Diagrams/Dev/Fixpoint

This page describes the motivation and design for a refactoring of diagrams, to give them a semantics based on computing fixed points of functions from "context" information to raw tree of primitives together with some summary information.

Reference

See the original "manifesto" and ensuing mailing list discussion here: http://thread.gmane.org/gmane.comp.lang.haskell.diagrams/383

See also later IRC discussion beginning here: http://ircbrowse.net/browse/diagrams?events_page=935

Detailed design

Most of the changes should be in the diagrams-core package, though a few things in diagrams-lib may need to change as well.

diagrams-core

No changes should be necessary to the following modules (all prefixed by Diagrams.Core): Envelope, HasOrigin, Juxtapose, Names, Points, Query, Trace, Transform, V.

I'm not sure about Style yet.

Diagrams.Core.Compile

• Change the name of UpAnnots to Summary.
• Change the name of DownAnnots to Context, and change its definition to

 type Context b v m = Style v
                    ::: Name
                    ::: SubMap b v m
                    ::: ()

The addition of SubMap is so that we can use the positions of laid-out subdiagrams to compute the positions of others.

• transfToAnnot and transfFromAnnot can be deleted.
• QDiaLeaf and withQDiaLeaf can be deleted.

• Create new definitions

 type ContextualT b v q m a = ReaderT (Context b v q) m a

 type Contextual b v q a = ContextualT b v q Identity a

One could imagine making ContextualT a newtype but that would necessitate writing lots of instances for things like MonadState, MonadReader, and so on.

• The definition of QDiagram should be changed to something like

 type QDiagram b v m = Contextual b v m (RTree b v Annotation, Summary b v m) 

It's important that this is NOT a newtype, so we can freely use the Monad instance for Contextual when working with diagrams.