Extractor for fractions, where numerator and denominator are expressions from the underlying ring
Extractor for fractions, where numerator and denominator are expressions from the underlying ring
Addition gives rise to an Abelian group
Addition gives rise to an Abelian group
Axioms defining the theory; such axioms are simply added as formulae to the problem to be proven, and thus handled using the standard reasoning techniques (including e-matching).
Function used internally to represent the unique denominator for all fractions
Function used internally to represent the unique denominator for all fractions
Optionally, other theories that this theory depends on.
Division operation
Division operation
Domain of the ring
Domain of the ring
Optionally, a function evaluating theory functions applied to concrete arguments, represented as constructor terms.
Optionally, a function evaluating theory functions applied to concrete arguments, represented as constructor terms.
Optionally, a function evaluating theory predicates applied to concrete arguments, represented as constructor terms.
Optionally, a function evaluating theory predicates applied to concrete arguments, represented as constructor terms.
Add the symbols defined by this theory to the order
Add the symbols defined by this theory to the order
Function to represent fractions, where numerator and denominator are expressions from the underlying ring
Function to represent fractions, where numerator and denominator are expressions from the underlying ring
Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).
Information which of the predicates satisfy the functionality axiom; at some internal points, such predicates can be handled more efficiently
Interpreted functions of the theory
If this theory defines any Theory.Decoder
, which
can translate model data into some theory-specific representation,
this function can be overridden to pre-compute required data
from a model.
If this theory defines any Theory.Decoder
, which
can translate model data into some theory-specific representation,
this function can be overridden to pre-compute required data
from a model.
Greater-than-or-equal operator
Greater-than-or-equal operator
Greater-than operator
Greater-than operator
Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination.
Optionally, a post-processor that is applied to formulas output by the
prover, for instance to interpolants or the result of quantifier
elimination. This method will be applied to the formula after
calling Internal2Inputabsy
.
Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.
Optionally, a stream of the constructor terms for this domain can be defined (e.g., the fractions with co-prime numerator and denominator).
Function to embed integers in the ring of fractions
Function to embed integers in the ring of fractions
Conversion of an integer term to a ring term
Conversion of an integer term to a ring term
Test whether a rational is integer.
Test whether a rational is integer.
Check whether we can tell that the given combination of theories is sound for checking satisfiability of a problem, i.e., if proof construction ends up in a dead end, can it be concluded that a problem is satisfiable.
Less-than-or-equal operator
Less-than-or-equal operator
Less-than operator
Less-than operator
Additive inverses
Additive inverses
Difference between two terms
Difference between two terms
Ring multiplication
Ring multiplication
Non-zero elements now give rise to an Abelian group
Non-zero elements now give rise to an Abelian group
Multiplication gives rise to an Abelian monoid
Multiplication gives rise to an Abelian monoid
The one element of this ring
The one element of this ring
Optionally, a plug-in implementing reasoning in this theory
Ring addition
Ring addition
Optionally, simplifiers that are applied to formulas output by the prover, for instance to interpolants or the result of quantifier.
Optionally, simplifiers that are applied to formulas output by the
prover, for instance to interpolants or the result of quantifier. Such
simplifiers are invoked by with ap.parser.Simplifier
.
Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination.
Optionally, a post-processor that is applied to formulas output by the
prover, for instance to interpolants or the result of quantifier
elimination. This method will be applied to the raw formulas, before
calling Internal2Inputabsy
.
Information how interpreted predicates should be handled for e-matching.
Interpreted predicates of the theory
Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.
Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.
N-ary sums
N-ary sums
Optionally, a plugin for the reducer applied to formulas both before and during proving.
Optionally, a plugin for the reducer applied to formulas both before and during proving.
Conversion of a rational term to an integer term, the floor operator.
Conversion of a rational term to an integer term, the floor operator.
Method that can be overwritten in sub-classes to term concrete fractions into canonical form.
When instantiating existentially quantifier formulas,
EX phi
, at most one instantiation is necessary
provided that all predicates in phi
are contained
in this set.
When instantiating existentially quantifier formulas,
EX phi
, at most one instantiation is necessary
provided that all predicates in phi
are contained
in this set.
N-ary sums
N-ary sums
num * s
num * s
Additional axioms that are included if the option
+genTotalityAxioms
is given to Princess.
A list of functions that should be considered in automatic trigger generation
The zero element of this ring
The zero element of this ring
The theory and field of rational numbers.