From 3f01bac76d7ab5d0668eb2d09dc7ef0758c195c6 Mon Sep 17 00:00:00 2001 From: Brian Picciano Date: Thu, 4 Mar 2021 17:21:00 -0700 Subject: ginger conditionals errata --- .../2021-03-04-conditionals-in-ginger-errata.md | 195 +++++++++++++++++++++ 1 file changed, 195 insertions(+) create mode 100644 src/_posts/2021-03-04-conditionals-in-ginger-errata.md diff --git a/src/_posts/2021-03-04-conditionals-in-ginger-errata.md b/src/_posts/2021-03-04-conditionals-in-ginger-errata.md new file mode 100644 index 0000000..b4c0007 --- /dev/null +++ b/src/_posts/2021-03-04-conditionals-in-ginger-errata.md @@ -0,0 +1,195 @@ +--- +title: >- + Conditionals in Ginger, Errata +description: >- + Too clever by half. +series: ginger +tags: tech +--- + +After publishing the last post in the series I walked away from my computer +feeling that I was very clever and had made a good post. This was incorrect. + +To summarize [the previous post][prev], it's not obvious which is the best way +to structure conditionals in a graphical programming language. My favorite +solution looked something like this: + +``` + in -> } -> } -if-> } -0-> } -add-> out +in -1-> } -> } } } -1-> } -sub-> out +in -0-> } } + } + in -lt-> } +``` + +Essentially an `if` operator which accepts a value and a boolean, and which has +two output edges. If the boolean is true then the input value is sent along the +first output edge, and if it's false it's sent along the second. + +This structure is not possible, given the properties of ginger graphs that have +been laid out in [other posts in the series][other]. + +## Nodes, Tuples, and Edges + +A ginger graph, as it has been presented so far, is composed of these three +elements. A node has a value, and its value is unique to the graph; if two nodes +have the same value then they are the same node. Edges connect two nodes or +tuples together, and have a value and direction. Tuples are, in essence, a node +whose value is its input edges. + +The `if` operation above lies on an edge, not a node or tuple. It cannot have +multiple output edges, since it cannot have any edges at all. It _is_ an edge. + +So it's back to the drawing board, to some extent. But luckily I've got some +more ideas in my back pocket. + +## Forks and Junctions + +In an older conception of ginger there was no tuple, but instead there were +forks and junctions. A junction was essentially the same as a tuple, just named +differently: a node whose value is its input edges. A fork was just the +opposite, a node whose value is its output edges. Junctions and forks naturally +complimented each other, but ultimately I didn't find forks to be useful for +much because there weren't cases where it was necessary to have a single edge be +split across multiple output edges directly; any case which appeared to require +a fork could be satisfied by directing the edge into a 1-tuple and using the +output edges of the 1-tuple. + +But now we have such a case. The 1-tuple won't work, because the `if` operator +would only see the 1-tuple, not its edges. It could be supposed that the graph +interpreter could say that an `if` operation must be followed by a 1-tuple, and +that the 1-tuple's output edges have a special meaning in that circumstance. But +making the output edges of a 1-tuple have different meaning in different +circumstances isn't very elegant. + +So a fork might be just the thing here. For the example I will represent a +fork as the opposite of a tuple: a vertical column of `{` characters. + +``` + in -> } -> } -if-> { -0-> } -add-> out +in -1-> } -> } } { -1-> } -sub-> out +in -0-> } } + } + in -lt-> } +``` + +It _looks_ elegant, which is nice. I am curious though if there's any other +possible use-case where a fork might be useful... if there's not then it seems +odd to introduce an entire new element just to support a single operation. Why +not just make that operation itself the new element? + +## Switch it Up + +In most conceptions of a flowchart that I've seen a conditional is usually +represented as a node with a different shape than the other nodes (often a +diamond). Ginger could borrow this idea for itself, and declare a new graph +element, alongside nodes, tuples, and edges, called a switch. + +Let's say a switch is simply represented by a `-<>`, and acts like a node in all +aspects except that it has no value and is not unique to the graph. + +The example presented in the [previous post][prev] would look something like +this: + +``` + in -> } -> } -<> -0-> } -add-> out +in -1-> } -> } } -1-> } -sub-> out +in -0-> } } + } + in -lt-> } +``` + +This isn't the _worst_. Like the fork it's adding a new element, but that +element's existence is required and its usage is very specific to that +requirement, whereas the fork's existence is required but ambiguously useful +outside of that requirement. + +On the other hand, there are macros to consider... + +## Macrophillic + +Ginger will certainly support macros, and as alluded to in the last post I'd +like even conditional operations to be fair game for those who want to construct +their own more complex operators. In the context of the switch `-<>` element, +would someone be able to create something like a pattern matching conditional? +If the builtin conditional is implemented as a new graph element then it seems +that the primary way to implement a custom conditional macro will also involve a +new graph element. + +While I'm not flat out opposed to allowing for custom graph elements, I'm +extremely skeptical that it's necessary, and would like it to be proven +necessary before considering it. So if we can have a basic conditional, _and_ +custom conditional macros built on top of the same broadly useful element, that +seems like the better strategy. + +So all of that said, it seems I'm leaning towards forks as the better strategy +in this. But I'd like a different name. "Fork" was nice as being the compliment +of a "junction", but I like "tuple" way more than "junction" because the term +applies well both to the structural element _and_ to the transformation that +element performs (i.e. a tuple element combines its input edges' values into a +tuple value). But "tuple" and "fork" seem weird together... + +## Many Minutes Later... + +A brief search of the internet reveals no better word than "fork". A place +where a tree's trunk splits into two separate trunks is called a "fork". A +place where a river splits into two separate rivers is called a "fork". +Similarly with roads. And that _is_ what's happening, from the point of view of +the graph's structure: it is an element whose only purpose is to denote multiple +outward edges. + +So "fork" it is. + +## Other considerations + +A 1-tuple is interesting in that it acts essentially as a concatenation of two +edges. A 1-fork could, theoretically, do the same thing: + +``` +a -foo-> } -bar-> b + +c -far-> { -boo-> d +``` + +The top uses a tuple, the bottom a fork. Each is, conceptually, valid, but I +don't like that two different elements can be used for the exact same use-case. + +A 1-tuple is an established concept in data structures, so I am loath to give it +up. A 1-fork, on the other hand, doesn't make sense structurally (would you +point to any random point on a river and call it a "1-fork"?), and fork as a +whole doesn't really have any analog in the realm of data structures. So I'm +prepared to declare 1-forks invalid from the viewpoint of the language +interpreter. + +Another consideration: I already expect that there's going to be confusion as to +when to use a fork and when to use multiple outputs from a node. For example, +here's a graph which uses a fork: + +``` +a -> { -op1-> foo + { -op2-> bar +``` + +and here's a graph which has multiple outputs from the same node: + +``` +a -op1-> foo + -op2-> bar +``` + +Each could be interpreted to mean the same thing: "set `foo` to the result of +passing `a` into `op1`, and set `bar` to the result of passing `a` into `op2`." +As with the 1-tuple vs 1-fork issue, we have another case where the same +task might be accomplished with two different patterns. This case is trickier +though, and I don't have as confident an answer. + +I think an interim rule which could be put in place, subject to review later, is +that multiple edges from a node or tuple indicate that that same value is being +used for multiple operations, while a fork indicates something specific to the +operation on its input edge. It's not a pretty rule, but I think it will do. + +Stay tuned for next week when I realize that actually all of this is wrong and +we start over again! + +[prev]: {% post_url 2021-03-01-conditionals-in-ginger %} +[other]: {% post_url 2021-01-09-ginger %} -- cgit v1.2.3