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--- prs [2020/04/29 16:55] – created rajit
+++ prs [2020/04/29 16:57] (current) – removed rajit
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-===== The prs sublanguage =====
-The ''prs'' sublanguage is used to specify production rules. Production rules are the syntax used by ACT to specify pull-up and pull-down networks for a gate. For example, an inverter with input ''a'' and output ''b'' would be specified by the following production rule:
-<code>
-   a -> b-
-  ~a -> b+
-</code>
-The left-hand side of a production rule is a Boolean expression, and the right hand side specifies the action to be taken when the Boolean expression is true. A more complete example of an inverter in ACT would be:
-<code>
-bool a, b;
-prs {
-   a -> b-
-  ~a -> b+
-}
-</code>
-A two-input NAND gate with inputs ''a'' and ''b'' and output ''c'' would be:
-<code>
-prs {
-  a & b -> c-
- ~a | ~b -> c+
-}
-</code>
-A two-input inverting C-element would be:
-<code>
-prs {
-  a & b -> c-
-~a & ~b -> c+
-}
-</code>
-Note that the expressive power of production rules makes it equally easy to specify state-holding gates (like an inverting C-element) and combinational gates (like a NAND gate).
-==== The three types of arrows ====
-The syntax above is sufficient to be able to specify the Boolean conditions for arbitrary pull-up and pull-down networks, and uses a "simple" arrow (''- >''). In addition, there are two common cases of gates for which the prs language has special syntax.
-The first common case is a combinational gate like an inverter or NAND. In a combinational gate, the Boolean expression for the pull-up is the complement of the Boolean expression for the pull-down. In this case we can simply specify one, and use the ''= >'' arrow to let ACT know that this is a combinational gate---i.e., the second production rule can be automatically generated from the given rule. The following is the same two-input NAND gate specified using a more compact syntax:
-<code>
-prs {
-   a & b => c-
-}
-</code>
-Note that this is the same as specifying
-<code>
-prs {
-   ~a | ~b => c+
-}
-</code>
-In both cases, ACT generates the second production rule from the first one by complementing the Boolean expression and changing the direction of the signal transition (''+'' to ''-'' and vice versa).
-The second common case is that of C-elements. To specify the two-input C-element above, you can also write
-<code>
-prs {
-   a & b #> c-
-}
-</code>
-In this case, ACT generates the second production rule by complementing each variable in the Boolean expression.
-==== Loops ====
-When defining parameterized circuits, it is helpful to also have the corresponding parametrized production rules that implement the circuit. There are two loop constructs available that use the same "repetition" syntax within the body of the prs sublanguage.
-<code>
-bool x[5], y[5];
-prs {
-  (i:5: x[i] => y[i]-)
-}
-</code>
-The example above creates five inverters when the circuit is expanded. ''i'' is the loop variable, and the body of the loop is simply replicated.
-<code>
-bool x[5], y;
-prs {
-  (&i:5: x[i]) => y-
-}
-</code>
-The example above is a 5-input NAND gate. Here the replication construct is used with ''&'' as the separator, which is the same as:
-<code>
-...
-prs {
-  x[0] & x[1] & x[2] & x[3] & x[4] => y-
-}
-</code>
-Similarly, ''|'' can also be used as a separator. Note that these can be combined with other expressions as needed, as in the following example:
-<code>
-prs {
-  en & (|i:5: x[i]) -> y-
-  ~en -> y+
-}
-</code>
-==== CMOS implementation ====
-The ACT tools provide automated support for converting production rules into a transistor-level implementation. This is done in a way that is entirely under user control, so the way the production rules are written is strictly followed when creating the transistors that implement the production rules.
-=== Implementable rules ===
-In what follows, we assume that the production rule expression is written in negation-normal form((Negation-normal form for a Boolean expression corresponds to a Boolean expression where the negation symbol can only appear on a variable. In other words, an expression like ''~(a|b)'' is not in negation-normal form; it can easily be converted to negation-normal form using DeMorgan's rule to obtain ''~a&~b''.)).
-For a production rule to be //CMOS-implementable//, we require that all variables in the pull-up network are inverted, and all variables in the pull-down network are un-inverted. So in the example  below, the first rule is not CMOS-implementable while the second and third rules are.
-<code>
-  a & b -> c+
-  a & b -> d-
-  ~a | ~b -> e+
-</code>
-=== Transistor sizing and flavors ===
-The width, length, flavor, and folding of a transistor can be specified as part of the syntax of production rules. The following examples illustrate the syntax.
-<code>
-  a <10> & b <10> -> c-
-</code>
-In this example, the widths of the transistor for ''a'' and ''b'' are both 10 units. The value is dimensionless, and is converted into physical dimensions using the ''lambda'' parameter specified in the [[config:netlist|netlist configuration options]] file.
-<code>
-  a <20,4> & b <20,4> -> c-
-</code>
-In this example, the transistor specified is one with a width of 20 units and length of 4 units. The default values of width and length for p-type and n-type devices are specified in the [[config:netlist|netlist configuration file]]. In the earlier example, the standard length for the transistors would be used (which is typically set to the minimum valid length for the technology in the case of digital circuits).
-<code>
-  a <10,lvt> & b<10,lvt> -> c-
-</code>
-Transistors come in different //flavors// in a modern technology. The flavors supported by ACT are specified in the top-level ACT [[config:start|configuration]]. Here, the ''lvt'' flavor is being specified. The standard names that we use are ''svt'' (for standard Vt), ''lvt'', and ''hvt'' but these are configuration options.
-Finally, it is often the case that multiple transistors in an expression use the same sizing information.
-<code>
- a <10> & b -> c-
-</code>
-In this example, the sizing for ''b'' is omitted. However, it inherits the sizing for ''a''. This //implicit// sizing only applies to a single production rule.
-=== Gate ordering ===
-A rule of the form
-<code>
- a & b -> c-
-</code>
-it could be implemented with a series transistor chain. However, if the gates of the two series transistors are exchanged, the Boolean expression is still logically the same value although the circuit characteristics (e.g. delay) might be different.
-ACT imposes a strict interpretation on gate ordering, since a circuit designer might have carefully chosen the gate ordering for their circuit. The interpretation is that, since the output is on the right hand side of the production rule, the gate closest to the output corresponds to the rightmost variable. So, in the example above, the gate order would be that ''a'' is closest to ground, and ''b'' is closest to ''c''.
-=== Multi-finger transistors ===
-A multi-fingered transistor can be manually specified if necessary. The example
-<code>
-  (a <10> | a<10>) & (b<10> | b<10>) -> c-
-</code>
-would have the effect of using two multi-fingered transistors, with an effective width of 20 units each. This can be also specified as follows:
-<code>
-  a<20;2> & b<20;2> -> c-
-</code>
-or, using the implicit sizing rules, as
-<code>
- a<20;2> & b -> c-
-</code>