Release Notes

Version 0.28

Moved the PicoSAT and Espresso code to a top-level thirdparty directory.

Did lots of work in the boolexpr library. Primary change was to get rid of all dynamic stack allocations, replacing them with heap allocations. Most of this was internal stuff which won’t be noticeable at the UI. This includes a mega rename of boolexpr public functions and variables to have a BX_* prefix.

Also added a new simplification:

>>> Xor(a, Xnor(b, c))
Not(Xor(a, b, c))

Release 0.27

Version 0.27.5

Fixed Issue 121.

Version 0.27.4

Fixed an invalid memory access with PicoSAT extension:

Version 0.27.3

Fixed two more issues with C extensions:

Version 0.27.2


Version 0.27.1

Fixed a segfault issue with the to_dnf and to_cnf functions. See Issue 109 for details.

Version 0.27.0


This release involves many backwards-incompatible changes, so please browse through these release notes when upgrading from 0.26 to 0.27.

The major new feature in this release is the addition of a high performance C extension for Boolean expressions. See Issue 98 for some details, but the idea is fairly simple. Since expressions are basically the central data type of PyEDA, it was about time they received the proper performance attention. So I spent a couple months hacking on a C extension located in extension/boolexpr. Now most of the expensive transformations are handled at the C level. For example, simplification and conversion to DNF/CNF are much faster.

The C library uses reference counting for memory management, and I have done some extensive testing to make sure it doesn’t leak memory. The API isn’t documented to the level of a finished product, but if you want to figure out the broad strokes just read the boolexpr.h header file. The algorithms are all single-threaded at the moment. In a future release I would like to experiment with using OpenMP tasks to accelerate the work.

With that said, here’s a list of changes.

The deprecated Expression.factor method went away, replaced by the to_nnf method.

Also, the deprecated Expression.invert method went away. The simplification and NNF transformation algorithms are more efficient now, so you really don’t need this anyways.

The Expression.to_unicode and Expression.to_latex methods went away. They may come back in the future, but they were undocumented and broken anyways.

The Expression class hierarchy is now completely different. Expressions are split up into two categories: Atom and Operator. Atoms are sub-divided into Constant and Literal, and literals are further subdivided into Complement, and Variable. Note that it is Variable, not ExprVariable. Operators now have completely different class names. Instead of ExprOr, it is now OrOp. ExprNot becomes NotOp, etc.

Probably the other most noticeable change to the UI is that using overloaded operators no longer automatically simplifies expressions. For example:

>>> a, b, c, d = map(exprvar, 'abcd')
>>> a & b & c & d
And(And(And(a, b), c), d)

The reason I made this change is that simplification costs a bit of CPU time, and we should avoid that when creating large expressions. The factory operators still simplify by default:

>>> And(a, b, c, d)
And(a, b, c, d)

You can no longer count on the ordering of clauses in a two-level expression. This was done for performance reasons as well. It is very wasteful to to the computations necessary for figuring out a canonical ordering, and the return on investment isn’t very high. If you have written tests that rely on some fixed operand ordering, they will probably break. Literals within clauses, on the other hand, are still ordered by their uniqid values.

There is now an Expression.size method, which returns the number of nodes in the tree. This number is a nice proxy for memory usage if you multiply it by the size of a BoolExpr node.

The Expression.absorb method is now gone, but if you use Expression.to_dnf or Expression.to_cnf, it will automatically apply absorption for you. Also, it is much faster than it was before.

My apologies to anybody using Windows, because I have not had the necessary machines for testing a build on that platform. Feel free to submit a pull request if you find something that is not portable.

Though this addition is very exciting, there is still plenty of room for improvement in the performance area. I would like to experiment with using OpenMP “tasks” to accelerate big tree transformations. Currently, the SAT implementation does not happen directly in the C layer. That requires further integration between the two C APIs. Also, annoyingly, the Tseitin transformation code is still written in Python. This is due to the problem that this transformation requires the ability to create new variable objects, which is currently handled at the Python level. This is not an unsolvable problem, but requires some work.

I’m almost positive I missed a few details. Feel free to email with comments and suggestions.

Happy programming!

Version 0.26

Another small, incremental release.

The most important changes were related to Issue 99. Simplified the expression class hierarchy a bit. Got rid of Nor, Nand, and Xnor expression classes, because they’re not all that useful. Eliminated auto-simplification of degenerate forms.

