syndi - synthesizer of delay insensitive circuits

This file documents syndi version 0.2.0, which is a compiler that translates a specification language to Petri nets, delay insensitive circuit netlists, or virtual code executable files.

1. Usage

syndi is a compiler that generates Delay Insensitive circuits or Petri nets from a high level specification language. This document is intended mainly as a reference manual for users already familiar with the language, but it may be of some assistance to new users who consider themselves a quick study.

1.1 Options

The following command line options are recognized.

--help

Show a short summary of syndi's usage and options.

--version

Show the version number and the date of the syndi source file from which the compiler was built.

--warranty

Show a short copyleft message and a reminder about the lack of a warranty.

--main=definition

Include the given definition among those to be compiled, which may be any expression or equation in syndi syntax. It will usually be necessary to quote the expression to suppress interpretation by the shell.

--display

Display the type and value of the last symbol defined, either in a source file or with the --main option, with names and numeric subexpressions evaluated, variables transformed out, and recursive equations solved. This option disables the writing of all output files.

--phase n

Write a core dump file, where n is from 0 to 10. This option may be time consuming due to file compression, and will be of interest only to developers working on the syndi compiler itself.

--preamble-only

With regard to the --phase option, write an empty core dump file except for the front matter, so as to save time on compression.

--library

Compile all source files into reusable binary modules (may be time consuming due to output file compression).

--petrinet

Generate a Petri net listing for each statement or circuit defined in a source file or --main option and write it to a file named after the identifier.

--circuit

Generate a DI netlist for each statement or circuit defined in a source file or --main option and write it to a file named after the identifier.

--executable

Compile each function defined in a source file or --main option whose result type is a statement or circuit to a stand-alone executable file (may be time consuming for large functions due to output file compression).

The last four can be applied selectively to definitions in the source by using the corresponding compiler directives instead, but directives are overridden by command line options. If --main is specified with no other options and no files or with only binary files, --display is implied. More about directives and executable files is explained in 2.3 Directives.

1.2 Files

Any number of input files may be specified on the command line, which may be any combination of source and binary files. Expressions in source files may refer to identifiers defined in other source files or exported from binary files. Binary files are required to be libraries produced by previous runs of syndi using the library option or directive.

Input file names are normally assumed to be relative to the current directory, but on GNU systems, the AVMINPUTS environment variable may be used to store a colon separated list of additional directories that will be searched. This feature applies to binary files only.

Output files are written to the current directory. In the case of library files, an output file with a .slf suffix is written for each source file in which any #library+ directive is used, or for all source files if the --library option is given on the command line. In all other cases, a separate file is written for each relevant declaration, with a file name derived from the identifier of the declaration. Output file formats for Petri nets and DI netlists are documented in the diana manual.

A file called profile.txt is written to the current directory on every run, which tabulates the time spent on various aspects of the compilation.

2. Syntax

A source file is organized as a sequence of equations interspersed with directives. Each equation is of the form lvalue = expression, where

lvalue ::= identifier | (lvalue) | lvalue params
params ::= variable | (params[,params]*)
expression ::= identifier | variable | number | name | tuple | list |
    application | abstraction | expression operator expression
operator ::= ^ | : | - | .
tuple ::= () | (expression[,expression]*)
list ::= nil | <> | <expression[,expression]*>
application::= expression [whitespace] expression
abstraction ::= params . whitespace expression

An lvalue can therefore contain only one identifier, which is said to be the identifier declared by the equation. The terms equations, declarations, and definitions are used interchangeably in this document.

Note that the . is an overloaded operator, which is disambiguated according to whether it is followed immediately by an operand or by white space. In the latter case, it stands for functional abstraction, also known as lambda abstraction.

An equation of the form f x = g is syntactic sugar for f = x. g, just as g(x) y = h represents g = x. y. h, and so on. The identifier on the left may also appear on the right, in which case the equation is interpreted as a recurrence to be solved. Recurrences can be solved over functions and statements, and may involve multiple equations. However, other types of recurrences such as "lazy lists" are not supported.

There are two forms of function application, one with white space and one without. The latter has higher precedence and is left associative. All other operators including application with a space are right associative. Hence, g(x) y is equivalent to (g x) y, not g(x(y)).

In order of decreasing precedence, the operators are tight application, - , . , : , ^ , loose application, and functional abstraction. The operator symbols - , . , :, and ^ are semantically equivalent to the built in functions range, dot, cat, and cons, respectively, except when the . represents functional abstraction.

(note to functional programmers: in Haskell, unlike syndi, function application is always left associative. This feature of Haskell seeks an accommodation with a historical accident whereby languages based on lambda calculi compel the simulation tuples through higher order functions.)

2.1 Lexical Elements

As the above grammar suggests, the main lexical classes are identifiers, numbers, variables, and names.

identifiers

are case-sensitives strings of letters, digits, or underscores. The identifier declared by an equation must not coincide with any pre-defined functions or constants listed in the subsequent sections. Any identifier in any expression may always be replaced with the right side of the equation declaring it without changing the meaning of the expression (subject to minor rewriting where the lvalue contains variables).

numbers

are non-negative integers expressed as decimal strings, with unlimited precision up to the available host memory.

variables

are expressed as strings of characters enclosed in double quotes, which may include any characters except double quotes themselves. Any expression containing variables must either be a subexpression of an abstraction whose params contain the variables, or must be part of an equation whose lvalue contains them. That is to say, no unbound variables are allowed.

names

represent signals in syndi and are syntactically similar to identifiers. A name is recognized as such by not being a pre-defined identifier and not being declared in any equation.

