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