A list of (other) theories that are implicitly declared as a side-effect of declaring this theory. We assume that theories can implicitly define some of their dependencies, but not vice versa.

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).

The number of elements per sort, or None for infinite sorts.

The constructors of the ADT

Function symbols representing the index of the head symbol of a constructor term

List the constructors belonging to each sort; the constructors are identified with the position of a constructor in the sequence ctorSignatures.

Compute the size (number of constructor occurrences) of a constructor term; return None if parts of the term are symbolic, and the size cannot be determined.

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.

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

Translate a function belonging to this theory to an SMT-LIB identifier.

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.

Get the constructor number ctorNum of sort sortNum.

Query the constructor type of a term; the given id is the position of a constructor in the sequence ctorSignatures.

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.

Enum sorts, i.e., sorts with only nullary constructors.

Recursive sorts, i.e., sorts that can appear (directly or indirectly) as sort of subterms of its own terms.

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.

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.

Optionally, a plug-in implementing reasoning in this theory

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.

Translate a predicate belonging to this theory to an SMT-LIB identifier.

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.

Print an SMT-LIB declaration of this theory; do not output anything if the theory does not need to be declared.

Optionally, a plugin for the reducer applied to formulas both before and during proving.

Rewrite a formula prior to solving; e.g., add selector and tester constraints

The selectors of the ADT

When instantiating existentially quantifier formulas, EX phi, at most one instantiation is necessary provided that all predicates in phi are contained in this set.

Translate a sort belonging to this theory to an SMT type.

The sort sorts(n) belonging to the constructor constructors(ctorNum).

The strongly connected components among the ADTs sorts.

Function symbols representing (relative) depth of constructor terms. The symbols are only available for measure == ADT.TermMeasure.RelDepth

Function symbols representing absolute size of constructor terms. The symbols are only available for measure == ADT.TermMeasure.Size

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

Extractor to recognise sorts belonging to this ADT.