[Agda] A frontend for the semiring solver using the reflection API

Altenkirch Thorsten psztxa at exmail.nottingham.ac.uk
Mon Apr 2 10:14:13 CEST 2012

Hi Wojciech,

you are correct this was one of the motivating examples but as far as I
know nobody  has yet implemented such an interface. Thank you very much!


On 01/04/2012 23:46, "Wojciech Jedynak" <wjedynak at gmail.com> wrote:

>Hello everybody,
>last week my sanity has been saved by the stdlib's semiring solver. To
>make it more convenient to use, and as an exercise in Agda's
>reflection API,  I wrote a simple front-end for the solver today.
>I guess that this was one of motivating examples for introducing the
>API to Agda in the first place, so others must have created similar
>modules before - it might be interesting to compare different
>approaches, so please share if you can.
>The code is available at
>It has been checked with the latest darcs version of Agda & stdlib.
>Long story short, instead of
>stdlib : ∀ m n → suc (m + n + (m + n)) ≡ m + m + suc (n + n)
>stdlib = solve 2 (λ m n → con 1 :+ (m :+ n :+ (m :+ n)) := m :+ m :+
>(con 1 :+ (n :+ n))) refl
>one can simply say
>notbad : ∀ m n → suc (m + n + (m + n)) ≡ m + m + suc (n + n)
>notbad = quoteGoal e in ring e refl refl refl refl
>The right hand side is the same regardless of the goal, so we can use
>it like the ring tactic in Coq.
>It would be nice to replace it with a one-word notation, but I don't
>know how to do it, so it's either
>snippets or copy&paste for now.
>The code should be simlifiable, so I would appreciate any comments.
>PS. Pattern-matching lambdas in Agda 2.3 are awesome - it's very neat
>to use them for trivial inversion properties instead of writing many
>Agda mailing list
>Agda at lists.chalmers.se

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