X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=advanced_topics%2Fcalculator_improvements.mdwn;h=68bd39d8b44a8886bf2d0be673b33426ed12bc3e;hp=cbf4c89cfffd331d93abf855f3a6e9385014c501;hb=2cef07bcbf221a75e0cf0da553be6566a206d68f;hpb=3a2af9fce8aa8b45c0e5bd9774cff980dd5ed6f2 diff --git a/advanced_topics/calculator_improvements.mdwn b/advanced_topics/calculator_improvements.mdwn index cbf4c89c..68bd39d8 100644 --- a/advanced_topics/calculator_improvements.mdwn +++ b/advanced_topics/calculator_improvements.mdwn @@ -184,7 +184,7 @@ Here is the expanded definition for our language type: | Apply of (term * term) | Letrec of (char * term * term);; -Now consider what we'll need to do when evaluating a term like `Letrec ('f', Lambda (...), t2)`. The subterm `Lambda (...)` will evaluate to something of the form `Closure ('y', body, savedg)`, where `f` may occur free in `body`. What we'll want to do is to ensure that when `body` is applied, it's applied using not the assignment `savedg` but a modified assignment `savedg'` which binds `f` to this very function value. That is, we want to bind `f` not to: +Now consider what we'll need to do when evaluating a term like `Letrec ('f', Lambda (...), t2)`. The subterm `Lambda (...)` will evaluate to something of the form `Closure ('y', body, savedg)`, where `Variable 'f'` may occur free in `body`. What we'll want to do is to ensure that when `body` is applied, it's applied using not the assignment `savedg` but a modified assignment `savedg'` which binds `'f'` to this very function value. That is, we want to bind `'f'` not to: Closure ('y', body, savedg) @@ -197,9 +197,9 @@ but instead to: Except, this isn't quite right. It's almost what we want, but not exactly. Can you see the flaw? -The flaw is this: inside `new_closure`, what is `f` bound to? It's bound by `savedg'` to `orig_closure`, which in turn leaves `f` free (or bound to whatever existing value it had according to `savedg`). This isn't what we want. It'll break if we need to make recursive calls to `f` which go more than two levels deep. +The flaw is this: inside `new_closure`, what is `'f'` bound to? It's bound by `savedg'` to `orig_closure`, which in turn leaves `'f'` free (or bound to whatever existing value it had according to `savedg`). This isn't what we want. It'll break if we need to make applications of `Variable 'f'` which recurse more than once. -What we really want is for `f` to be bound to `new_closure`, something like this: +What we really want is for `'f'` to be bound to `new_closure`, something like this: let rec new_closure = Closure ('y', body, ('f', new_closure) :: savedg) in new_closure @@ -222,12 +222,12 @@ If we implemented assignments as functions rather than as lists of pairs, the co | Let (var_to_bind, t1, t2) -> let value1 = eval t1 g - in let g' = fun var -> if var = var_to_bind value1 else g var + in let g' = fun var -> if var = var_to_bind then value1 else g var in eval t2 g' ... | Letrec (var_to_bind, t1, t2) -> let Closure (arg_var, body, savedg) = eval t1 g - in let rec savedg' = fun var -> if var = var_to_bind Closure (arg_var, body, savedg') else savedg var + in let rec savedg' = fun var -> if var = var_to_bind then Closure (arg_var, body, savedg') else savedg var in let g' = fun var -> if var = var_to_bind then Closure (arg_var, body, savedg') else g var in eval t2 g';; @@ -245,7 +245,7 @@ The way we'll do this is that, when we bind a value to a variable, we'll keep tr Letrec ('f', Lambda ('y', Variable 'f')), ...) -In the first case, an application of `f` to any argument should evaluate to `Int 1`; in the second case, it should evaluate to the same function closure that `f` evaluates to. We'll keep track of which way a variable was bound by expanding our `bound_value` type: +In the first case, an application of `Variable 'f'` to any argument should evaluate to `Int 1`; in the second case, it should evaluate to the same function closure that `Variable 'f'` evaluates to. We'll keep track of which way a variable was bound by expanding our `bound_value` type: type expressed_value = Int of int | Bool of bool | Closure of char * term * assignment and bound_value = Nonrecursive of expressed_value | @@ -253,7 +253,7 @@ In the first case, an application of `f` to any argument should evaluate to `Int and assignment = (char * bound_value) list;; -Since we're not permitting ourselves OCaml's ability to recursively define cyclical lists, we're not going to be able to update the saved assignment in a closure when that closure is recursively bound to a variable. Instead, we'll just make a note of what variable `f` is supposed to be the recursively bound one---by binding it not to `Nonrecursive (Closure (arg_var, body, savedg))` but rather to `Recursive_Closure ('f', arg_var, body, savedg)`. We'll do the work to make the saved assignment recursive in the right way *later*, when we *evaluate* `f`. The result will look like this: +Since we're not permitting ourselves OCaml's ability to recursively define cyclical lists, we're not going to be able to update the saved assignment in a closure when that closure is recursively bound to a variable. Instead, we'll just make a note that variable `'f'` is supposed to be the recursively bound one---by binding it not to `Nonrecursive (Closure (arg_var, body, savedg))` but rather to `Recursive_Closure ('f', arg_var, body, savedg)`. We'll do the work to make the saved assignment recursive in the right way *later*, when we *evaluate* `Variable 'f'`. The result will look like this: let rec eval (t : term) (g: assignment) = match t with ...