Those are some very interesting visual languages, Miguel! I remember drawing some diagrams when I was teaching myself Haskell, but I never actually tried to create a formal visual language. Since my background is in hardware engineering, I would naturally gravitate toward schematic diagrams. I am also familiar with the graphical programming language of LabView.
After reading Miguel's exposition, I thought about how I might draw a picture of map1. map1 :: (a -> b) -> [a] -> [b] map1 f [] = [] map1 f (x:xs) = (f x) : map1 f xs [image: map1.png] (Image created with Inkscape) Here is what I'm thinking: * Green boxes represent inputs and outputs. * Inputs are always on the left, outputs are always on the right. * Inputs appear in top-to-bottom order. * Data always flows left to right. * Arrows represent data flow. * A named white rectangle represents application of the named function. * A gray rectangle represents a function that arrives through data flow. * A filled-in arrowhead means the data "in" the arrow is to be "unpacked" and used as a function. * A named light-blue rectangle (such as on the left, with a colon in it) represents a pattern match operation. In thinking about this, I can sense that there are MANY issues with using a visual language to represent Haskell. Some issues I can think of: * How to represent pattern matching? * How to represent partial application? * How to represent data types or class constraints in the diagram? * How to represent a list comprehension or a do statement? (These might require special visual syntax) * Will the data flow always take the form of a directed acyclic graph, so that data never has to flow right-to-left? (Perhaps there's a way to "tie the knot" and get a cycle in the data flow graph.) * Whether to create special symbols for certain commonly used functions? (In digital circuit schematics, AND, OR, and NOT gates have special symbols, but most compound circuits are represented with labeled rectangles.) Also, if I want to automatically generate an image from a Haskell function, then my image generator needs to automatically place and route all those boxes. I'll have to give more thought to the other versions of map, and maybe make some more diagrams. -- Ron
<<map1.png>>
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