Merge pull request #10 from jakewilliami/dev

Dev

README.md

@@ -14,54 +14,27 @@ This is a minimal package for a pure Julia implementation of tools used in [Comp
 julia> pair_tuple(5,7) # code pair of natural numbers as a natural number
 83
 
-julia> pair_tuple(5,7,20)
-5439
-
-julia> π(83, 2) # code a natural number into a 2-tuple
-(5, 7)
-
-julia> π(83)
+julia> π(83) # code a natural number into a 2-tuple
 (5, 7)
 
-julia> π(83, 2, algebraic)
+julia> π(83, 2, algebraic) # use algebraic method of depairing rather than search (much faster)
 (5, 7)
 
-julia> π(83, 3, algebraic) # code a natural number into a 3-tuple
-(2, 0, 7)
-
 julia> π(83, 2, 1) # code a natural number into a 2-tuple and get the the number in the tuple indexed by 1 (index starting from zero)
 7
 
 julia> cℤ(-10) # code integer as a natural number
 19
 
-julia> cℤ((-1,2))
+julia> cℤ((-1,2)) # cℤ pairs the code of each
 16
 
-julia> cℤ(-1, 2)
-(1, 4)
-
 julia> cℤ⁻¹(19)
 -10
 
-julia> Sequence(121).length
-1
-
 julia> Sequence(972292871301644916468488152875266508938968846389326007980307063346008398713128885682044504108288931767348821063618087715644933567266540511345568504718733339523678538338052787779884557674350959673597803113281693069940562881722205193604550737455583875504348606989700013337656597740101535).instructions
 (328, 4, 531, 4, 5, 0, 14)
 
-julia> Sequence(121).instructions
-(14,)
-
-julia>  Instruction(7).instruction
-(1, 2)
-
-julia>  Instruction(14).instruction
-(4, 0)
-
-julia>  Instruction(58).instruction
-(3, (1, 2))
-
 julia> Instruction((3, (1, 2))).I
 58
 
@@ -75,20 +48,16 @@ julia> Programme(121).instructions
 julia> show_programme(121)
 0    halt
 
-julia> show_programme(972292871301644916468488152875266508938968846389326007980307063346008398713128885682044504108288931767348821063618087715644933567266540511345568504718733339523678538338052787779884557674350959673597803113281693069940562881722205193604550737455583875504348606989700013337656597740101535)
-0    if R1 = 0 goto 5
-1    R1 := R1 - 1
-2    if R1 = 0 goto 6
-3    R1 := R1 - 1
-4    goto 0
-5    R0 := R0 + 1
-6    halt
-
 julia> run_goto_programme(363183787614755732766753446033240)
 (1, 0)
 
