Church numerals: Difference between revisions
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Church 3 ^ Church 4 = 81
</pre>
===Extended Church Functions in Julia===
<lang julia>id = x -> x
always(f) = d -> f
struct Church # used for "infinite" Church type resolution
unchurch::Function
end
(cn::Church)(ocn::Church) = cn.unchurch(ocn)
compose(cnl::Church) = cnr::Church -> Church(f -> cnl(cnr(f)))
(cn::Church)(fn::Function) = cn.unchurch(fn)
(cn::Church)(i::Int) = cn.unchurch(i)
zero = Church(always(Church(id)))
one = Church(id)
succ(cn::Church) = Church(f -> (x -> f(cn(f)(x))))
add(m::Church) = n::Church -> Church(f -> n(f) ∘ m(f))
mult(m::Church) = n::Church -> Church(f -> m(n(f)))
exp(m::Church) = n::Church -> Church(n(m))
iszero(n::Church) = n.unchurch(Church(always(zero)))(one)
pred(n::Church) = Church(f -> Church(x -> n(
g -> (h -> h(g(f))))(Church(always(x)))(Church(id))))
subt(n::Church) = m::Church -> Church(f -> m(pred)(n)(f))
divr(n::Church) = d::Church ->
Church(f -> ((v::Church -> v(Church(always(succ(divr(v)(d)))))(zero))(
subt(n)(d)))(f))
div(dvdnd::Church) = dvsr::Church -> divr(succ(dvdnd))(dvsr)
church2int(cn::Church) = cn(i -> i + 1)(0)
int2church(n) = n <= 0 ? zero : succ(int2church(n - 1))
function runtests()
church3 = int2church(3)
church4 = succ(church3)
church11 = int2church(11)
church12 = succ(church11)
println("Church 3 + Church 4 = ", church2int(add(church3)(church4)))
println("Church 3 * Church 4 = ", church2int(mult(church3)(church4)))
println("Church 3 ^ Church 4 = ", church2int(exp(church3)(church4)))
println("Church 4 ^ Church 3 = ", church2int(exp(church4)(church3)))
println("isZero(Church 0) = ", church2int(iszero(zero)))
println("isZero(Church 3) = ", church2int(iszero(church3)))
println("pred(Church 4) = ", church2int(pred(church4)))
println("pred(Church 0) = ", church2int(pred(zero)))
println("Church 11 - Church 3 = ", church2int(subt(church11)(church3)))
println("Church 11 / Church 3 = ", church2int(div(church11)(church3)))
println("Church 12 / Church 3 = ", church2int(div(church12)(church3)))
end
runtests()</lang>
{{out}}
<pre>Church 3 + Church 4 = 7
Church 3 * Church 4 = 12
Church 3 ^ Church 4 = 81
Church 4 ^ Church 3 = 64
isZero(Church 0) = 1
isZero(Church 3) = 0
pred(Church 4) = 3
pred(Church 0) = 0
Church 11 - Church 3 = 8
Church 11 / Church 3 = 3
Church 12 / Church 3 = 4</pre>
Note that this is very slow due to that, although function paradigms can be written in Julia, Julia isn't very efficient at doing FP: This is because Julia has no type signatures for functions and must use reflection at run time when the types are variable as here (as to function kind ranks) for a slow down of about ten times as compared to statically known types. This is particularly noticeable for the division function where the depth of function nesting grows exponentially.
=={{header|Lambdatalk}}==
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