语境
我正在尝试实现一个与 IBM 的 OLP（线性编程建模语言）松散相似的 EDSL。
代码
Haskell EDSL 代码
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleInstances #-}
-- Numbers at the type level
data Peano = Zero | Successor Peano
-- Counting Vector Type. Type information contains current length
data Vector peanoNum someType where
Nil :: Vector Zero someType
(:+) :: someType
-> Vector num someType
-> Vector (Successor num) someType
infixr 5 :+
-- Generate Num-th nested types
-- For example: Iterate (S (S Z)) [] Double => [[Double]]
type family Iterate peanoNum constructor someType where
Iterate Zero cons typ = typ
Iterate (Successor pn) cons typ =
cons (Iterate pn cons typ)
-- DSL spec
data Statement =
DecisionVector [Double]
| Minimize Statement
| Iteration `Sum` Expression
| Forall Iteration Statement
| Statement :| Statement
| Constraints Statement
infixl 8 `Sum`
infixl 3 :|
data Iteration =
String `In` [Double]
| String `Ins` [String]
data Expression where
EString :: String -> Expression
EFloat :: Double -> Expression
(:?) :: Vector n Expression -> Iterate (n) [] Double -> Expression
(:*) :: Expression -> Expression -> Expression
Lt :: Expression -> Expression -> Expression
Gt :: Expression -> Expression -> Expression
Id :: String -> Expression
infixr 5 `Lt`
infixr 5 `Gt`
infixr 6 :*
infixr 7 :?
test :: Statement
test =
let rawMaterial = 205
products = ["light", "medium", "heavy"]
demand = [59, 12, 13]
processes = [1, 2]
production = [[12,16], [1,7], [4,2]]
consumption = [25, 30]
-- foo = (EId "p" :+ EId "f" :+ Nil) `Subscript` production
-- bar = (EId "p" :+ Nil) `Subscript` cost
run = []
cost = [300, 400]
in
DecisionVector run :|
Minimize
(Sum ("p" `In` processes)
((Id "p" :+ Nil) :? cost :*
(Id "p" :+ Nil) :? run)) :|
Constraints
(Sum ("p" `In` processes)
((Id "p" :+ Nil) :? consumption :*
(Id "p" :+ Nil) :? run `Lt` EFloat rawMaterial) :|
Forall ("q" `Ins` products)
(Sum ("p" `In` processes)
((Id "q" :+ Id "p" :+ Nil) :? production :*
(Id "p" :+ Nil) :? run `Gt`
(Id "q" :+ Nil) :? demand)))
instance Show Statement where
show (DecisionVector v) = show v
show (Minimize s) = "(Minimize " ++ show s ++ ")"
show (i `Sum` e) = "(" ++ show i ++ " `Sum` " ++ show e ++ ")"
show (Forall i e) = "(Forall " ++ show i ++ show e ++ ")"
show (sa :| sb) = "(" ++ show sa ++ show sb ++ ")"
show (Constraints s) = "(Constraints " ++ show s ++ ")"
instance Show Iteration where
show (str `In` d) = "(" ++ show str ++ " `In` " ++ show d ++ ")"
show (str `Ins` d) = "(" ++ show str ++ " `Ins` " ++ show d ++ ")"
instance Show Expression where
show (EString s) = "(EString " ++ show s ++ ")"
show (EFloat f) = "(EFloat " ++ show f ++ ")"
show (Lt ea eb) = "(" ++ show ea ++ " `Lt` " ++ show eb ++ ")"
show (Gt ea eb) = "(" ++ show ea ++ " `Gt` " ++ show eb ++ ")"
show (ea :* eb) = "(" ++ show ea ++ " :* " ++ show eb ++ ")"
show (Id s) = "(Id " ++ show s ++ ")"
show (vec :? dbl) = "(" ++ show vec ++ " :? " ++ "dbl" ++ ")"
instance Show (Vector p Expression) where
show (Nil) = "Nil"
show (e :+ v) = "(" ++ show e ++ " :+ " ++ show v ++ ")"
-- eval_opl :: Statement -> [Double]
EDSL 与 OPL 比较
let rawMaterial = 205
products = ["light", "medium", "heavy"]
demand = [59, 12, 13]
processes = [1, 2]
production = [[12,16], [1,7], [4,2]]
consumption = [25, 30]
-- foo = (EId "p" :+ EId "f" :+ Nil) `Subscript` production
-- bar = (EId "p" :+ Nil) `Subscript` cost
run = []
cost = [300, 400]
in
DecisionVector run :|
Minimize
(Sum ("p" `In` processes)
((Id "p" :+ Nil) :? cost :*
(Id "p" :+ Nil) :? run)) :|
Constraints
(Sum ("p" `In` processes)
((Id "p" :+ Nil) :? consumption :*
(Id "p" :+ Nil) :? run `Lt` EFloat rawMaterial) :|
Forall ("q" `Ins` products)
(Sum ("p" `In` processes)
((Id "q" :+ Id "p" :+ Nil) :? production :*
(Id "p" :+ Nil) :? run `Gt`
(Id "q" :+ Nil) :? demand)))
对应opl码
float rawMaterial = 205;
{string} products = {"light","medium","heavy"};
float demand[products] = [59,12,13];
{string} processes = {"1","2"};
float production[products][processes] = [[12,16],[1,7],[4,2]];
float consumption[processes] = [25,30];
float cost[processes] = [300,400];
dvar float+ run[processes];
minimize sum (p in processes) cost[p] * run[p];
constraints {
sum (p in processes) consumption[p] * run[p] <= rawMaterial;
forall (q in products)
sum (p in processes) production[q][p] * run[p] >= demand[q];
}
相关部分
(:?) :: Vector n Expression -> Iterate (n) [] Double -> Expression
也
instance Show Expression where
[...]
show (vec :? dbl) = "(" ++ show vec ++ " :? " ++ "dbl" ++ ")"
问题描述
OPL 使用括号进行数组订阅，我尝试使用以下符号将订阅映射到我的 EDSL
((Id "p" :+ Id "f" :+ Nil) :? consumption
这在以下意义上对应于 OPL：
consumption[p][f]
在前者中， (Id "p" :+ Id "f" :+ Nil) 构造一个 Vector 类型的值，其中包含有关所述向量长度的类型级别信息。根据构造函数:?的定义，可以看到，Iterate(n)[] Double 会展开为[[Double]]。这可以按预期巧妙地工作。然而，反过来使用生成的语法树，我需要对实际值进行模式匹配。
show (vec :? dbl) = "(" ++ show vec ++ " :? " ++ "dbl" ++ ")"
问题：以上行有效，但我不知道如何使用实际数据。如何进行模式匹配？无论如何都可以使用数据吗？通过明显的替换dbl
(Iterate (Successor (Successor Zero)) [] Double)
不起作用。我还尝试建立一个数据系列，但我无法找到一种方法来递归地创建一个包含所有任意嵌套的 Double 列表的系列：
Double
[Double]
[[Double]]
[[[Double]]]
...