Swish.Datatype

This module defines the structures used to represent and manipulate datatypes. It is designed as a basis for handling datatyped RDF literals, but the functions in this module are more generic.

Documentation

data Datatype ex lb vn

Datatype wraps a DatatypeVal value, hiding the value type that is used only in implementations of the datatype. Users see just the datatype name and associated ruleset.

Constructors

forall vt. Datatype (DatatypeVal ex vt lb vn)

typeName :: Datatype ex lb vn -> ScopedName

Get type name from Datatype value

typeRules :: Datatype ex lb vn -> Ruleset ex

Get static rules from Datatype value

typeMkRules :: Datatype ex lb vn -> ex -> [Rule ex]

Make rules for Datatype value based on supplied expression

typeMkModifiers :: Datatype ex lb vn -> [OpenVarBindingModify lb vn]

Make variable binding modifiers based on values supplied

typeMkCanonicalForm :: Datatype ex lb vn -> Text -> Maybe Text

Get the canonical form of a datatype value.

getTypeAxiom :: ScopedName -> Datatype ex lb vn -> Maybe (Formula ex)

Get the named axiom from a Datatype value.

getTypeRule :: ScopedName -> Datatype ex lb vn -> Maybe (Rule ex)

Get the named rule from a Datatype value.

data DatatypeVal ex vt lb vn

DatatypeVal is a structure that defines a number of functions and values that characterize the behaviour of a datatype.

A datatype is specified with respect to (polymophic in) a given type of (syntactic) expression with which it may be used, and a value type (whose existence is hidden as an existential type within DatatypeMap).

(I tried hiding the value type with an internal existential declaration, but that wouldn't wash. Hence this two-part structure with Datatype in which the internal detail of the value type is hidden from users of the Datatype class.)

The datatype characteristic functions have two goals:

1. to support the general datatype entailment rules defined by the RDF semantics specification, and
2. to define additional datatype-specific inference patterns by means of which provide additional base functionality to applications based on RDF inference.

Datatype-specific inferences are provided using the DatatypeRel structure for a datatype, which allows a number of named relations to be defined on datatype values, and provides mechanisms to calculate missing values in a partially-specified member of a relation.

Note that rules and variable binding modifiers that deal with combined values of more than one datatype may be defined separately. Definitions in this module are generally applicable only when using a single datatype.

An alternative model for datatype value calculations is inspired by that introduced by CWM for arithmetic operations, e.g.

    (1 2 3) math:sum ?x => ?x rdf:value 6

(where the bare integer n here is shorthand for "n"^^xsd:integer).

Datatype-specific inference patterns are provided in two ways:

• by variable binding modifiers that can be combined with the query results during forward- for backward-chaining of inference rules, and
• by the definition of inference rulesets that involve datatype values.

I believe the first method to be more flexible than the second, in that it more readily supports forward and backward chaining, but can be used only through the definition of new rules.

Type parameters:

ex

is the type of expression with which the datatype may be used.

vt

is the internal value type with which the labels are associated.

lb

is the type of label that may be used as a variable in an expression or rule.

vn

is the type of node that may be used to carry a value in an expression or rule.

Constructors

DatatypeVal

Fields

• tvalName :: ScopedName

  Identifies the datatype, and also its value space class.

• tvalRules :: Ruleset ex

  A set of named expressions and rules that are valid in in any theory that recognizes the current datatype.

• tvalMkRules :: ex -> [Rule ex]

  A function that accepts an expression and devives some datatype-dependent rules from it. This is provided as a hook for creating datatyped class restriction rules.

• tvalMkMods :: [OpenVarBindingModify lb vn]

  Constructs a list of open variable binding modifiers based on tvalMod, but hiding the actual value type.

• tvalMap :: DatatypeMap vt

  Lexical to value mapping, where vt is a datatype used within a Haskell program to represent and manipulate values in the datatype's value space

• tvalRel :: [DatatypeRel vt]

  A set of named relations on datatype values. Each relation accepts a list of Maybe vt, and computes any unspecified values that are in the relation with values supplied.

