IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically. The system provides an interactive tracing tool that allows you to interact the proof planning attempt. (see the screenshot of IsaPlanner being used with Isabelle and Proof General) It is based on the Isabelle theorem prover and the Isar language. The main proof technique written in IsaPlanner is an inductive theorem prover based on Rippling. This is applicable within Isabelle's Higher Order Logic, and can easily be adapted to Isabelle's other logics. The system now the main platform for proof planning research in the Edinburgh mathematical reasoning group
In the fully expansive (or LCF-style) approach to theorem proving, theorems are represented by an abstract type whose primitive operations are the axioms and inference rules of a logic. Theorem proving tools are implemented by composing together the inference rules using ML programs. This idea can be generalised to computing valid judgements that represent other kinds of information. In particular, consider judgements (a,r,t,b), where a is a set of boolean terms (assumptions) that are assumed true, r represents a variable order, t is a boolean term all of whose free variables are boolean and b is a BDD. Such a judgement is valid if under the assumptions a, the BDD representing t with respect to r is b, and we will write a r t --> b when this is the case. The derivation of "theorems" like a r t --> b can be viewed as "proof" in the style of LCF by defining an abstract type term_bdd that models judgements a r t --> b analogously to the way the type thm models theorems |- t.
HOL4 is the latest version of the HOL interactive proof assistant for higher order logic: a programming environment in which theorems can be proved and proof tools implemented. Built-in decision procedures and theorem provers can automatically establish many simple theorems (users may have to prove the hard theorems themselves!) An oracle mechanism gives access to external programs such as SAT and BDD engines. HOL 4 is particularly suitable as a platform for implementing combinations of deduction, execution and property checking. several widely used versions of the HOL system: 1. HOL88 from Cambridge; 2. HOL90 from Calgary and Bell Labs; 3. HOL98 from Cambridge, Glasgow and Utah. HOL 4 is the successor to these. Its development was partly supported by the PROSPER project. HOL 4 is based on HOL98 and incorporates ideas and tools from HOL Light. The ProofPower system is another implementation of HOL.