We have data packets with different structures. They are supposed to be read/written in different languages. Example:
| ClassId | Data |
ClassId = "datapoint" (Data structure):
temperature - 1bytes
elevation - 2bytes
gradient - 1bytes
ClassId = "config" (Data structure):
frequency - 1bytes
deviceId - 3bytes
ClassId = "accelerometer" (Data structure):
time - 2bytes
x - 2bytes
y - 2bytes
z - 2bytes
Rather than manually writing the code that parses each data packet based on its class (which is error prone and time-consuming), I would expect to have a configuration file and then the code (python/c/etc.) is generated automatically that can read and write packets. Something along these lines:
lib.set(packet, "datapoint", {
elevation: 933,
temperature: 18,
gradient: 20
});
lib.get(packet, "datapoint");
=>
{
elevation: 933,
temperature: 18,
gradient: 20
}
Googling it did not bring me anywhere. Any pointers would be very helpful.
You need a code generation system, that compiles a packet specification into code to parse/unparse the packets.
You can build one ad hoc using a parser generator, and write ad hoc code to procedurally walk a parse tree and spit out relevant code.
Or you can use a program transformation system (PTS), which treats your packet specifications like source code, and transforms to source code in your target language. You explain the syntax of the packets to the PTS pretty much the same way you explain the syntax to a parser generator.
But with a PTS, you can write transformation rules in surface syntax notation that recognizes the packet-system syntax and maps it to target langauge function syntax. That makes writing and maintaining such a tool a lot easier, especially if the packet syntax changes, and/or you change the target language infrastructure to parse the packets in different ways.
EDIT 10/3: OP asks for a concrete example, presumably with a PTS.
I'm going to show what this looks like for our DMS Software Reengineering Toolkit (see bio for more about DMS).
First you need an (DMS-compatible) grammar for the packet languages. Based on what I see, it is pretty simple:
Packets = Packet ;
Packets = Packets Packet ; -- allow a list of packet defintions
Packet = 'ClassID' '=' STRING members ;
members = ;
members = members member ; -- allow list of members
member = IDENTIFIER '-' NATURAL 'bytes' ;
I think this grammar is naive in that packet members in practice may have different types (maybe strings, floats, booleans, ...); OP's example only shows what I'm assuming are N-byte binary integer numbers. You also need grammars for your various target languages. I'm going to assume you have these grammars (and that's quite the assumption); lets work with C for the moment. [DMS does have many of these].
We also have to assume a representation of the transmitted data. OP suggests something but I think he is trying to hint at generated code ("lib.set...").
Instead I'm going to assume that packet content is being read from a Stream as binary bytes simply appended together; this makes for the smallest packet size possible and thus fast transmission times.
So, now we to specify our code generator, as set of rewrite rules that map packet definitions to code.
For background, a rewrite rule for a PTS typically looks like this:
if you see *this*, replace it by *that*
So you are essentially replacing one structure by another. These typically operate on ASTs, but use surface syntax for this and that for readability.
What follows are DMS's source to source rewrite rules; they look like they operate on text but in fact they operate on ASTs produced by DMS's parser.
DMS has its own syntax for rules but it essentially follows the typical style above:
rule rule_name( pattern_variables ):
source_syntax_category -> target_syntax_category =
" this_pattern " -> " that_pattern " ;
Source and target patterns are enclosed in *metaquotes" "; actual literal quote characters are thus escaped as \".
