From 3ae2b6a91a7bacea08d522cb94f78b2c7b2d95c9 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Thu, 25 Nov 2010 11:31:30 -0500 Subject: [PATCH] tweak calc improvements Signed-off-by: Jim Pryor --- advanced_topics/calculator_improvements.mdwn | 52 ++++++++++++++-------------- 1 file changed, 26 insertions(+), 26 deletions(-) diff --git a/advanced_topics/calculator_improvements.mdwn b/advanced_topics/calculator_improvements.mdwn index 4ddff279..e22afb1a 100644 --- a/advanced_topics/calculator_improvements.mdwn +++ b/advanced_topics/calculator_improvements.mdwn @@ -57,7 +57,7 @@ We'll switch over to using variable `g` for assignment functions, which is a con type bound_value = expressed_value;; type assignment = (char * bound_value) list;; -Here's where we should be now. We expand some of the clauses in the `eval` function for clarity: +Here's where we should be now. We expand some of the clauses in the `eval` function for clarity, and we rename a few variables: type term = Constant of int | Multiplication of (term * term) @@ -79,14 +79,14 @@ Here's where we should be now. We expand some of the clauses in the `eval` funct let Int value1 = eval t1 g in let Int value2 = eval t2 g in Int (value1 + value2) - | Variable c -> - (* we don't handle cases where g doesn't bind c to any value *) - List.assoc c g - | Let (c, t1, t2) -> - (* evaluate t2 under a new assignment where c has been bound to + | Variable var -> + (* we don't handle cases where g doesn't bind var to any value *) + List.assoc var g + | Let (var_to_bind, t1, t2) -> + (* evaluate t2 under a new assignment where var_to_bind has been bound to the result of evaluating t1 under the current assignment *) let value1 = eval t1 g - in let g' = (c, value1) :: g + in let g' = (var_to_bind, value1) :: g in eval t2 g' | Iszero t1 -> (* we don't handle cases where t1 doesn't evaluate to an Int *) @@ -143,7 +143,7 @@ Now our evaluation function needs two further clauses to interpret the two new e let rec eval (t : term) (g: assignment) = match t with ... - | Lambda(c, t1) -> Closure (c, t1, g) + | Lambda(arg_var, t1) -> Closure (arg_var, t1, g) | Apply(t1, t2) -> let value2 = eval t2 g (* we don't handle cases where t1 doesn't evaluate to a function value *) @@ -208,11 +208,11 @@ And as a matter of fact, OCaml *does* permit us to recursively define cyclical l let rec eval (t : term) (g: assignment) = match t with ... - | Letrec (c, t1, t2) -> + | Letrec (var_to_bind, t1, t2) -> (* we don't handle cases where t1 doesn't evaluate to a function value *) let Closure (arg_var, body, savedg) = eval t1 g - in let rec new_closure = Closure (arg_var, body, (c, new_closure) :: savedg) - in let g' = (c, new_closure) :: g + in let rec new_closure = Closure (arg_var, body, (var_to_bind, new_closure) :: savedg) + in let g' = (var_to_bind, new_closure) :: g in eval t2 g';; However, this is a somewhat exotic ability in a programming language, so it would be good to work out how to interpret `Letrec(...)` forms without relying on it. @@ -220,15 +220,15 @@ However, this is a somewhat exotic ability in a programming language, so it woul If we implemented assignments as functions rather than as lists of pairs, the corresponding move would be less exotic. In that case, our `Let(...)` and `Letrec(...)` clauses would look something like this: - | Let (c, t1, t2) -> + | Let (var_to_bind, t1, t2) -> let value1 = eval t1 g - in let g' = fun var -> if var = c then value1 else g var + in let g' = fun var -> if var = var_to_bind value1 else g var in eval t2 g' ... - | Letrec (c, t1, t2) -> + | Letrec (var_to_bind, t1, t2) -> let Closure (arg_var, body, savedg) = eval t1 g - in let rec savedg' = fun var -> if var = c then Closure (arg_var, body, savedg') else savedg var - in let g' = fun var -> if var = c then Closure (arg_var, body, savedg') else g var + in let rec savedg' = fun var -> if var = var_to_bind 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';; and this is just a run-of-the-mill use of recursive functions. However, for this exercise we'll continue using lists of pairs, and work out how to interpret `Letrec(...)` forms using them. @@ -257,24 +257,24 @@ Since we're not permitting ourselves OCaml's ability to recursively define cycli let rec eval (t : term) (g: assignment) = match t with ... - | Variable c -> ( - (* we don't handle cases where g doesn't bind c to any value *) - match List.assoc c g with + | Variable var -> ( + (* we don't handle cases where g doesn't bind var to any value *) + match List.assoc var g with | Nonrecursive value -> value | Recursive_Closure (self_var, arg_var, body, savedg) as rec_closure -> (* we update savedg to bind self_var to rec_closure here *) let savedg' = (self_var, rec_closure) :: savedg in Closure (arg_var, body, savedg') ) - | Let (c, t1, t2) -> - (* evaluate t2 under a new assignment where c has been bound to + | Let (var_to_bind, t1, t2) -> + (* evaluate t2 under a new assignment where var_to_bind has been bound to the result of evaluating t1 under the current assignment *) let value1 = eval t1 g (* we have to wrap value1 in Nonrecursive *) - in let g' = (c, Nonrecursive value1) :: g + in let g' = (var_to_bind, Nonrecursive value1) :: g in eval t2 g' ... - | Lambda(c, t1) -> Closure (c, t1, g) + | Lambda(arg_var, t1) -> Closure (arg_var, t1, g) | Apply(t1, t2) -> let value2 = eval t2 g (* we don't handle cases where t1 doesn't evaluate to a function value *) @@ -282,11 +282,11 @@ Since we're not permitting ourselves OCaml's ability to recursively define cycli (* evaluate body under savedg, except with arg_var bound to Nonrecursive value2 *) in let savedg' = (arg_var, Nonrecursive value2) :: savedg in eval body savedg' - | Letrec (c, t1, t2) -> + | Letrec (var_to_bind, t1, t2) -> (* we don't handle cases where t1 doesn't evaluate to a function value *) let Closure (arg_var, body, savedg) = eval t1 g - (* evaluate t2 under a new assignment where c has been recursively bound to that function value *) - in let g' = (c, Recursive_Closure(c, arg_var, body, savedg)) :: g + (* evaluate t2 under a new assignment where var_to_bind has been recursively bound to that function value *) + in let g' = (var_to_bind, Recursive_Closure(var_to_bind, arg_var, body, savedg)) :: g in eval t2 g';; -- 2.11.0