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September 10, 2020 13:31
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Reto N.2 7-9-2020
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Reduzca a forma normal las siguientes abstracciones: | |
1. (\x.xx)(\x.xx) | |
2. (\x.xxx)(\x.xxx) | |
3. (\x.\y.xy)(\y.y)e # Para evitar confusion, use una abstraccion Alpha-equivalente para el combinador Identidad | |
4. (\m.\n.( | |
(n (\a.\b.\c. | |
( | |
b((ab)c) | |
) | |
))m | |
) | |
) (\f.\n.n) (\f.\n.fx) | |
5. (\a.a)(\b.b)(\c.cc)(\d.d) |
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Reduzca a forma normal las siguientes abstracciones:
aplicacion de funciones
(\x.xx)(\x.xx) --> M := e | x | MM | \x.M
(\x.xx)(\x.xx)
(\a.aa)(\b.bb)
(\b.bb)(\b.bb)
(\x.xxx)(\x.xxx)
(\c.c c c)(\a.aaa)
(\a.aaa) (\a.aaa) (\a.aaa)
(\x.xxx)(\x.xxx)
(\b.bbb)(\w.www) (\a.aaa)
(\z.zzz)(\p.ppp)(\w.www)(\a.aaa)
(\p.ppp)(\p.ppp)(\p.ppp)(\w.www)(\a.aaa)
Halting problem
(\x.\z.xz)(\y.y)e # Para evitar confusion, use una abstraccion Alpha-equivalente para el combinador Identidad
(\z.(\y.y)z)e
(\y.y)e
e
Funciones (de) punto fijo
Fixed point functions
(\a.aa)(\b.bb) --> quan
(\y.y)e
(n (\a.\b.\c.
(
b((ab)c)
)
))m
)
) (\f.\n.n) (\f.\n.fx)
M::(\f.\n.n)
N::(\f.\n.fn)
F::(\a.\b.\c.(b((ab)c)))
(\m.\n.( (n F )m)) M N
(\n.( (n F )M)) N
(NF)M
( (\f.\n.fn)(\a.\b.\c.(b((ab)c))) )M
( (\n.(\a.\b.\c.(b((ab)c)))n) )M
(\n.(\a.\b.\c.(b((ab)c)))n) M
(\a.\b.\c.(b((ab)c)))M
(\b.\c.(b((Mb)c)))
(\b.\c. (b( ( (\f.\n.n) b) c) ))
(\b.\c. (b( (\n.n)c ) ))
(\b.\c.bc) --> Beta normal
1+0=1
Peano numerals
"0" :: (\f.\x.x)
"1" :: (\f.\x.fx)
"2" :: (\f.\x.ffx)
(N+1)th :: SUCC N -> (\a.\b.\c.(b((ab)c)))
SUCC 2 ->> (\f.\x.fffx)
(\a.\b.\c.(b((ab)c))) 2
\b.\c.b(2b)c
\b.\c.b( (\f.\x.ffx) b)c
\b.\c.b (\x.bbx)c
\b.\c.b bbc
\b.\c.bbbc == (\f.\x.fffx)
(\b.b)(\c.cc)(\d.d)
(\c.cc)(\d.d)
(\d.d)(\d.d)
(\d.d)