Delete old half-baked files.
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wan-may
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c24f86500e
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--Dependencies for displaying things.
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local backend = {}
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return backend
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132
rapport.lua
132
rapport.lua
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local function Gap(t, i)
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if not t[i] then return i else return Gap(t, i + 1) end
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end
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local function Gaps(t, i)
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return Gap, t, i
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end
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--Data structure supporting fast ordered insertion and search.
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local function Order()
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local o = {}
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local list = { val = nil, prev = nil, next = nil }
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o.Get = function( x )
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end
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o.GetAdjacent = function( node )
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return node.prev.val, node.next.val
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end
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o.Insert = function( x )
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if not list.val then
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list.val = x
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return list
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end
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local node = list
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while node and node.val < x do node = node.next end
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end
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return o
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end
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--Construct an isomorphism between two countable dense total orders
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--these orders are specified by functions which return the next element in some enumeration
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--these elements must be comparable with comparison operators <, >, &c.
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local function Isomorphism( Enumeration, InverseEnumeration, inv )
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--Exported table.
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local t = {}
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local enum, order, mapping, inverse
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--Another Isomorphism structure,
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--which contains the image of this isomorphism and the inverse
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--isomorphism mapping back to our dense countable linear order.
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inverse = inv or Isomorphism( InverseEnumeration, nil, t )
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--Array for caching and lazily evaluating the supplied Enumeration,
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--an iterator that enumerates the elements of a dense countable linear order.
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enum = { Enumeration() }
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setmetatable(enum, {__index = function(_, i)
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for j = #enum + 1, i do
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enum[j] = Enumeration()
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end
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return rawget( enum, i )
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end})
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t.enum = enum --Expose as field
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--Structure supporting fast ordered insertion and search.
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--Values are i such that mapping[order[i]] is not nil,
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--sorted according to getmetatable( enum[i] ).__lt
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order = { 1 }
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--Find the indices i and k such that
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--enum[i] is the greatest lower bound on enum[j] in the mapping's support
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--enum[k] is the least upper bound on enum[j] in the mapping's support
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local function GetBounds( leaf )
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end
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--Array defining isomorphism mapping this dense countable order to the one in inverse.
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--If mapping[i] = j, then f(enum[i]) = inverse.enum[j]
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mapping = { 1 }
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setmetatable( mapping, {__newindex = function(map, k, v)
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rawset(mapping, k, v)
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end})
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--Iterates over the natural numbers outside the isomorphism's support,
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--so returns the least n such that n >= i and mapping[n] == nil.
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--(Warning, infinite loop! Make sure to break out of this.)
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local function NextGap(i)
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if not mapping[i] then return i else return NextGap(i + 1) end --tail-recursive
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end
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--Include another point in the mapping's support.
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--Infinite loop: ))<<>>((
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function t.ExpandMap()
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local gapIdx = NextGap(1)
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local pred, succ = GetBounds( OrderedInsertion( gapIdx ) )
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mapping[gapIdx] = inverse.AddNextBetween( i, mapping[pred], mapping[succ] )
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return inverse.ExpandMap()
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end
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--Find the first j such that mapping[j] == nil,
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--enum[lower] < enum[j] < enum[upper]
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--Then map j to i, and add j to the order.
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function t.AddNextBetween( i, lower, upper )
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local p, q, r, j = enum[lower], nil, enum[upper], nil
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for k in Gaps( 1 ) do
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q = enum[k]
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if ((not p) or (p < q))
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and ((not r) or (q < r)) then
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j = k
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break
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end
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end
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mapping[j] = i
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OrderedInsertion(j)
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return j
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end
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--Get the isomorphism as a dictionary, for plotting.
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function t.GetMapping( )
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local map = {}
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for idx, imageIdx in pairs( mapping ) do
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map[ enum[ idx ] ] = inverse.enum[ imageIdx ]
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end
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return map
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end
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return t
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end
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return setmetatable( { Isomorphism = Isomorphism }, {__call = Isomorphism } )
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