swish-0.10.9.0: A semantic web toolkit.
Copyright(c) 2003 Graham Klyne 2009 Vasili I Galchin 2011 2012 2022 Douglas Burke
LicenseGPL V2
MaintainerDouglas Burke
Stabilityexperimental
PortabilityCPP, DerivingStrategies, OverloadedStrings
Safe HaskellSafe-Inferred
LanguageHaskell2010

Swish.Rule

Description

This module defines a framework for defining inference rules 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.

Synopsis

Documentation

class Eq ex => Expression ex where Source #

Expression is a type class for values over which proofs may be constructed.

Methods

isValid :: ex -> Bool Source #

Is expression true in all interpretations? If so, then its truth is assumed without justification.

Instances

Instances details
(LDGraph lg lb, Eq (lg lb)) => Expression (lg lb) Source #

Instances of LDGraph are also instance of the Expression class, for which proofs can be constructed. The empty RDF graph is always True (other enduring truths are asserted as axioms).

Instance details

Defined in Swish.RDF.Proof

Methods

isValid :: lg lb -> Bool Source #

data Formula ex Source #

A Formula is a named expression.

Constructors

Formula 

Fields

Instances

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

Defined in Swish.Rule

Methods

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

show :: Formula ex -> String #

showList :: [Formula ex] -> ShowS #

Eq (Formula ex) Source #

Define equality of formulae as equality of formula names

Instance details

Defined in Swish.Rule

Methods

(==) :: Formula ex -> Formula ex -> Bool #

(/=) :: Formula ex -> Formula ex -> Bool #

Ord (Formula ex) Source #

Define ordering of formulae based on formula names

Instance details

Defined in Swish.Rule

Methods

compare :: Formula ex -> Formula ex -> Ordering #

(<) :: Formula ex -> Formula ex -> Bool #

(<=) :: Formula ex -> Formula ex -> Bool #

(>) :: Formula ex -> Formula ex -> Bool #

(>=) :: Formula ex -> Formula ex -> Bool #

max :: Formula ex -> Formula ex -> Formula ex #

min :: Formula ex -> Formula ex -> Formula ex #

data Rule ex Source #

Rule is a data type for inference rules that can be used to construct a step in a proof.

Constructors

Rule 

Fields

  • ruleName :: ScopedName

    Name of rule, for use when displaying a proof

  • fwdApply :: [ex] -> [ex]

    Forward application of a rule, takes a list of expressions and returns a list (possibly empty) of forward applications of the rule to combinations of the antecedent expressions. Note that all of the results returned can be assumed to be (simultaneously) true, given the antecedents provided.

  • bwdApply :: ex -> [[ex]]

    Backward application of a rule, takes an expression and returns a list of alternative antecedents, each of which is a list of expressions that jointly yield the given consequence through application of the inference rule. An empty list is returned if no antecedents will allow the consequence to be inferred.

  • checkInference :: [ex] -> ex -> Bool

    Inference check. Takes a list of antecedent expressions and a consequent expression, returning True if the consequence can be obtained from the antecedents by application of the rule. When the antecedents and consequent are both given, this is generally more efficient that using either forward or backward chaining. Also, a particular rule may not fully support either forward or backward chaining, but all rules are required to fully support this function.

    A default implementation based on forward chaining is given below.

Instances

Instances details
Show (Rule ex) Source # 
Instance details

Defined in Swish.Rule

Methods

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

show :: Rule ex -> String #

showList :: [Rule ex] -> ShowS #

Eq (Rule ex) Source #

Define equality of rules as equality of the rule names.

Instance details

Defined in Swish.Rule

Methods

(==) :: Rule ex -> Rule ex -> Bool #

(/=) :: Rule ex -> Rule ex -> Bool #

Ord (Rule ex) Source #

Define ordering of rules based on the rule names.

Instance details

Defined in Swish.Rule

Methods

compare :: Rule ex -> Rule ex -> Ordering #

(<) :: Rule ex -> Rule ex -> Bool #

(<=) :: Rule ex -> Rule ex -> Bool #

(>) :: Rule ex -> Rule ex -> Bool #

(>=) :: Rule ex -> Rule ex -> Bool #

max :: Rule ex -> Rule ex -> Rule ex #

min :: Rule ex -> Rule ex -> Rule ex #

type RuleMap ex = Map ScopedName (Rule ex) Source #

A set of rules labelled with their name.

nullScope :: Namespace Source #

The namespace http://id.ninebynine.org/2003/Ruleset/null with the prefix null:.

nullSN Source #

Arguments

:: LName

local name.

-> ScopedName 

Create a scoped name with the null namespace.

nullFormula :: Formula ex Source #

The null formula.

nullRule :: Rule ex Source #

The null rule.

fwdCheckInference Source #

Arguments

:: Eq ex 
=> Rule ex

rule

-> [ex]

antecedants

-> ex

consequence

-> Bool 

Checks that consequence is a result of applying the rule to the antecedants.

bwdCheckInference Source #

Arguments

:: Eq ex 
=> Rule ex

rule

-> [ex]

antecedants

-> ex

consequence

-> Bool 

Checks that the antecedants are all required to create the consequence using the given rule.

showsFormula Source #

Arguments

:: ShowLines ex 
=> String

newline

-> Formula ex

formula

-> ShowS 

Create a displayable form of a labelled formula

showsFormulae Source #

Arguments

:: ShowLines ex 
=> String

newline

-> [Formula ex]

the formulae to show

-> String

text to be placed after the formulae

-> ShowS 

Return a displayable form of a list of labelled formulae

showsWidth :: Int -> String -> ShowS Source #

Show a string left justified in a field of at least the specified number of characters width.