The built in names + and * have particular algebraic properties. Any name of the form a.+.n, where n is a number and . is the dot operator, is equivalent to a.successor(n), and any name of the form a.*.n is equivalent to a.double(n). If n is a list of numbers, then the expressions are equivalent to a.((map successor) n) and a.((map double) n), respectively. More about names is explained in 3.7 Names.

2.2 Comments

There are five forms of comments in syndi. New users only need to learn the first one.

• The delimiters (# and #) may be used in matched pairs to indicate a comment anywhere in a source file, and may be nested.
• A hash character # followed by white space or a non-alphabetic character other than a hash designates the remainder of the line as a comment. A backslash at the end of the line may be used as a comment continuation character.
• Two consecutive dashes designate the remainder of the line as a comment, and it may also have a comment continuation character at the end.
• Three consecutive hashes, ###, indicate that the remainder of the file is a comment.
• A pair of hashes, ##, followed by anything other than a third hash indicates a smart comment, which may be used to "comment out" a section of syntactically correct code. A smart comment between declarations comments out the next declaration, and a smart comment appearing anywhere within a list or tuple comments out the remainder of the item in which it appears up to the terminating comma or closing delimiter, taking nested lists or tuples into account.

Standard caveats apply with regard to comment delimiters inside of quoted strings.

2.3 Directives

The following directives may be used within a source file to control the production of output files by syndi during a compilation. Directives begin with a hash, followed with no intervening spaces by the directive name, and concluded with either a plus or a minus sign. They may appear only between declarations. By default, all directives are disabled except sometimes for #eager+. Where a directive is specified with a plus sign, it is enabled for all declarations following it until its next occurrence with a minus sign.

#petrinet+

Write a file containing a Petri net listing for each statement or circuit declared following this directive. (The file name will be the same as the identifier of the declaration, unless that name clashes with the name of the source file, in which case a prefix of petrinet- will be added.)

#circuit+

Write a file containing a DI circuit netlist for each statement or circuit declared following this directive, using a file name derived from the identifier prepended with circuit-.

#library+

Include the declarations following this directive in a binary library file to be produced from this source, named after the source file with a suffix of .slf added.

#blackbox+

Do not synthesize a circuit for any statement declared following this directive, but instead list it as a primitive component in any netlist where it would otherwise occur. A comment will be added to the netlist to document the pin assignment chosen for the component.

#executable+

Write a stand-alone executable file in avram virtual machine code format for each function following this directive whose result type is either circuit or statement, naming the executable file after the identifier with a prefix of executable- if necessary to avoid a clash with the source file name.

#eager+

Synthesize a sub-circuit corresponding to each part of a statement, which will be combined with other sub-circuits when the parts are combined.

#lazy+

Disable the #eager+ directive if it would otherwise be enabled by default, which is for any declaration using the circuit function or the #circuit+ directive.

2.3.1 Executable Files

Any executable file written by syndi is based on a function. The code generated will automatically incorporate a wrapper that enables it to read and parse a single expression in a subset of syndi syntax from standard input. The expression in the input text may include numbers, names, infix operators, lists, tuples, and comments, but no pre-defined identifiers or variables. The value obtained for this expression will be used as an argument to the function. Run time error messages including parsing errors will be written to standard error.

If the function in an executable file is evaluated successfully with the argument obtained from standard input, an automatically supplied back end will write the result to standard output as either a Petri net or a netlist, depending on the function result type. The output file formats are documented in the diana manual. In the case of a netlist, a comment will be included in the output displaying the identifier of the function and its argument.

If the result type is anything other than a statement or a circuit, the back end will attempt to write it to standard output as an expression in syndi syntax. If that is not possible due to it being of an unprintable type, an error message displaying the type expression will be written to standard error.

Executable files produced in this way may of course be used for any purpose, but they are also compatible with diana for use as virtual code input files. In this case, the text parameter following the --dimensions option on the diana command line will be used as the input text.

2.3.2 Eagerness

One way syndi synthesizes circuits more efficiently is by synthesizing them in parts and then putting the parts together. When the list function is used to make a list of copies of a statement, all of which are to be synthesized as circuits, syndi will synthesize the circuit just once, and then make copies of it, rather than synthesizing a circuit for each copy of the statement. When the doall function is used to express a list of concurrently executing statements, which is then translated into a circuit, syndi will synthesize a circuit for each statement individually, and form parallel combinations of those circuits that have no inputs in common, rather than synthesizing a circuit from the combined statement. This strategy saves time during synthesis and may also lead to better circuits, and is designated as eager evaluation in this document.

However, synthesizing a circuit in advance for each part of a statement is a waste of time if the statement is not going to be translated into a circuit, so syndi tries to determine whether or not it will be required and performs no circuit synthesis if it is not.

This determination is based on three criteria by default. An eager evaluation strategy is precluded in any declaration for which the #blackbox+ directive is selected. Otherwise, it is indicated if the #circuit+ directive is selected for the declaration, or if the circuit function is used anywhere in the declaration.

Although it is not usually necessary, the user can force eager evaluation by using the #eager+ directive, or forcibly inhibit it using the #lazy+ directive. Inhibiting eagerness when it should have been left alone may cause an exponential increase in the time needed to synthesize a circuit or in the size of the circuit. In other cases it may save time to inhibit eagerness, such as when most of the constituent statements in a doall statement have shared inputs and therefore can not be synthesized as separate circuits.

