Data commit

Task/Amb/Lua/amb-1.lua

@@ -0,0 +1,21 @@
+function amb (set)
+    local workset = {}
+    if (#set == 0) or (type(set) ~= 'table') then return end
+    if #set == 1 then return set end
+    if #set > 2 then
+        local first = table.remove(set,1)
+        set = amb(set)
+        for i,v in next,first do
+            for j,u in next,set do
+                if v:byte(#v) == u[1]:byte(1) then table.insert(workset, {v,unpack(u)}) end
+            end
+        end
+        return workset
+    end
+    for i,v in next,set[1] do
+        for j,u in next,set[2] do
+            if v:byte(#v) == u:byte(1) then table.insert(workset,{v,u}) end
+        end
+    end
+    return workset
+end

Task/Amb/Lua/amb-2.lua

@@ -0,0 +1,8 @@
+result = amb({{'the','that','a'},{'frog','elephant','thing'},{'walked','treaded','grows'},{'slowly','quickly'}})
+for i,v in next,result do
+    io.write (i,':\t')
+    for j,u in next,v do
+        io.write (u,' ')
+    end
+    io.write ('\n')
+end

Task/Amb/Lua/amb-3.lua

@@ -0,0 +1,21 @@
+function T(t) return setmetatable(t, {__index=table}) end
+table.each = function(t,f) for i=1,#t do f(t[i]) end return t end
+table.map = function(t,f) local s=T{} for i=1,#t do s[i]=f(t[i]) end return s end
+table.clone = function(t) local s=T{} for k,v in ipairs(t) do s[k]=v end return s end
+table.filter = function(t,f) local s=T{} for i=1,#t do if f(t[i]) then s[#s+1]=t[i] end end return s end
+
+function Amb(f, ...)
+  local function cartprod(...)
+    local sets, temp, prod = {...}, T{}, T{}
+    local function descend(depth)
+      for k,v in pairs(sets[depth]) do
+        temp[depth] = v
+        if (depth==#sets) then prod[#prod+1] = temp:clone() else descend(depth+1) end
+        temp[depth] = nil
+      end
+    end
+    descend(1)
+    return prod
+  end
+  return type(f)=='function' and cartprod(...):filter(f) or {f,...}
+end

Task/Amb/Lua/amb-4.lua

@@ -0,0 +1,69 @@
+print("Per task requirements:")
+w1 = Amb('the','that','a')
+w2 = Amb('frog','elephant','thing')
+w3 = Amb('walked','treaded','grows')
+w4 = Amb('slowly','quickly')
+function rule(t) local a,b,c,d = unpack(t) return a:byte(#a)==b:byte(1) and b:byte(#b)==c:byte(1) and c:byte(#c)==d:byte(1) end
+answers = Amb(rule, w1, w2, w3, w4)
+answers:map(function(t) return t:concat(" ") end):each(print)
+
+print()
+
+print("Modified task, seek equal length of words:")
+w1 = Amb('the','that','a','which')
+w2 = Amb('red','green','blue','yellow')
+w3 = Amb('frog','elephant','cow','thing')
+w4 = Amb('walked','treaded','grew','shrunk')
+w5 = Amb('slow','quick','moderately')
+function rule(t) local a,b,c,d,e = unpack(t) return #a==#b and #b==#c and #c==#d and #d==#e end
+answers = Amb(rule, w1, w2, w3, w4, w5)
+answers:map(function(t) return t:concat(" ") end):each(print)
+
+print()
+
+print("Modified example, seek product of 12:")
+x = Amb(1,2,3)
+y = Amb(4,5,6)
+function rule(t) local x,y = unpack(t) return x*y==12 end
+answers = Amb(rule, x, y)
+answers:map(function(t) return t:concat(" ") end):each(print)
+
+print()
+
+print("Pythagorean triples:")
+x = Amb(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
+y = Amb(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
+z = Amb(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
+function rule(t) local x,y,z = unpack(t) return x^2 + y^2 == z^2 end
+answers = Amb(rule, x, y, z)
+answers:map(function(t) return t:concat(" ") end):each(print)
+
+print()
+
+print("When there is no solution:")
+x = Amb(1,2,3)
+y = Amb(4,5,6)
+function rule(t) local x,y = unpack(t) return x*y==7 end
+answers = Amb(rule, x, y, z)
+print("#answers = " .. #answers)
+
+print()
+
+print("send + more = money:")
+-- intuitive simplification applied:  m must be 1 ==> others may not be 1 (reduces complexity from 10^8 to 9^7)
+-- ("m is allowed to be leading zero" solutions exist, e.g. 2 8 1 7 0 3 6 5, and this could find them, but why?)
+s = Amb(0,2,3,4,5,6,7,8,9)
+e = Amb(0,2,3,4,5,6,7,8,9)
+n = Amb(0,2,3,4,5,6,7,8,9)
+d = Amb(0,2,3,4,5,6,7,8,9)
+m = Amb(1)
+o = Amb(0,2,3,4,5,6,7,8,9)
+r = Amb(0,2,3,4,5,6,7,8,9)
+y = Amb(0,2,3,4,5,6,7,8,9)
+function rule(t)
+  for i=1,#t do for j=i+1,#t do if t[i]==t[j] then return false end end end
+  local s,e,n,d,m,o,r,y = unpack(t)
+  return s*1000 + e*100 + 10*n + d + m*1000 + o*100 + r*10 + e == m*10000 + o*1000 + n*100 + e*10 + y
+end
+answers = Amb(rule, s, e, n, d, m, o, r, y)
+answers:map(function(t) return t:concat(" ") end):each(print)