Theorem Prover using Isabelle

1
Theorem Prover using Isabelle

• Saravanakumar Chandran
• Under Guidance from
• Dr. S Toida

2
Isabelle

• A generic proof assistant
• Easier to use than others e.g., TPS
• Comes with large theories of formally verified
  mathematics, including elementary number theory,
  algebra and set theory. (Main, Set, HOL, TypeDef
  .)
• Developed at Cambridge Univ. and TU Munich
• Free for academic users

3
Project Goals

• Develop a web interface to Isabelle, for proofs
  involving Sets and logic.
• Allow users to use Math Symbols which they are
  aware of.
• Transform the result back into Math symbols.
• Provide feedback to user as to correctness for
  current line of proof (Undo the line)
• Capability to correct mistakes.
• Allow user to refer any previous lines
• Maximize ease of use, minimize loss of
  functionality through interface

4
Major Components

• Client Interface
• Message/Communication (Socket)
• Server to interact with Isabelle
• Symbol Filter between client and server

5
User Interface

• Java Applet on browser
• Proof statement section
• Math Symbols for Sets and Logics
• Dynamically adds boxes/text areas based on proof
  status
• Communicates to Isabelle via a server residing
  on web-server host. (Proof content object)

6
Socket communication

• Simple java object holds current state of proof
  (ProofContent)
• Filter intercepts the ProofContent object from
  the client and transforms the Math symbol into
  Isabelle equivalent and sends it on to the
  Server.
• Server executes the proof line and modifies the
  ProofContent object and sends it to the Filter.
  Filter again converts it back into Human
  understandable Math Symbol format and passes it
  on to the client to display.

7
Symbol Filter

• Proof content object is modified by the filter
  from client to server and vice versa.
• Unicode Mapping

8
Server

• Process that receives requests from clients and
  interacts with Isabelle
• Makes Unix calls using java runtime exec
• Each request spawns a thread which invokes
  Isabelle
• Reads Isabelles stdout/stderr to determine
  correctness
• Modifies ProofContent object and returns to
  client
• Theory toy Main.

9
Server Code

• theory Toy Main
• lemma "x - (A Int B) gt x A Int B"
• ML "set trace_simp"
• apply(auto)
• After this code is executed by the server if the
  result is that No subgoals then the step is
  proved.

10
Proof Checker

• Demo URL
• http//tango.cs.odu.edu29082/symbolmap/index.html
  

11
References

• HOL libraries
• http//www.cl.cam.ac.uk/Research/HVG/Isabelle/dist
  /library/HOL/
• Isabelle
• http//www.cl.cam.ac.uk/Research/HVG/Isabelle/