Solution2012-08-15-V3B
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Transcript of Solution2012-08-15-V3B
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8/12/2019 Solution2012-08-15-V3B
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Z,B, . . .
f : Z Z f(x) =
1 x Z x 0
0
g : (Z Z) Z g(h) =
0
h(x)= x Z
t s t s
f S={, 0}
f(S) ={0, 1} f(S) =f(S)
fi(x) = 0 x i
S = {f1, f2, . . .} S = f f(x) = 0 x Z g(S) = = 0 = g(S)
g
(x.42) bot bot bot
42
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> 1
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D f : D D {fi()| i N}
f
D = 2N D
S D
D
(D, )
f : D D f
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f mult nf mult
()
n N
n f mult
f mult
S(S (S ))S (S Z)
Z
S(S)S Z
S
seln,i isaconstr argofconstr
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fi() fi+1()
i N
i= 0 f0() = f1()
i >0
fi1() fi() f
f
f(fi1()) f(fi()) fi() fi+1()
{fi() | i N} D {fi() | i N}
f
f({fi()| i N}) =f({fi()| i N}) (f )
={fi+1()| i N}
=({fi+1()| i N} { })
={fi()| i N}
d
f
{fi()| i N} d
fi() d f0() = d
fi() d f f(fi()) f(d)
d
f
fi+1
()d
S= {M1, M2, . . .} Mi Mi+1
S=
Mi Mi
Mi B
Mi B e
Mi\ B k
e Mk eB Mk B B S
Mi D
D
Ni := {k N | k i} Ni Ni+1 {N1, N2, . . .}
f(M) = M
{42}
g
(nf mult
())(x, y) =
0
x= 0 n > 0
x y
0< x < n y=
f mult
g(x, y) =
0
x= 0
x y 0< x y=
h(x, y) =
0 x= 0
x y x= y=
x= (x= 0 y = ) (
)
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f
f(c1, c2) = f mult(f)(c1, c2) f(c1, c2) = 0 c1 = 0
c1 = 0 f(c1, c2) =c2+f(c11, c2) c1 = c1 1 c2 = c1 = 0
c2+f(c1 1, c2)
h
c1, c2 Z f(c1, c2) = c2+ f(c1 1, c2)
B H
A (A ) A (E )A (B )
A B
B(E)A H
isaZ
isaS
argofS
isaZ
argofS
Lam
t= fact.(x.(If(LessThanOrEx 1) 1 (Timesx (fact (Minusx 1)))))
= { If True x y.x,
If Falsex y.y,
fix f.f(fixf)}
{ Minus x y z | x, y Z z= x y}
{Times
x y z | x, y Z
z= x y} { LessThanOrE x y b | x, y Z ((x y b= True) (x > y b= False))}
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fixt 1
t
(fix(quot x y.If(LessThanx y) 0 (Plus1 (quot (Minusx y) y )))) v w
fixt 1
(f.(f (fixf))) t 1
t (fixt) 1
(x.(If(LessThanOrEx 1) 1 (Timesx (fixt (Minusx 1))))) 1
If(LessThanOrE1 1) 1 (Times1 (fixt (Minus1 1))) ()
If True 1 (Times1 (fixt (Minus1 1))) (x.(y.x)) 1 (Times1 (fixt (Minus1 1)))
(y.1) (Times1 (fixt (Minus1 1)))
1
If if
()
A0 := {x:: a.a Int} y.y x W
W(A0, y.y x)W(A0+ {y:: b1}, y x)
W(A0+ {y:: b1}, y) = (id,b1)W(A0+ {y:: b1}, x) = (id,b2 Int)
mgu(b1, (b2 Int)b3) = [b1/(b2 Int) b3])= ([b1/(b2 Int) b3], b3)
= ([b1/(b2 Int) b3], ((b2 Int) b3) b3)
