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).
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).
Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).
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
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
Interpreted functions of the theory
Symbol representing proper (non-linear) multiplication
Optionally, a plug-in implementing reasoning in this theory
Optionally, a plug-in implementing reasoning in this theory
Information how interpreted predicates should be handled for e-matching.
Information how interpreted predicates should be handled for e-matching.
Interpreted predicates of the theory
Interpreted predicates of the theory
Additional axioms that are included if the option
+genTotalityAxioms
is given to Princess.
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
A list of functions that should be considered in automatic trigger generation
Convert the given expression to this multiplication theory
Convert the given expression to this multiplication theory
Convert the given expression to this multiplication theory
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.
Euclidian division
Euclidian remainder
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
Floor division
Floor remainder
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 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 pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover. This method will be applied very early in the translation process.
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.
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.
Multiply two terms, using the mul
function if necessary;
if any of the two terms is constant, normal Presburger
multiplication will be used.
Multiply two terms, using the mul
function if necessary;
if any of the two terms is constant, normal Presburger
multiplication will be used.
Multiply two terms, using the mul
function if necessary;
if any of the two terms is constant, normal Presburger
multiplication will be used, and simple terms will directly be simplified.
Multiply two terms, using the mul
function if necessary;
if any of the two terms is constant, normal Presburger
multiplication will be used, and simple terms will directly be simplified.
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
.
Exponentiation, with non-negative exponent
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.
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.
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.
Truncation division
Truncation remainder
Trait for theories providing general, non-linear multiplication.