For DMS rules this is always a fragment of the Packet notation, and that is always a fragment of our chosen target language (C). Pattern variable names in the rule head are given syntactic types and can only match the corresponding type in the AST. Pattern variables found inside metaquotes are written as \variable. Metafunctions can compute derived results; they are invoked inside patterns as "\function( args )". See DMS Rewrite Rules for more details.
source domain Packet; -- the little language we defined
target domain C; -- what we will generate code for
-- you'll write one of these rulesets for each target language
rule top_level(pl: Packets): Packets -> Statements =
" \pl "
-> " ReadPacketType(stream, packet_type);
switch(packet_type) {
\pl
default: Panic(\"unrecognized packet type\");
}" if IsRoot(pl); -- do this once [at root of tree]
rule translate_packet_definitions(p: Packet, pl: packet_list): Packets -> switch_case_list
" \p \pl ";
rule translate_packet_definition(s:STRING, ms: members, pl: Packets): Packets -> switch_case =
" ClassID = \s \m \pl "
-> " case \concatenate\(\"enum_\"\,\string_to_identifier\(\s\)\): {
\string_to_identifier\(\s\)* p=malloc(sizeof(\string_to_identifier\(\s\)));
\m
return p;
}
";
rule translate_members(m: member, ms: members) : members -> Statements
= " \m \ms ";
rule translate_member(i: IDENTIFIER, n: NATURAL) = member -> StatementList =
" \i - \n bytes " ->
" p-> \toCIdentifer\(\i\) = ReadNByteValue(stream,\toCNatural\(\n\)) ; "
This isn't complete (in particular, I need anther set of rules to generate the enum declaration for the set of packet types) and I doubt if it is exactly right but it give the flavor of the rules. With these rules, OP's example input would generate this C code:
ReadPacketType(stream, packet_type);
switch(packet_type) {
case enum_datapoint: {
datapoint* p=malloc(sizeof(datapoint));
p->temperature=ReadNByteValue(stream,1);
p->elevation=ReadNByteValue(stream,2);
p->gradient=ReadNByteValue(stream,2);
return p;
}
case enum_config: {
config* p=malloc(sizeof(config));
p->frequency=ReadNByteValue(stream,1);
p->deviceId=ReadNByteValue(stream,3);
return p;
}
case enum_accelerometer: {
accelerometer* p=malloc(sizeof(accelerometer));
p-time>=ReadNByteValue(stream,2);
p->x=ReadNByteValue(stream,2);
p->y=ReadNByteValue(stream,2);
p->z=ReadNByteValue(stream,2);
return p;
}
default: Panic(\"unrecognized packet type\");
}
Related
I am writing a simple compiler as a school work. I am looking for an automated approach to generate both positive and negative testing data to test my compiler, given the formal grammar and other specification. The language I am dealing with is of mediate size with 38 or so non-terminals. For the sake of illustration, here is a snapshot of the grammar:
program: const_decl* declaration* ENDMARKER
# statement
stmt: flow_stmt | '{' stmt* '}' | NAME [stmt_trailer] ';' | ';'
stmt_trailer: arglist | ['[' expr ']'] '=' expr
flow_stmt: if_stmt | for_stmt | while_stmt | read_stmt ';' | write_stmt ';' | return_stmt ';'
return_stmt: 'return' ['(' expr ')']
if_stmt: 'if' '(' condition ')' stmt ['else' stmt]
condition: expr ('<'|'<='|'>'|'>='|'!='|'==') expr | expr
for_stmt: ('for' '(' NAME '=' expr ';' condition ';'
NAME '=' NAME ('+'|'-') NUMBER ')' stmt)
Is there any tools to generate input file with the help of the grammar? The hand-written tests are too tedious or too weak to discover problems. An example of this language here:
void main() {
int N;
int temp;
int i, j;
int array_size;
reset_heap;
scanf(N);
for (i = 0; i < N; i = i + 1) {
scanf(array_size);
if (array_size > max_heap_size) {
printf("array_size exceeds max_heap_size");
} else {
for (j = 0; j < array_size; j = j + 1) {
scanf(temp);
heap[j] = temp;
}
heap_sort(array_size);
print_heap(array_size);
}
}
}
Generating controllable testing data automatically can save the days. Given the simplicity of the language, there must be some way to effectively do this. Any pointer and insight is greatly appreciated.
Any pointer and insight is greatly appreciated.
This should have the subtopic of How to avoid combinatorial explosion when generating test data.
While I would not be surprised if there are tools to do this having had the same need to generate test data for grammars I have created a few one off applications.
