is this type heaven or type hell?

Author: jeffwack

src/sequences/Sequences.jl

@@ -1,6 +1,18 @@
 using Primes
 using IterTools
 
+struct Digit{N} <: Integer
+    value::Int
+    function Digit{N}(value::Int) where N
+        m = N-1
+        0 <= value < N || error("Value must be in range [0, $m]")
+        new{N}(value)
+    end
+end
+
+Base.show(io::IO, d::Digit{N}) where {N} = print(io, d.value)
+Base.Int(d::Digit{N}) where {N} = d.value
+
 struct Sequence{T}
     items::Vector{T}
     preperiod::Int
@@ -36,6 +48,79 @@ struct Sequence{T}
     end
 end
 
+const BinaryExpansion = Sequence{Digit{2}}
+
+function BinaryExpansion(theta::Rational)    
+    orb = orbit(theta)
+    itinerary = Digit{2}[]
+    zero = Digit{2}(0)
+    one = Digit{2}(1)
+    for theta in orb.items
+        if theta < 1//2
+            push!(itinerary,zero)
+        else
+            push!(itinerary,one)
+        end
+    end
+    return Sequence{Digit{2}}(collect(itinerary),orb.preperiod)
+end
+
+function orbit(angle::Rational)
+    items = Rational[]
+
+    while isempty(findall(x->x==angle,items))
+        push!(items,angle)
+        angle = angle*2
+        angle = angle%1//1
+    end
+
+    preperiod = findall(x->x==angle,items)[1] - 1
+
+    return Sequence{Rational}(items,preperiod)
+    
+end
+
+abstract type KneadingSymbol end
+
+struct A <: KneadingSymbol end
+struct B <: KneadingSymbol end
+struct star <: KneadingSymbol end
+
+Base.show(io::IO, symb::KneadingSymbol) = print(io, repr(typeof(symb)))
+
+const KneadingSequence = Sequence{KneadingSymbol}
+
+function thetaitinerary(theta::Rational,orb::Sequence)
+    a = theta/2
+    b = (theta+1)/2
+    itinerary = KneadingSymbol[]
+
+    for angle in orb.items
+        if angle == a
+            push!(itinerary,star())
+        elseif angle == b
+            push!(itinerary,star())
+        elseif angle > a && angle < b
+            push!(itinerary,A())
+        else
+            push!(itinerary,B())
+        end
+    end
+    
+    return Sequence{KneadingSymbol}(itinerary,orb.preperiod)
+end
+
+function thetaitinerary(theta::Rational,angle::Rational)
+    return thetaitinerary(theta,orbit(angle))
+end
+
+function KneadingSequence(angle::Rational)
+    orb = orbit(angle)
+    return thetaitinerary(angle,orb)
+end
+
+
+
 function Sequence(str::String,preperiod::Int)
     return Sequence{Char}(Vector{Char}(str),preperiod)
 end
@@ -103,21 +188,6 @@ function shiftby(seq::Sequence,n::Int)
     end
 end
 
-function divisors(n)
-    d = Int64[1]
-    for (p, e) in factor(n)
-        r = 1
-        l = length(d)
-        for i in 1:e
-            r *= p
-            for j in 1:l
-                push!(d, d[j]*r)
-            end
-        end
-    end
-    return sort(d)
-end
-
 function prepend(K::Sequence,thing)
     return Sequence{Char}(pushfirst!(copy(K.items),thing),K.preperiod+1)
 end