78 lines
2.2 KiB
Markdown
78 lines
2.2 KiB
Markdown
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기본적인 정의를 합니다.
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```my-ml-like-sudo-language
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// fg is shortest available pathes function that returns a path from pos to target.
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// type cmd :: enum {
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// up'^', down'v', right'<', left'>', accept'A'
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// }
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// type path_set = set of list of cmd;
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```
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이제 헬퍼 함수를 정이합니다.
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```
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// \product is a function that returns a list of all possible combinations of two lists.
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// \product :: path_set -> path_set -> path_set
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// \product [] ys = []
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// \product xs [] = []
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// \product (x:xs) y = (concat x y) ++ (\product xs y)
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// infix 5 \product // associativity is not important. because it commutative.
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// ++ is union of two sets.
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// concat :: cmd -> path_set -> path_set
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// concat x [] = [x]
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// concat x (y:ys) = (x:y) ++ (concat x ys)
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// product :: path_set -> path_set -> path_set
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// product a b = a \product b
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```
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```my-ml-like
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type start_pos = cmd
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type target_pos = cmd
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type next_pos = cmd
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available_paths :: start_pos -> target_pos -> path_set
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type Handler 'T :: start_pos -> ('T, next_pos)
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// define unit, mappend. these are monoid.
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//
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// unit :: Handler of path_set
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// unit = s -> t -> (t, s)
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// mappend :: Handler of path_set -> Handler of path_set -> Handler of path_set
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// mappend f g = s ->
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// let (t, s') = f s in
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// let (a ,s'') = g s'
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// in ( (product t a ) , s'')
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//
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// move :: Handler of (cmd -> set of list of cmd)
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// move s cmds x = available_paths x \product
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// accept :: Handler of (list of cmd -> list of cmd)
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// f = fg 'A'
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// f :: (list of cmd) -> set of (list of cmd)
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// statement execute 'A' (f (x)) = x
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// f x = move x; accept;
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// f x:tails = (move x; accept; f tails) 'A'
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// sl is get shortest path length
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// sl :: list of cmd -> Int
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// sl cmd = (f cmd) |> (foldr (x,y) -> min(x,y), INF)
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// operator \product is a function that returns a list of all possible combinations of two lists.
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// \product :: list of cmd -> list of cmd -> list of cmd
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// \product [] ys = ys
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// \product xs [] = xs
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// \product (x:xs) (y:ys) = x \product (y:ys) ++ xs \product (y:ys)
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// infixr 5 \product
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// sl (a \product b) = sl a + sl b
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// f /(.*)A/:rest = f '$1A' \product f rest
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// sl(f /(.*)A/:rest)) = sl (f '$1A' \product f rest)
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// = sl (f '$1A') + sl (f rest)
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//
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```
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