IsaPlanner is a
proof planner for the interactive
proof assistant
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor ...
,
Isabelle
Isabel is a female name of Spanish origin. Isabelle is a name that is similar, but it is of French origin. It originates as the medieval Spanish form of '' Elisabeth'' (ultimately Hebrew ''Elisheva''), Arising in the 12th century, it became popul ...
. Originally developed by Lucas Dixon
[A Proof Planning Framework for Isabelle. Lucas Dixon. PhD Thesis, University of Edinburgh. 2005.] as part of his PhD thesis at the
University of Edinburgh
The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...
, it is now maintained by members of the Mathematical Reasoning Group, in the
School of Informatics at Edinburgh.
IsaPlanner is the latest of a series of proof planners written at Edinburgh. Earlier planners include Clam and LambdaClam.
Features
IsaPlanner allows the user to encode reasoning techniques, using a
combinator
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of comput ...
language, for
conjecturing and
proving theorems. IsaPlanner works by manipulating reasoning states, records of open goals, the current proof plan and other important information, and combinators are functions mapping reasoning states to
lazy lists of successor reasoning states.
IsaPlanner's library supplies combinators for branching and
iteration
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
, amongst other tasks, and powerful reasoning techniques can be created by combining simpler reasoning techniques with these combinators.
Several reasoning techniques come ready implemented within IsaPlanner, notably, IsaPlanner features an implementation of dynamic
rippling, a rippling
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
capable of working in
higher order settings, a
best-first rippling heuristic and a reasoning technique for proofs by
induction
Induction, Inducible or Inductive may refer to:
Biology and medicine
* Labor induction (birth/pregnancy)
* Induction chemotherapy, in medicine
* Induced stem cells, stem cells derived from somatic, reproductive, pluripotent or other cell t ...
.
Additional features include an interactive tracing tool, for manually stepping through proof attempts and a module for viewing and manipulating
hierarchical
A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important ...
proofs.
Planned features
Features currently being implemented, or planned for the future, are an expanded set of
proof critics, suitable for use in higher order domains, dynamic relational rippling, a
rippling heuristic suitable for rippling over
relational expressions as opposed to
functional
Functional may refer to:
* Movements in architecture:
** Functionalism (architecture)
** Form follows function
* Functional group, combination of atoms within molecules
* Medical conditions without currently visible organic basis:
** Functional sy ...
expressions, again suitable for use in higher order domains, and integration of IsaPlanner with
Proof General.
References
{{Reflist
External links
IsaPlanner project pageMathematical Reasoning Group
Automated theorem proving