One of the best series of articles I have found on this is by Eric Lippert, Every Binary Tree There Is, think BNF converted to binary operators then converted to AST when you read tree. However he uses Catalan (every branch has two leaves) and when I wrote my app I preferred Motzikin (a branch can have one or two leaves).
Also he did his in C# with LINQ and I did mine in Prolog using DCG.
Generating the data based on the BNF or DCG is not hard, the real trick is to limit the area of expansion and the size of the expansion and to inject bad data.
By area of expansion lets say you want to test nested if statements three levels deep, but have to have valid code that compiles. Obviously you need the boilerplate code to make it compile then you start changing the deeply nested if by adding or removing the else clause. So you need to put in constraints so that the boilerplate code is constant and the testing part is variable.
By size of expansion lets say that you want to test conditional expressions. You can easily calculate that if you have many operators and you want to test them all in combinations you soon run into combinatorial explosion. The trick is to ensure you test deep enough and with enough breadth but not every combination. Again the judicial use of constraints helps.
So the point of all of this is that you start with a tool that takes in the BNF and generates valid code. Then you modify the BNF to add constraints and modify the generator to understand the constraints to generate the code examples.
Then you modify the BNF for invalid data and likewise the generator to understand those rules.
After that is working you can then start layering on levels of automation.
If you do go this route and decide that you will have to learn Prolog, take a look at Mercury first. I have not done this with Mercury, but if I do it again Mercury is high on the list.
While my actual code is not public, this and this is the closest to it that is public.
Along the way I had some fun with it in Code Golf.
When generating terminals such as reserved words or values for types, you can use predefined list with both valid and invalid data, e.g. for if if the language is case sensitive I would include in the list if,If,IF,iF, etc. For value types such as unsigned byte I would include -1,0,255 and 256.
When I was testing basic binary math expressions with +, -, * and ^ I generated all the test for with three basic numbers -2,-1,0,1, and 2. I thought it would be useless since I already had hundreds of test cases, but since it only took a few minutes to generate all of the test cases and several hours to run it, to my surprise it found a pattern I did not cover. The point here is that contrary what most people say about having to many test cases, remember that it is only time on a computer by changing a few constraints so do the large number of test.
I am using Menhir to parse a DSL. My parser builds an AST using an elaborate collection of nested types. During later typecheck and other passes in error reports generated for a user, I would like to refer to source file position where it occurred. These are not parsing errors, and they generated after parsing is completed.
A naive solution would be to equip all AST types with additional location information, but that would make working with them (e.g. constructing or matching) unnecessary clumsy. What are the established practices to do that?
I don't know if it's a best practice, but I like the approach taken in the abstract syntax tree of the Frama-C system; see https://github.com/Frama-C/Frama-C-snapshot/blob/master/src/kernel_services/ast_data/cil_types.mli
This approach uses "layers" of records and algebraic types nested in each other. The records hold meta-information like source locations, as well as the algebraic "node" you can match on.
For example, here is a part of the representation of expressions:
type ...
and exp = {
eid: int; (** unique identifier *)
enode: exp_node; (** the expression itself *)
eloc: location; (** location of the expression. *)
}
and exp_node =
| Const of constant (** Constant *)
| Lval of lval (** Lvalue *)
| UnOp of unop * exp * typ
| BinOp of binop * exp * exp * typ
...
So given a variable e of type exp, you can access its source location with e.eloc, and pattern match on its abstract syntax tree in e.enode.
So simple, "top-level" matches on syntax are very easy:
let rec is_const_expr e =
match e.enode with
| Const _ -> true
| Lval _ -> false
| UnOp (_op, e', _typ) -> is_const_expr e'
| BinOp (_op, l, r, _typ) -> is_const_expr l && is_const_expr r
To match deeper in an expression, you have to go through a record at each level. This adds some syntactic clutter, but not too much, as you can pattern match on only the one record field that interests you:
let optimize_double_negation e =
match e.enode with
| UnOp (Neg, { enode = UnOp (Neg, e', _) }, _) -> e'
| _ -> e
For comparison, on a pure AST without metadata, this would be something like:
let optimize_double_negation e =
match e.enode with
| UnOp (Neg, UnOp (Neg, e', _), _) -> e'
| _ -> e
I find that Frama-C's approach works well in practice.
