ModuloArithmetic
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package bitvectors
Generic class to represent families of functions, indexed by a vector of bit-widths.
Modulo sorts, representing the interval
[lower, upper] with wrap-around arithmetic.
Modulo sorts, representing the interval
[lower, upper] with wrap-around arithmetic.
Object to create and recognise modulo sorts representing signed bit-vectors.
Object to create and recognise modulo sorts representing unsigned bit-vectors.
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).
Cast a term to an integer term.
Cast a term to an integer interval, with modulo semantics.
Cast a term to a signed bit-vector term.
Cast a term to a modulo sort.
Cast a term to an unsigned bit-vector term.
Compute the smallest number n such that all numbers in the
interval [min(a, b), max(a, b)] have bits at and above
n in common.
For instance, commonBitsLB(11, 14) == Some(3)
and commonBitsLB(1, -1) == None.
11 = 1011_2
14 = 1110_2
Compute the smallest number n such that all numbers in the
interval [min(a, b), max(a, b)] have bits at and above
n in common.
For instance, commonBitsLB(11, 14) == Some(3)
and commonBitsLB(1, -1) == None.
11 = 1011_2
14 = 1110_2
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.
Evaluate bv_extract with concrete arguments
Evaluate bv_extract with concrete arguments
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.
Evaluate mod_cast with concrete arguments
Evaluate mod_cast with concrete arguments
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.
A simplification function that applies the methods evalFun
and evalPred to some given expression (but not recursively).
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
Add the symbols defined by this theory to the order
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
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.
Function to map the modulo-sorts back to integers.
Function to map the modulo-sorts back to integers. Semantically this is just the identify function
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.
Function for multiplying any number t with 2^n
and mapping to an interval [lower, upper].
Function for multiplying any number t with 2^n
and mapping to an interval [lower, upper].
The function is applied as l_shift_cast(lower, upper, t, n).
Function for mapping any number to an interval [lower, upper].
Function for mapping any number to an interval [lower, upper].
The function is applied as mod_cast(lower, upper, number)
Optionally, a set of predicates used by the theory to tell the
PresburgerModelFinder about terms that will be handled
exclusively by this theory.
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, 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.
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.
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.
Information how interpreted predicates should be handled for e-matching.
Interpreted predicates of the theory
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.
Function for dividing any number t by 2^n,
rounding towards negative, and mapping to an interval [lower, upper].
Function for dividing any number t by 2^n,
rounding towards negative, and mapping to an interval [lower, upper].
The function is applied as r_shift_cast(lower, upper, t, n).
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.
Run-length encoding of the least-significant size bits of
a number, starting with the number of least-significant zeroes.
Run-length encoding of the least-significant size bits of
a number, starting with the number of least-significant zeroes. Bits beyond
size are ignored.
Shift the term shifted a number of bits to the left,
staying within the given sort.
Shift the term shifted a number of bits to the left,
staying within the given sort.
Shift the term shifted a number of bits to the right,
staying within the given sort.
Shift the term shifted a number of bits to the right,
staying within the given sort.
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.
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.
Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.
Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.
A list of functions that should be considered in automatic trigger generation
A list of functions that should be considered in automatic trigger generation
(Since version ) see corresponding Javadoc for more information.
Theory for performing bounded modulo-arithmetic (arithmetic modulo some number N). This in particular includes bit-vector/machine arithmetic.