• tvalMod :: [DatatypeMod vt lb vn]

  A list of named values that are used to construct variable binding modifiers, which in turn may be used by a rule definition.

  TODO: In due course, this value may be calculated automatically from the supplied value for tvalRel.

getDTMod :: ScopedName -> DatatypeVal ex vt lb vn -> Maybe (DatatypeMod vt lb vn)

Return the named datatype value modifier, if it exists.

getDTRel :: ScopedName -> DatatypeVal ex vt lb vn -> Maybe (DatatypeRel vt)

Return the named datatype relation, if it exists.

tvalMkCanonicalForm :: DatatypeVal ex vt lb vn -> Text -> Maybe Text

Get the canonical form of a datatype value, or Nothing.

data DatatypeMap vt

DatatypeMap consists of methods that perform lexical-to-value and value-to-canonical-lexical mappings for a datatype.

The datatype mappings apply to string lexical forms which are stored as Text.

Constructors

DatatypeMap

Fields

• mapL2V :: Text -> Maybe vt

  Function to map a lexical string to the datatype value. This effectively defines the lexical space of the datatype to be all strings for which yield a value other than Nothing.

• mapV2L :: vt -> Maybe Text

  Function to map a value to its canonical lexical form, if it has such.

data DatatypeRel vt

Datatype for a named relation on values of a datatype.

Constructors

DatatypeRel

Fields

• dtRelName :: ScopedName
• dtRelFunc :: DatatypeRelFn vt

type DatatypeRelFn vt = [Maybe vt] -> Maybe [[vt]]

Type for a datatype relation inference function.

A datatype relation defines tuples of values that satisfy some relation. A datatype relation inference function calculates values that complete a relation with values supplied.

The function accepts a list of Maybe vt, where vt is the datatype value type. It returns one of:

• Just a list of lists, where each inner list returned is a complete set of values, including the values supplied, that are in the relation.
• Just an empty list is returned if the supplied values are insufficient to compute any complete sets of values in the relation.
• Nothing if the supplied values are not consistent with the relation.

type DatatypeRelPr vt = [vt] -> Bool

Type for datatype relation predicate: accepts a list of values and determines whether or not they satisfy the relation.

altArgs

Arguments

:: Eq vt

=> DatatypeRelPr vt

-> [(vt -> Bool, [b])]

a list of argument value predicates and function descriptors. The predicate indicates any additional constraints on argument values (e.g. the result of abs must be positive). Use (const True) for the predicate associated with unconstrained relation arguments. For each argument, a list of function descriptors is supplied corresponding to alternative values (e.g. a square relation would offer two alternative values for the root.)

-> ((vt -> Bool) -> b -> [Maybe vt] -> Maybe [vt])

a function that takes an argument value predicate, a function descriptor and applies it to a supplied argument list to return: Just a calculated list of one or more possible argument values, Just [] indicating insufficient information provided, or Nothing indicating inconsistent information provided. May be one of unaryFnApp, binaryFnApp, listFnApp or some other caller-supplied value.

-> DatatypeRelFn vt

The return value can be used as the dtRelFunc component of a DatatypeRel value.

Given a list of argument values and a list of functions for calculating new values from supplied values, return a list of argument values, or Nothing if the supplied values are inconsistent with the calculations specified.

Each list of values returned corresponds to a set of values that satisfy the relation, consistent with the values supplied.

Functions are described as tuple consisting of:

(a) a predicate that the argument is required to satisfy

(b) a function to apply,

(c) a function to apply function (b) to a list of arguments

(d) argument list index values to which the function is applied.

Each supplied argument is of the form Maybe a, where the argument has value type a. Nothing indicates arguments of unknown value.