The main use for these directives is in compiling a library containing functions returning statements as their results, which are not actually evaluated on any arguments at compile time. The #eager+ directive might not be enabled by default in this case, but it should be specified explicitly unless it is known that the functions will be used only for Petri nets and not circuits. The #lazy+ directive might be used if it is known that a library function will not be used for circuits despite meeting some of the above criteria, as it will allow a considerable reduction in code size and time needed for library file compression.

3. Semantics

The remainder of this document catalogs the pre-defined functions and constants in syndi, starting with those that are likely to be most familiar.

For illustrative purposes, functions are shown as the left side of an application expression with an example argument on the right, as in double(n). However, functions in syndi are first class objects and may appear in other contexts. For example, the list of functions <half,not,double> is a perfectly valid expression (although not itself a function).

3.1 Arithmetic Operators

The following arithmetic functions are useful for manipulating compile-time constants.

double(n)

multiply a number by two and return the result

half(n)

divide a number by two and return the truncated result

not(x)

return one if the argument is zero or an empty list of any type, otherwise return zero

odd(n)

return zero for even arguments and one for odd arguments

predecessor(n)

subtract one from a number and return the result, or throw exception in the case of zero

successor(n)

add one to a number and return the result

equal(x,y)

take any pair of arguments of the same type and return one if they have the same concrete representations, otherwise return zero (N.B. entities with non-unique representations, such as functions, could be equal but not equal; due apologies to theoreticians)

sum(n,m)

return the sum of two numbers

product(n,m)

return the product of two numbers

quotient(n,m)

divide n by m, and return the truncated quotient, or throw an exception if m is zero

mod(n,m)

divide n by m, and return the remainder, or throw an exception if m is zero

difference(n,m)

subtract m from n, returning the difference if non-negative and throwing an exception otherwise

range(n,m)

take a pair of numbers to the inclusive list of consecutive numbers obtained by counting either up or down as necessary from n to m

3.2 Projection Functions

Some general functions are provided for building lists and tuples or extracting their components.

In the following descriptions, (x1..xn) is written for an n-tuple, and <x1..xn> for a list of n items. Only binary tuples are actually provided in syndi, but expressions like (x1,x2,x3) may be written as an abbreviated form of (x1,(x2,x3)).

There is no semantic distinction between an expression x and the unary tuple (x), but the unit list <x> differs from x.

A non-empty tuple is any tuple other than (), and a non-empty list is any list other than nil or <>. Functions defined only for non-empty lists or tuples will throw an exception in the alternative.

left(x1..xn)

extract the left side of an n-tuple, where n is greater than one, returning x1

right(x1..xn)

extract the right side of an n-tuple, where n is greater than one, which will be the n-1 tuple (x2..xn)

swap(x1..xn)

interchange the left and right sides of a pair, returning ((x2..xn),x1)

head<x1..xn>

return the first item in a non-empty list, x1

tail<x1..xn>

take a non-empty list and return the list obtained by deleting the first item, which will be <x2..xn>

identity(x)

return the whole argument x, which may be of any type

cat(<x1..xn>,<y1..yn>)

return the concatenation of a pair of lists of the same type, <x1..xn,y1..yn>

cons(x0,<x1..xn>)

take a pair whose right side is a list of items of a type matching that of the left, and return a list whose head is the left and whose tail is the right, i.e., <x0,x1..xn>

3.3 List Mutators

Continuing with the conventions of the previous section, a few more operations particular to lists are also available.

reverse<x1..xn>

reverse the order of the items in a list, to obtain <xn..x1>

roll<x1..xn>

move the first item of a non-empty list to the end, returning <x2..xn,x1>, or return the empty list if the argument is empty.

flat<<a0..an>..<z0..zm>>

take a list of lists to one long list by concatenating all the items in order, to obtain <a0..zm>

transpose<<a0..an>..<z0..zn>>

take a list of equal-length lists, and form the list whose head is the list of their heads, whose next item is the list of all their next items, and so on, i.e., <<a0..z0>,<a1..z1>..<an..zn>>

unzip<(x0,y0)..(xn,yn)>

take a list of pairs to a pair of lists by forming the list of all the left sides and the list of all the right sides, which is (<x0..xn>,<y0..yn>)

distribute(d,<x0..xn>)

take any datum and any list to a list of pairs, all of whose left sides are the given datum, and whose right sides are the corresponding item of the original list, to obtain <(d,x0)..(d,xn)>

zip(<x0..xn>,<y0..yn>)

take a pair of equal length lists to a list of pairs, in which the left side of each item is the corresponding item from the left list, and the right side of each item is that of the other, i.e., <(x0,y0)..(xn,yn)>

3.4 Functional Combinators

A number of functions that take functions as arguments or return functions as results lend themselves to a particularly expressive style of programming, and are provided in syndi for the benefit of users who are disposed to take advantage of them.

apply(f,x)

given a function f and an argument x, return the value of the function application f(x)

apply_to(x) f

given an argument x, return a function that will take a function f as an argument and return the result obtained by applying it to x. Hence, writing apply_to(x) f is just an alternative way of writing apply(f,x).

