# Qi-circuit - A domain specific language to create signal flow graphs **URL:** \ **Category:** Show & Tell\ **Tags:** qi, stream, dsl, circuit\ **Created:** [December 18, 2023, 7:13pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610 "2023-12-18T19:13:52Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![chansey97](https://avatars.discourse-cdn.com/v4/letter/c/e480ec/32.png) [@chansey97](https://racket.discourse.group/u/chansey97)\ **Post date:** [December 18, 2023, 7:13pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/1 "2023-12-18T19:13:52Z")
Hello everyone, I'm excited to share a package that I've recently developed, built on top of [Qi](https://docs.racket-lang.org/qi/index.html), called Qi-circuit: [https://github.com/chansey97/qi-circuit](https://github.com/chansey97/qi-circuit "https://github.com/chansey97/qi-circuit") Qi-circuit a domain-specific language designed for creating stream circuits; in some literature, they are also referred to as signal flow graphs. The main aim of this package is to reveal the connection between Qi and signal flow graphs. A quick example of calculating the Fibonacci sequence by Qi-circuit. ```scheme #lang racket (require qi) (require "../qi-circuit-lib/circuit.rkt") (define zero (stream-cons 0 zero)) (define one (~>> (zero) (c-reg 1))) (define-flow sf (~>> (c-loop (~>> (== _ (c-reg 0)) (c-add +) (c-loop (~>> (== _ (c-reg 0)) (c-add +) (-< _ _))) (c-reg 0) (-< _ _))))) (define fib ((☯ sf) one)) (~>> (fib) (stream-take _ 20) stream->list) ;; '(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181) ``` I have written a [tutorial](https://github.com/chansey97/qi-circuit) about it, including many examples, such as integral, factorial, fibonacci, catalan numbers, and ODE. Each example contains a step-by-step diagram reasoning to transform a general circuit to Qi-circuit. Give it a try and let me know what you think about. Any insights, suggestions, and criticism are highly appreciated. Thanks! ---
**Author:** ![benknoble](https://yyz2.discourse-cdn.com/free1/user_avatar/racket.discourse.group/benknoble/32/16_2.png) [@benknoble](https://racket.discourse.group/u/benknoble)\ **Post date:** [December 18, 2023, 7:27pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/2 "2023-12-18T19:27:21Z")
It seems to me that your definition of `sf` repeats the body a bit? ```scheme (define-flow sf (~>> (c-loop (~>> (== _ (c-reg 0)) (c-add +) (c-loop (~>> (== _ (c-reg 0)) (c-add +) (-< _ _))) (c-reg 0) (-< _ _))))) ``` I wonder if that was intentional, and if so, why? ---
**Author:** ![chansey97](https://avatars.discourse-cdn.com/v4/letter/c/e480ec/32.png) [@chansey97](https://racket.discourse.group/u/chansey97)\ **Post date:** [December 18, 2023, 8:39pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/3 "2023-12-18T20:39:57Z")
Thanks for your feedback! What do you mean by " `sf` repeats the body a bit?" ? Note that the same stream function can have different circuits, but they are equivalent. For Fibonacci sequence, you might write a different circuit. The circuit in the example uses a general circuit for any rational stream. More details, see [qi-circuit/qi-circuit-examples/fibonacci.md at main · chansey97/qi-circuit · GitHub](https://github.com/chansey97/qi-circuit/blob/main/qi-circuit-examples/fibonacci.md) ---
**Author:** ![benknoble](https://yyz2.discourse-cdn.com/free1/user_avatar/racket.discourse.group/benknoble/32/16_2.png) [@benknoble](https://racket.discourse.group/u/benknoble)\ **Post date:** [December 18, 2023, 9:43pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/4 "2023-12-18T21:43:20Z")
The pattern `(~>> (== _ (c-reg 0) (c-add +) (-< _ _))` looks nested within itself a bit, modulo an extra `(c-reg 0)` and placement of threading. ---
**Author:** ![chansey97](https://avatars.discourse-cdn.com/v4/letter/c/e480ec/32.png) [@chansey97](https://racket.discourse.group/u/chansey97)\ **Post date:** [December 18, 2023, 9:52pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/5 "2023-12-18T21:52:58Z")
This is `c-loop` construct. ![image](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/a/a78eee2af0df0e73fe41d4136fe339dab2a334d0.png) The `(~>> (== _ (c-reg 0) (c-add +) (-< _ _))` is the `sf` in `c-loop` (blue dashed rectange), so it has two inputs and two outputs. Maybe I misunderstood your question. ---
