X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=hints%2Fassignment_7_hint_6.mdwn;h=344451a80a6200dbce92ea34d47652a9c7659032;hp=ed3828b7e83fb5059212f02f145dd932697ac3ea;hb=efa4651049a770c2935ebc11770bbdb23b8a3c6d;hpb=f212354152a53c6a3ab018c7874570c600f463b9

diff --git a/hints/assignment_7_hint_6.mdwn b/hints/assignment_7_hint_6.mdwn
index ed3828b7..344451a8 100644
--- a/hints/assignment_7_hint_6.mdwn
+++ b/hints/assignment_7_hint_6.mdwn
@@ -5,26 +5,17 @@
 
 	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;;
 
 		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 extensions set = List.filter (fun one_dpm -> let (truth_value, _, _) = one_dpm (r, h) in truth_value) set
+					in let truth_value' = extensions (phi one_dpm) = []
+                    in (truth_value', r, h)
+            )
 
 
 *	Representing \[[and &phi; &psi;]] is simple:
@@ -32,13 +23,24 @@
 		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) ->
+                    let extensions set = List.filter (fun one_dpm -> let (truth_value, _, _) = one_dpm (r, h) in truth_value) set
+					in let truth_value' = extensions (phi one_dpm) <> [] || extensions (bind_set (negate_op phi one_dpm) psi) <> []
+                    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) ->
+                    let extensions set = List.filter (fun one_dpm -> let (truth_value, _, _) = one_dpm (r, h) in truth_value) set
+					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) <> []) (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 +118,10 @@
 		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! *)