The basic idea is that, for each argument position in the relation, a function may be supplied to calculate that argument's possible values from some combination of the other arguments. The results calculated in this way are compared with the original arguments provided: if the values conflict then the relation is presumed to be unsatisfiable with the supplied values, and Nothing is returned; if there are any calculated values for arguments supplied without any values, then tbe calculated values are used. If there are any arguments for which no values are supplied or calculated, then the relation is presumed to be underdetermined, and Just [] is returned.

type UnaryFnDescr a = (a -> a, Int)

altArgs support for unary functions: function descriptor type

type UnaryFnTable a = [(a -> Bool, [UnaryFnDescr a])]

altArgs support for unary functions: function descriptor table type

type UnaryFnApply a = (a -> Bool) -> UnaryFnDescr a -> [Maybe a] -> Maybe [a]

altArgs support for unary functions: function applicator type

unaryFnApp :: UnaryFnApply a

altArgs support for unary functions: function applicator

type BinaryFnDescr a = (a -> a -> a, Int, Int)

altArgs support for binary functions: function descriptor type

type BinaryFnTable a = [(a -> Bool, [BinaryFnDescr a])]

altArgs support for binary functions: function descriptor table type

type BinaryFnApply a = (a -> Bool) -> BinaryFnDescr a -> [Maybe a] -> Maybe [a]

altArgs support for binary functions: function applicator type

binaryFnApp :: BinaryFnApply a

altArgs support for binary functions: function applicator

type BinMaybeFnDescr a = (a -> a -> Maybe [a], Int, Int)

altArgs support for binary function with provision for indicating inconsistent supplied values: function descriptor type

type BinMaybeFnTable a = [(a -> Bool, [BinMaybeFnDescr a])]

altArgs support for binary function with provision for indicating inconsistent supplied values: function descriptor table type

type BinMaybeFnApply a = (a -> Bool) -> BinMaybeFnDescr a -> [Maybe a] -> Maybe [a]

altArgs support for binary function with provision for indicating inconsistent supplied values: function applicator type

binMaybeFnApp :: BinMaybeFnApply a

altArgs support for binary function with provision for indicating inconsistent supplied values: function applicator

type ListFnDescr a = (a -> a -> a, a, a -> a -> a, Int)

altArgs support for list functions (e.g. sum over list of args), where first element of list is a fold over the rest of the list, and remaining elements of list can be calculated in terms of the result of the fold and the remaining elements

List function descriptor is

(a) list-fold function, f (e.g. (+)

(b) list-fold identity, z (e.g. 0)

(c) list-fold-function inverse, g (e.g. (-))

(d) index of element to evaluate

such that:

   (a `f` z) == (z `f` a) == a
   (a `g` c) == b <=> a == b `f` c
   (a `g` z) == a
   (a `g` a) == z

and the result of the folded function does not depend on the order that the list elements are processed.

NOTE: the list of ListFnDescr values supplied to altArgs must be at least as long as the argument list. In many cases, Haskell lazy evaluation can be used to supply an arbitrarily long list. See test cases in spike-altargs.hs for an example.

Function descriptor type

type ListFnTable a = [(a -> Bool, [ListFnDescr a])]

Function table type

type ListFnApply a = (a -> Bool) -> ListFnDescr a -> [Maybe a] -> Maybe [a]

altArgs support for list functions: function applicator type

listFnApp :: ListFnApply a

altArgs support for list functions: function applicator

data DatatypeMod vt lb vn

Wrapper for data type variable binding modifier included in a datatype value.

Constructors

DatatypeMod

Fields

• dmName :: ScopedName
• dmModf :: [ModifierFn vt]
• dmAppf :: ApplyModifier lb vn

type ModifierFn vn = [vn] -> [vn]

Datatype value modifier functions type

Each function accepts a list of values and returns a list of values. The exact significance of the different values supplied and returned depends on the variable binding pattern used (cf. ApplyModifier), but in all cases an empty list returned means that the corresponding inputs are not consistent with the function and cannot be used.

type ApplyModifier lb vn = ScopedName -> [ModifierFn vn] -> OpenVarBindingModify lb vn

Type of function used to apply a data value modifier to specified variables in a supplied variable binding. It also accepts the name of the datatype modifier and carries it into the resulting variable binding modifier.

(Note that vn is not necessarily the same as vt, the datatype value type: the modifier functions may be lifted or otherwise adapted to operate on some other type from which the raw data values are extracted.)

nullDatatypeMod :: DatatypeMod vt lb vn

Null datatype value modifier

makeVmod11inv :: (Ord lb, Ord vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a 1->1 function and inverse, such as negate.

