Computational Logic A “Hands-on” Introduction to Logic Programming

Exercises on Unification
• Get the m.g.u. of:
1. p(X, Y ) and p(f(Y ), f(Z))
2. p(f(X), Y ) and p(Y, g(X))
3. p(X, Y, f(X, Y )) and p(f(A, B), B, A)
4. p(f(X, Y ), g(Z, X), h(V ), a, W ) and p(Z, W, Y, V, g(f(V, Y ), X))
5. conv(us(Month, Day, Y ear), eur(Day, Month, Y ear)) and
conv(us(jan, 25, Y ear), D)
6. conv(us(Month, Day, Y ear), eur(Day, Month, Y ear)) and
conv(D, eur(22, may, 2002))
7. third(l(A, l(B, l(X, C))), X) and third(l(one, l(two, l(three, void))), Y )
8. third(l(A, l(B, l(X, C))), X) and third(l(one, l(two, void)), Y )
9. third(l(A, l(B, l(X, C))), X) and third(L, a)
Computational Logic
A “Hands-on” Introduction to Logic Programming
Exercises
2

Exercises on unification — Solutions (Contd.)
• p(X, Y, f(X, Y )) and p(f(A, B), B, A)
θ E T S
{} { p(X,Y,f(X,Y))=p(f(A,B),B,A) } p(X,Y,f(X,Y)) p(f(A,B),B,A)
{} { X=f(A,B), Y=B, f(X,Y)=A } X f(A,B)
{ X=f(A,B) } { Y=B, f(f(A,B),Y)=A } Y B
{ X=f(A,B), Y=B } { f(f(A,B),B)=A } f(f(A,B),Y) A
fail
Exercises on unification — Solutions
• p(X, Y ) and p(f(Y ), f(Z))
θ E T S
{} { p(X,Y)=p(f(Y),f(Z)) } p(X,Y) p(f(Y),f(Z))
{} { X=f(Y), Y=f(Z) } X f(Y)
{ X=f(Y) } { Y=f(Z) } Y f(Z)
{ X=f(f(Z)), Y=f(Z) } {}
• p(f(X), Y ) and p(Y, g(X))
θ E T S
{} { p(f(X),Y)=p(Y,g(X)) } p(f(X),Y) p(Y,g(X))
{} { f(X)=Y, Y=g(X) } f(X) Y
{ Y=f(X) } { f(X)=g(X) } f(X) g(X)
fail
4

