Lecture 6 Monadic Staging of the RE language

Lecture 6: Monadic Staging of the RE language Tim Sheard Oregon Graduate Institute CSE 510 Section FSC Winter 2004 Algorithms CSE 532, Spring 2000

Assignments Assignment 4 is now posted on webpage n Due in 1 week on Feb 1, 2005 Reading Assignment now on webpage n n Staging Algebraic Datatypes By Tim Sheard and Iavor Diatchki Must be read by next Tueday Feb. 1 Volunteers for presentation? Cs 510 FSC Winter 2005 2

Recall RE Language datatype 'a Maybe = Just of 'a | Nothing; datatype RE = Lit of string | Or of (RE*RE) | Concat of (RE*RE) | Star of RE; fun prefix [] xs = | prefix (y: : ys) if y=x then | prefix ys xs = Cs 510 FSC Winter 2005 Just xs (x: : xs) = prefix ys xs else Nothing; 3

One interpreter fun eval (Lit s) input = (case prefix (explode s) input of Just more => Just(s, more) | Nothing => Nothing) | eval (Or(a, b)) input = (case eval a input of Nothing => eval b input | Just pair => Just pair) | eval (Concat(a, b)) input = (case (eval a input) of Just(zs, rest) => (case eval b rest of Just (bs, more) => Just (zs ^ bs, more) | Nothing => Nothing) | eval (Star x) input = let fun f input = case eval x input of Nothing => ("", input) | Just (cs, zs) => let val (bs, ws) = f zs in (cs ^ bs, ws) end in Just(f input) end; Cs 510 FSC Winter 2005 4

Staging it fun Seval (Lit s) input = <case prefix (explode ~(lift s)) ~input of Just more => Just(~(lift s), more) | Nothing => Nothing> | Seval (Or(a, b)) input = <case ~(Seval a input) of Nothing => ~(Seval b input) | Just pair => Just pair> | Seval (Concat(a, b)) input = <case ~(Seval a input) of Just(zs, rest) => (case ~(Seval b <rest>) of Just (bs, more) => Just (zs ^ bs, more) | Nothing => Nothing> Cs 510 FSC Winter 2005 5

Staging continued Note how the helper | Seval (Star x) input = function “f” is in the generated code. <let fun f input = case ~(Seval x <input>) Nothing => ("", input) | Just (cs, zs) => let val (bs, ws) = f zs in (cs ^ bs, ws) end in Just(f ~input) end>; Cs 510 FSC Winter 2005 6

What does it generate? val t 1 = Concat(Or(Lit "tim", Lit "mary") , Star (Lit "x")); fun test x = <fn s => ~(Seval x <s>)>; fun f x = (run(test t 1)) (explode x); test t 1; Cs 510 FSC Winter 2005 7

-| test t 1; val it = <(fn a => (case %prefix (%explode "tim") a of Just o => Just("tim", o) | Nothing => Nothing) of Nothing => (case %prefix (%explode "mary") a of Just n => Just("mary", n) | Nothing => Nothing) | Just m => Just m) of Just(c, b) => (case let fun f g = (case %prefix (%explode "x") g of Just l => Just("x", l) | Nothing => Nothing) of Nothing => ("", g) | Just(i, h) => let val (k, j) = f h in (i %^ k, j) end) in Just (f b) end of Just(e, d) => Just(c %^ e, d) | Nothing => Nothing))> : <char list -> (string * char list) Maybe> Cs 510 FSC Winter 2005 8

Monadic version <Do %mm { a <- %try (%prefix 2 (%explode "tim")) (%prefix 2 (%explode "mary")) ; b <- %star (%prefix 2 (%explode "x")) ; Return %mm (a %@ %concat b) }> : <char list M> What is the Monad used here? Cs 510 FSC Winter 2005 9

The “meaning” type Eval : : RE -> char list -> (string * char list) Maybe datatype 'a M = M of (char list -> ('a* char list) Maybe); fun un. M (M x) = x; Eval 2 : : RE -> char list M Cs 510 FSC Winter 2005 10

Implementing the Monad val mm = let fun return x = M (fn s => Just(x, s)); fun bind (M f) g = let fun h s = case f s of Just(a, s 2) => un. M (g a) s 2 | Nothing => Nothing in M h end in Mon(return, bind) end; Cs 510 FSC Winter 2005 11

Operations on the monad fun test (M f) = let fun h s = case f s of Nothing => Just(Nothing, s) | Just(a, rest) => Just(Just a, rest) in M h end; fun prefix 2 s = let fun h x = case prefix s x of Nothing => Nothing | Just m => Just(s, m) in M h end; fun try (M f) (M g) = let fun h s = case f s of Nothing => g s | Just pair => Just pair in M h end Cs 510 FSC Winter 2005 12

Monadic Version fun star m = Do mm { mx <- test m ; case mx of Just x => Do mm { xs <- star m ; Return mm (x: : xs) } | Nothing => Return mm []}; fun eval 2 (Lit s) = prefix 2 (explode s) | eval 2 (Or(a, b)) = try (eval 2 a) (eval 2 b) | eval 2 (Concat(a, b)) = Do mm { x <- eval 2 a ; y <- eval 2 b ; Return mm (x@y)} | eval 2 (Star x) = Do mm { xss <- star (eval 2 x) ; Return mm (concat xss) } Cs 510 FSC Winter 2005 13

Staged Monadic Version fun Seval 2 (Lit s) = <prefix 2 (explode ~(lift s))> | Seval 2 (Or(a, b)) = <try ~(Seval 2 a) ~(Seval 2 b)> | Seval 2 (Concat(a, b)) = <Do mm { x <- ~(Seval 2 a) ; y <- ~(Seval 2 b) ; Return mm (x@y)}> | Seval 2 (Star x) = <Do mm { xss <- star ~(Seval 2 x) ; Return mm (concat xss) }>; Cs 510 FSC Winter 2005 14

Results -| Seval 2 t 1; val it = <Do %mm { a <- %try (%prefix 2 (%explode "tim")) (%prefix 2 (%explode "mary")) ; b <- %star (%prefix 2 (%explode "x")) ; Return %mm (a %@ %concat b) }> : <char list M> Note calls to the monadic operators “try”, “star”, “test” (embedded in call to “star”), and “prefix 2” Cs 510 FSC Winter 2005 15

Cs 510 FSC Winter 2005 16