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [x,y] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if x and y are in the appropriate relationship.
2. is [y] -> [x], used to perform the calculation in a forward direction.
3. is [x] -> [y], used to perform the calculation in a backward direction. This may be the same as (2) (e.g. for negation) or may be different (e.g. increment).

lbs

is a list of specific label values for which a variable binding modifier will be generated. (The intent is that a variable-free value can be generated as a Curried function, and instantiated for particular variables as required.)

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

makeVmod11 :: (Ord lb, Ord vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a non-invertable 1->1 injection, such as absolute value.

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [x,y] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if x and y are in the appropriate relationship.
2. is [x] -> [y], used to perform the calculation.

lbs

is a list of specific label values for which a variable binding modifier will be generated.

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

makeVmod21inv :: (Ord lb, Ord vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a 2->1 invertable function, such as addition or subtraction.

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [x,y,z] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if x, y and z are in the appropriate relationship.
2. is [y,z] -> [x], used to perform the calculation in a forward direction.
3. is [x,z] -> [y], used to run the calculation backwards to determine the first input argument
4. is [x,y] -> [z], used to run the calculation backwards to determine the second input argument

lbs

is a list of specific label values for which a variable binding modifier will be generated.

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

makeVmod21 :: (Ord lb, Ord vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a 2->1 non-invertable function, such as logical AND or OR.

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [x,y,z] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if x, y and z are in the appropriate relationship.
2. is [y,z] -> [x], used to perform the calculation in a forward direction.

lbs

is a list of specific label values for which a variable binding modifier will be generated.

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

makeVmod20 :: (Eq lb, Show lb, Eq vn, Show vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a simple comparson of two values.

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [x,y] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if x and y are in the appropriate relationship.

lbs

is a list of specific label values for which a variable binding modifier will be generated.

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

makeVmod22 :: (Ord lb, Ord vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a 2->2 non-invertable function, such as quotient/remainder

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [w,x,y,z] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if w, x, y and z are in the appropriate relationship.
2. is [y,z] -> [w,x], used to perform the calculation given two input values.

lbs

is a list of specific label values for which a variable binding modifier will be generated.

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

NOTE: this might be generalized to allow one of w or x to be specified, and return null if it doesn't match the calculated value.

makeVmodN1 :: (Ord lb, Ord vn) => ApplyModifier lb vn

ApplyModifier function for use with DatatypeMod in cases when the value mapping is a N->1 function, such as Sigma (sum) of a vector.

nam

is the name from the DatatypeMod value that is carried into the resulting variable binding modifier.

fns

are functions used to implement details of the variable binding modifier:

1. is [x,y...] -> [?], used as a filter (i.e. not creating any new variable bindings), returning a non-empty list if x and y... are in the appropriate relationship.
2. is [y...] -> [x], used to perform the calculation.

lbs

is a list of specific label values for which a variable binding modifier will be generated.

Note: an irrefutable pattern match for lbs is used so that a name for the VarBindingModify value can be extracted using an undefined label value.

data DatatypeSub ex lb vn supvt subvt

Describe a subtype/supertype relationship between a pair of datatypes.

Originally, I had this as a supertype field of the DatatypeVal structure, but that suffered from some problems:

• supertypes may be introduced retrospectively,
• the relationship expressed with respect to a single datatype cannot indicate how to do injections/restrictions between the underlying value types.

ex

is the type of expression with which the datatype may be used.

lb

is the type of the variable labels used.

vn

is the type of value node used to contain a datatyped value

supvt

is the internal value type of the super-datatype

subvt

is the internal value type of the sub-datatype

Constructors

DatatypeSub

Fields

• trelSup :: DatatypeVal ex supvt lb vn

  Datatype that is a supertype of trelSub, having value space supvt.

• trelSub :: DatatypeVal ex subvt lb vn

  Datatype that is a subtype of trelSup, having value space supvt.

• trelToSup :: subvt -> supvt

  Function that maps subtype value to corresponding supertype value.

• trelToSub :: supvt -> Maybe subvt

  Function that maps supertype value to corresponding subtype value, if there is such a value.