**Author:** ![chansey97](https://avatars.discourse-cdn.com/v4/letter/c/e480ec/32.png) [@chansey97](https://racket.discourse.group/u/chansey97)\ **Post date:** [December 20, 2023, 6:48am UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/8 "2023-12-20T06:48:15Z")
I deleted the previous reply, which is a bit confusing; here is the updated answer. For Fibonacci sequence, its generating function is F = \frac{X}{1 - X - X^2}. We can derive the recursive equation F = X + F X + F X^2 from it. One way to solve the recursive equation is to use stream algorithms, i.e. ```scheme (define F (stream-cons 0 (stream-cons 1 (map + F (stream-rest F))))) (~>> (F) (stream-take _ 20) stream->list) ;; '(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181) ``` However, the recursive equation can also be represented as circuits. For example, ![image-20231220140125664](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/5/50e67f8996a0616e538cc13ffbf3298ed1c1962f.png) It's obvious that it has two loops. However, there are many ways for solving the same recursive equation; this is just one of them. i.e. F = (X + F X) + F X^2. As follows are other possible implementations: F = (X + F X^2) + F X ![image-20231220140434941](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/4/48dfc235be219845f25efa11a68b2dc34152a372.png) F = (F X + F X^2) + X ![image-20231220135853380](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/c/c7fd80478eea9f82aafad9d439a668445a85ea02.png) F = (1 + F X + F) X ![image-20231220135548419](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/a/ad2b80c51c91b6714963f38385effb9b741c1f53.png) F = X + F (X + X^2) ![image-20231220115342196](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/2/2819e2905b757c708aa0f7da93b48ac790844b4d.png) Look the last one, which has only one loop. We can use the circuit as a template to create Qi-circuit. ![image-20231220115612955](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/3/3ae675c944e5e18e83f252e87cd1d772ff25b552.png) ```scheme (define fib (~>> (one) (c-reg 0) (c-loop (~>> (== _ (~>> (-< (c-reg 0) (~>> (c-reg 0) (c-reg 0))) (c-add +))) (c-add +) (-< _ _))))) (~>> (fib) (stream-take _ 20) stream->list) ;; '(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181) ``` This answer your question "why there are two loops". * * * BTW, in the latest Qi-circuit, I added a new form `c-loop-gen`. ![image-20231220133353173](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/7/7a63e05f0d89c25c1a51420ea21079ba9ed81114.png) It can output signals without any input. Now, there's no longer to use a dummy input (such as zero) and `>2` as was required previously. The Fibonacci sequence can also be defined as follows: F = (F + (FX + 1)) X ![image-20231220132518110](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/7/7a045cfbe0f252bdb3307d436c9aad9c8d013336.png) ![image-20231220132553877](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/1/19da087d868957676c3528f633502c347e02a895.png) ```scheme (define fib (~>> () (c-loop-gen (~>> (c-reg 0) (-< _ (c-reg 1)) (c-add +) (-< _ _))) (c-reg 0) )) (~>> (fib) (stream-take _ 20) stream->list) ;; '(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181) ``` This circuit seems more readable. ---
**Author:** ![robby](https://yyz2.discourse-cdn.com/free1/user_avatar/racket.discourse.group/robby/32/7_2.png) [@robby](https://racket.discourse.group/u/robby)\ **Post date:** [December 20, 2023, 4:49pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/9 "2023-12-20T16:49:29Z")
All the talk of circuits and streams reminds me of the Lustre programming language. Do you guys know it? Here's how to implement fib in it: ```scheme node fib () returns (f: int); let f = 1 -> pre(f + (0 -> pre f)); tel ``` Here's a transcript of what running this in [lv6](https://gricad-gitlab.univ-grenoble-alpes.fr/verimag/synchrone/lustre-v6) looks like: ```scheme $ lv6 -cc -2c -n fib fib.lus W: fib_fib_loop.c has been generated. W: fib_fib.h has been generated. W: fib_fib.c has been generated. + '[' -z ']' + C_COMPILER=gcc + '[' -z ']' + MAIN_FILE=fib_fib_loop.c + gcc -o fib.exec lustre_consts.c fib_fib.c fib_fib_loop_io.c fib_fib_loop.c fib_fib_loop.c:11:48: warning: passing arguments to 'fib_fib_ctx_new_ctx' without a prototype is deprecated in all versions of C and is not supported in C2x [-Wdeprecated-non-prototype] fib_fib_ctx_type* ctx = fib_fib_ctx_new_ctx(NULL); ^ 1 warning generated. sys call: 'sh fib.sh' $ ./fib.exec #inputs #outputs "f":int #step 1 1 #step 2 1 #step 3 2 #step 4 3 #step 5 5 #step 6 8 #step 7 13 #step 8 21 #step 9 34 #step 10 55 #step 11 89 #step 12 144 ``` ---
