package chase

Chase: A Model Finder for Finitary Geometric Logic

John D. Ramsdell
The MITRE Corporation

Chase is a model finder for first order logic with equality. It finds minimal models of a theory expressed in finitary geometric form, where functions in models may be partial. A formula is in finitary geometric form if it is a sentence consisting of a single implication, the antecedent is a conjunction of atomic formulas, and the consequent is a disjunction. Each disjunct is a possibly existentially quantified conjunction of atomic formulas. A function is partial if it is defined only on a proper subset of its domain.

Installing From OPAM

$ opam install chase

Installing From Sources

This software uses ocaml, opam, and dune. See http://ocaml.org for ocaml installation instructions. Install dune with:

$ opam install dune

Install the programs with:

$ dune build
$ dune install

Usage

The user guide is in chase.xhtml.

$ chase -h
Usage: chase [OPTIONS] [INPUT]
Options:
  -o FILE  --output=FILE  output to file (default is standard output)
  -t       --terse        use terse output -- print only models
  -j       --just-one     find just one model
  -i       --input-order  use input order to select formulas
  -b INT   --bound=INT    set structure size bound (default 250)
  -l INT   --limit=INT    set step count limit (default 2000)
  -c       --compact      print structures compactly
  -s       --sexpr        print structures using S-expressions
  -m INT   --margin=INT   set output margin
  -q       --quant        read formulas using quantifier syntax
  -e       --explicit     print formulas using quantifier syntax
  -f       --flatten      print flattened formulas
  -p       --proc-time    print processor time in seconds
  -v       --version      print version number
  -h       --help         print this message

$ chasetree -h
Usage: chasetree [OPTIONS] [INPUT]
Options:
  -o FILE  --output=FILE  output to file (default is standard output)
  -r INT   --ratio=INT    set ratio between window heights (default 20%)
  -v       --version      print version number
  -h       --help         print this message

Example

The syntax used for geometric theories is Geolog, a Prolog-like syntax. What follows is an example of a theory for conference management.

$ cat cm.gl
% Conference Management

author(X) & paper(Y) & assigned(X, Y).
author(X) & paper(Y) => read_score(X, Y) | conflict(X, Y).
assigned(X, Y) & author(X) & paper(Y) => read_score(X, Y).
assigned(X, Y) & conflict(X, Y) => false.
$

A run of Chase produces the following output.

$ chase cm.gl
% chase version 1.5
% bound = 50, limit = 500, input_order = false
% ********
% author(X) & paper(Y) & assigned(X, Y). % (0)
% author(X) & paper(Y) => read_score(X, Y) | conflict(X, Y). % (1)
% assigned(X, Y) & author(X) & paper(Y) => read_score(X, Y). % (2)
% assigned(X, Y) & conflict(X, Y) => false. % (3)
% ********

(0)[]

(1,0){0}[assigned(x, y), author(x), paper(y)]

(2,1){1}![assigned(x, y), author(x), paper(y), read_score(x, y)]

(3,1){1}[assigned(x, y), author(x), conflict(x, y), paper(y)]

(4,3){2}[assigned(x, y), author(x), conflict(x, y), paper(y),
  read_score(x, y)]

A run of Chase produces structures assembled into a tree. The root of the tree is labeled (0). A label of the form (n, p) gives the node number of the tree node and its parent. The form {r} records the rule used to produce this structure. A structure marked with ! is a model. Thus in this output, there are two paths explored, <0,1,2> and <0,1,3,4>, and one model found (2).

More examples are in the tst directory.

A graphical view of Chase output is constructed by chasetree.

$ chase -o cm.text cm.gl
$ chasetree -o cm.xhtml cm.text

Makefile

The file chase.mk contains make rules for Chase. A sample makefile that uses chase.mk follows.

include chase.mk

TXTS	:= $(patsubst %.gl,%.txt,$(wildcard *.gl)) \
		$(patsubst %.glx,%.txt,$(wildcard *.glx))

all:	$(TXTS)

clean:
	-rm $(TXTS)

Literate Theories Using Markdown

When the Chase input file name has the extension ".md", the input syntax is treated as Markdown, and Chase input is extracted from fenced code blocks. Examples of literate theories is in the markdown directory.

Emacs Users

Syntax error messages produced by Chase include Emacs style location information. Use M-x compile to run Chase and C-x ` to move to the sequent that caused the error message. When other error messages include position information, it points to the position of period in the formula that caused the problem.

Development

The software uses ocamlbuild for development and testing. To run the tests in the tst directory, type:

$ make; (cd tst; make)

To generate documentation using ocamldoc, type:

$ make chase.docdir/index.html

The instructions for debugging the program is in debug.txt.