Updated to PicoSAT version 960.

Got rid of some old DPLL cruft. The PicoSAT extension is so superior to my amateurish Python implementation, no point in keeping it around anymore.

Changed the names of various exceptions from something like LexError to lex.Error. I was influenced by the Exceptions section from the Google Python Style Guide.

Deprecated expression factor methods in favor of the more hip negation normal form (NNF) terminology. See Issue 101 for details.

Updated the formatting of truth table strings. Now the inputs are aligned beneath their variable names.


inputs: x2 x1 x0
000 0
001 0
010 0
011 1
100 0
101 1
110 1
111 1


x2 x1 x0
 0  0  0 : 0
 0  0  1 : 0
 0  1  0 : 0
 0  1  1 : 1
 1  0  0 : 0
 1  0  1 : 1
 1  1  0 : 1
 1  1  1 : 1

Version 0.25

This is a small, incremental release. I recently changed jobs and moved, so development will definitely slow down for a while.

Function array concatenation and repetition for MDAs is now a bit smarter (Issue 96). Rather than simply flattening, the operators will attempt to retain the shape of the MDAs if possible. For example, a 2x6x7 + 2x6x7 concatenation will return 4x6x7, and 2x6x7 * 2 repetition will return 4x6x7.

Got rid of a[0][1][2] expression parsing syntax. Use a[0,1,2] instead. Also got rid of the bitvec function. Use the exprvars function (or bddvars, ttvars) instead. Finally all vestiges of the legacy BitVector MDA methodology are gone.

Everything else was just miscellaneous code/test/documentation cleanup.

Version 0.24

Variables names are now required to be C-style identifiers. I.e., [a-zA-Z_][a-zA-Z0-9_]*.

The expression parser now handles both a[1][2][3] and a[1,2,3] syntaxes (Issue 91). The a[1][2][3] is deprecated.

Got rid of expression is_neg_unate, is_pos_unate, and is_binate functions. I haven’t been able to find an efficient algorithm for this, so just convert expressions and BDDs to truth tables first. If your function is too big to fit in a truth table, it’s probably also too big to expand to a canonical expression.

Not(Not(...)) double negation is now automatically reduced, just like Not(Nand(...)), etc.

Cleaned up the definition of expression depth (Issue 92). This is not backwards compatible.

Fixed Issue 93, picosat script fails with trivial zero input:

$ picosat
p cnf 0 1

Changed RegexLexer to yield EndToken at the end of a token stream. This makes parsing nicer, avoiding catching StopIteration everywhere.

Got rid of factor=False on expression factory functions. This was overly designed UI.

The expression restrict method is a little faster now. Especially for big functions.

Added lots of new reference documentation.

Added new farray documentation chapter. Fixed several little issues with function arrays during this process. The constructor now takes an ftype=None parameter. Negative indices make more sense now. Slices behave more like Python tuple slices. Fixed several inconsistencies with empty arrays.

Deprecated bitvec function.

Version 0.23

This version introduces a new picosat script. Now you can solve DIMACS CNF files from the command-line. See for details.

Finally there is a proper documentation chapter for binary decision diagrams! While writing this documentation, I noticed, and fixed some obscure bugs related to incorrect usage of weak references to BDD nodes.

Made some minor changes to the public interface of the bdd module.

Replaced the traverse method with three options for BDD iteration:

  • bdd.dfs_preorder - Depth-first search pre-order traversal
  • bdd.dfs_postorder - Depth-first search post-order traversal
  • bdd.bfs() - Breadth-first search

Got rid of the deprecated uint2bv and int2bv functions. Use the uint2exprs, int2exprs functions instead.

Changed the pyeda.parsing.parse_pla function so it takes a string input. This makes it much easier to test.

Deprecated the is_neg_unate, is_pos_unate, is_binate methods for expressions. I haven’t found a correct algorithm that is better than just 1) converting to a truth table, and 2) checking for monotonicity in the cofactors.

As of this release, I will be dropping support for Python 3.2.

Version 0.22

A couple features, and some good bug-fixes in this release.

Fixed Issue 80. Apparently, I forgot to implement the right-side version of XOR operator: 0 ^ x.

Fixed Issue 81. I continue finding bugs with degenerate forms. This particular one comes up when you try to do something similar to Or(Or(a, b)). The __new__ method was implemented incorrectly, so I moved the Or(a) = a (and similar) rules to the simplify method.