fix(h)

take a second order function h as an argument and return the first order function f such that f(x) = h(f) x for all x. Alternatively, if h is a function from statements to statements, return the least deterministic statement p that is observationally equivalent to h(p)

map(f)

take a function f to the function that would transform a list <x1..xn> to <f(x1)..f(xn)>

constant(k)

take any constant k to the function that always returns k regardless of its argument

lift(f)

given any binary operator f, return a higher order function v such that (v(g,h))(x) = f(g x,h x) for all functions g, h, and all arguments x

bu(f,k)

given a binary operator f and a left argument k, construct a function g to satisfy g(x) = f(k,x) for all right arguments x

fold(f,k)

given a binary operator f and a vacuous case result k, construct a function g that operates on lists such that g(nil) = k, and g(cons(h,t)) = f(h,g(t))

tuple(f1..fk)

given any k-tuple of functions (f1..fk), construct a function g such that g(x) = (f1(x)..fk(x)) for all arguments x

follow<f0..fn>

given any list of functions <f0..fn>, construct a function g such that g(x) = f0(..fn(x)) for all arguments x, or is the identity function if the list of functions is empty

if_then_else(p,f,g)

given a triple of functions (p,f,g) construct a function h such that h(x) = g(x) for values of x where p(x) has a value of 0 or nil, but h(x) = f(x) whenever p(x) has some other value

3.5 Components

Components are a primitive data type in syndi that may be used for constructing circuits. A component is best envisioned as a box with a fixed number of terminals, of which some are inputs and some are outputs.

Although the terminals are anonymous, they are ordered, so it is meaningful to speak of the first input terminal on a component, the last output terminal, etc..

It is possible for an output terminal on a component to be connected to an input terminal on the same or another component to form a network, but such a network may be viewed as yet another component. Different terminals on the same component are not necessarily equivalent for the purpose of connections.

Components interact with their environment or with other components with which they are connected by sending and receiving signals or transitions on their terminals.

3.5.1 Primitive Components

The following components are pre-defined. These are useful mainly as degenerate case results when defining component-valued functions, similarly to the way zero is useful in mathematics.

dead_source

has no inputs and a single output, which never transmits

diverter

has two inputs and two outputs. See the diana manual for the semantics.

iwire

has one input and one output terminal, initially sends a transition and then behaves as a wire

wire

has one input and one output terminal, engages in passive handshakes

live_source

has no inputs and one output, which initially sends one transition and then remains quiescent

sink

has one input and no outputs, and may safely receive at most one transition during its life.

unsafe_sink

has one input and no outputs, but may never safely receive any transitions at all

3.5.2 Component Families

These functions map numeric arguments to components whose input and output arity depends on the arguments. Components obtained from these functions have efficient DI decompositions that will be used by syndi in the construction of any netlist derived from them, as well as an efficient Petri net representation. It is therefore more efficient to use these where possible than to obtain equivalent circuits by other means.

arbiter(n)

Given a number n, this function returns a component with n request inputs and n grant outputs, and one acknowledge input. It responds to a transition on any request eventually with the corresponding grant, but will serve only one at a time in the event of concurrent requests, requiring an acknowledgment input after each grant.

celement(n)

This function takes a number n to a device with n inputs and one output, which waits for n concurrent input transitions and then responds with the output.

decision_wait(n,m)

Given a pair of numbers n and m, this function returns a decision wait element with n rows and m columns. The row inputs are first, followed by the columns, and the outputs are in row major order. The device responds to a concurrent input on row i and column j with a transition from the i,j-th output.

fork(n)

This function takes a number n to a component with one input and n outputs. Each input transition results in n concurrent output transitions.

majority(k,n)

Given a pair of numbers (k,n) this function returns a k-of-n majority gate. The device has n inputs and one output. It acknowledges with a transition on the output whenever any k of the inputs is signaled.

sparse_decision_wait<(r,c)...>

This function returns a restricted form of a decision wait element in which only certain combinations of row and column inputs are valid. The argument to the function is a list of pairs of numbers giving the valid combinations. Every row and every column is required to have at least one entry, or else an exception of "unused input" is thrown. The number of outputs on the device is equal to the length of the parameter list.

mutex(n)

This function takes a number n to a mutual exclusion element with n inputs and n outputs. Each input and output pair forms a passive four phase handshaking port. Concurrent inputs are allowed but only one handshake at a time may be completed.

random(n)

Given a number n, this function returns a device with one input and n outputs. A transition on the input is acknowledged with one transition on one of the outputs chosen at random.

sequencer(n)

This device is similar to an arbiter but requires an initial input transition on the acknowledgment input before behaving like one.

toggle(n)

This function takes a number n to a device with one input and n outputs. Each time an input transition is given, it is acknowledged with a transition from the next output in the sequence of outputs, which recycles after n transitions.

waveform(<<t1..tn>...>,<<s1..sn>...>)

This function requires an argument in the form of a pair of lists. Each item in the lists is a list of ones and zeros, not all of which are zero, and can be envisioned as the instantaneous amplitude of a waveform at a particular time step. The left list in the pair represents a transient waveform and the right represents the steady state. All of the lists of ones and zeros must have the same length. The device returned by this function will have one input, and a number of outputs equal to the length of the lists of ones and zeros, n. Each time an input transition is received by the device, it will respond with transitions on the outputs in the positions of the 1's in the current time step. The transient wave is emitted only once, and the steady state recycles indefinitely. Either may be empty.

xor(n)

Given a number n, this function returns an n-way exclusive or gate, which has n inputs and one output. It responds to a transition on any input with the output. Concurrent input transitions are not allowed.

