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Task/Execute-a-Markov-algorithm/Lua/execute-a-markov-algorithm.lua

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+-- utility method to escape punctuation
+function normalize(str)
+	local result = str:gsub("(%p)", "%%%1")
+	-- print(result)
+	return result
+end
+
+-- utility method to split string into lines
+function get_lines(str)
+	local t = {}
+	for line in str:gmatch("([^\n\r]*)[\n\r]*") do
+		table.insert(t, line)
+	end
+	return t
+end
+
+local markov = {}
+local MARKOV_RULE_PATTERN = "(.+)%s%-%>%s(%.?)(.*)"
+
+function markov.rule(pattern,replacement,terminating)
+	return {
+		pattern = pattern,
+		replacement = replacement,
+		terminating = (terminating == ".")
+	}, normalize(pattern)
+end
+
+function markov.make_rules(sample)
+	local lines = get_lines(sample)
+	local rules = {}
+	local finders = {}
+	for i,line in ipairs(lines) do
+		if not line:find("^#") then
+		s,e,pat,term,rep = line:find(MARKOV_RULE_PATTERN)
+		if s then
+			r, p = markov.rule(pat,rep,term)
+			rules[p] = r
+			table.insert(finders, p)
+		end
+		end
+	end
+	return {
+		rules = rules,
+		finders = finders
+	}
+end
+
+function markov.execute(state, sample_input)
+
+local rules, finders = state.rules, state.finders
+local found = false -- did we find any rule?
+local terminate = false
+
+repeat
+found = false
+
+for i,v in ipairs(finders) do
+	local found_now = false -- did we find this rule?
+	if sample_input:find(v) then
+		found = true
+		found_now = true
+	end
+	sample_input = sample_input:gsub(v, rules[v].replacement, 1)
+	-- handle terminating rules
+	if found_now then
+		if rules[v].terminating then terminate = true end
+		break
+	end
+end
+
+until not found or terminate
+
+return sample_input
+end
+------------------------------------------
+------------------------------------------
+
+local grammar1 = [[
+# This rules file is extracted from Wikipedia:
+# http://en.wikipedia.org/wiki/Markov_Algorithm
+A -> apple
+B -> bag
+S -> shop
+T -> the
+the shop -> my brother
+a never used -> .terminating rule
+]]
+
+local grammar2 = [[
+# Slightly modified from the rules on Wikipedia
+A -> apple
+B -> bag
+S -> .shop
+T -> the
+the shop -> my brother
+a never used -> .terminating rule
+]]
+
+local grammar3 = [[
+# BNF Syntax testing rules
+A -> apple
+WWWW -> with
+Bgage -> ->.*
+B -> bag
+->.* -> money
+W -> WW
+S -> .shop
+T -> the
+the shop -> my brother
+a never used -> .terminating rule
+]]
+
+local grammar4 = [[
+### Unary Multiplication Engine, for testing Markov Algorithm implementations
+### By Donal Fellows.
+# Unary addition engine
+_+1 -> _1+
+1+1 -> 11+
+# Pass for converting from the splitting of multiplication into ordinary
+# addition
+1! -> !1
+,! -> !+
+_! -> _
+# Unary multiplication by duplicating left side, right side times
+1*1 -> x,@y
+1x -> xX
+X, -> 1,1
+X1 -> 1X
+_x -> _X
+,x -> ,X
+y1 -> 1y
+y_ -> _
+# Next phase of applying
+1@1 -> x,@y
+1@_ -> @_
+,@_ -> !_
+++ -> +
+# Termination cleanup for addition
+_1 -> 1
+1+_ -> 1
+_+_ ->
+]]
+
+local grammar5 = [[
+# Turing machine: three-state busy beaver
+#
+# state A, symbol 0 => write 1, move right, new state B
+A0 -> 1B
+# state A, symbol 1 => write 1, move left, new state C
+0A1 -> C01
+1A1 -> C11
+# state B, symbol 0 => write 1, move left, new state A
+0B0 -> A01
+1B0 -> A11
+# state B, symbol 1 => write 1, move right, new state B
+B1 -> 1B
+# state C, symbol 0 => write 1, move left, new state B
+0C0 -> B01
+1C0 -> B11
+# state C, symbol 1 => write 1, move left, halt
+0C1 -> H01
+1C1 -> H11
+]]
+
+local text1 = "I bought a B of As from T S."
+local text2 = "I bought a B of As W my Bgage from T S."
+local text3 = '_1111*11111_'
+local text4 = '000000A000000'
+
+------------------------------------------
+------------------------------------------
+
+function do_markov(rules, input, output)
+	local m = markov.make_rules(rules)
+	input = markov.execute(m, input)
+	assert(input == output)
+	print(input)
+end
+
+do_markov(grammar1, text1, 'I bought a bag of apples from my brother.')
+do_markov(grammar2, text1, 'I bought a bag of apples from T shop.')
+-- stretch goals
+do_markov(grammar3, text2, 'I bought a bag of apples with my money from T shop.')
+do_markov(grammar4, text3, '11111111111111111111')
+do_markov(grammar5, text4, '00011H1111000')