swish-0.10.0.3: A semantic web toolkit.

Copyright (c) 2003 Graham Klyne 2009 Vasili I Galchin2011 2016 Douglas Burke GPL V2 Douglas Burke experimental H98 None Haskell98

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 FieldsproofContext :: [Ruleset ex]Proof context: list of rulesets, each of which provides a number of axioms and rules.proofInput :: Formula exGiven expressionproofResult :: Formula exResult expressionproofChain :: [Step ex]Chain of inference rule applications progressing from input to result

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 FieldsstepRule :: Rule exInference rule usedstepAnt :: [Formula ex]Antecedents of inference rulestepCon :: Formula exNamed consequence of inference rule
Instances
 Show ex => Show (Step ex) Source # Instance detailsDefined in Swish.Proof MethodsshowsPrec :: 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.

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.

Arguments

 :: ShowLines ex => String newline string -> Proof ex -> String

Returns a simple string representation of a proof.

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.

Arguments

 :: ShowLines ex => String newline -> Formula ex formula -> ShowS

Create a displayable form of a labelled formula