Extractor for fractions, where numerator and denominator are expressions from the underlying ring.

Object to construct and identify fractions, consisting of a numerator and a denominator. Fractions are internally represented using either the function frac, for proper fractions, or function fromRing for ring elements cast to a fraction.

The theory is not complete for the full first-order case; check whether the denom function occurs in the scope of a quantifier.

Extractor for ring elements embedded into the ring of fractions.

Function to represent sums of terms.

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. 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

Divide each term of a sum by the denom() term, rewriting accordingly. Constant terms are dropped and their sum is returned as the second result.

Function to represent division.

Domain of the ring

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.

A simplification function that applies the methods evalFun and evalPred to some given expression (but not recursively). This is used in the Theory.postSimplifiers methods.

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 embed ring elements in the ring of fractions.

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.

Greater-than-or-equal 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. 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. This method will be applied very early in the translation process.

Hack to enable other theories to use rationals even in axioms with quantifiers. This should be removed as soon as the incompatibility of rationals and quantifiers has been resolved.

Optionally, a stream of the constructor terms for this domain can be defined (e.g., the fractions with co-prime numerator and denominator).

Conversion of an integer term to a ring term

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 predicate.

Less-than-or-equal predicate.

Less-than operator

Additive inverses

Difference between two terms

Optionally, a set of predicates used by the theory to tell the PresburgerModelFinder about terms that will be handled exclusively by this theory. If a proof goal in model generation mode contains an atom p(x), for p in this set, then the PresburgerModelFinder will ignore x when assigning concrete values to symbols.

Ring multiplication

Function to represent a product of a fraction, represented using numerator and denominator, with a fraction term.

Function to represent a product of a ring term with a fraction term.

Function to represent products of terms.

Non-zero elements now give rise to an Abelian group

Multiplication gives rise to an Abelian monoid

The one element of this ring

Optionally, a plug-in implementing reasoning in this theory

Ring addition

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 ap.parser.Simplifier. By default, this list will only include the evaluatingSimplifier.

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.

N-ary sums

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.

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.

N-ary sums

num * s, where num must be an integer term.

num * s

Additional axioms that are included if the option +genTotalityAxioms is given to Princess.

Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.

A list of functions that should be considered in automatic trigger generation

The zero element of this ring