18 pointsby matt_d3 hours ago2 comments

deepsunan hour ago
Full syntax of λλ (from the paper):
```
   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)
```
- trompan hour 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).
- pjmlp15 minutes ago
  So simplified, a bit like System F.
trompan hour 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.