(set-box! ycell 3)
(+ x (unbox ycell)))
-(C has explicit-style mutable variables, too, which it calls *pointers*. But simple variables in C are already mutable, in the implicit style.)
+C has explicit-style mutable variables, too, which it calls *pointers*. But simple variables in C are already mutable, in the implicit style. Scheme also has both styles of mutation. In addition to the explicit boxes, Scheme also lets you mutate unboxed variables:
+
+ (begin
+ (define x 1)
+ (set! x 2)
+ x)
+ ; evaluates to 2
When dealing with explicit-style mutation, there's a difference between the types and values of `ycell` and `!ycell` (or in Scheme, `(unbox ycell)`). The former has the type `int ref`: the variable `ycell` is assigned a reference cell that contains an `int`. The latter has the type `int`, and has whatever value is now stored in the relevant reference cell. In an implicit-style framework though, we only have the resources to refer to the contents of the relevant reference cell. `y` in fragment [G] or the C snippet above has the type `int`, and only ever evaluates to `int` values.
Let's consider how to interpet our new syntactic forms `newref`, `deref`, and `setref`:
-1. \[[newref starting_val]] should allocate a new reference cell in the store and insert `starting_val` into that cell. It should return some "key" or "index" or "pointer" to the newly created reference cell, so that we can do things like:
+1. When `expr` evaluates to `starting_val`, **newref expr** should allocate a new reference cell in the store and insert `starting_val` into that cell. It should return some "key" or "index" or "pointer" to the newly created reference cell, so that we can do things like:
let ycell = newref 1
in ...
in (Index new_index, s'')
...
-2. When `expr` evaluates to a `store_index`, then `deref expr` should evaluate to whatever value is at that index in the current store. (If `expr` evaluates to a value of another type, `deref expr` is undefined.) In this operation, we don't change the store at all; we're just reading from it. So we'll return the same store back unchanged (assuming it wasn't changed during the evaluation of `expr`).
+2. When `expr` evaluates to a `store_index`, then **deref expr** should evaluate to whatever value is at that index in the current store. (If `expr` evaluates to a value of another type, `deref expr` is undefined.) In this operation, we don't change the store at all; we're just reading from it. So we'll return the same store back unchanged (assuming it wasn't changed during the evaluation of `expr`).
let rec eval expression g s =
match expression with
in (List.nth s' n, s')
...
-3. When `expr1` evaluates to a `store_index` and `expr2` evaluates to an `int`, then `setref expr1 expr2` should have the effect of changing the store so that the reference cell at that index now contains that `int`. We have to make a decision about what value the `setref ...` call should itself evaluate to; OCaml makes this `()` but other choices are also possible. Here I'll just suppose we've got some appropriate value in the variable `dummy`.
+3. When `expr1` evaluates to a `store_index` and `expr2` evaluates to an `int`, then **setref expr1 expr2** should have the effect of changing the store so that the reference cell at that index now contains that `int`. We have to make a decision about what value the `setref ...` call should itself evaluate to; OCaml makes this `()` but other choices are also possible. Here I'll just suppose we've got some appropriate value in the variable `dummy`.
let rec eval expression g s =
match expression with
(* evaluate expr2 using original assignment function and new store *)
in eval expr2 g s''
+Note: Chris uses this kind of machinery on the third page of the Nov 22 handout. Except he implements `Let` the way we here implement `Change`. And he adds an implementation of `Alias` (see below). Some minor differences: on his handout (and following Groenendijk, Stokhof and Veltman), he uses `r` and `g` where we use `g` and `s` respectively. Also, he implements his `r` with a function from `char` to `int`, instead of a `(char * int) list`, as we do here. It should be obvious how to translate between these. His implementation requires that variables always already have an associated peg. So that when we call `Let(c, expr1, expr2)` for the first time with `c`, there's a peg whose value is to be updated. That's easier to ensure when you implement the assignment as a function than as a `(char * int) list`.
+
##How to implement mutation with a State monad##
(* alternatively, an env could be implemented as type char -> int *)
type 'a reader = env -> 'a;;
- let unit_reader (value : 'a) : 'a reader =
+ let reader_unit (value : 'a) : 'a reader =
fun e -> value;;
- let bind_reader (u : 'a reader) (f : 'a -> 'b reader) : 'b reader =
+ let reader_bind (u : 'a reader) (f : 'a -> 'b reader) : 'b reader =
fun e -> let a = u e
in let u' = f a
in u' e;;
(* this corresponds to having only a single mutable variable *)
type 'a state = store -> ('a, store);;
- let unit_state (value : 'a) : 'a state =
+ let state_unit (value : 'a) : 'a state =
fun s -> (value, s);;
- let bind_state (u : 'a state) (f : 'a -> 'b state) : 'b state =
+ let state_bind (u : 'a state) (f : 'a -> 'b state) : 'b state =
fun s -> let (a, s') = u s
in let u' = f a
in u' s';;
in computation initial_store;;
+* See also our [[State Monad Tutorial]].