3.5.3 Component Constructors

A small selection of functions operating on components is sufficient to allow arbitrarily complex components to be built from simpler ones. In fact, only the first two are really necesary.

zed(x)

This function takes a single component with at least one input and one output. The result is the component obtained by connecting the first unconnected output to the last unconnected input, which therefore will have one less externally available input and one less output.

arr<x1..xn>

This function takes a list of components and forms a single component by putting them together in order but not making any connections. The first input in the resulting component will be the first input on the first component in the argument, and the last input will be the last input on the last component.

popout(n) x

This function takes a number n to a function that will operate on any component x by reordering the outputs. The function will move the first n outputs of the component to the last positions, but otherwise preserve their order.

pushin(n) x

This function is analogous to popout, but pertains to inputs rather than outputs, and moves the last inputs to the first positions instead of the first to the last.

route(<x1..xn>,<y1..ym>) z

This function takes a pair of lists of numbers, both forming a consecutive set starting from zero, to a function that permutes the input and output terminals of a component accordingly. The length of each permutation must equal the corresponding number of terminals on the component to which the resulting function is applied, with the exception that an empty list is taken to mean that the order should remain unchanged.

snip(<a1..an>,<b1..bm>) x

This function takes a pair of lists of names to a function that will turn a circuit or a statement into a component, in effect by making the signals anonymous and imposing an order on them. The signal names in the lists must be a permutation on the actual signal names of the circuit or statement to which the resulting function is applied, as they serve to indicate the ordering on the terminals.

3.6 Circuits

Circuits are another primitive type in syndi, that are similar to components in that they can be envisioned as boxes that interact with their environment by sending and receiving signals on their terminals. However, unlike a component, the terminals on a circuit are unordered, and have names associated with them. Furthermore, whereas a component can not be written to a file with the #petrinet+ or #circuit+ directives, a circuit can. (Either can always be included in binary library files, as definitions of any type can.)

There are no pre-defined circuits, but there are three functions that allow circuits to be constructed.

circuit(x)

take a statement x and return a circuit having the same observable behavior

pins(<a1..an>,<b1..bm>) x

Given a pair of lists of names, pins returns a function that transforms a component to a circuit (c.f., snip). The names of the input terminals <a1..an> are on the left and the names of the output terminals <b1..bm> are on the right. The names are required to be mutually distinct. The function returned by pins may only be applied to a component x having matching numbers of input and output terminals, n and m, or else an exception will be thrown.

connected<x1..xn>

This function takes a list of circuits and returns the circuit obtained by connecting them according to their terminal names.

• If an input terminal on a circuit in the list has the same name as an output terminal on any circuit in the list, the two terminals are wired together, and are no longer accessible for further connections.
• If multiple circuits in the list have outputs with the same name, the terminals are merged through an exclusive-or gate.
• If multiple circuits in the list have inputs with the same name, an exception is thrown.
• Terminals with distinct names become terminals on the result.

The appropriate operation with shared inputs (i.e., the one to make all the commutative diagrams commute) would call for some sort of non-blocking arbitration between them, which does not have any reasonable circuit-level semantics, and hence causes an exception.

However, the connected function is polymorphic and will also operate on lists of statements to give a combined statement. In this case, shared inputs are allowed, and the statement can then be converted to a circuit.

3.7 Names

Names are not only a lexical class but a primitive data type in syndi, and have a few operations intended to make them more useful. These may assist in the management of large specifications by allowing their names to be handled with some uniformity.

instance(n) x

This function takes a name, n, to a function that will operate on a circuit or statement x by changing the names of its signals. The value of instance(n) x will be a circuit or statement similar to x, except that wherever a signal name s appears in x, the name n.s will appear in instance(n) x. Multiple instances of the same circuit or statement with different values of n could therefore be used in the same context without having any names in common. Nested instances are also acceptable.

list(n) x

This function takes a number, n, to a function that will operate on a value x of any type, and return a list containing n identical or similar copies of x. The contents of the list depend on the type of x.

• If x is a number, the result will be the list of consecutive numbers from x to x+n-1 in the case of positive n, or the empty list if n is zero (cf. range).
• If x is a name, the result will be a list of names of the form x.i, where i is a number from zero to n-1, in order of increasing i.
• If x is a component or a function, the result will be a list of n identical copies of x.
• If x is a statement or a circuit, the result will be a list of n statements or circuits, respectively, in which each item is a copy of x whose signal names have been subscripted with a different value of i ranging from zero to n-1. The first item in the list will have all signal names s changed to s.0, the second will have s.1, etc..
• If x is a tuple (y,z), the result will be a list of tuples whose left sides are the items of list(n) y and whose right sides are the items of list(n) z.
• If x is a list <y0..yn>, the result will be a list of lists, whose k-th item will be list(n) yk

dot(x,y)

This function is equivalent to the built in . operator, and is used for combining names. Both arguments should be either names, numbers, lists of names, or lists of numbers. Alternatively, the right argument could be a pair thereof, (w,z), and the result will be dot(x,dot(w,z)). The reserved names + and * have a special interpretation as explained in 2.1 Lexical Elements. Otherwise, the following rules apply.

• If x and y are both names or numbers, the result can not be expanded further and is denoted simply as x.y.
• If x is a name or number and y is a list <y0..yn>, the result is the list of names <x.y0..x.yn>
• If x is a list <x0..xn> and y is a name or number, the result is the list of names <x0.y..xn.y>
• If x is a list <x0..xn> and y is a list <y0..ym>, the result is the lists of all names xi.yj, where i ranges from zero to n, and j ranges from zero to m, in the order <x0.y0,x0.y1...>

rename<(a0,b0)..(an,bn)> x

This function takes a list of pairs of names (ai,bi) to a function that changes the names of the signals in a circuit or statement x. Every name ai in x is changed to the corresponding bi. The assignment of names must be unambiguous and the names in the result must be unique, or else an exception is thrown. However, it is not required to rename every signal in x, nor is every ai required to appear in x. Those that are not renamed retain their original values.