To match the notation used by Univ of Illinois VLSI class, I changed BDD low/high nodes to “lo”, and “hi”.

Got rid of the “minus” operator, a - b. This was previously implemented as a | ~b, but I don’t think it has merit anymore.

The farray type now uses the + operator for concatenation, and * for repetition. These are very important features in SystemVerilog. See Issue 77 for details.

Implemented the farray.__setitem__ method. It is very useful to instantiate an farray using exprzeros, and then programmatically assign indices one-by-one. See Issue 78 for details.

To demonstrate some of the fancy, new farray features, I added the AES algorithm to the logic package. It manages to complete all the logic assignments, but I haven’t been able to test its correctness yet, because it explodes the memory on my machine. At a bare minimum, it will be a nice test case for performance optimizations necessary to handle large designs.

Version 0.21

Important bug fix! Issue 75. Harnesser pointed out that Espresso was returning some goofy results for degenerate inputs (a literal or AND(lit, lit, ...)).

The major new feature in this release is the farray mult-dimensional array (MDA) data type. The implementation of BitVector was a kludge – it was built around the Expression function type, and didn’t support all the fancy things you could do with numpy slices. All usage of the old Slicer and BitVector types has been eliminated, and replaced by farray. This includes the bitvec, uint2bv, and int2bv functions, and the contents of the pyeda.logic package (addition, Sudoku, etc).

Both uint2bv and int2bv are deprecated, superceded by uint2exprs and int2exprs (or uint2bdds, etc). So far I haven’t deprecated bitvec, because it’s a very commonly-used function.

See Issue 68 for some details on the farray type. My favorite part is the ability to multiplex an farray using Python’s slice syntax:

>>> xs = exprvars('x', 4)
>>> sel = exprvars('s', 2)
>>> xs[sel]
Or(And(~s[0], ~s[1], x[0]), And(s[0], ~s[1], x[1]), And(~s[0], s[1], x[2]), And(s[0], s[1], x[3]))

This even works with MDAs:

>>> xs = exprvars('x', 4, 4)
>>> sel = exprvars('s', 2)
>>> xs[0,sel]
Or(And(~s[0], ~s[1], x[0][0]), And(s[0], ~s[1], x[0][1]), And(~s[0], s[1], x[0][2]), And(s[0], s[1], x[0][3]))

Added AchillesHeel function to expression parsing engine.

Eliminated the + and * operators for Boolean OR, AND, respectively. This is annoying, but I need these operators for Issue 77. Sorry for any trouble, but that’s what major version zero is for :).

Version 0.20

Probably the most useful feature in this release is the espresso script:

$ espresso -h
usage: espresso [-h] [-e {fast,ness,nirr,nunwrap,onset,strong}] [--fast]
                [--no-ess] [--no-irr] [--no-unwrap] [--onset] [--strong]

Minimize a PLA file

positional arguments:
  file                  PLA file (default: stdin)

optional arguments:

This script implements a subset of the functionality of the original Espresso command-line program. It uses the new parse_pla function in the pyeda.parsing.pla module to parse common PLA files. Note that the script only intends to implement basic truth-table functionality at the moment. It doesn’t support multiple-valued variables, and various other Espresso built-in features.

Added Espresso get_config and set_config functions, to manipulate global configuration

New Bitvector methods:

  • unor - unary nor
  • unand - unary nand
  • uxnor - unary xnor

Made BitVector an immutable type. As a result, dropped item assignment X[0] = a, zero extension X.zext(4), sign extension X.sext(4), and append method.

The BitVector type now supports more overloaded operators:

  • X + Y concatenate two bit vectors
  • X << n return the bit vector left-shifted by n places
  • X >> n return the bit vector right-shifted by n places

Both left shift and right shift are simple shifts–they use the default “carry-in” of zero.

Got rid of boolify utility function. It had been replaced over time by more sophisticated techniques.

There is a new Mux factory function, for multiplexing arbitrarily many input functions.

Update to PicoSAT 959. Check the homepage for details, but it looks like the only changes were related to header file documentation.

Added a neat capability to specify assumptions for SAT-solving using a with statement. It supports both literal and product-term forms:

>>> f = Xor(a, b, c)
>>> with a, ~b:
...     print(f.satisfy_one())
{a: 1, b: 0, c: 0}
>>> with a & ~b:
...     print(f.satisfy_one())
{a: 1, b: 0, c: 0}

At the moment, this only works for the satisfy_one method, because it is so handy and intuitive.

