Train Tables: Difference between revisions
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==Introduction== | |||
The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct the Train which corresponds to more complicated expressions. For example, the expression | The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct the Train which corresponds to more complicated expressions. For example, the expression | ||
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may be expressed as a Train as follows: | may be expressed as a Train as follows: | ||
<apll> | {| border="0" | ||
<apll> | | || <apll>L e (L f R) g L h R</apll> | ||
<apll> | |- | ||
|<apll>←→</apll> || <apll>L e L (f g h) R</apll> || || using the definition of Dyadic Fork | |||
|- | |||
|<apll>←→</apll> || <apll>L (⊣ e (f g h)) R</apll> || || using the Train for <apll>L g L h R</apll> | |||
|} | |||
==Tables== | |||
<apll>gR:</apll><br /> | <apll>gR:</apll><br /> | ||
g R g | |||
R g R (g ⊢) | |||
Other <apll>gR</apll> forms using <apll>g</apll> twice may be obtained from <apll>ghR</apll> below. | Other <apll>gR</apll> forms using <apll>g</apll> twice may be obtained from <apll>ghR</apll> below. | ||
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g L (⊢ g)⍨ | g L (⊢ g)⍨ | ||
R g R (⊢ g ⊢) (⊢ g⍨) | R g R (⊢ g ⊢) (⊢ g⍨) | ||
R g L (⊢ | R g L g⍨ (g ⊢)⍨ (⊢ g ⊣) | ||
L g L (⊣ g ⊣) | L g L (⊣ g ⊣) | ||
L g R (g ⊢) | L g R g (g ⊢) | ||
Other <apll>LgR</apll> forms using <apll>g</apll> twice may be obtained from <apll>LghR</apll> below. | Other <apll>LgR</apll> forms using <apll>g</apll> twice may be obtained from <apll>LghR</apll> below. | ||
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(L f R) g L h R (f g h) Dyadic Fork | (L f R) g L h R (f g h) Dyadic Fork | ||
==Further Study== | |||
If you want to better understand this feature, the following [http://www.nars2000.org/download/workspaces/trains.ws.nars workspace] might be helpful. It contains functions to aid in understanding Trains such that you can enter a Train (say) <apll>L (f g h ⊢) R</apll> and it'll output the equivalent expression <apll>L f (g R) h R</apll>. | |||
Latest revision as of 16:57, 5 March 2009
Introduction
The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct the Train which corresponds to more complicated expressions. For example, the expression
L e (L f R) g L h R
may be expressed as a Train as follows:
| L e (L f R) g L h R | |||
| ←→ | L e L (f g h) R | using the definition of Dyadic Fork | |
| ←→ | L (⊣ e (f g h)) R | using the Train for L g L h R |
Tables
gR:
g R g
R g R (g ⊢)
Other gR forms using g twice may be obtained from ghR below.
LgR:
L (⊣ ⊣)
R (⊢ ⊢)
g R (⊢ g)
g L (⊢ g)⍨
R g R (⊢ g ⊢) (⊢ g⍨)
R g L g⍨ (g ⊢)⍨ (⊢ g ⊣)
L g L (⊣ g ⊣)
L g R g (g ⊢)
Other LgR forms using g twice may be obtained from LghR below.
ghR:
g h R ((⊢ g) h)
R g h R (g h) Monadic Hook
g R h R ((⊢ g) (h ⊢))
(g R) h R (g h ⊢) (h⍨ g)
R g R h R (g (h ⊢))
(R g R) h R ((g ⊢) h ⊢)
LghR:
g h R ((⊢ g) h) g L h R (⊢ (⊢ g) h) (g L) h R (h⍨ g)⍨ L g h L (⊣ g (⊢ h)⍨) L g h R (g h) Dyadic Hook R g h R (⊢ g (⊢ h)) R g h L (g h)⍨ L g L h L (⊣ g ⊣ h ⊣) L g L h R (⊣ g h) L g R h L (⊢ g h)⍨ L g R h R (g (h ⊢)) R g L h L (g (h ⊢))⍨ R g L h R (⊢ g h) R g R h L (⊣ g h)⍨ R g R h R (⊢ g ⊢ h ⊢) (L g L) h L ((⊢ g⍨) h ⊢)⍨ (L g L) h R (h⍨ (g ⊢))⍨ (L g R) h L (g h ⊣) (L g R) h R (g h ⊢) (R g L) h L (g h ⊢)⍨ (R g L) h R (g h ⊣)⍨ (R g R) h L (h⍨ (g ⊢)) (R g R) h R ((⊢ g⍨) h ⊢)
fghR:
(f R) g h R (f g h) Monadic Fork
LfghR:
(L f R) g L h R (f g h) Dyadic Fork
Further Study
If you want to better understand this feature, the following workspace might be helpful. It contains functions to aid in understanding Trains such that you can enter a Train (say) L (f g h ⊢) R and it'll output the equivalent expression L f (g R) h R.
