Church numerals: Difference between revisions
→{{header|Elm}}: correct order of exponent calls and add Crystal extended version...
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64</pre>
=={{header|Crystal}}==
Although the Crystal language is by no means a functional language, it does offer the feature of "Proc"'s/lambda's which are even closures, meaning that they can capture environment state from outside the scope of their body. Using these plus a structure to act as a wrapper for the recursive typed Church functions and the Union types to be able to eliminate having to use side effects, the following code for the Extended Church Numeral functions was written (this wasn't written generically, but that isn't that important to the Task):
{{trans|F#}}
<lang crystal>struct Church # can't be generic!
getter church : (Church -> Church) | Int32
def initialize(@church) end
def apply(ch)
chf = @church
chf.responds_to?(:call) ? chf.call(ch) : self
end
def compose(chr)
chlf = @church
chrf = chr.church
if chlf.responds_to?(:call) && chrf.responds_to?(:call)
Church.new(-> (f : Church) { chlf.call(chrf.call(f)) })
else
self
end
end
end
# Church Numeral constants...
CHURCH_ZERO = begin
Church.new(-> (f : Church) {
Church.new(-> (x : Church) { x }) })
end
CHURCH_ONE = begin
Church.new(-> (f : Church) { f })
end
# Church Numeral functions...
def succChurch
-> (ch : Church) {
Church.new(-> (f : Church) { f.compose(ch.apply(f)) }) }
end
def addChurch
-> (cha : Church, chb : Church) {
Church.new(-> (f : Church) { cha.apply(f).compose(chb.apply(f)) }) }
end
def multChurch
-> (cha : Church, chb : Church) { cha.compose(chb) }
end
def expChurch
-> (chbs : Church, chexp : Church) { chexp.apply(chbs) }
end
def isZeroChurch
liftZero = Church.new(-> (f : Church) { CHURCH_ZERO })
-> (ch : Church) { ch.apply(liftZero).apply(CHURCH_ONE) }
end
def predChurch
-> (ch : Church) {
Church.new(-> (f : Church) { Church.new(-> (x : Church) {
prd = Church.new(-> (g : Church) { Church.new(-> (h : Church) {
h.apply(g.apply(f)) }) })
frst = Church.new(-> (d : Church) { x })
id = Church.new(-> (a : Church) { a })
ch.apply(prd).apply(frst).apply(id)
}) }) }
end
def subChurch
-> (cha : Church, chb : Church) {
chb.apply(Church.new(predChurch)).apply(cha) }
end
def divr # can't be nested in another def...
-> (n : Church, d: Church) {
tstr = -> (v : Church) {
loopr = Church.new(-> (a : Church) {
succChurch.call(divr.call(v, d)) }) # recurse until zero
v.apply(loopr).apply(CHURCH_ZERO) }
tstr.call(subChurch.call(n, d)) }
end
def divChurch
-> (chdvdnd : Church, chdvsr : Church) {
divr.call(succChurch.call(chdvdnd), chdvsr) }
end
# conversion functions...
def intToChurch(i) : Church
rslt = CHURCH_ZERO
cntr = 0
while cntr < i
rslt = succChurch.call(rslt)
cntr += 1
end
rslt
end
def churchToInt(ch) : Int32
succInt32 = Church.new(-> (v : Church) {
vi = v.church
vi.is_a?(Int32) ? Church.new(vi + 1) : v })
rslt = ch.apply(succInt32).apply(Church.new(0)).church
rslt.is_a?(Int32) ? rslt : -1
end
# testing...
ch3 = intToChurch(3)
ch4 = succChurch.call(ch3)
ch11 = intToChurch(11)
ch12 = succChurch.call(ch11)
add = churchToInt(addChurch.call(ch3, ch4))
mult = churchToInt(multChurch.call(ch3, ch4))
exp1 = churchToInt(expChurch.call(ch3, ch4))
exp2 = churchToInt(expChurch.call(ch4, ch3))
iszero1 = churchToInt(isZeroChurch.call(CHURCH_ZERO))
iszero2 = churchToInt(isZeroChurch.call(ch3))
pred1 = churchToInt(predChurch.call(ch4))
pred2 = churchToInt(predChurch.call(CHURCH_ZERO))
sub = churchToInt(subChurch.call(ch11, ch3))
div1 = churchToInt(divChurch.call(ch11, ch3))
div2 = churchToInt(divChurch.call(ch12, ch3))
print("#{add} #{mult} #{exp1} #{exp2} #{iszero1} #{iszero2} ")
print("#{pred1} #{pred2} #{sub} #{div1} #{div2}\r\n")</lang>
{{out}}
<pre>7 12 81 64 1 0 3 0 8 3 4</pre>
=={{header|Elm}}==
Line 502 ⟶ 628:
in [ addChurch chThree chFour
, multChurch chThree chFour
, expChurch chThree chFour
, expChurch chFour chThree
, isZeroChurch churchZero
, isZeroChurch chThree
Line 513 ⟶ 639:
|> String.join ", " |> text</lang>
{{out}}
<pre>7, 12,
The "churchToInt" function works by applying an integer successor function which takes an "arity zero" value and returns an "arity zero" containing that value plus one, then applying an "arity zero" wrapped integer value of zero to the resulting Church value; the result of that is unwrapped to result in the desired integer returned value. The idea of using "arity zero" values as function values is borrowed from Haskell, which wraps all values as data types including integers, etc. (all other than primitive values are thus "lifted"), which allows them to be used as functions. Since Haskell has Type Classes which F# and Elm do not, this is not so obvious in Haskell code which is able to treat values such as "lifted" integers as functions automatically, and thus apply the same Type Class functions to them as to regular (also "lifted") functions. Here in the F# code, the necessary functions that would normally be part of the Functor and Applicative Type Classes as applied to Functions in Haskell are supplied here to work with the Discriminated Union/custom type wrapping of this Function idea.
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