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
Optionally, other theories that this theory depends on.
Optionally, other theories that this theory depends on. Specified dependencies will be loaded before this theory, but the preprocessors of the dependencies will be called after the preprocessor of this theory.
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
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.
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).
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
Conversion of an integer term to a ring term
Conversion of an integer term to a ring term
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.
Additive inverses
Additive inverses
Difference between two terms
Difference between two terms
Ring multiplication
Ring multiplication
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
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.
Method that can be overwritten in sub-classes to term concrete fractions into canonical form.
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 of fractions
s / t
, withs, t
taken from some ring. The theory uses an encoding in which the same (fixed, but arbitrary) denominator is used for all expressions. The range of considered denominators is described by thedenomConstraint
argument over the variable_0
.