swish- A semantic web toolkit.

Copyright(c) 2003, Graham Klyne, 2009 Vasili I Galchin, 2011 Douglas Burke
LicenseGPL V2
MaintainerDouglas Burke
Safe HaskellNone



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.



data Proof ex Source

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




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.




stepRule :: Rule ex

Inference rule used

stepAnt :: [Formula ex]

Antecedents of inference rule

stepCon :: Formula ex

Named consequence of inference rule


Show ex => Show (Step ex) 

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


:: (Expression ex, Ord ex) 
=> [Rule ex]


-> [ex]


-> 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


:: ShowLines ex 
=> String

newline string

-> Proof ex 
-> String 

Returns a simple string representation of a proof.

showsProof Source


:: 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


:: ShowLines ex 
=> String


-> Formula ex


-> ShowS 

Create a displayable form of a labelled formula