 julia> run_goto_programme(363183787614755732766753446033240, Register(0, 0, 0 ,0))
 (1, 0, 0, 0)
+
+julia> show_programme(rand(GoToProgramme), 3) # a reasonably small random programme with 3 lines
+0    R3 := R3 + 1
+1    if R0 = 0 goto 1
+2    halt
 ```
 
 [code-style-img]: https://img.shields.io/badge/code%20style-blue-4495d1.svg

examples/basic.jl

@@ -85,16 +85,6 @@ function programme_ui()
 
 end
 
-function test_random(d::Integer)
-    # random = abs(rand(Int)) + 121
-    random = rand(121:2000)
-
-    println("The programme coded by the number $random is shown in $d instructions as follows:\n")
-
-    show_programme(pair_tuple(d, pair_tuple(random, pair_tuple(4, 0))))
-end
-
-
 # helper
 function binary_search(a::BigInt, b::BigInt) # useful for bug fixing
     while a != b
@@ -110,4 +100,4 @@ function binary_search(a::BigInt, b::BigInt) # useful for bug fixing
     return a
 end
 
-programme_ui()
+# programme_ui()

src/ComputabilityTheory.jl

@@ -6,16 +6,20 @@
 
 module ComputabilityTheory
 
+include(joinpath(dirname(@__FILE__), "abstract_types.jl"))
 include(joinpath(dirname(@__FILE__), "coding.jl"))
 include(joinpath(dirname(@__FILE__), "machines.jl"))
 include(joinpath(dirname(@__FILE__), "goto.jl"))
 
+export Machine, TuringMachine, MachineComponent, Programme,
+        ProgrammeComponent
+
 export ∸, pair_tuple, algebraic, π, cℤ, cℤ⁻¹
 
 export Tape, Left, Stay, Right, MachineState, Rule, TMProgramme,
         run_turing_machine, RegisterMachine, run_goto_programme
 
 export Sequence, Instruction, GoToProgramme, increment, decrement,
-        goto, ifzero_goto, halt, show_programme
+        goto, ifzero_goto, halt, show_programme, rand
 
 end # end module

src/abstract_types.jl

@@ -0,0 +1,11 @@
+#!/usr/bin/env bash
+    #=
+    exec julia --project="$(realpath $(dirname $0))" --color=yes --startup-file=no -e 'include(popfirst!(ARGS))' \
+    "${BASH_SOURCE[0]}" "$@"
+    =#
+
+abstract type Machine end
+abstract type TuringMachine <: Machine end
+abstract type MachineComponent end
+abstract type Programme end
+abstract type ProgrammeCompoment end

src/goto.jl

@@ -23,6 +23,7 @@ It should also be noted that the sequence code for some base cases is defined as
  - if d = 1, for a ∈ ℕ, the sequence code [a] for the sequence (a) of length 1, is <1, a>.
 =#
 
+include(joinpath(dirname(@__FILE__), "abstract_types.jl"))
 include(joinpath(dirname(@__FILE__), "coding.jl"))
 
 using Printf: @printf
@@ -33,7 +34,7 @@ const __goto_identifier = 2
 const __ifzero_goto_identifier = 3
 const __halt_identifier = (4, 0)
 
-struct Instruction
+struct Instruction <: ProgrammeCompoment
 	I::Integer
 	first::Integer
 	second::Integer
@@ -82,7 +83,7 @@ struct Instruction
 	Instruction(i::Integer, j::Integer...) = Instruction((i, j...))
 end # end struct
 
-struct Sequence
+struct Sequence <: ProgrammeCompoment
 	q::Integer
 	seq_length::Integer
 	instructions::Tuple
@@ -97,30 +98,23 @@ struct Sequence
 	function Sequence(t::Tuple)
 		q = nothing
 		seq_length, instructions = t[1], t[2]
-
-		sequence_length_error = "The first number in your sequence should match the length of your sequence."
-		seq_length ≠ length(instructions) && throw(error("$(sequence_length_error)"))
 
 		if eltype(instructions) <: Integer
 			q = pair_tuple(t[1], t[2]...)
 		end
 
 		if eltype(instructions) <: Tuple
-			q = pair_tuple(t[1], pair_tuple(pair_tuple.(t[2])))
+			# q = pair_tuple(t[1], pair_tuple(pair_tuple.(t[2])))
+			q = pair_tuple(t[1], pair_tuple(t[2]))
 		end
-
-
-
-		# if isone(length(t[2]))
-		# 	q = pair_tuple(t[1], t[2]...)
-		# else
-		# 	q = pair_tuple(t[1], pair_tuple(t[2]))
-		# end
+
+		# sequence_length_error = "The first number in your sequence should match the length of your sequence."
+		# seq_length ≠ length(instructions) && throw(error("$(sequence_length_error)"))
 
 		new(q, seq_length, instructions)
 	end
 
-	Sequence(i::Integer, j::Tuple) = Sequence((i, j))
+	Sequence(i::Integer, j::Tuple) = Sequence(pair_tuple(i, pair_tuple(j...)))
 	Sequence(i::Integer, j::Integer...) = Sequence((i, tuple(j...)))
 end # end struct
 
@@ -131,7 +125,7 @@ ifzero_goto(t::Tuple) = Instruction(__ifzero_goto_identifier, (t[1], t[2])...)
 ifzero_goto(n::Integer, k::Integer) = Instruction(__ifzero_goto_identifier, (n, k)...)
 halt() = Instruction(__halt_identifier...)
 
-struct GoToProgramme
+struct GoToProgramme <: Programme
     P::Integer
     programme_length::Integer
     instructions::Vector{<:Tuple}
@@ -149,9 +143,7 @@ struct GoToProgramme
         programme_length = sequence_dump.seq_length
 
         # construct list of codes for each instruction
-        if iszero(programme_length)  instructions = 0  end
-        instructions = [i.instruction for i in snapshot]
-
+        instructions = iszero(programme_length) ? 0 : [i.instruction for i in snapshot]
         # check that the programme halts at the end
     	instructions[end] ≠ halt().instruction && throw(error("Goto programmes neccesarily have a halting instruction."))
 
@@ -224,3 +216,17 @@ show_programme(io::IO, P::Integer) = show_programme(io::IO, GoToProgramme(P))
 # Fall back to standard output
 show_programme(P::GoToProgramme) = show_programme(stdout, P)
 show_programme(P::Integer) = show_programme(stdout, GoToProgramme(P))
+
+function Base.rand(::Type{T}, d::Integer; upper_bound::Integer=200) where T <: GoToProgramme
+	return pair_tuple(d, pair_tuple(rand(1:upper_bound), halt().I))
+	return Sequence((d, (rand(1:upper_bound), halt().I))).q
+end
+
+function Base.rand(::Type{T}) where T <: GoToProgramme
+	while true
+		try
+			return rand(T, rand(2:10))
+		catch
+		end
+	end
+end

src/machines.jl

@@ -3,7 +3,8 @@
     exec julia --project="$(realpath $(dirname $0))" --color=yes --startup-file=no -e 'include(popfirst!(ARGS))' \
     "${BASH_SOURCE[0]}" "$@"
     =#
-
+
+include(joinpath(dirname(@__FILE__), "abstract_types.jl"))
 include(joinpath(dirname(@__FILE__), "coding.jl"))
 include(joinpath(dirname(@__FILE__), "goto.jl"))
 include(joinpath(dirname(@__FILE__), "utils.jl"))
@@ -15,21 +16,21 @@ include(joinpath(dirname(@__FILE__), "utils.jl"))
 @enum Move Left=1 Stay Right
 
 # defing structs
-mutable struct MachineState
+mutable struct MachineState <: MachineComponent
     state::String
     tape::Dict{Int, String}
     headpos::Int
 end
 
-struct Rule
+struct Rule <: MachineComponent
     instate::String
     outstate::String
     s1::String
     s2::String
     move::Move
 end
- 
-struct TMProgramme
+
+struct TMProgramme <: TuringMachine
     title::String
     initial::String
     final::String
@@ -85,7 +86,7 @@ end
 
 #--Register Machines--------------------------------------------------------------------------
 
-mutable struct RegisterMachine
+mutable struct RegisterMachine <: Machine
     contents::AbstractArray#Vector{<:Integer}
 
     function RegisterMachine(contents::AbstractArray)