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Expressing Imperative Programs Functionally (4 of 4)

lDefine the functions according to the state transformations in boxes.

x = 1;

a = 1;

a = a*x;

x = x+1;

x <= n

yes

input n

output a

fac(n)

f1(a, n, x)

f2(a, n, x)

f1(a, n, x)

This arc is regarded as the same as the one above.

fac(n) = f1(1, n, 1);

f1(a, n, x) = x <= n ? f2(a, n, x)

: a;

f2(a, n, x) = f1(a*x, n, x+1);

This is called “McCarthy’s transformation principle in the text.