+
##Aliasing or Passing by reference##
Terminological note: in OCaml, `=` and `<>` express the qualitative (in)discernibility relations, also expressed in Scheme with `equal?`. In OCaml, `==` and `!=` express the numerical (non)identity relations, also expressed in Scheme with `eq?`. `=` also has other syntactic roles in OCaml, such as in the form `let x = value in ...`. In other languages, like C and Python, `=` is commonly used just for assignment (of either of the sorts we've now seen: `let x = value in ...` or `change x to value in ...`). The symbols `==` and `!=` are commonly used to express qualitative (in)discernibility in these languages. Python expresses numerical (non)identity with `is` and `is not`. What an unattractive mess. Don't get me started on Haskell (qualitative discernibility is `/=`) and Lua (physical (non)identity is `==` and `~=`).
- Note that neither of the equality predicates here being considered are the same as the "hyperequals" predicate mentioned above. For example, in the following (fictional) language:
+ Because of the particular way the numerical identity predicates are implemented in all of these languages, it doesn't quite match our conceptual expectations. For instance, For instance, if `ycell` is a reference cell, then `ref !ycell` will always be a numerically distinct reference cell containing the same value. We get this pattern of comparisons in OCaml:
+
+ ycell == ycell
+ ycell != ref !ycell (* true, these aren't numerically identical *)
+
+ ycell = ycell
+ ycell = ref !ycell (* true, they are qualitatively indiscernible *)
+
+ But now what about?
+
+ (0, 1, ycell) ? (0, 1, ycell)
+ (0, 1. ycell) ? (0, 1. ref !ycell)
+
+ You might expect the first pair to be numerically identical too---after all, they involve the same structure (an immutable triple) each of whose components is numerically identical. But OCaml's "physical identity" predicate `==` does not detect that identity. It counts both of these comparisons as false. OCaml's `=` predicate does count the first pair as equal, but only because it's insensitive to numerical identity; it also counts the second pair as equal. This shows up in all the other languages I know, as well. In Python, `y = []; (0, 1, y) is (0, 1, y)` evaluates to false. In Racket, `(define y (box 1)) (eq? (cons 0 y) (cons 0 y))` also evaluates to false (and in Racket, unlike traditional Schemes, `cons` is creating immutable pairs). They chose an implementation for their numerical identity predicates that is especially efficient and does the right thing in the common cases, but doesn't quite match our mathematical expectations.
+
+ Additionally, note that none of the equality predicates so far considered is the same as the "hyperequals" predicate mentioned above. For example, in the following (fictional) language:
let ycell = ref 1
in let xcell = ref 1
in let (adder', setter') = factory 1
in ...
- Of course, in most languages you wouldn't be able to evaluate a comparison like `getter = getter'`, because in general the question whether two computations always return the same values for the same argument is not decidable. So typically languages don't even try to answer that question. However, it would still be true that `getter` and `getter'` (and `adder` and `adder'`) were extensionally equivalent.
+ Of course, in most languages you wouldn't be able to evaluate a comparison like `getter = getter'`, because in general the question whether two functions always return the same values for the same arguments is not decidable. So typically languages don't even try to answer that question. However, it would still be true that `getter` and `getter'` (and `adder` and `adder'`) were extensionally equivalent.
However, they're not numerically identical, because by calling `setter 2` (but not calling `setter' 2`) we can mutate the function value `getter` (and `adder`) so that it's *no longer* qualitatively indiscernible from `getter'` (or `adder'`).
We use the `None`/`Some factorial` option type here just as a way to ensure that the contents of `fact_cell` are of the same type both at the start and the end of the block.
+* Now would be a good time to go back and review some material from [[week1]], and seeing how much we've learned. There's discussion back then of declarative or functional languages versus languages using imperatival features, like mutation. Mutation is distinguished from shadowing. There's discussion of sequencing, and of what we mean by saying "order matters."
+
+ In point 7 of the Rosetta Stone discussion, the contrast between call-by-name and call-by-value evaluation order appears (though we don't yet call it that). We'll be discussing that more in coming weeks. In the [[damn]] example, continuations and other kinds of side-effects (namely, printing) make an appearance. These too will be center-stage in coming weeks.
+
+* Now would also be a good time to read [Calculator Improvements](/week10). This reviews the different systems discussed above, as well as other capabilities we can add to the calculators introduced in [week7](/reader_monad_for_variable_binding). We will be building off of that in coming weeks.
+
##Offsite Reading##