assignment7 tweaks

[lambda.git] / hints / assignment_7_hint_6.mdwn

diff --git a/hints/assignment_7_hint_6.mdwn b/hints/assignment_7_hint_6.mdwn
index ed3828b..740eba2 100644 (file)
--- a/hints/assignment_7_hint_6.mdwn
+++ b/hints/assignment_7_hint_6.mdwn
@@ -5,26 +5,19 @@
 
        where `i` *subsists* in <code>s[&phi;]</code> if there are any `i'` that *extend* `i` in <code>s[&phi;]</code>.
 
------- wrong....
-
-       In our framework, we just have to convert the operation <code>>>= \[[&psi;]]</code> into another operation <code>>>= \[[&psi;]] >>= neg</code>, where `neg` flips the truth-value of all the `bool dpm`s it operates on:
+       Here's how to do that in our framework:
 
                type clause_op = bool dpm -> bool dpm set;;
+               
+               (* filter out which bool dpms in a set are true when receiving (r, h) as input *)
+               let extensions set (r, h) = List.filter (fun one_dpm -> let (truth_value, _, _) = one_dpm (r, h) in truth_value) set;;
 
                let negate_op (phi : clause_op) : clause_op =
-                       let neg : clause_op = fun one_dpm ->
-                                               unit_set (fun (r, h) ->
-                                                       let (truth_value, r', h') = one_dpm (r, h)
-                                                       in (not truth_value, r', h'))
-                       in fun one_dpm -> bind_set (phi one_dpm) neg;;
-
-
-               let negate_op (phi : clause_op) : clause_op =
-                       fun one_dpm ->
-                               if blah
-                               then unit_set one_dpm
-                               else empty_set
-------
+                       fun one_dpm -> unit_set (
+                fun (r, h) ->
+                                       let truth_value' = extensions (phi one_dpm) (r, h) = []
+                    in (truth_value', r, h)
+            )
 
 
 *      Representing \[[and &phi; &psi;]] is simple:
@@ -32,13 +25,25 @@
                let and_op (phi : clause_op) (psi : clause_op) : clause_op =
                        fun one_dpm -> bind_set (phi one_dpm) psi;;
 
-*      We define the other connectives in terms of `not` and `and`:
+*      Here are `or` and `if`:
 
                let or_op (phi : clause_op) (psi : clause_op) =
-                       negate_op (and_op (negate_op phi) (negate_op psi))
+                       (* NOT: negate_op (and_op (negate_op phi) (negate_op psi)) *)
+            fun one_dpm -> unit_set (
+                fun (r, h) ->
+                                       in let truth_value' = extensions (phi one_dpm) (r, h) <> [] || extensions (bind_set (negate_op phi one_dpm) psi) (r, h) <> []
+                    in (truth_value', r, h))
+
+               let if_op (phi : clause_op) (psi : clause_op) : clause_op =
+                       (* NOT: negate_op (and_op phi (negate_op psi)) *)
+            fun one_dpm -> unit_set (
+              fun (r, h) ->
+                                       in let truth_value' = List.for_all (fun one_dpm ->
+                                                       let (truth_value, _, _) = one_dpm (r, h)
+                                                       in truth_value = false || extensions (psi one_dpm) (r, h) <> []
+                                               ) (phi one_dpm)
+                    in (truth_value', r, h));;
 
-               let if_op (phi : clause_op) (psi : clause_op) =
-                       negate_op (and_op phi (negate_op psi));;
 
 *      Now let's test everything we've developed:
 
@@ -116,10 +121,10 @@
                let antecedent = fun one_dpm -> exists 'x' one_dpm >>= lift_predicate male getx >>= exists 'y' >>= lift_predicate2 wife_of getx gety;;
                
                (* "if a man x has a wife y, x kisses y" *)
-               run (initial_set >>= if_op antecedent lift_predicate2 kisses getx gety);;
+               run (initial_set >>= if_op antecedent (lift_predicate2 kisses getx gety));;
                (* Bob has wife Carol, and kisses her; and Ted has wife Alice and kisses her; so this is true! *)
 
                (* "if a man x has a wife y, x misses y" *)
-               run (initial_set >>= if_op antecedent lift_predicate2 misses getx gety);;
+               run (initial_set >>= if_op antecedent (lift_predicate2 misses getx gety));;
                (* Bob has wife Carol, and misses her; but Ted misses only Carol, not his wife Alice; so this is false! *)