Hets - the Heterogeneous Tool Set

Safe HaskellSafe

Logic

Description

The folder Logic contains the infrastructure needed for presenting a logic to Hets. A logic here is understood in the theory of institutions. More precisely, a logic is an entailment system in the sense of Meseguer. An entailment system consists of a category of signatures and signature morphisms, a set of sentences for each signature, a sentence translation map of each signature morphism, and an entailment relation between sets of sentences and sentences for each signature.

The module Logic.Logic contains all the type classes for interfacing entailment systems in this sense, including the type class Logic. The entailment relation is given by one or more theorem provers, rewriters, consistency checkers, model checkers. The module Logic.Prover is for the interface to these. The data types Proof_Status and Prover provides the interface to provers. In case of a successful proof, also the list of axioms that have been used in the proof can be returned.

Note that the type class Logic contains much more than just an entailment system. There is infrastructure for parsing, printing, static analysis (of both basic specifications and symbols maps) , conversion to ATerms, sublogic recognition etc. You see that in order to really work with it, one needs much more than just an entailment system in the mathematical sense. We will use the term logic synonymously with an extended entailment system in this sense.

The type class LogicalFramework is an interface for the logics which can be used as logical frameworks, in which object logics can be specified by the user. Its methods are used in the analysis of newlogic definitions, in Framework.Analysis.

The method base_sig returns the base signature of the framework The method write_logic constructs the contents of the Logic_L file, where L is the name of the object logic passed as an argument. Typically, this file will declare the lid of the object logic L and instances of the classes Language, Syntax, Sentences, Logic, and StaticAnalysis. The instance of Category is usually inherited from the framework itself as the object logic reuses the signatures and morphisms of the framework. The function write_syntax constructs the contents of the file declaring the Ltruth morphism. Currently we simply store the morphism using its representation as a Haskell datatype value.

Module Logic.Comorphism provides type classes for the various kinds of mappings between logics, and module Logic.Grothendieck realizes the Grothendieck logic and also contains a type LogicGraph.

How to add a new logic to Hets

A good idea is to look at an existing logic, say Propositional or CASL, and look how it realizes the abstract interface given in Logic.Logic - this is done in Propositional.Logic_Propositional resp. CASL.Logic_CASL, where the whole of the Propositional resp. CASL folder is imported.

You also should have a look at some of the Common modules, providing data structures for identifiers (Common.Id), results (Common.Result), and relations (Common.Lib.Rel). These are used quite frequently.