[Haskell-cafe] From function body to DAG and back again?

[Mario Lang]

Hi.

I have a binary instance for a file format[1] which describes
a graph of DSP primitives.  This DAG was generated from a function body[2]
(in another programming language).  I think that language
can be boiled down to a pure language with let expressions,
to allow an output to be consumed by several inputs.
And there the trouble starts.  I am working on this without the usual
theoretical background.  I am not a PLD student, I am a self-taught Haskell fan.

The function body is basically a very neat way to make a DAG readable
without using visualisation.  Since I am blind, this topic has always
fascinated me.

Since I have this bidirectional binary instance, and
Haskell is supposed to be great at writing small languages,
I wonder what would be required to
* write a decompiler which would generate a version of the original function body
as a data structure and
* write a compiler which would translate that data structure back to the graph.

This is very much for my own learning experience, especially
since there is already a Haskell library which implements at least the
compilation part, and more.  However, I always found it very fascinating
to try to understand how this translation works, so I'd finally
like to take a stab at implementing it myself.

I have now searched a day for matching learning material which
would shed some light on the problem for me, without any great success.
Most SLC-examples I stumbled across immediately proceed to
implement an evaluation fucntion, which is not quite what I need.
For both directions, I need to work out the data structure
for my small language first, which is where I am stuck.
I have a feeling the decompiler might be easier to write then
the compiler.  My intuition says all I need to do is work backwards from
the last graph node, resolving all inputs until I am done.
However, I am stuck on the data structure and the compiler part.

Any hints on what could help me to get a better grasp on the problem and
how to solve it in Haskell are greatly appreciated.


[1] https://github.com/mlang/sound-supercollider/blob/master/Sound/SuperCollider/SynthDef.hs

[2]

SynthDef(\default, { arg out=0, freq=440, amp=0.1, pan=0, gate=1;
	var z = LPF.ar(
		Mix.new(
			VarSaw.ar(freq + [0, Rand(-0.4,0.0), Rand(0.0,0.4)], 0, 0.3, 0.3)
		),
		XLine.kr(Rand(4000,5000), Rand(2500,3200), 1)
	) * Linen.kr(gate, 0.01, 0.7, 0.3, 2);
	OffsetOut.ar(out, Pan2.ar(z, pan, amp));
}, [\ir]).writeDefFile;

Which translates to the following graph.  The pairs are inputs, pointing
at the corresponding outputs in the graph, -1 refering to the list of
constants at the beginning.

defaultSynthDef :: SynthDef
defaultSynthDef = SynthDef
  [ GraphDef
    "default"
    [-0.4,0.0,0.4,0.3,4000.0,5000.0,2500.0,3200.0,1.0,1.0e-2,0.7,2.0]
    [0.0,440.0,0.1,0.0,1.0]
    [("out",0),("freq",1),("amp",2),("pan",3),("gate",4)]
    [ UGen "Control" Scalar 0 [] [Scalar]
    , UGen "Control" Control 1 [] [Control,Control,Control,Control]
    , UGen "VarSaw" Audio 0 [(1,0),(-1,1),(-1,3)] [Audio]
    , UGen "BinaryOpUGen" Audio 2 [(2,0),(-1,3)] [Audio]
    , UGen "Linen" Control 0 [(1,3),(-1,9),(-1,10),(-1,3),(-1,11)] [Control]
    , UGen "Rand" Scalar 0 [(-1,0),(-1,1)] [Scalar]
    , UGen "BinaryOpUGen" Control 0 [(1,0),(5,0)] [Control]
    , UGen "VarSaw" Audio 0 [(6,0),(-1,1),(-1,3)] [Audio]
    , UGen "BinaryOpUGen" Audio 2 [(7,0),(-1,3)] [Audio]
    , UGen "Rand" Scalar 0 [(-1,1),(-1,2)] [Scalar]
    , UGen "BinaryOpUGen" Control 0 [(1,0),(9,0)] [Control]
    , UGen "VarSaw" Audio 0 [(10,0),(-1,1),(-1,3)] [Audio]
    , UGen "BinaryOpUGen" Audio 2 [(11,0),(-1,3)] [Audio]
    , UGen "Sum3" Audio 0 [(12,0),(8,0),(3,0)] [Audio]
    , UGen "Rand" Scalar 0 [(-1,4),(-1,5)] [Scalar]
    , UGen "Rand" Scalar 0 [(-1,6),(-1,7)] [Scalar]
    , UGen "XLine" Control 0 [(14,0),(15,0),(-1,8),(-1,1)] [Control]
    , UGen "LPF" Audio 0 [(13,0),(16,0)] [Audio]
    , UGen "BinaryOpUGen" Audio 2 [(17,0),(4,0)] [Audio]
    , UGen "Pan2" Audio 0 [(18,0),(1,2),(1,1)] [Audio,Audio]
    , UGen "OffsetOut" Audio 0 [(0,0),(19,0),(19,1)] []
    ]
    []
  ]

-- 
CYa,
  ⡍⠁⠗⠊⠕