Version 0.19

Release 0.19.3

Enhanced error handling in the Espresso C extension.

Release 0.19.2

Added the espresso_tts function, which allows you to run Espresso on one or more TruthTable instances.

Release 0.19.1

Fixed a bone-headed mistake: leaving espresso.h out of the source distribution. One of these days I will remember to test the source distribution for all the necessary files before releasing it.

Release 0.19.0

This is a very exciting release! After much hard work, PyEDA now has a C extension to the famous Espresso logic minimization software from Berkeley! See the new chapter on two-level logic minimization for usage information.

Also, after some feedback from users, it became increasingly obvious that using the -+* operators for NOT, OR, AND was a limitation. Now, just like Sympy, PyEDA uses the ~|&^ operators for symbolic algebra. For convenience, the legacy operators will issue deprecation warnings for now. In some upcoming release, they will no longer work.

After other feedback from users, I changed the way Expression string representation works. Now, the __str__ method uses Or, And, etc, instead of ascii characters. The idea is that the string representation now returns valid Python that can be parsed by the expr function (or the Python interpreter). To provide support for fancy formatting in IPython notebook, I added the new to_unicode and to_latex methods. These methods also return fancy string representations.

For consistency, the uint2vec and int2vec functions have been renamed to uint2bv and int2bv, respectively.

Since is_pos_unate, is_neg_unate, and is_binate didn’t seem like fundamental operations, I remove them from the Function base class.

Version 0.18

Release 0.18.1

Three minor tweaks in this release:

  • expr/bdd to_dot methods now return undirected graphs.
  • Added AchillesHeel factory function to expr.
  • Fixed a few obscure bugs with simplification of Implies and ITE.

Release 0.18.0

New stuff in this release:

  • Unified the Expression and Normalform expression types, getting rid of the need for the nfexpr module.
  • Added to_dot methods to both Expression and BinaryDecisionDiagram data types.

Mostly incremental changes this time around. My apologies to anybody who was using the nfexpr module. Lately, Expression has gotten quite fast, especially with the addition of the PicoSAT C extension. The normal form data type as set(frozenset(int)) was not a proper implementation of the Function class, so finally did away with it in favor of the new “encoded” representation that matches the Dimacs CNF convention of mapping an index 1..N to each variable, and having the negative index correspond to the complement. So far this is only useful for CNF SAT-solving, but may also come in handy for any future, fast operations on 2-level covers.

Also, somewhat awesome is the addition of the to_dot methods. I was playing around with IPython extensions, and eventually hacked up a neat solution for drawing BDDs into the notebook. The magic functions are published in my ipython-magic repo. See the usage notes. Using subprocess is probably not the best way to interface with Graphviz, but it works well enough without any dependencies.

Version 0.17

Release 0.17.1

Got rid of the assumptions parameter from boolalg.picosat.satisfy_all function, because it had no effect. Read through picosat.h to figure out what happened, and you need to re-apply assumptions for every call to picosat_sat. For now, the usage model seems a little dubious, so just got rid of it.

Release 0.17.0

New stuff in this release:

  • Added assumptions=None parameter to PicoSAT satisfy_one and satisfy_all functions. This produces a very nice speedup in some situations.
  • Got rid of extraneous Python wrapper module. Now the PicoSAT Python interface is implemented by picosatmodule.c.
  • Updated Nor/Nand operators to secondary status. That is, they now can be natively represented by symbolic expressions.
  • Added a Brent-Kung adder to logic.addition module
  • Lots of other miscellaneous cleanup and better error handling

Version 0.16

Release 0.16.3

Fixed bug: absorption algorithm not returning a fully simplified expression.

Release 0.16.2

Significantly enhance the performance of the absorption algorithm

Release 0.16.1

Fixed bug: PicoSAT module compilation busted on Windows

Release 0.16.0

New stuff in this release:

  • Added Expression complete_sum method, to generate a normal form expression that contains all prime implicants.
  • Unicode expression symbols, because it’s awesome
  • Added new Expression ForEach, Exists factory functions.
  • Changed frozenset implementation of OrAnd and EqualBase arguments back to tuple. The simplification aspects had an unfortunate performance penalty. Use absorb to get rid of duplicate terms in DNF/CNF forms.
  • Added flatten=False/True to Expression to_dnf, to_cdnf, to_cnf, to_ccnf methods. Often, flatten=False is faster at reducing to a normal form.
  • Simplified absorb algorithm using Python sets.
  • Expression added a new splitvar property, which implements a common heuristic to find a good splitting variable.

