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PiMachine

Guides

  • Evaluation
  • Terms
  • Types

Tech Notes

  • Diagrams
  • SAT

Symbols

  • PiChoice
  • PiCombinator
  • PiContinuation
  • PiEval
  • PiEvalTrace
  • PiFunction
  • PiHole
  • PiInverse
  • PiMachineDiagram
  • PiMachinePort
  • PiMinus
  • PiOne
  • PiPlus
  • PiReduce
  • PiState
  • PiStateQ
  • PiTerm
  • PiTermQ
  • PiTimes
  • PiTypeQ
  • PiUnit
  • PiZero
WolframInstitute`PiMachine`
PiCombinator
​
PiCombinator
[name]
basic combinator terms.
​
Examples  
(2)
Basic Examples  
(2)
List and construct basis combinators:
In[1]:=
PiCombinator
[]
Out[1]=
{Identity,ZeroElimination,ZeroIntroduction,PlusSwap,PlusLeftAssociation,PlusRightAssociation,ZeroAbsorb,ZeroFactor,UnitElimination,UnitIntroduction,TimesSwap,TimesLeftAssociation,TimesRightAssociation,Distribution,Factorization,PlusCup,PlusCap,TimesCup,TimesCap,EvalForward,EvalBackward}
In[2]:=
PiCombinator
/@
PiCombinator
[]
Out[2]=

id
,
unite
+
l
,
uniti
+
l
,
swap
+
,
assocl
+
,
assocr
+
,PiCombinator[ZeroAbsorb],PiCombinator[ZeroFactor],
unite
*
l
,
uniti
*
l
,
swap
*
,
assocl
*
,
assocr
*
,
dist
,
factor
,
η
+
,
ϵ
+
,PiCombinator[TimesCup],PiCombinator[TimesCap],
eval
,
†
eval

In[3]:=
PiCombinator
"ZeroAbsorb"
PiOne

Out[3]=
absorbz
1

In[4]:=
PiCombinator
"ZeroFactor"
PiOne

Out[4]=
factorz
1

In[5]:=
PiCombinator
["TimesCap"[PiFalse]]
Out[5]=
ϵ
*



In[6]:=
PiCombinator
["TimesCup"[PiFalse]]
Out[6]=
η
*



​
Import shortcut names for combinators:
In[1]:=
Needs["WolframInstitute`PiMachine`Programs`"]
In[2]:=
swap[PiFalse]
Out[2]=

In[3]:=
uniti[PiFalse]
Out[3]=
1
⊗

In[4]:=
zeroi[PiTrue]
Out[4]=
2

""

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