You need somehow to attach the location information to your nodes. The usual solution is to encode your AST node as a record, e.g.,
type node =
| Typedef of typdef
| Typeexp of typeexp
| Literal of string
| Constant of int
| ...
type annotated_node = { node : node; loc : loc}
Since you're using records, you can still pattern match without too much syntactic overhead, e.g.,
match node with
| {node=Typedef t} -> pp_typedef t
| ...
Depending on your representation, you may choose between wrapping each branch of your type individually, wrapping the whole type, or recursively, like in Frama-C example by #Isabelle Newbie.
A similar but more general approach is to extend a node not with the location, but just with a unique identifier and to use a final map to add arbitrary data to nodes. The benefit of this approach is that you can extend your nodes with arbitrary data as you actually externalize node attributes. The drawback is that you can't actually guarantee the totality of an attribute since finite maps are no total. Thus it is harder to preserve an invariant that, for example, all nodes have a location.
Since every heap allocated object already has an implicit unique identifier, the address, it is possible to attach data to the heap allocated objects without actually wrapping it in another type. For example, we can still use type node as it is and use finite maps to attach arbitrary pieces of information to them, as long as each node is a heap object, i.e., the node definition doesn't contain constant constructors (in case if it has, you can work around it by adding a bogus unit value, e.g., | End can be represented as | End of unit.
Of course, by saying an address, I do not literally mean the physical or virtual address of an object. OCaml uses a moving GC so an actual address of an OCaml object may change during a program execution. Moreover, an address, in general, is not unique, as once an object is deallocated its address can be grabbed by a completely different entity.
Fortunately, after ephemera were added to the recent version of OCaml it is no longer a problem. Moreover, an ephemeron will play nicely with the GC, so that if a node is no longer reachable its attributes (like file locations) will be collected by the GC. So, let's ground this with a concrete example. Suppose we have two nodes c1 and c2:
let c1 = Literal "hello"
let c2 = Constant 42
Now we can create a location mapping from nodes to locations (we will represent the latter as just strings)
module Locations = Ephemeron.K1.Make(struct
type t = node
let hash = Hashtbl.hash (* or your own hash if you have one *)
let equal = (=) (* or a specilized equal operator *)
end)
The Locations module provides an interface of a typical imperative hash table. So let's use it. In the parser, whenever you create a new node you should register its locations in the global locations value, e.g.,
let locations = Locations.create 1337
(* somewhere in the semantics actions, where c1 and c2 are created *)
Locations.add c1 "hello.ml:12:32"
Locations.add c2 "hello.ml:13:56"
And later, you can extract the location:
# Locations.find locs c1;;
- : string = "hello.ml:12:32"
As you see, although the solution is nice in the sense, that it doesn't touch the node data type, so the rest of your code can pattern match on it nice and easy, it is still a little bit dirty, as it requires global mutable state, that is hard to maintain. Also, since we are using an object address as a key, every newly created object, even if it was logically derived from the original object, will have a different identity. For example, suppose you have a function, that normalizes all literals:
let normalize = function
| Literal str -> Literal (normalize_literal str)
| node -> node
It will create a new Literal node from the original nodes, so all the location information will be lost. That means, that you need to update the location information, every time you derive one node from another.
Another issue with ephemera is that they can't survive the marshaling or serialization. I.e., if you store your AST somewhere in a file, and then you restore it, all nodes will loose their identity, and the location table will become empty.
