Deducteam / predicativize

A tool for sharing proofs with predicative systems

Predicativize: A tool for sharing proofs with predicative system

We refer to the paper Translating proofs from an impredicative type system to a predicative one for an introduction to the tool.

Predicativize was used to translate Matita's arithmetic library to Agda, the translated proofs can be found here.

Installation

First start by installing Dedukti (https://github.com/Deducteam/Dedukti hash c65e7e) and then simply run make. In order to test the tool, run make test_agda which will predicativize the Fermat's little theorem library. If Agda is installed, then you can also run make test_agda_with_typecheck, which also translates the results to Agda files and typechecks them.

You can also test the tool with Matita's arithmetic library, by running make matita_agda, and with a fragment of Isabelle's library, by running make isabelle_agda. However, be advised that these take a lot of time.

Modes

By running dune exec -- predicativize --help we can see that the following modes are available.

  -a      Automatically translates the output to agda files
  -at     Automatically translates the output to agda files and typechecks them
  --eta   Uses eta equality
  --cstr  A file containing extra constraints to be taken into account
  --meta  A file containing metarules to be applied to the files
  --path  Paths to look for .dko files

The --path option should be used to point to the theory files defining the encoding.

The meta file supplied to --meta should be used to translate from the source file's syntax to the theory/pts.dk syntax, which is the one used. You can look at metas/sttfa_to_pts.dk for a meta file allowing to translate from the syntax of theory/sttfa.dk to the syntax of theory/pts.dk.

In order to see an example of cstr file, you can look at extra_cstr/matita.dk.

You can look at the makefile to see examples of how these options are used.

Times

• matita - with lt_4_to_fact and le_fact_10 : ~37 min
• matita - without lt_4_to_fact and le_fact_10 : ~7 min
• test (fermat's little theorem proof in hol) : ~2 min