))) ,. ':'"_) ,. 2&({::) >@:(((
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48 + ]) { a."_)@[ ; (] $ ' '"_) , '^'"_) 3&({::))@:([ (0 0 $ 1!:2&2)@:(
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'A changeless cycle was detected!'"_)^:(-.@:(_1"_ = 1&({::))))@:((((3&(
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{::) + 8&({::)) ; 1 + 9&({::)) 3 9} ])@:(<@:((0: 0&({::)@]`(<@(1&({::))
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@])`(2&({::)@])} ])@:(7 3 2&{)) 2} ])@:(<"0@:(6&({::) (<@[ { ]) 0&({::)
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) 7 8 1} ])@:([ (0 0 $ 1!:2&2)@:(((":@:(]&:>)@:(6&({::)) ,: (":@] 9&({:
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:))) ,. ':'"_) ,. 2&({::) >@:(((48 + ]) { a."_)@[ ; (] $ ' '"_) , '^'"_
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) 3&({::))^:(0 = 4&({::) | 9&({::)))@:(<@:(1&({::) ; 3&({::) { 2&({::))
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6} ])@:(<@:(3&({::) + _1 = 3&({::)) 3} ])@:(<@:(((_1 = 3&({::)) {:: 5&
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({::)) , 2&({::) , (3&({::) = #@:(2&({::))) {:: 5&({::)) 2} ])^:(-.@:(_
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1"_ = 1&({::)))^:_)@:((0 ; (({. , ({: % 3:) , 3:)@:$ $ ,)@:(}."1)@:(".;
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._2)@:(0&({::))) 9 0} ])@:(<@:('' ; 0"_) 5} ])@:(5&(] , a: $~ [))@:(,~)
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NB. Local...
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B - Blank defaults
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M - State and tape symbol read
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PRINT - Printing symbol
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MOVE - Tape head moving instruction
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C - Step Counter
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)
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'Q S T P F B M PRINT MOVE C'=. 10 Fetch NB. Fetching 10 Boxes
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DisplayTape=. > o (((48 + ]) { a.c)@[ ; ((] $ ' 'c) , '^'c))
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display=. ((((": o (]&:>) o M) ,: (":@] C)) ,. ':'c ) ,. (T DisplayTape P))
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NB. Displaying state, symbol, tape / step and pointer
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amend=. 0 (0 {:: ])`(<@:(1 {:: ]))`(2 {:: ])} ]
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NB. execute (monadic verb)...
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FillLeft=. (_1 = P ) {:: B NB. Expanding and filling the tape
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FillRight=. ( P = # o T) {:: B NB. with 0's (if necessary)
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ia=. <@[ { ] NB. Selecting by the indices of an array
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execute is
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T`(FillLeft , T , FillRight)h NB. Adjusting the tape
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P`(P + _1 = P) h NB. and the pointer (if necessary)
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M`(S ; P { T) h NB. Updating the state and reading the tape symbol
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[ (smoutput o display)^:(0 = F | C) NB. Displaying intermediate cycles
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(PRINT MOVE S)`(<"0 o (M ia Q))h NB. Performing the printing, moving and state actions
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T`(amend o ((PRINT P T)f)) h NB. Printing symbol on tape at the pointer position
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(P C)`((P + MOVE) ; 1 + C) h NB. Updating the pointer and the counter
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)
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cc=. 'A changeless cycle was detected!'c
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halt=. _1 c = S NB. Halting when the current state is _1
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rt=. ((({. , ({: % 3:) , 3:) o $) $ ,) o (}."1) o (". ;. _2)
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NB. Reshaping the transition table as a 3D array (state,symbol,action)
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utm is NB. Universal Turing Machine (dyadic verb)
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,~ NB. Appending the arguments in reverse order
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,&(;:5$',') NB. Appending 5 local boxes (B M PRINT MOVE C)
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B`('' ; 0 c) h NB. Setting empty blank defaults as 0
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(C Q)`(0 ; rt o Q)h NB. Setting the counter and the transition table
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execute^:(-. o halt)^:_ NB. Executing until a halt instruction is issued
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[ smoutput o cc ^: (-. o halt) NB. or a changeless single cycle is detected
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display NB. Displaying (returning) the final status
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)
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utm=. utm f. NB. Fixing the universal Turing machine code
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NB. The simulation code is produced by 77 (-@:[ ]\ 5!:5@<@:]) 'utm'
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