Speaking of the "monadic approach" that you mentioned in comments. Though monads are magic, they still can't magically solve all the problems. They are not silver bullets :) In order to attach something to a node we still need to extend it with an extra attribute - either a location information directly or an identity through which we can attach properties indirectly. The monad can be useful for the latter though, as instead of having a global reference to the last assigned identifier, we can use a state monad, to encapsulate our id generator. And for the sake of completeness, instead of using a state monad or a global reference to generate unique identifiers, you can use UUID and get identifiers that are not only unique in a program run, but are also universally unique, in the sense that there are no other objects in the world with the same identifier, no matter how often you run your program (in the sane world). And although it looks like that generating the UUID doesn't use any state, underneath the hood it still uses an imperative random number generator, so it is sort of cheating, but still can seen as pure functional, as it doesn't contain observable effects.
So the question is about the grammar below. I'm working on a mini-interpreted language for fun (we learned about some compiler design in class, so I want to take it to the next level and try something on my own). I'm stuck trying to make the non-terminal symbol Expr.
Statement ::= Expr SC
Expr ::= /* I need help here */
Assign ::= Name EQUAL Expr
AddSub ::= MulDiv {(+|-) AddSub}
MulDiv ::= Primary {(*|/) MulDiv}
Primary ::= INT | FLOAT | STR | LP Expr RP | Name
Name ::= ID {. Name}
Expr has to be made such that Statement must allow for the two cases:
x = 789; (regular assignment, followed by semicolon)
x+2; (no assignment, just calculation, discarded; followed by a semicolon)
The purpose of the second case is to setup the foundation for more changes in the future. I was thinking about unary increment and decrement operators, and also function calls; both of which don't require assignment to be meaningful.
I've looked at other grammars (C# namely), but it was too complicated and lengthy to understand. Naturally I'm not looking for solutions, but only for guidance on how I could modify my grammar.
All help is appreciated.
EDIT: I should say that my initial thought was Expr ::= Assign | AddSub, but that wouldn't work since it would create ambiguity since both could start with the non-terminal symbol Name. I have made my tokenizer such that it allows one token look ahead (peek), but I have not made such a thing for the non terminals, since it would be trying to fix a problem that could be avoided (ambiguity). In the grammar, the terminals are the ones that are all-caps.
The simplest solution is the one actually taken by the designers of C, and thus by the various C derivatives: treat assignment simply as yet another operator, without restricting it to being at the top-level of a statement. Hence, in C, the following is unproblematic:
while ((ch = getchar()) != EOF) { ... }
Not everyone will consider that good style, but it is certainly common (particularly in the clauses of the for statement, whose syntax more or less requires that assignment be an expression).
There are two small complications, which are relatively easy to accomplish:
Logically, and unlike most operators, assignment associates to the right so that a = b = 0 is parsed as a = (b = 0) and not (a = b) = 0 (which would be highly unexpected). It also binds very weakly, at least to the right.
Opinions vary as to how tightly it should bind to the left. In C, for the most part a strict precedence model is followed so that a = 2 + b = 3 is rejected since it is parsed as a = ((2 + b) = 3). a = 2 + b = 3 might seem like terrible style, but consider also a < b ? (x = a) : (y = a). In C++, where the result of the ternary operator can be a reference, you could write that as (a < b ? x : y) = a in which the parentheses are required even thought assignment has lower precedence than the ternary operator.
None of these options are difficult to implement in a grammar, though.
In many languages, the left-hand side of an assignment has a restricted syntax. In C++, which has reference values, the restriction could be considered semantic, and I believe it is usually implemented with a semantic check, but in many C derivatives lvalue can be defined syntactically. Such definitions are unambiguous, but they are often not amenable to parsing with a top-down grammar, and they can create complications even for a bottom-up grammar. Doing the check post-parse is always a simple solution.