**Author:** ![chansey97](https://avatars.discourse-cdn.com/v4/letter/c/e480ec/32.png) [@chansey97](https://racket.discourse.group/u/chansey97)\ **Post date:** [December 23, 2023, 9:26am UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/10 "2023-12-23T09:26:56Z")
Thank you for telling me the Lustre language. I read some articles online about Lustre, and it's very cool! Inspired by [Lustre](https://homepage.cs.uiowa.edu/~tinelli/classes/181/Spring10/Notes/03-lustre.pdf) , I added two new forms to Qi-circuit. ![image-20231223151615811](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/4/4874398ccbe2d92c8c25ff871d85637faac3d7b9.png) ![image-20231223150807313](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/a/a9430736f741fd3436b1a9e2af951eb462bdcf00.png) They correspond to `->` and `if then else` in Lustre. Now we can create more interesting circuits. For example, the bistable switch: ![image-20231223144005731](https://global.discourse-cdn.com/free1/uploads/racket/original/2X/0/0fa9c7a267494efcd6790fb4832dd528ac511d62.png) ```scheme (define (bistable-switch on off) (~>> (on off) ▽ (c-loop (~>> (== △ (~>> (-< (gen false) (c-reg 0)) c-->)) (c-switch (% 3> _) [_ (~>> 2> NOT)] [else 1>]) (-< _ _) )))) ``` In Lustre, it would be write ```scheme node Switch(on,off: bool) returns (s: bool); let s = if(false -> pre s) then not off else on; tel ``` Qi-circuit seems more cumbersome than Lustre. BTW, do you think Lustre is readable? or some one has to draw out the diagram for understanding? Qi-circuit at least maintains the shape of the circuit. ---
**Author:** ![chansey97](https://avatars.discourse-cdn.com/v4/letter/c/e480ec/32.png) [@chansey97](https://racket.discourse.group/u/chansey97)\ **Post date:** [December 23, 2023, 9:27am UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/11 "2023-12-23T09:27:05Z")
Next task is adding Lustre's Clock to Qi-circuit. But before that, I have to think about the issue of modularity. Currently Qi-circuit seems [not suitable for modularization (e.g. the ODE example)](https://github.com/chansey97/qi-circuit/blob/main/qi-circuit-examples/ode-1st.md) because Qi is strict in Racket: > Note that this example also shows that you cannot treat `integral` as an independent component, because `(c-reg y0)` must be on the leftmost side of `sf` in the `c-loop` or `c-loop-gen`. In other words, you often have to slide the `c-reg` to the left. I haven't tried the same example with Arrow in Haskell, but it might be related. Naively use `#lang lazy` with `list` doesn't work at the moment, I have not explored deeply though. Anyone has idea about it? Thanks. ---
**Author:** ![robby](https://yyz2.discourse-cdn.com/free1/user_avatar/racket.discourse.group/robby/32/7_2.png) [@robby](https://racket.discourse.group/u/robby)\ **Post date:** [December 23, 2023, 2:28pm UTC](https://racket.discourse.group/t/qi-circuit-a-domain-specific-language-to-create-signal-flow-graphs/2610/12 "2023-12-23T14:28:35Z")
> [@chansey97](#): > > BTW, do you think Lustre is readable? or some one has to draw out the diagram for understanding? Qi-circuit at least maintains the shape of the circuit. I know only very little about Lustre. It is a storied programming language, however, dating back to the 1980s and with a lot of very serious people using it for safety-critical things and studying its properties and making it more and more robust. There is an annual meeting called [Synchron](https://www.rtsys.informatik.uni-kiel.de/en/synchron-2023/) where many of the people who go work full-time on Lustre and related things. I don't know if it has an industrial community, tho. That's an academic community. I'm guessing that they would welcome a presentation on your work if you can manage a trip to Europe and are intersted in talking with them. (I don't know an online way to connect to that community, however.)