Tim%20Sheard

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Fundamentals of
Staged Computation
Lecture 6 Monadic Staging of the RE language

• Tim Sheard
• Oregon Graduate Institute

CSE 510 Section FSC Winter 2004
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Assignments

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

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Recall RE Language

• datatype 'a Maybe Just of 'a Nothing
• datatype RE
• Lit of string
• Or of (RERE)
• Concat of (RERE)
• Star of RE
• fun prefix xs Just xs
• prefix (yys) (xxs)
• if yx then prefix ys xs else Nothing
• prefix ys xs Nothing

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One interpreter

• fun eval (Lit s) input
• (case prefix (explode s) input of
• Just more gt Just(s,more)
• Nothing gt Nothing)
• eval (Or(a,b)) input
• (case eval a input of
• Nothing gt eval b input
• Just pair gt Just pair)
• eval (Concat(a,b)) input
• (case (eval a input) of
• Just(zs,rest) gt
• (case eval b rest of
• Just (bs,more) gt Just (zs bs,more)
• Nothing gt Nothing)
• Nothing gt Nothing)
• eval (Star x) input
• let fun f input case eval x input of
• Nothing gt ("",input)
• Just (cs,zs) gt let val
  (bs,ws) f zs

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Staging it

• fun Seval (Lit s) input
• ltcase prefix (explode (lift s)) input of
• Just more gt Just((lift s),more)
• Nothing gt Nothinggt
• Seval (Or(a,b)) input
• ltcase (Seval a input) of
• Nothing gt (Seval b input)
• Just pair gt Just pairgt
• Seval (Concat(a,b)) input
• ltcase (Seval a input) of
• Just(zs,rest) gt
• (case (Seval b ltrestgt) of
• Just (bs,more) gt Just (zs bs,more)
• Nothing gt Nothing)
• Nothing gt Nothinggt

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Staging continued
Note how the helper function f is in the
generated code.

• Seval (Star x) input
• ltlet fun f input
• case (Seval x ltinputgt)
• Nothing gt ("",input)
• Just (cs,zs) gt
• let val (bs,ws) f zs
• in (cs bs,ws) end
• in Just(f input) endgt

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What does it generate?

• val t1
• Concat(Or(Lit "tim",Lit "mary")
• ,Star (Lit "x"))
• fun test x
• ltfn s gt (Seval x ltsgt)gt
• fun f x (run(test t1)) (explode x)
• test t1

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• - test t1
• val it
• lt(fn a gt
• (case (case (case prefix (explode "tim") a
  of
• Just o gt Just("tim",o)
• Nothing gt Nothing) of
• Nothing gt
• (case prefix (explode "mary") a
  of
• Just n gt Just("mary",n)
• Nothing gt Nothing)
• Just m gt Just m) of
• Just(c,b) gt
• (case let fun f g (case (case prefix
  (explode "x") g of
• Just l gt
  Just("x",l)
• Nothing gt
  Nothing) of
• Nothing gt
  ("",g)
• Just(i,h) gt let
  val (k,j) f h
• in
  (i k,j) end)
• in Just (f b) end of

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Monadic version

• ltDo mm
• a lt- try (prefix2 (explode "tim"))
• (prefix2 (explode "mary"))
• b lt- star (prefix2 (explode "x"))
• Return mm (a _at_ concat b)
• gt
• ltchar list Mgt
• What is the Monad used here?

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The meaning type

• Eval RE -gt char list -gt
• (string char list) Maybe
• datatype 'a M
• M of (char list -gt ('a char list) Maybe)
• fun unM (M x) x
• Eval2 RE -gt char list M

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Implementing the Monad

• val mm
• let fun return x M (fn s gt Just(x,s))
• fun bind (M f) g
• let fun h s
• case f s of
• Just(a,s2) gt unM (g a) s2
• Nothing gt Nothing
• in M h end
• in Mon(return,bind) end

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Operations on the monad

• fun test (M f)
• let fun h s case f s of
• Nothing gt Just(Nothing,s)
• Just(a,rest) gt Just(Just
  a,rest)
• in M h end
• fun prefix2 s
• let fun h x case prefix s x of
• Nothing gt Nothing
• Just m gt Just(s,m)
• in M h end
• fun try (M f) (M g)
• let fun h s case f s of
• Nothing gt g s
• Just pair gt Just pair
• in M h end

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Monadic Version

• fun star m
• Do mm mx lt- test m
• case mx of
• Just x gt Do mm xs lt- star m
• Return mm (xxs)
• Nothing gt Return mm
• fun eval2 (Lit s) prefix2 (explode s)
• eval2 (Or(a,b)) try (eval2 a) (eval2 b)
• eval2 (Concat(a,b))
• Do mm x lt- eval2 a
• y lt- eval2 b
• Return mm (x_at_y)
• eval2 (Star x)
• Do mm xss lt- star (eval2 x)
• Return mm (concat xss)

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Staged Monadic Version

• fun Seval2 (Lit s) ltprefix2 (explode (lift
  s))gt
• Seval2 (Or(a,b))
• lttry (Seval2 a) (Seval2 b)gt
• Seval2 (Concat(a,b))
• ltDo mm x lt- (Seval2 a)
• y lt- (Seval2 b)
• Return mm (x_at_y)gt
• Seval2 (Star x)
• ltDo mm xss lt- star (Seval2 x)
• Return mm (concat xss)
• gt

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Results

• - Seval2 t1
• val it
• ltDo mm
• a lt- try (prefix2 (explode "tim"))
• (prefix2 (explode "mary"))
• b lt- star (prefix2 (explode "x"))
• Return mm (a _at_ concat b)
• gt
• ltchar list Mgt
• Note calls to the monadic operators try,
  star, test (embedded in call to star), and
  prefix2

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