If you really want to distinguish assignment statements from expression statements, then you indeed run into the problem of prediction failure (not ambiguity) if you use a top-down parsing technique such as recursive descent. Since the grammar is not ambiguous, a simple solution is to use an LALR(1) parser generator such as bison/yacc, which has no problems parsing such a grammar since it does not require an early decision as to which kind of statement is being parsed. On the whole, the use of LALR(1) or even GLR parser generators simplifies implementation of a parser by allowing you to specify a grammar in a form which is easily readable and corresponds to the syntactic analysis. (For example, an LALR(1) parser can handle left-associative operators naturally, while a LL(1) grammar can only produce right-associative parses and therefore requires some kind of reconstruction of the syntax tree.)
A recursive descent parser is a computer program, not a grammar, and its expressiveness is thus not limited by the formal constraints of LL(1) grammars. That is both a strength and a weakness: the strength is that you can find solutions which are not limited by the limitations of LL(1) grammars; the weakness is that it is much more complicated (even, sometimes, impossible) to extract a clear statement about the precise syntax of the language. This power, for example, allows recursive descent grammars to handle left associativity in a more-or-less natural way despite the restriction mentioned above.
If you want to go down this road, then the solution is simple enough. You will have some sort of function:
/* This function parses and returns a single expression */
Node expr() {
Node left = value();
while (true) {
switch (lookahead) {
/* handle each possible operator token. I left out
* the detail of handling operator precedence since it's
* not relevant here
*/
case OP_PLUS: {
accept(lookahead);
left = MakeNode(OP_PLUS, left, value());
break;
}
/* If no operator found, return the current expression */
default:
return left;
}
}
}
That easily be modified to be able to parse both expressions and statements. First, refactor the function so that it parses the "rest" of an expression, given the first operator. (The only change is a new prototype and the deletion of the first line in the body.)
/* This function parses and returns a single expression
* after the first value has been parsed. The value must be
* passed as an argument.
*/
Node expr_rest(Node left) {
while (true) {
switch (lookahead) {
/* handle each possible operator token. I left out
* the detail of handling operator precedence since it's
* not relevant here
*/
case OP_PLUS: {
accept(lookahead);
left = MakeNode(OP_PLUS, left, value());
break;
}
/* If no operator found, return the current expression */
default:
return left;
}
}
}
With that in place, it is straightforward to implement both expr and stmt:
Node expr() {
return expr_rest(value());
}
Node stmt() {
/* Check lookahead for statements which start with
* a keyword. Omitted for simplicity.
*/
/* either first value in an expr or target of assignment */
Node left = value();
switch (lookahead) {
case OP_ASSIGN:
accept(lookahead);
return MakeAssignment(left, expr())
}
/* Handle += and other mutating assignments if desired */
default: {
/* Not an assignment, just an expression */
return MakeExpressionStatement(expr_rest(left));
}
}
}
In a functional program I have an API that provides functions on complex state implemented as a record:
let remove_number nr {counter ; numbers ; foo } = {counter ; numbers = IntSet.remove nr numbers ; foo}
let add_fresh {counter ; numbers ; foo } = { counter = counter + 1 ; numbers = IntSet.add counter numbers ; foo }
I know, I can use the simplified record modification syntax like this:
let remove_number nr state = { state with numbers = IntSet.remove nr numbers }
When the record type grows, the latter style is actually more readable. Hence, I will probably use it anyway. But out of curiosity, I wonder, whether it also allows the compiler to detect possible memory reusage more easily (my application is written in a monadic style, so there will usually only be one record that is passed along, hence an optimizing compiler could remove all allocations but one and do in-place-mutation instead). In my limited view, the with-syntax gives a good heuristic for places to apply such optimization, but is that true?
Does OCaml even optimize (unneeded) record allocations?
Is the record modification syntax lowered before any optimizations apply?
And finally, is there any pattern recognition implemented in the ocaml
compiler, that tells it that there is a "cheap" way to create one
record expression by modifying a "dead" value in place (and how is
that optimization usually called)?
The two versions of remove_number that you give are equivalent. The { expr with ... } notation doesn't modify a record. It creates a new record.
Record modification looks like this:
let remove_number nr rec = rec.numbers <- IntSet.remove nr rec.numbers
I don't think OCaml does the sort of optimization you describe. The plan with OCaml is to generate code that's close to what you write.