3.8 Statements

Statements are another primitive type in syndi, and are comparable to circuits in that they represent entities that interact with their environment or with other statements by exchanging named input and output signals. A statement can also be written to a file as a Petri net or a netlist by way of the #petrinet+ and #circuit+ directives. Unlike circuits, statements are specified in a procedural style as the term suggests, making them a more abstract description, and are supported by certain combining forms that are not applicable to circuits.

By analogy with conventional programming languages, statements in syndi may be considered to begin executing and perhaps to terminate. Unlike conventional languages, statements are not inherently constrained to execute sequentially or at predictable intervals.

3.8.1 Communicating Statements

The following functions take a list of signal names to a statement that engages in an input or output transaction with its environment. In the case of an empty argument, each of these functions returns a statement that starts executing and then immediately finishes. (The distinction between such a statement and one that never even begins executing is important for reasons discussed in 3.8.2 Compound Statements.)

get<s1..sn>

If all signals named in the list have been transmitted by the environment or by some other statement executing concurrently, and if no other statement receives any of them first, the statement returned by the get function will eventually receive them as a group and then terminate. If none of the signals or only some of the signals are available, the statement will be unable even to begin executing, and therefore will not receive any signals such as may be available.

getany<s1..sn>

If any of the signals in the list has been transmitted from elsewhere, the statement returned by getany may take the opportunity to begin executing, receive it, and then terminate. If multiple signals in the list are available, the statement may make a non-deterministic choice as to which one to receive. If no other concurrently executing statement is able to receive them, the getany statement eventually will.

getput<s1..sn>

This function takes a list of alternating input and output signal names, beginning with an input. The statement it returns will wait indefinitely to receive the first signal in the list, whereupon it will transmit the next signal in the list, if any, and then wait for the next one, and so on. The statement will not begin executing unless the first input signal is available, and will not terminate until it has reached the end of the list.

put<s1..sn>

The statement returned by this function will immediately begin executing, transmit the whole list of signals concurrently, and then terminate.

putany<s1..sn>

The statement returned by this function will immediately begin executing, transmit one signal chosen at random from the list, and then terminate.

putget<s1..sn>

The putget statement is analogous to getput, except that it begins by transmitting rather than receiving, and then alternately transmits and receives. It is therefore free to begin executing regardless of whether any of the inputs in the list is available at the time.

unget<s1..sn>

This function takes a list of signals to a statement whose execution renders them receivable by other concurrently executing statements. It differs from a put statement only in that the signals in the list are nevertheless regarded as inputs.

It is almost always a programming error for the argument to any of these functions except getput and putget to contain repeated signals, but this condition is not checked.

3.8.2 Compound Statements

There are three basic ways of combining statements so as to influence their schedule of execution relative to one another. Each of these functions takes a list of statements as an argument and returns a statement as a result.

do<s1..sn>

The statement returned by this function proceeds by executing each of the statements in the list sequentially starting with the first one, much like a standard imperative programming language. The do statement is not able to begin executing unless the first statement in the list is able to begin. Subsequent statements in the list that would normally be able to begin immediately, such as put and unget, are not able to begin until their predecessor in the list terminates. The do statement itself terminates when the last statement in the list terminates.

doall<s1..sn>

The doall statement works by allowing all of its constituent statements to begin concurrently executing immediately. The entire statement is considered to have begun executing as soon as any one of the statements in the list begins, but does not terminate until all of them begin and then terminate.

doany<s1..sn>

A doany statement also allows all of the statements in the list to begin executing immediately, but as soon as one of them begins, the others are barred from beginning. The whole statement terminates when the single statement that began executing terminates.

With any of these functions, the statements in the argument list may have some signals in common. Any signal that is an input on one statement and an output on another is exchanged internally and becomes neither an input nor an output for the resulting statement. Any output signal common to multiple statements may be transmitted to the environment by any of them, but multiple concurrent transmissions of the same output are always an error. Any input signal common to multiple statements will be received by at most one of them for each time it is transmitted. If more than one is concurrently executing, the recipient will be determined at random.

The issue of precise criteria whereby statements are said to begin execution is important mainly because of the doany statement, which has no equivalent in conventional programming languages but is essential for concurrent systems. The foregoing specifications imply that the statement doany<get<a,b>,get<b,c>> will always terminate successfully if either group of signals <a,b> or <b,c> is sent to it. On the other hand, doany<doall<get<a>,get<b>>,doall<get<b>,get<c>>> might not. In this case, either statement may begin executing if b arrives first. With no possibility of backtracking after it begins, deadlock occurs if the next signal to arrive does not match the one required by the statement that has already started. Note also that by design there is no provision in the language to stipulate the order in which signals will arrive, regardless of when they are sent.

Whether a doany statement behaves deterministically or not depends on the starting criteria of its constituent statements and the signals provided by the environment. Normal practice would impose determinacy by having each statement within the doany begin with an indivisible input operation (e.g., a get statement) whose signals are not a subset of the ones in any of the other statements. Non-determinacy prevails only when multiple statements are initially enabled, for example when they all begin with an output.

