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 Representation 5!:

 x 5!:0 Define. 5!:0 is an adverb and provides a complete inverse of 5!:1. That is, (5!:1 <'f') 5!:0 equals f for all f . 5!:1 y Atomic. The atomic representation of the entity named y and is used in gerunds. The result is a single box containing a character list of the symbol (if primitive) or a two-element boxed list of the symbol and atomic representation of the arguments (if not primitive). Symbol-less entities are assigned the following encodings: 0  Noun 2  Hook 3  Fork 4  Bonded conjunction or train of adverbs For example: ``` plus=: + 5!:1 <'plus' +-+ |+| +-+ noun=: 3 1 4 1 5 9 5!:1 <'noun' +---------------+ |+-+-----------+| ||0|3 1 4 1 5 9|| |+-+-----------+| +---------------+ increment=: 1&+ 5!:1 <'increment' +-------------+ |+-+---------+| ||&|+-----+-+|| || ||+-+-+|+||| || |||0|1|| ||| || ||+-+-+| ||| || |+-----+-+|| |+-+---------+| +-------------+ ``` 5!:2 y Boxed. ``` nub=: (i.@# = i.~) # ] 5!:2 <'nub' +-------------------+-+-+ |+--------+-+------+|#|]| ||+--+-+-+|=|+--+-+|| | | |||i.|@|#|| ||i.|~||| | | ||+--+-+-+| |+--+-+|| | | |+--------+-+------+| | | +-------------------+-+-+ ``` 5!:4 y Tree. A literal matrix that represents the named entity in tree form. Thus: ``` 5!:4 <'nub' +- i. +- @ -+- # +---+- = | +- ~ --- i. --+- # +- ] ``` 5!:5 y Linear. The linear representation is a string which, when interpreted, produces the named object. For example: ``` 5!:5 <'nub' (i.@# = i.~) # ] 5!:5 <'a' [ a=: o. i. 3 4 3.14159265358979324*i.3 4 lr=: 3 : '5!:5 <''y''' lr 10000\$'x' 10000\$'x' ``` 5!:6 y Paren. Like the linear representation, but is fully parenthesized. ``` 5!:6 <'nub' ((i.@#) = (i.~)) # ] ``` x 5!:7 y Explicit. The left argument is 1 (monadic) or 2 (dyadic); the right argument is the boxed name of a verb, adverb, or conjunction. For example: ``` perm=: 3 : 0 z=. i.1 0 for. i.y do. z=.,/(0,.1+z){"2 1\:"1=i.>:{:\$z end. ) 1 (5!:7) <'perm' +-+----------+-------------------------------+ |0|1 _1 0 |z=.i.1 0 | +-+----------+-------------------------------+ |1|65536 2 1 |for. | +-+----------+-------------------------------+ |2|2 _1 1 |i.y | +-+----------+-------------------------------+ |3|131072 6 1|do. | +-+----------+-------------------------------+ |4|1 _1 1 |z=.,/(0,.1+z){"2 1\:"1=i.>:{:\$z| +-+----------+-------------------------------+ |5|32 3 1 |end. | +-+----------+-------------------------------+ ``` The result of 5!:7 is a 3-column boxed matrix. Column 0 are the boxed integers 0 1 2 ... n-1. Column 1 are boxed 3-element integer vectors of control information: control word code, goto line number, and source line number. Column 2 are boxed control words and sentences. The result of 5!:7 is a 0 3 empty matrix if the named object is not an explicit definition, or is undefined for the specified valence.

For all but the noun case, the default displays established by 9!:3 provide convenient experimentation with all representations. For example, 9!:3 (6 4 2) specifies that the paren, tree, and boxed representations are all to be displayed.

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