Toma 0.4

Teppei Saito
Japan Advanced Institute of Science and Technology, Japan

Architecture

Toma 0.4 is an automatic equational theorem prover. It proves unsatisfiability of a UEQ problem as follows: A given problem is transformed into a word problem whose validity entails unsatisfiability of the original problem. The word problem is solved by a new variant of maximal (ordered) completion [WM18, Hir21].

Strategies

Toma performs ordered completion in the following way: (1) Given an equational system E, the tool constructs a lexicographic path order > that maximizes reducibility of the ordered rewrite system (E, >) [WM18]. (2) Using the order >, the tool runs ordered completion [BDP89] on E without the deduce rule (critical pair generation). Such a run eventually ends with an inter-reduced version (E', >). (3) Then the tool checks joinability of the goal. If the goal is joinable with respect to (E', >), the tool outputs the proof and terminates. Otherwise, assigning the union of E' and a set of critical pairs of (E', >) to E, the tool goes back to the first step (1). After a certain number of iterations of the loop, the tool skips the order generation step (1) and repeats only (2)(3) with a fixed lexicographic path order.

Implementation

Toma is written in Haskell. Z3 is used to solve maximization problems of reducibility. The source code is available at:

    https://www.jaist.ac.jp/project/maxcomp/

Expected Competition Performance

Toma is still in the experimental stage and unable to compete with matured tools. The tool would solve several easy problems from the categories BOO, GRP and RNG.