swish-0.10.0.0: A semantic web toolkit.

Copyright(c) 2003 Graham Klyne 2009 Vasili I Galchin
2011 2016 Douglas Burke
LicenseGPL V2
MaintainerDouglas Burke
Stabilityexperimental
PortabilityH98
Safe HaskellNone
LanguageHaskell98

Swish.Proof

Description

This module defines a framework for constructing proofs over some expression form. It is intended to be used with RDF graphs, but the structures aim to be quite generic with respect to the expression forms allowed.

It does not define any proof-finding strategy.

Synopsis

Documentation

data Proof ex Source #

Proof is a structure that presents a chain of rule applications that yield a result expression from a given expression

Constructors

Proof 

Fields

data Step ex Source #

Step in proof chain

The display name for a proof step comes from the display name of its consequence formula.

Constructors

Step 

Fields

Instances
Show ex => Show (Step ex) Source # 
Instance details

Defined in Swish.Proof

Methods

showsPrec :: Int -> Step ex -> ShowS #

show :: Step ex -> String #

showList :: [Step ex] -> ShowS #

checkProof :: (Expression ex, Ord ex) => Proof ex -> Bool Source #

Check consistency of given proof. The supplied rules and axioms are assumed to be correct.

explainProof :: (Expression ex, Ord ex) => Proof ex -> Maybe String Source #

Check proof. If there is an error then return information about the failing step.

checkStep Source #

Arguments

:: Ord ex 
=> [Rule ex]

rules

-> [ex]

antecedants

-> Step ex

the step to validate

-> Bool

True if the step is valid

A proof step is valid if rule is in list of rules and the antecedents are sufficient to obtain the conclusion and the antecedents are in the list of formulae already proven.

Note: this function depends on the ruleName of any rule being unique among all rules. In particular the name of the step rule being in correspondence with the name of one of the indicated valid rules of inference.

showProof Source #

Arguments

:: ShowLines ex 
=> String

newline string

-> Proof ex 
-> String 

Returns a simple string representation of a proof.

showsProof Source #

Arguments

:: ShowLines ex 
=> String

newline string

-> Proof ex 
-> ShowS 

Create a displayable form of a proof, returned as a ShowS value.

This function is intended to allow the calling function some control of multiline displays by providing:

  1. the first line of the proof is not preceded by any text, so it may be appended to some preceding text on the same line,
  2. the supplied newline string is used to separate lines of the formatted text, and may include any desired indentation, and
  3. no newline is output following the final line of text.

showsFormula Source #

Arguments

:: ShowLines ex 
=> String

newline

-> Formula ex

formula

-> ShowS 

Create a displayable form of a labelled formula