AR 20/12/2005

This is a translator of a part of the proof system
by Claes Strannegård, as defined in the manuscript
"Translating Formal Proofs into English".

The functionality is to translate between a formal
and an informal notation for proofs.

As examples, we provide 3 of the 4 examples in
Strannegård's paper. His example 3 is left as exercise.

A good way to start is

  % gf <test.gfs

which will translate the proofs back and forth.

If you modify the grammars and want to compile from source, you also need

  % export GF_LIB_PATH=/home/aarne/GF/lib -- set to the path in your system

Files:

  ex1eng.txt      -- the 3 tests
  ex1.txt    
  ex2eng.txt
  ex2.txt
  ex4eng.txt
  ex4.txt

  Formula.gf      -- abstract syntax of formulas
  FormulaSymb.gf  -- concrete syntax of formulas
  Precedence.gf   -- precedence package
  ProofEng.gf     -- top concrete syntax, English
  Proof.gf        -- top abstract syntax
  ProofSymb.gf    -- top concrete syntax, symboli

  proof.gfcm      -- precompiled translator

  README          -- this file
  test.gfs        -- the test script


Notes:

1. The abstract syntax does not do proof checking.

2. de Morgan labels have been disambiguated with "1" and "2".

3. The symbolic Ex falso quodlibet rule needs to show the
   conclusion formula in the label to make linearization 
   possible (in the absence of smart proof checking).

4. The English concrete syntax needs some extra formula
   arguments for the same reason. These arguments can be
   omitted, but the resulting parser returns some 
   metavariables.

An interesting further task would be to implement the
proof checker and a proof search procedure, in Haskell or,
even better, in the GF Transfer Language.

Another nice thing would be to linearize the formulas
into real English.