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Scalar function: Difference between revisions
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Only a particular [[valence]] of a function is labelled "scalar". The scalar monad [[Not]] usually shares the glyph <source lang=apl inline>~</source> with non-scalar dyad [[Without]], and similarly scalar [[Roll]] and non-scalar [[Deal]] are both written <source lang=apl inline>?</source>. | Only a particular [[valence]] of a function is labelled "scalar". The scalar monad [[Not]] usually shares the glyph <source lang=apl inline>~</source> with non-scalar dyad [[Without]], and similarly scalar [[Roll]] and non-scalar [[Deal]] are both written <source lang=apl inline>?</source>. | ||
== Standard scalar functions == | == Standard scalar functions == | ||
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== User defined scalar functions == | |||
In [[nested array model]] dialects with the [[Depth (operator)|Depth]] operator (<source lang=apl inline>⍥</source> or in J, ''Level at'' <source lang=j inline>L:</source> ), any function can be used as a scalar function (that is, be applied to all simple scalars) using the [[derived monadic operator]] <source lang=apl inline>perv←⍥0</source>: | |||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qKPtUduE6kd9U4HUo56mlMzigke9u2ofdbcAxYJdgUR4sLprWWpeibqGenBqcXFmfl5AUSaQq6AO1KyuyfWoo70CqNk5PyVVoeJ/QWpRGcio3qUGXH75ecHJiTmJRW55YEt6t1qpA/UBzVZQT1OvRZZXAOlT0DBQMNRUMFTQeNTVZKhgoAl0XjsXyOBHvWv@AwA Try it online!] | |||
<source lang=apl> | |||
perv←⍥0 | |||
NonScalarFn←{⍵:'t' ⋄ 'f'} | |||
NonScalarFn perv (0 1) 1 (⊂1 0) | |||
┌──┬─┬────┐ | |||
│ft│t│┌──┐│ | |||
│ │ ││tf││ | |||
│ │ │└──┘│ | |||
└──┴─┴────┘ | |||
</source> | |||
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | |||
In dialects that support [[dfn]]s, this operator can be defined<ref>[[John Scholes]], [https://dfns.dyalog.com/n_perv.htm perv] (Scalar pervasion). dfns workspace, 2019-02-17.</ref> as: | |||
<!-- [https://tio.run/##VZGxTsMwEIb3PMVtlwygZo3EVJURIWVAjFbsQKTItpwQFaEuCCUhKKgLIwOwMLB26cij@EXSc6IIasn23e@77@wz0/kJv2e5uhlsW9t6@2Bf32jjWaFtv7fdFzoTSV1eI09lgRv78kRuvKLlKsZVJWSJPsaiKDIlL01GLiDRMPBs26yJtlRcwHrQwlRjCQLXW9t9wvGw/TvECcuZARfKHM9zB@GZff6gLIrYuRlN9n6W5mTfCUzyYFS50OUtLCJQRCMVUglM6zxLWDmT/9UmVNv8fs@8P6AyM08QKAIjkjtTZJWA0rBKmILlp97Gu1Byuvy5nB65i5A6Qd0CTPHofHwe@AsIAwipSPcYwiKgH2g81yrb/wwH Try it online!] --> | |||
<source lang=apl> | |||
perv←{⍺←⊢ ⍝ Scalar pervasion | |||
1=≡⍺ ⍵ ⍵:⍺ ⍺⍺ ⍵ ⍝ (⍺ and) ⍵ depth 0: operand fn application | |||
⍺ ∇¨⍵ ⍝ (⍺ or) ⍵ deeper: recursive traversal. | |||
} | |||
</source> | |||
{{Works in|[[Dyalog APL]]}} | |||
== External links == | == External links == | ||