Exercises on unification — Solutions (Contd.)
Exercises on unification — Solutions (Contd.)
• conv(us(Month, Day, Y ear), eur(Day, Month, Y ear)) and conv(us(jan, 25, Y ear), D)
• p(f(X, Y ), g(Z, X), h(V ), a, W ) and p(Z, W, Y, V, g(f(V, Y ), X))
θ E T S
{} { conv(us(Month,Day,Year), conv(...) conv(...)
eur(Day,Month,Year))=
conv(us(jan,25,Year),D) }
{} { us(Month,Day,Year)= us(...) us(...),
us(jan,25,Year),
eur(Day,Month,Year)=D }
{} { Month=jan, Day=25, Year=Year, Month jan
eur(Day,Month,Year)=D }
{Month=jan} { Day=25, Year=Year, Day 25
eur(Day,jan,Year)=D }
{ Month=jan, Day=25} { Year=Year, Year Year
eur(25,jan,Year)=D }
{Month=jan, Day=25} { eur(25,jan,Year)=D } eur(25,jan,Year) D
θ E T S
{} { p(f(X,Y),g(Z,X),h(V),a,W)= p(...) p(...)
p(Z,W,Y,V,g(f(V,Y),X)) }
{} { f(X,Y)=Z, g(Z,X)=W, h(V)=Y, f(X,Y) Z
a=V, W=g(f(V,Y),X) }
{Z=f(X, Y)} { g(f(X,Y),X)=W, h(V)=Y, g(f(X,Y),X) W
a=V, W=g(f(V,Y),X) }
{ Z=f(X,Y), { h(V)=Y, a=V, h(V) Y
W=g(f(X,Y),X) } g(f(X,Y),X)=g(f(V,Y),X) }
{ Z=f(X,Y), { a=V, g(f(X,h(V)),X)= a V
W=g(f(X,Y),X), Y=h(V) } g(f(V,h(V)),X) }
{ Z=f(X,Y), W=g(f(X,Y),X), { g(f(X,h(a)),X)= g(...) g(...)
Y=h(V), V=a } g(f(a,h(a)),X) }
{ Z=f(X,Y), W=g(f(X,Y),X), { f(X,h(a))=f(a,h(a)), X=X } f(X,h(a)) f(a,h(a))
Y=h(V), V=a }
{ Z=f(X,Y), W=g(f(X,Y),X), { X=a, X=X, h(a)=h(a) } X a
Y=h(V), V=a }
{ Z=f(X,Y), W=g(f(X,Y),X), { X=X, h(a)=h(a) }
Y=h(V), V=a, X=a }
{Month=jan, Day=25, {}
D=eur(25,jan,Year)}
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Exercises on unification — Solutions (Contd.)
Exercises on unification — Solutions (Contd.)
• third(l(A, l(B, l(X, C))), X) and third(l(one, l(two, l(three, void))), Y )
θ E T S
{} { third(l(A,l(B,l(X,C))),X)= third(...) third(...)
third(l(one,l(two,
l(three,void))),Y) }
{} { l(A,l(B,l(X,C)))= l(A,...) l(one,...)
l(one,l(two,l(three,void))),
X=Y }
{} { A=one, l(B,l(X,C))= A one
l(two,l(three,void)), X=Y }
{A=one} { l(B,l(X,C))= l(B,l(X,C)) l(two,l(three,void))
l(two,l(three,void)), X=Y }
{A=one} { B=two, B two
l(X,C)=l(three,void), X=Y }
{A=one, B=two } {l(X,C)=l(three,void), X=Y } l(X,C) l(three,void)
{A=one, B=two } {X=three, C=void, X=Y } X three
{A=one, B=two, {C=void, three=Y } C void
X=three }
{A=one, B=two, { three=Y } three Y
X=three, C=void }
{A=one, B=two, {}
X=three, C=void,
Y=three }
• conv(us(Month, Day, Y ear), eur(Day, Month, Y ear)) and conv(D, eur(22, may, 2002))
θ E T S
{} { conv(us(Month,Day,Year), conv(...) conv(..
eur(Day,Month,Year))=
conv(D,eur(22,may,2002)) }
{} { us(Month,Day,Year)=D, us(Month,Day,Year) D
eur(Day,Month,Year)=
eur(22,may,2002) }
{D=us(Month,Day,Year)} { eur(Day,Month,Year)= eur(...) eur(..
eur(22,may,2002) }
{D=us(Month,Day,Year)} {Day=22, Month=may, Day 22
Year=2002 }
{D=us(Month,22,Year), { Month=may, Year=2002} Month may
Day=22}
{D=us(may,22,Year), { Year=2002} Year 2002
Day=22, Month=may}
{D=us(may,22,2002), {}
Day=22, Month=may,
Year=2002}
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Exercises on execution, strategies, trees
Exercises on unification — Solutions (Contd.)
• Given the following logic program:
eats(X,Y)

Exercises on execution, strategies, trees – Solutions (Contd.)
Exercises on execution, strategies, trees – Solutions
• Resolution tree:

Exercises on execution, strategies, trees – Solutions (Contd.)
Exercises on execution, strategies, trees – Solutions (Contd.)
• Search tree:

Exercises on execution, strategies, trees – Solutions (Contd.)
Exercises on execution, strategies, trees – Solutions (Contd.)
• Solution space tree:

Exercises on Modelling
Exercises on execution, strategies, trees – Solutions (Contd.)
falta
• Solution space tree:

Exercises on lists and trees
Exercises on ADTs, recursion, and types
falta
falta
20

Exercises on structures
falta