Calvin-L / snf

A Coq tactic to convert your goal to skolem normal form (SNF)

The snf Tactic

This is a Coq tactic that converts your goal into skolem normal form (SNF):

Coq < Require Import SNF.


Coq < Goal exists x:nat, forall y:nat, x < y \/ y >= x.
1 goal
  
  ============================
  exists x : nat, forall y : nat, x < y \/ y >= x


Unnamed_thm < snf.
1 goal
  
  x : nat -> nat
  H0 : forall x0 : nat, ~ x0 < x x0 /\ ~ x x0 >= x0
  ============================
  False

The snf tactic assumes classical logic and indefinite description.

You'll need Coq 8.14 or higher to use it.

Getting Started

Install Coq 8.14+, then run make.

You can mess around with the tactic in src/Example.v.

I don't (yet) have any specific advice on how to use snf in another project.

Why?

Normal forms are incredibly important in automatic theorem proving. If someone wanted to, say, write an SMT solver in Gallina that can be used to solve Coq proof obligations, they will need to implement something like this as a starting point.

Mostly this project is a demonstration of proof by reflection. It shows a relatively clean way to (1) reflect quantified propositions into concrete datatypes using Ltac2 (see DataProp.v) and (2) write Gallina functions to manipulate those terms, with proofs that validity is preserved (see e.g. NNFProp.v).