e ::= v | x | input(p)
| let x = e1 in e2
| (e1, e2)
| unpack e1 as (x1, x2) in e2
| phase(θ, e)
| split(r, e)
| unitary(U, (e1, e2))
| output(p) <- e1; e2
v ::= r ↓ ℝ | p ↓ Port | U ↓ Unitary | ()
τ ::= ℝ | Port | Opt | Unitary | Unit |(τ1 * τ2)
tromp 1 days ago [-]
Note that this is not an extension of the pure λ-calculus.
Abstraction (λx.e) and application (f a) are missing,
although the let construct "let x = e1 in e2" is equivalent to their combination
((λx.e2) e1).
The paper has few details on the higher-level specification language in which users specify desired behaviour:
> Specification Language. Specifications are written as relations between input and output ports, expressed using linear expressions. On their own, specifications are not λ _λ programs. It is the job of the synthesizer to find λ _λ programs that realize a given specification. For example, a simple switching behavior can be specified as output[i] = input[j], while a 2x2 AllReduce operation can be written as output[1] = (input[1] + input[2])/sqrt(2) and output[2]= (input[1] - input[2])/sqrt(2).
pjmlp 1 days ago [-]
So simplified, a bit like System F.
tromp 1 days ago [-]
The second λ is subscripted. As footnote 1 in the paper says:
> Pronounced “lambda lambda”. One λ refers to the λ-calculus and the other refers to an optical wavelength.
sunrunner 23 hours ago [-]
Or, in French, Lambdeux.
tromp 21 hours ago [-]
That also sounds like a good french name for Binary Lamda Calculus.
iLemming 19 hours ago [-]
"Lambda" is from Greek, so plural would be something like "Lambdada".
noworld 23 hours ago [-]
Ah, the bi-lams.
esseph 21 hours ago [-]
lambdi!
wigster 21 hours ago [-]
how do i search for a character i can't even type?
are people in this field just able to jump into Greek mode?
ktallett 1 days ago [-]
I am curious why develop a new language instead of building a library for an existing language. What are the benefits as I didn't see this in the paper? Can it interact with other languages?
flossly 24 hours ago [-]
I understood this language like being something similar to assembly.
Many compiled languages can compile down to assembly and which can be used to debug/optimize/understand the compilation process.
Assembly is so close to the underlying hardware that it's not very practical for us humans to write software with it.
> Can it interact with other languages?
I'd say this is probably similar to the story with assembly. Assembly cannot interop with C. But C can be compiled down to assembly (not sure that counts as "interact" to you).
tekne 23 hours ago [-]
Assembly can totally interop with C.
ktallett 23 hours ago [-]
Well the logical step would be that you are creating a silicon photonics environment that has comparable input and output to the real world (classical computing) which is always into another system to appropriately input, readout, and feedback into the system. Hence why interaction with the languages that readout and input will involve are essential.
black_knight 1 days ago [-]
The first sentence of the abstract gives a motivation: "λλ uses a linear type system to encode the physical constraints of optics, rejecting unrealizable programs at compile time."
The fact that it its own language does not preclude using it within the context of a different language. You can embed a domain specific language into a general purpose one.
ktallett 23 hours ago [-]
I read that but unless they are able to encode construction, input, output, material, and packaging restraints which I'm not sure this does then I can't see the benefit. It's only ever going to be idealised which are realistically unrealizable.
A key focus of silicon photonics is that it has to interact with classical systems to do readout and input right now so it would be logical to design with that built in.
opengrass 18 hours ago [-]
I'm a retard so I'm gonna call it Half Life.
Rendered at 11:33:15 GMT+0000 (Coordinated Universal Time) with Vercel.
Abstraction (λx.e) and application (f a) are missing, although the let construct "let x = e1 in e2" is equivalent to their combination ((λx.e2) e1).
The paper has few details on the higher-level specification language in which users specify desired behaviour:
> Specification Language. Specifications are written as relations between input and output ports, expressed using linear expressions. On their own, specifications are not λ _λ programs. It is the job of the synthesizer to find λ _λ programs that realize a given specification. For example, a simple switching behavior can be specified as output[i] = input[j], while a 2x2 AllReduce operation can be written as output[1] = (input[1] + input[2])/sqrt(2) and output[2]= (input[1] - input[2])/sqrt(2).
> Pronounced “lambda lambda”. One λ refers to the λ-calculus and the other refers to an optical wavelength.
are people in this field just able to jump into Greek mode?
Many compiled languages can compile down to assembly and which can be used to debug/optimize/understand the compilation process.
Assembly is so close to the underlying hardware that it's not very practical for us humans to write software with it.
> Can it interact with other languages?
I'd say this is probably similar to the story with assembly. Assembly cannot interop with C. But C can be compiled down to assembly (not sure that counts as "interact" to you).
The fact that it its own language does not preclude using it within the context of a different language. You can embed a domain specific language into a general purpose one.
A key focus of silicon photonics is that it has to interact with classical systems to do readout and input right now so it would be logical to design with that built in.