Given the following grammar:
S -> L=L
s -> L
L -> *L
L -> id
What are the first and follow for the non-terminals?
If the grammar is changed into:
S -> L=R
S -> R
L -> *R
L -> id
R -> L
What will be the first and follow ?
When I took a compiler course in college I didn't understand FIRST and FOLLOWS at all. I implemented the algorithms described in the Dragon book, but I had no clue what was going on. I think I do now.
I assume you have some book that gives a formal definition of these two sets, and the book is completely incomprehensible. I'll try to give an informal description of them, and hopefully that will help you make sense of what's in your book.
The FIRST set is the set of terminals you could possibly see as the first part of the expansion of a non-terminal. The FOLLOWS set is the set of terminals you could possibly see following the expansion of a non-terminal.
In your first grammar, there are only three kinds of terminals: =, *, and id. (You might also consider $, the end-of-input symbol, to be a terminal.) The only non-terminals are S (a statement) and L (an Lvalue -- a "thing" you can assign to).
Think of FIRST(S) as the set of non-terminals that could possibly start a statement. Intuitively, you know you do not start a statement with =. So you wouldn't expect that to show up in FIRST(S).
So how does a statement start? There are two production rules that define what an S looks like, and they both start with L. So to figure out what's in FIRST(S), you really have to look at what's in FIRST(L). There are two production rules that define what an Lvalue looks like: it either starts with a * or with an id. So FIRST(S) = FIRST(L) = { *, id }.
FOLLOWS(S) is easy. Nothing follows S because it is the start symbol. So the only thing in FOLLOWS(S) is $, the end-of-input symbol.
FOLLOWS(L) is a little trickier. You have to look at every production rule where L appears, and see what comes after it. In the first rule, you see that = may follow L. So = is in FOLLOWS(L). But you also notice in that rule that there is another L at the end of the production rule. So another thing that could follow L is anything that could follow that production. We already figured out that the only thing that can follow the S production is the end-of-input. So FOLLOWS(L) = { =, $ }. (If you look at the other production rules, L always appears at the end of them, so you just get $ from those.)
Take a look at this Easy Explanation, and for now ignore all the stuff about ϵ, because you don't have any productions which contain the empty-string. Under "Rules for First Sets", rules #1, #3, and #4.1 should make sense. Under "Rules for Follows Sets", rules #1, #2, and #3 should make sense.
Things get more complicated when you have ϵ in your production rules. Suppose you have something like this:
D -> S C T id = V // Declaration is [Static] [Const] Type id = Value
S -> static | ϵ // The 'static' keyword is optional
C -> const | ϵ // The 'const' keyword is optional
T -> int | float // The Type is mandatory and is either 'int' or 'float'
V -> ... // The Value gets complicated, not important here.
Now if you want to compute FIRST(D) you can't just look at FIRST(S), because S may be "empty". You know intuitively that FIRST(D) is { static, const, int, float }. That intuition is codified in rule #4.2. Think of SCT in this example as Y1Y2Y3 in the "Easy Explanation" rules.
If you want to compute FOLLOWS(S), you can't just look at FIRST(C), because that may be empty, so you also have to look at FIRST(T). So FOLLOWS(S) = { const, int, float }. You get that by applying "Rules for follow sets" #2 and #4 (more or less).
I hope that helps and that you can figure out FIRST and FOLLOWS for the second grammar on your own.
If it helps, R represents an Rvalue -- a "thing" you can't assign to, such as a constant or a literal. An Lvalue can also act as an Rvalue (but not the other way around).
a = 2; // a is an lvalue, 2 is an rvalue
a = b; // a is an lvalue, b is an lvalue, but in this context it's an rvalue
2 = a; // invalid because 2 cannot be an lvalue
2 = 3; // invalid, same reason.
*4 = b; // Valid! You would almost never write code like this, but it is
// grammatically correct: dereferencing an Rvalue gives you an Lvalue.