Version 0.15

Release 0.15.1

Release 0.15.0

This is probably the most exciting release of PyEDA yet! Integration of the popular PicoSAT fast C SAT solver makes PyEDA suitable for industrial-strength applications. Unfortunately, I have no idea how to make this work on Windows yet.

Here are the full release notes:

  • Drop support for Python 2.7. Will only support Python 3.2+ going forward.
  • Integrate PicoSAT, a compact SAT solver written in C.
  • Added lots of new capabilities to Boolean expression parsing:
    • s ? d1 : d0 (ITE), p => q (Implies), and p <=> q (Equal) symbolic operators.
    • Full complement of explicit form Boolean operators: Or, And, Xor, Xnor, Equal, Unequal, Nor, Nand, OneHot0, OneHot, Majority, ITE, Implies, Not
    • The expr function now simplifies by default, and has simplify=True, and factor=False parameters.
  • New Unequal expression operator.
  • New Majority high-order expression operator.
  • OneHot0, OneHot, and Majority all have both disjunctive (conj=False) and conjunctive (conj=True) forms.
  • Add new Expression.to_ast method. This might replace the expr2dimacssat function in the future,
  • Fixed bug: Xor.factor(conj=True) returns non-equivalent expression.
  • Changed the meaning of conj parameter in Expression.factor method. Now it is only used by the top-level, and not passed recursively.
  • Normal form expression no longer inherit from Function. They didn’t implement the full interface, so this just made sense.
  • Replaced pyeda.expr.expr2dimacscnf with a new pyeda.expr.DimacsCNF class. This might be unified with normal form expressions in the future.

Version 0.14

Release 0.14.2

Fixed Issue #42.

There was a bug in the implementation of OrAnd, due to the new usage of a frozenset to represent the argument container.

With 0.14.1, you could get this:

>>> And('a', 'b', 'c') == Or('a', 'b', 'c')


>>> And('a', 'b', 'c') == Or('a', 'b', 'c')

The == operator is only used by PyEDA for hashing, and is not overloaded by Expression. Therefore, this could potentially cause some serious issues with Or/And expressions that prune arguments incorrectly.

Release 0.14.1

Fixed Issue #41. Basically, the package metadata in the 0.14.0 release was incomplete, so the source distribution only contained a few modules. Whoops.

Release 0.14.0

This release reorganizes the PyEDA source code around quite a bit, and introduces some awesome new parsing utilities.

Probably the most important new feature is the addition of the pyeda.boolalg.expr.expr function. This function takes int or str as an input. If the input is a str instance, the function parses the input string, and returns an Expression instance. This makes it easy to form symbolic expression without even having to declare variables ahead of time:

>>> from pyeda.boolalg.expr import expr
>>> f = expr("-a * b + -b * c")
>>> g = expr("(-x[0] + x[1]) * (-x[1] + x[2])")

The return value of expr function is not simplified by default. This allows you to represent arbitrary expressions, for example:

>>> h = expr("a * 0")
>>> h
0 * a
>>> h.simplify()
  • Reorganized source code:
    • Moved all Boolean algebra (functions, vector functions) into a new package, pyeda.boolalg.
    • Split arithmetic into addition and gray_code modules.
    • Moved all logic functions (addition, gray code) into a new package, pyeda.logic.
    • Created new Sudoku module under pyeda.logic.
  • Awesome new regex-based lexical analysis class, pyeda.parsing.RegexLexer.
  • Reorganized the DIMACS parsing code:
    • Refactored parsing code to use RegexLexer.
    • Parsing functions now return an abstract syntax tree, to be used by pyeda.boolalg.ast2expr function.
    • Changed dimacs.load_cnf to pyeda.parsing.dimacs.parse_cnf.
    • Changed dimacs.load_sat to pyeda.parsing.dimacs.parse_sat.
    • Changed dimacs.dump_cnf to pyeda.boolalg.expr2dimacscnf.
    • Changed dimacs.dump_sat to pyeda.boolalg.expr2dimacssat.
  • Changed constructors for Variable factories. Unified namespace as just a part of the name.
  • Changed interactive usage. Originally was from pyeda import *. Now use from pyeda.inter import *.
  • Some more miscellaneous refactoring on logic expressions:
    • Fixed weirdness with Expression.simplified implementation.
    • Added new private class _ArgumentContainer, which is now the parent of ExprOrAnd, ExprExclusive, ExprEqual, ExprImplies, ExprITE.
    • Changed ExprOrAnd argument container to a frozenset, which has several nice properties for simplification of AND/OR expressions.
  • Got rid of pyeda.alphas module.
  • Preliminary support for logic expression complete_sum method, for generating the set of prime implicants.
  • Use a “computed table” cache in BDD restrict method.
  • Use weak references to help with BDD garbage collection.
  • Replace distutils with setuptools.
  • Preliminary support for Tseitin encoding of logic expressions.
  • Rename pyeda.common to pyeda.util.