An explicit means of expressing a non-deterministic choice among any list of statements regardless of their starting criteria is provided by the pre-defined start statement. A statement of the form do<start,s1..sn> is always free to start in any environment, and hence a list of them in a doany statement will mean that one is chosen entirely at random. As this effect is rarely intended, the explicit use of the start statement indicates clearly when it is.

3.8.3 Degenerate Statements

These statements have no useful purpose in themselves but are sometimes convenient for their algebraic properties.

start

The start statement does nothing but immediately start executing and then finish. This statement is a right identity but not a left identity in a do statement. That is, do<s,start> is equivalent to s, but do<start,s> is not, for reasons explained in 3.8.2 Compound Statements. However, it is a left and a right identity for doall.

hang

This statement begins executing but never finishes and never outputs. It has the property that do<s0..sn,hang,t0..tn> is equivalent to do<s0..sn,hang>. It can be used to make a statement deliberately deadlock.

fail

This statement behaves unpredictably. It has the same property as hang, and the additional properties that both expressions doany<s0..sn,fail,t0..tn> and doall<s0..sn,fail,t0..tn> are equivalent to fail. When used as part of a circuit specification, it may sometimes facilitate optimization during synthesis by explicitly indicating "don't care" states reached through prohibited input combinations.

In addition to these statements, it is possible to define an identity for doany as getput<x,x>, i.e., that which never starts and never finishes, where x is any name. This statement is not predefined because no English word adequately describes it, but it may also be expressed as doany<>. Analogous expressions for the above statements are also valid, e.g., putget<x,x>, doall<> or do<> for start, do<start,getput<x,x>> for hang, and doall<unget<x>,put<x>> among others for fail.

3.8.4 Predicates

Predicates are a primitive data type in syndi and are used in conditional statements, just as they are in conventional programming languages. Predicates are not statements themselves and are useful only within a statement.

A very informal description of predicates in syndi would be that they test whether certain combinations of signals are available to be received from the environment or from other concurrently executing statements, that they direct the flow of control in a statement depending on the test result, and that when a test is successful, they indivisibly receive the relevant signals on behalf of the statement as a side effect.

Four predicate constructors are provided.

got<s1..sn>

This function takes a list of signal names to the predicate that succeeds when all signals in the list are available to be received, in which case it receives them (cf. get).

gotany<s1..sn>

This function takes a list of signal names to the predicate that succeeds when one or more signals in the list are available to be received, in which case it receives one of the available ones chosen at random (cf. getany).

all<p1..pn>

This function takes a list of predicates to the predicate that succeeds only if all predicates in the list can succeed simultaneously. In the event of success, all signals that would be received by the predicates individually are received collectively. If only some of the predicates in the list would succeed, the all predicate as a whole does not succeed and no signals are received.

any<p1..pn>

This function takes a list of predicates to the predicate that succeeds only if at least one of the predicates in the list is able to succeed. In the event of success, the signals receivable by the member of the list that was able to succeed are received. If more than one predicate in the list is able to succeed, the any predicate still succeeds, but only the set of signals associated with one of the successful predicates in the list chosen at random is received.

Note that the availability of signals is the only condition that can be tested. A statement may use a predicate in order to wait for a combination of signals to become available and then do something. It could also go ahead and do something without waiting. In either case, there is no need for negation of predicates, and none is provided. (The not function described in 3.1 Arithmetic Operators pertains only to compile time constants.)

Unlike the situation with doall and get, a predicate of the form all<got<a>,got<b>> is semantically equivalent to got<a,b>. Predicates are always transformed internally by syndi to sum-of-products form according to Boolean algebra. A statement will never deadlock due to merely testing a predicate (but of course, a predicate receiving signals can cause other statements waiting for those signals to deadlock).

3.8.5 Loop Statements

As in conventional programming languages, statements in syndi can be made to execute repeatedly, either forever, for a fixed number of times, or until some condition is met. The following pre-defined functions accomplish these objectives.

forever(s)

This function takes a statement s as an argument and returns a statement as a result. The resulting statement will have the same starting criteria as s (see 3.8.2 Compound Statements), but will never terminate. (I.e., anything coming after it in a do statement would never execute.) The statement returned will be observationally equivalent to an endless list of copies of s in a do statement. E.g., if s performs a single handshake with its environment, the result will perform infinitely many. Often a statement intended for circuit synthesis will be of the form forever(s) at its top level.

for(n) s

This function takes a number n as an argument and returns a function from statements to statements as a result. The resulting function takes a statement s to a statement that performs the actions of s n times and then terminates. This statement is thus equivalent to do (map constant s) range(1,n). Large values of n may cause infeasibly large circuits.

until(p) s

This function takes a predicate p to a function from statements to statements. The resulting function takes a statement s as an argument, and returns a statement that behaves like s executing repeatedly, while concurrently listening for the signals conducive to the success of p. When these signals become available, the statement completes the current iteration, if any, receives the signals, and terminates. Note that sending the signals is no guarantee of receiving them immediately, and s could still appear to execute a few times even if the signals were sent by a statement that terminated before the loop began.

