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Explicit Definition | m : n _ _ _ |

As defined and illustrated in Section II H, the phrase`s=: 0 : 0` may be used to define`s` as a script, and the explicit definition conjunction can be further used to produce a dyadic-only verb`` (`4 : s`),`` verb`` (`3 : s`),`` conjunction`` (`2 : s`),`` adverb`` (`1 : s`),`` or noun`` (`0 : s`). The left argument`13` may be used instead of`3` to produce equivalent results in tacit form if possible. The right argument`0` may be used in each case to make the corresponding definitions directly from the keyboard:`k : 0` is equivalent to`k :(0 : 0)`. Furthermore, the boxed representation`b=: <;._2 s` or the table representation`t=: >b` (or`t=:[;._2 s`)`` may be used in lieu of the script`s` in every case. Thus:

       f=: 3 : 0
    a=: 2+b=. y. ^ 2
    a+a*b
    :
    x.*x.+y.
    )

       a=: b=: 19
       f 3
    110

       a,b                        Only the globally assigned name is changed.
    11 19

As illustrated by the foregoing:

1. | The definitions of the monadic and dyadic cases produced by`3 : 0` are separated by a colon on a line by itself; if none occurs, the domain of the dyadic case is empty.
2. | The explicit result is the result of the last non-test block sentence executed; that result must be a noun in the`3 :` and`4 :` cases. See Control Structures for the definition of a test block.
3. | A name assigned by the copula`=.` is made local; values assigned to it have no effect on the use of the same name without the entity defined or within other entities invoked by it. A name assigned by`=:` is global.
4. | A locative cannot be localized.
5. | The names`x.` and`y.` denote the left and right arguments. In defining a conjunction it may be necessary to refer to its left and right arguments (using`u.` and`v.`)`` as well as to the arguments of the resulting function`` (`x.` and`y.`).`` The use of`m.` instead of`u.` restricts the corresponding argument to being a noun, as does the use of`n.` instead of`v.` .`` For example:

       conj=: 2 : '(u. y.)+ (v. y.)'
       mc=: 2 : 0
    (u.y.)+(v.y.)
    )

       dc=: 2 : 0                 Dyadic case
    :
    (u.y.)+(v.x.)
    )

       (!conj% 2 4 5);(!mc% 2 4 5);(1 2 3 !dc% 2 4 5)
    +---------------+---------------+--------------+
    |2.5 24.25 120.2|2.5 24.25 120.2|3 24.5 120.333|
    +---------------+---------------+--------------+

Control Structures. The sequence of execution of an explicit definition may be determined by control words such as`if. do. else. end.` and`while.` .`` For example, a function to find the root of a function`f` from a two-element list that brackets the root may be written and executed as follows:

       root=: 3 : 0
    m=.+/%#while.~:/y.do.if.~:/*f b=.(m,{.)y.do.y.=.b else.y.=.(m,{:)y.end.end.m y.
    )

       f=: 4:-%:
       b=: 1 32
       root b
    16

Such a definition may also be written on successive lines by breaking it before or after any control word, and the foregoing definition may be made more readable as follows:

       root=: 3 : 0
    m=. +/ % #
    while. ~:/y.
       do. if. ~:/*f b=. (m,{.) y.
                do. y.=. b
              else. y.=. (m,{:) y.
           end.
    end. m y.
    )

As illustrated by the foregoing, the word`if.` and a matching`end.` mark the beginning and end of a control structure, as do`while.` and a matching`end.`;`` such structures may be nested as is the`if.` structure within the`while.` structure.
The control words`for.`,`if.`,`select.`,`try.`,`while.`,`` and`whilst.` mark the beginnings of control structures that are each terminated by a matching`end.`,`` and therefore provide a form of punctuation. In the foregoing example,`do.` and`else.` break the`if.` structure into three simple blocks, each comprising a sentence, whereas the`do.` in the`while.` structure breaks it into two blocks, the first being a simple sentence, and the second being itself an`if.` control structure.
In general, a block comprises zero or more simple sentences and control structures. The role of blocks is summarized as follows:

    for.     T do. B end.
    for_xyz. T do. B end.
    if. T do. B end.
    if. T do. B else. B1 end.
    if. T do. B elseif. T1 do. B1 elseif. T2 do. B2 end.
    select. T case. T0 do. B0 fcase. T1 do. B1 case. T2 do. B2 end.
    try. B catch. B1 end.
    while. T do. B end.
    whilst. T do. B end.          Like while., but Skips Test first time.

Words beginning with`B` or`T` denote blocks. The last sentence executed in a`T` block is tested for a non-zero value in its leading atom, and the result of the test determines the block to be executed next. (An empty`T` block result or an omitted`T` block tests true.) If an error occurs in a`try.` block, execution continues in the matching`catch.` block. The final result is the result of the last sentence executed that was not in a`T` block, and if there is no such last executed sentence, the final result is`i.0 0` .
The behaviour of the remaining control words may be summarized as follows:

`assert. T` | signal assertion failure if`T` is not all 1s
`break.` | Go to end of`for.`,`while.`,`` or`whilst.` control structure
`continue.` | Go to top of`for.`,`while.`,`` or`whilst.` control structure
`goto_name.` | Go to label of same name
`label_name.` | Target of`goto_name.`
`return.` | Exit the function

Additional explanations and examples can be found in the Control Structures section.
The following example uses control words as well as`u.` and`n.` in modelling the Level conjunction`L:` :

       Level=: 2 : 0
    m=. 0{ 3&$&.|. n.
    ly=. L. y. if. 0>m do. m=.0>.m+ly end.
    if. m>:ly do. u. y. else. u. Level m&.> y. end.
    :
    'l r'=. 1 2{ 3&$&.|. n.
    lx=. L. x.  if. 0>l do. l=.0>. l + lx end.
    ly=. L. y.  if. 0>r do. r=.0>. r + ly end.
    b=. (l,r)>:lx,ly
    if.     b-: 0 0 do. x.    u. Level(l,r)&.>y.
    elseif. b-: 0 1 do. x.    u. Level(l,r)&.>y.
    elseif. b-: 1 0 do. (<x.) u. Level(l,r)&.>y.
    elseif. 1       do. x. u. y.
    end.
    )

       ] a=: (i.2 3);(<<2 3 4) ; 3
    +-----+---------+-+
    |0 1 2|+-------+|3|
    |3 4 5||+-----+|| |
    |     |||2 3 4||| |
    |     ||+-----+|| |
    |     |+-------+| |
    +-----+---------+-+

       +: Level 0 a
    +------+---------+-+
    |0 2  4|+-------+|6|
    |6 8 10||+-----+|| |
    |      |||4 6 8||| |
    |      ||+-----+|| |
    |      |+-------+| |
    +------+---------+-+

       +: L: 0 a
    +------+---------+-+
    |0 2  4|+-------+|6|
    |6 8 10||+-----+|| |
    |      |||4 6 8||| |
    |      ||+-----+|| |
    |      |+-------+| |
    +------+---------+-+

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