Data update

Task/Church-numerals/FreeBASIC/church-numerals.basic

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+Type church
+    ' eg {r_add,1,{a,b}}
+    op As Integer
+    n As Integer
+    x(1 To 2) As Integer
+End Type
+
+Dim Shared As church zero = Type<church>(1, 0, {0, 1})
+
+Function succ(c As church) As church
+    ' eg {r_add,1,{a,b}} => {r_add,2,{a,b}}  aka  a+b -> a+b+b
+    c.n += 1
+    Return c
+End Function
+
+' three normal integer-handling routines...
+Function sum(n As Integer, a As Integer, b As Integer) As Integer
+    For i As Integer = 1 To n
+        a += b
+    Next i
+    Return a
+End Function
+
+Function mul(n As Integer, a As Integer, b As Integer) As Integer
+    For i As Integer = 1 To n
+        a *= b
+    Next i
+    Return a
+End Function
+
+Function pow(n As Integer, a As Integer, b As Integer) As Integer
+    For i As Integer = 1 To n
+        a = a ^ b
+    Next i
+    Return a
+End Function
+
+' ...and three church constructors to match
+'    (no maths here, just pure static data)
+Function churchSum(c As church, d As church) As church
+    Dim res As church
+    res.op = 1 ' 1 for add
+    res.n = 1
+    res.x(1) = c.n
+    res.x(2) = d.n
+    Return res
+End Function
+
+Function churchMul(c As church, d As church) As church
+    Dim res As church
+    res.op = 2 ' 2 for mul
+    res.n = 1
+    res.x(1) = c.n
+    res.x(2) = d.n
+    Return res
+End Function
+
+Function churchPow(c As church, d As church) As church
+    Dim res As church
+    res.op = 3 ' 3 for pow
+    res.n = 1
+    res.x(1) = c.n
+    res.x(2) = d.n
+    Return res
+End Function
+
+Function churchToNum(c As church) As Integer
+    ' note this is where the bulk of any processing happens
+    Select Case c.op
+    Case 1
+        Return sum(c.n, c.x(1), c.x(2))
+    Case 2
+        Return mul(c.n, c.x(1), c.x(2))
+    Case 3
+        Return pow(c.n, c.x(1), c.x(2))
+    End Select
+End Function
+
+Function numToChurch(i As Integer) As church
+    Return Iif(i = 0, zero, succ(numToChurch(i - 1)))
+End Function
+
+Dim As church three = succ(succ(succ(zero)))
+Dim As church four  = succ(three)
+Print "three        -> "; churchToNum(three)
+Print "four         -> "; churchToNum(four)
+Print "three + four -> "; churchToNum(churchSum(three, four))
+Print "three * four -> "; churchToNum(churchMul(three, four))
+Print "three ^ four -> "; churchToNum(churchPow(three, four))
+Print "four ^ three -> "; churchToNum(churchPow(four, three))
+Print "5 -> five    -> "; churchToNum(numToChurch(5))
+
+Sleep

Task/Church-numerals/Scala/church-numerals.scala

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+object Church {
+
+  trait ChurchNum extends (ChurchNum => ChurchNum)
+
+  def zero: ChurchNum = f => x => x
+
+  def next(n: ChurchNum): ChurchNum = f => x => f(n(f)(x))
+
+  def plus(a: ChurchNum)(b: ChurchNum): ChurchNum = f => x => b(f)(a(f)(x))
+
+  def mult(a: ChurchNum)(b: ChurchNum): ChurchNum = f => x => b(a(f))(x)
+
+  def pow(m: ChurchNum)(n: ChurchNum): ChurchNum = n(m)
+
+  def toChurchNum(n: Int): ChurchNum = if (n <= 0) zero else next(toChurchNum(n - 1))
+
+  def toInt(c: ChurchNum): Int = {
+    var counter = 0
+    val funCounter: ChurchNum = f => { counter += 1; f }
+    plus(zero)(c)(funCounter)(x => x)
+    counter
+  }
+
+  def main(args: Array[String]): Unit = {
+    val zero = Church.zero
+    val three = next(next(next(zero)))
+    val four = next(next(next(next(zero))))
+
+    println(s"3+4=${toInt(plus(three)(four))}") // prints 7
+    println(s"4+3=${toInt(plus(four)(three))}") // prints 7
+
+    println(s"3*4=${toInt(mult(three)(four))}") // prints 12
+    println(s"4*3=${toInt(mult(four)(three))}") // prints 12
+
+    // exponentiation. note the reversed order!
+    println(s"3^4=${toInt(pow(four)(three))}") // prints 81
+    println(s"4^3=${toInt(pow(three)(four))}") // prints 64
+
+    println(s"  8=${toInt(toChurchNum(8))}") // prints 8
+  }
+}