3.8.6 Conditional Statements

Conditional statements are provided in syndi using predicates, as well as by other means. Where predicates are concerned, there is an element of non-determinacy compared to what one might expect from conventional programming languages, because signals in transit are not ordinarily certain to be readily receivable.

if(p) s

This function takes a predicate p to a function that takes a statement s to a qualified version of s. In the resulting statement, the signals that cause p to succeed may be received if available, and in that case the statement will then behave as s. Otherwise, the statement does nothing but begin executing and immediately terminate. The statement is therefore always free to begin executing whether the signals of interest are available or not, and furthermore there is no assurance that they will be received even if they are.

wait_until(p)

This function takes a predicate p to a statement that starts and finishes executing only when the conditions for the success of p are met, at which time it receives the relevant signals.

hang_if(p)

This function returns a statement that tests the predicate p, and if successful, it receives the associated signals and deliberately deadlocks. Otherwise, it terminates. (cf. hang)

fail_if(p)

This function returns a statement that tests the predicate p, and if successful, it receives the associated signals and deliberately devolves to the form of statement that is identified with a don't-care circuit or an unsafe Petri net. Otherwise, it terminates. (cf. fail)

assuming(e) s

This function takes a statement e to a function that takes a statement s to a restricted form of s. The input signals of the statement e should be the outputs of s, and the outputs of e should be the inputs of s. The result assuming(e) s will be a statement that is able to interact with its environment in whatever ways s interacts with e, but eschews any capabilities of s that this interaction does not require.

Some comments on these statements are in order. Whereas if statements are very common in sequential programming, they would be used only in unusual circumstances in syndi. The method of choice for writing specifications requiring very complex conditions should be with a wait_until statement at the beginning of each do statement inside of a doany statement.

The assuming statement is useful for efficient verification. If a statement of the form assuming(e) s is written to a file as a Petri net listing using the #petrinet+ directive, the file will contain a closed Petri net rather than one with open transitions. No existing Petri net analysis tools other than diana can cope with open Petri nets, and closed Petri nets are helpful even for diana because their state space is often exponentially smaller.

The assuming statement is also useful for efficient circuit synthesis. A specification in the absence of any information to the contrary will call for the synthesis of a circuit that is as receptive as possible. That may mean arbitration between concurrent inputs and buffering of inputs received in advance of their use. If it is known that the deployment environment is less demanding, the incorporation of the actual requirements through the assuming function will allow syndi to synthesize a simpler circuit.

The fail_if statement should never be used in a practical circuit specification. The closest it comes to being useful is in expressing combinations of inputs at points in the code where the specification is not required to cope with them, allowing syndi to synthesize a more efficient circuit. However, this purpose is better served by the assuming statement, which is more general, more readable, and more efficient.

Where the fail_if statement should be used is in the specification of an environment that will be written to a Petri net file to be used as the test environment along with a circuit to be verified by diana. By making the environment fragile enough to fail on those combinations of outputs that the circuit is not supposed to send, bugs in the circuit can be easily detected.

The hang_if statement serves a similar purpose to fail_if. If verification is performed with diana, there is probably no good reason to use it. However, the hang_if statement effectively allows any circuit verification problem to be converted to a deadlock detection problem, and deadlock detection is a vigorously studied subject for which better tools than diana may well be possible to find. In this case, the hang_if statement might for example be used in constructing the environment e in a statement of the form assuming(e) s, which will yield a closed Petri net suitable for analysis by generic tools (subject to file format conversion).

4. Status

Circuits synthesized by syndi always look plausible, but until it reaches a 1.0 release, syndi can be recommended for production use only in conjunction with a strict policy of verifying these circuits using diana. (It is unlikely that separate bugs in these two programs would collaborate maliciously, and diana has also been somewhat more thoroughly tested.) This caveat is less of an issue when syndi is used for constructing Petri net models or for semi-automated design using component families, which have been subject to greater scrutiny.

On non-GNU systems, time stamps on files aren't detected properly, and dependences listed in library and netlist files will always indicate an unknown date. This problem is due to a portability issue with avram rather than a bug in syndi.

The type inference isn't fool-proof. There is a remote possibility of a statement recurrence being mistaken for a function, making it inexpressible as a circuit or Petri net.

No other specific bugs are known, but any error message that doesn't look like it's intended to be self-explanatory is probably a sign of a bug. Any feedback would be greatly appreciated.

GNU GENERAL PUBLIC LICENSE

Copyright © 1989, 1991 Free Software Foundation, Inc.
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Everyone is permitted to copy and distribute verbatim copies
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Preamble

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2. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program.

   You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee.

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   Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program.

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How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found.

one line to give the program's name and an idea of what it does.
Copyright (C) 19yy  name of author

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

Also add information on how to contact you by electronic and paper mail.

If the program is interactive, make it output a short notice like this when it starts in an interactive mode:

Gnomovision version 69, Copyright (C) 19yy name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details
type `show w'.  This is free software, and you are welcome
to redistribute it under certain conditions; type `show c' 
for details.

The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program.

You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names:

Yoyodyne, Inc., hereby disclaims all copyright
interest in the program `Gnomovision'
(which makes passes at compilers) written 
by James Hacker.

signature of Ty Coon, 1 April 1989
Ty Coon, President of Vice

This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License.

Table of Contents

1. Usage

1.1 Options
1.2 Files

2. Syntax

2.1 Lexical Elements
2.2 Comments
2.3 Directives

2.3.1 Executable Files
2.3.2 Eagerness

3. Semantics

3.1 Arithmetic Operators
3.2 Projection Functions
3.3 List Mutators
3.4 Functional Combinators
3.5 Components

3.5.1 Primitive Components
3.5.2 Component Families
3.5.3 Component Constructors

3.6 Circuits
3.7 Names
3.8 Statements

3.8.1 Communicating Statements
3.8.2 Compound Statements
3.8.3 Degenerate Statements
3.8.4 Predicates
3.8.5 Loop Statements
3.8.6 Conditional Statements

4. Status
GNU GENERAL PUBLIC LICENSE