Copyright	(c) 2003 Graham Klyne 2009 Vasili I Galchin 2011 2016 2022 2024 Douglas Burke
License	GPL V2
Maintainer	Douglas Burke
Stability	experimental
Portability	CPP, DerivingStrategies
Safe Haskell	Safe-Inferred
Language	Haskell2010

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

data Proof ex = Proof {
- proofContext :: [Ruleset ex]
- proofInput :: Formula ex
- proofResult :: Formula ex
- proofChain :: [Step ex]
}
data Step ex = Step {
- stepRule :: Rule ex
- stepAnt :: [Formula ex]
- stepCon :: Formula ex
}
checkProof :: (Expression ex, Ord ex) => Proof ex -> Bool
explainProof :: (Expression ex, Ord ex) => Proof ex -> Maybe String
checkStep :: Ord ex => [Rule ex] -> [ex] -> Step ex -> Bool
showProof :: ShowLines ex => String -> Proof ex -> String
showsProof :: ShowLines ex => String -> Proof ex -> ShowS
showsFormula :: ShowLines ex => String -> Formula ex -> ShowS

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 proofContext :: [Ruleset ex] Proof context: list of rulesets, each of which provides a number of axioms and rules. proofInput :: Formula ex Given expression proofResult :: Formula ex Result expression proofChain :: [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
Fields stepRule :: Rule ex Inference rule used stepAnt :: [Formula ex] Antecedents of inference rule stepCon :: Formula ex Named consequence of inference rule

Instances

Instances details

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:

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,
the supplied newline string is used to separate lines of the formatted text, and may include any desired indentation, and
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