blob: fc1b5769f6df500eb48d651882e904722dd4106c (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
{-# OPTIONS -Wall -fno-warn-name-shadowing #-}
module Dataflow (
fixedpoint
) where
-----------------------------------------------------------------------------
-- | Solve the fixed-point of a dataflow problem.
--
-- Complexity: O(N+H*E) calls to the update function where:
-- N = number of nodes,
-- E = number of edges,
-- H = maximum height of the lattice for any particular node.
--
-- Sketch for proof of complexity:
-- Note that the state is threaded through the entire execution.
-- Also note that the height of the latice at any particular node
-- is the number of times 'update' can return non-Nothing for a
-- particular node. Every call (except for the top level one)
-- must be caused by a non-Nothing result and each non-Nothing
-- result causes as many calls as it has out-going edges.
-- Thus any particular node, n, may cause in total at
-- most H*out(n) further calls. When summed over all nodes,
-- that is H*E. The N term of the complexity is from the initial call
-- when 'update' will be passed 'Nothing'.
fixedpoint ::
(node -> [node]) -- map from nodes to those who's
-- value depend on the argument node
-> (node -> Maybe node -> s -> Maybe s)
-- Given the node which needs to be
-- updated, and which node caused that node
-- to need to be updated, update the state.
--
-- The causing node will be 'Nothing' if
-- this is the initial/bootstrapping update.
--
-- Must return 'Nothing' if no change,
-- otherwise returrn 'Just' of the new state.
-> [node] -- Nodes that should initially be updated
-> s -- Initial state
-- (usually a map from node to
-- the value for that node)
-> s -- Final state
fixedpoint dependants update nodes state =
foldr (fixedpoint' Nothing) state nodes where
-- Use a depth first traversal of nodes based on the update graph.
-- Terminate the traversal when the update doesn't change anything.
fixedpoint' cause node state =
case update node cause state of
Nothing -> state
Just state' ->
foldr (fixedpoint' (Just node)) state' (dependants node)
|