Version 0.13

Wow, this release took a huge leap from version 0.12. We’re probably not ready to declare a “1.0”, but it is definitely time to take a step back from API development, and start focusing on producing useful documentation.

This is not a complete list of changes, but here are the highlights.

  • Binary Decision Diagrams! The recursive algorithms used to implement this datatype are awesome.
  • Unification of all Variable subclasses by using separate factory functions (exprvar, ttvar, bddvar), but a common integer “uniqid”.
  • New “untyped point” is an immutable 2-tuple of variable uniqids assigned to zero and one. Also a new urestrict method to go along with it. Most important algorithms now use untyped points internally, because the set operations are very elegant and avoid dealing with which type of variable you are using.
  • Changed the Variable’s namespace argument to a tuple of strings.
  • Restricting a function to a 0/1 state no longer returns an integer. Now every function representation has its own zero/one representations.
  • Now using the fantastic Logilab PyLint program!
  • Truth tables now use the awesome stdlib array.array for internal representation.
  • Changed the names of almost all Expression sublasses to ExprSomething. the Or/And/Not operators are now functions. This simplified lots of crummy __new__ magic.
  • Expression instances to not automatically simplify, but they do if you use Or/And/Not/etc with default **kwargs.
  • Got rid of constant and binop modules, of dubious value.
  • Added is_zero, is_one, box, and unbox to Function interface.
  • Removed reduce, iter_zeros, and iter_ones from Function interface.
  • Lots of refactoring of SAT methodology.
  • Finally implemented unate methods correctly for Expressions.

Version 0.12

  • Lots of work in pyeda.table:
    • Now two classes, TruthTable, and PCTable (for positional-cube format, which allows X outputs).
    • Implemented most of the boolfunc.Function API.
    • Tables now support -, +, *, and xor operators.
  • Using a set container for And/Or/Xor argument simplification results in about 30% speedup of unit tests.
  • Renamed boolfunc.iter_space to boolfunc.iter_points.
  • New boolfunc.iter_terms generator.
  • Changed dnf=True to conf=False on several methods that give the option of returnin an expression in conjunctive or disjunctive form.
  • Added conj=False argument to all expression factor methods.
  • New Function.iter_domain and Function.iter_image iterators.
  • Renamed Function.iter_outputs to Function.iter_relation.
  • Add pyeda.alphas module for a convenience way to grab all the a, b, c, d, … variables.
  • Xor.factor now returns a flattened form, instead of nested.

Version 0.11

Release 0.11.1

  • Fixed bug #16: Function.reduce only implemented by Variable

Release 0.11.0

  • In pyeda.dimacs changed parse_cnf method name to load_cnf
  • In pyeda.dimacs changed parse_sat method name to load_sat
  • In pyeda.dimacs added new method dump_cnf, to convert expressions to CNF-formatted strings.
  • In pyeda.dimacs added new method dump_sat, to convert expressions to SAT-formatted strings.
  • Variables now have a qualname attribute, to allow referencing a variable either by its local name or its fully-qualified name.
  • Function gained a reduce method, to provide a standard interface to reduce Boolean function implementations to their canonical forms.
  • Expressions gained a simplify parameter, to allow constructing unsimplified expressions.
  • Expressions gained an expand method, to implement Shannon expansion.
  • New if-then-else (ITE) expression type.
  • NormalForm expressions now both support -, +, and * operators.