groundness — an efficient groundness analyser for Prolog
Copyright 1998-2017 Peter Schachte
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this code except in compliance with the License.
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
This is the groundness analyser described in the paper:
Tania Armstrong, Kim Marriott, Peter Schachte, and Harald Søndergaard. Two classes of Boolean functions for dependency analysis. Science of Computer Programming, 31(1):3–45, May 1998.
It is based on the abstract domain Pos documented in the paper:
K. Marriott, H. Sondergaard, Precise and efficient groundness analysis for logic programs, ACM Letters on Programming Languages and Systems 2 (14) (1993) 181-196.
This is a two-phase abstract interpreter, meaning it first analyses the groundness relationships among the arguments of each predicate bottom-up over the program call graph (analysing one strongly connected component at a time), and then in the second, top-down, phase, uses the results computed in the first phase to determine the groundness of arguments to each predicate. This approach is sound, but loses precision unless the analysis domain is condensing, which the Pos domain is.
Building
You must have SWI Prolog version 7 installed.
This code uses my Reduced Ordered Binary Decision
Diagram
implementation written in C. This must be compiled before using the
analyzer. To compile, simply run make. This will build the shared library
needed to access the ROBDD code. Note that this assumes that SWI Prolog is
installed in your search path with the name swipl. This Makefile has only
been tested on Mac OS X version 10.12. I welcome pull requests with
adaptations to other OSes, and ports to other Prologs.
Running
To run the analyzer, load analyzer.pl and execute the query
anz([filename]).
This will analyze the file filename and all the files it loads and
print out the goal-independent (bottom-up relational) analysis of
each predicate, called (g.i.), then the least upper bound of all
calls of the predicate, called (call), and the answer groundness,
called (answ). The latter is the worst case groundness on completion of
all calls to the program, which is the lattice meet of the first two
analyses.
Analysis results are shown in disjunctive normal form, as either
TRUE or FALSE or as one or more parenthesized conjunctions of argument
numbers, separated by spaces, and the lists are disjoined. So for example,
the goal independent analysis result for append is shown as
(1 2 3) (1 ~2 ~3) (~1 ~3)
This means that when append/2 succeeds, either all three arguments are
ground, or the first argument is ground and the others are not
(necessarily) ground, or the first and third are not (necessarily) ground,
whether the second is ground or not. This is equivalent to the more
succinct statement (1 ∧ 2) ⇔ 3, which you can verify with
a truth table.
Known bugs
The top-down analysis does not give the strongest possible analysis.