X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=hints%2Fassignment_7_hint_6.mdwn;h=fd8f55d4ff6a160aea1b75693e22634993abe579;hp=38f6c2e09b38449cd7bdda53b8aeb7c8c6a6b9a9;hb=72cca371a48d35b0177427b35f23ae8cc704fdf2;hpb=767dc2f1f56176d59b16840613d6c0b170a229f3 diff --git a/hints/assignment_7_hint_6.mdwn b/hints/assignment_7_hint_6.mdwn index 38f6c2e0..fd8f55d4 100644 --- a/hints/assignment_7_hint_6.mdwn +++ b/hints/assignment_7_hint_6.mdwn @@ -19,35 +19,37 @@ let new_dpm = fun (r, h) -> (* if one_dpm isn't already false at (r, h), we want to check its behavior when updated with phi - bind_set (unit_set one_dpm) phi === phi one_dpm; do you remember why? *) - let (truth_value, _, _) = one_dpm (r, h) + set_bind (set_unit one_dpm) phi === phi one_dpm; do you remember why? *) + let (truth_value, r', h') = one_dpm (r, h) in let truth_value' = truth_value && (truths (phi one_dpm) (r, h) = []) (* new_dpm must return a (bool, r, h) *) - in (truth_value', r, h) - in unit_set new_dpm;; + in (truth_value', r', h') + in set_unit new_dpm;; - **Note: Simon pointed out a subtle error in this code, which we will look into fixing. At the moment, the subtle error is still there.** + **Thanks to Simon Charlow** for catching a subtle error in previous versions of this function. Fixed 1 Dec. * Representing \[[and φ ψ]] is simple: let and_op (phi : clause) (psi : clause) : clause = - fun one_dpm -> bind_set (phi one_dpm) psi;; + fun one_dpm -> set_bind (phi one_dpm) psi;; (* now u >>= and_op phi psi === u >>= phi >>= psi; do you remember why? *) * Here are `or` and `if`: + (These probably still manifest the bug Simon spotted.) + let or_op (phi : clause) (psi : clause) = - fun one_dpm -> unit_set ( + fun one_dpm -> set_unit ( fun (r, h) -> let truth_value' = ( truths (phi one_dpm) (r, h) <> [] || - truths (bind_set (negate_op phi one_dpm) psi) (r, h) <> [] + truths (set_bind (negate_op phi one_dpm) psi) (r, h) <> [] ) in (truth_value', r, h)) let if_op (phi : clause) (psi : clause) : clause = - fun one_dpm -> unit_set ( + fun one_dpm -> set_unit ( fun (r, h) -> let truth_value' = List.for_all (fun one_dpm -> let (truth_value, _, _) = one_dpm (r, h) @@ -63,17 +65,17 @@ type assignment = char -> int;; type store = entity list;; type 'a dpm = assignment * store -> 'a * assignment * store;; - let unit_dpm (x : 'a) : 'a dpm = fun (r, h) -> (x, r, h);; - let bind_dpm (u: 'a dpm) (f : 'a -> 'b dpm) : 'b dpm = + let dpm_unit (x : 'a) : 'a dpm = fun (r, h) -> (x, r, h);; + let dpm_bind (u: 'a dpm) (f : 'a -> 'b dpm) : 'b dpm = fun (r, h) -> let (a, r', h') = u (r, h) in let u' = f a in u' (r', h') type 'a set = 'a list;; - let empty_set : 'a set = [];; - let unit_set (x : 'a) : 'a set = [x];; - let bind_set (u : 'a set) (f : 'a -> 'b set) : 'b set = + let set_empty : 'a set = [];; + let set_unit (x : 'a) : 'a set = [x];; + let set_bind (u : 'a set) (f : 'a -> 'b set) : 'b set = List.concat (List.map f u);; type clause = bool dpm -> bool dpm set;; @@ -91,18 +93,18 @@ fun entity_dpm -> let eliminator = fun truth_value -> if truth_value = false - then unit_dpm false - else bind_dpm entity_dpm (fun e -> unit_dpm (f e)) - in fun one_dpm -> unit_set (bind_dpm one_dpm eliminator);; + then dpm_unit false + else dpm_bind entity_dpm (fun e -> dpm_unit (f e)) + in fun one_dpm -> set_unit (dpm_bind one_dpm eliminator);; (* doing the same thing for binary predicates *) let lift_predicate2 (f : entity -> entity -> bool) : entity dpm -> entity dpm -> clause = fun entity1_dpm entity2_dpm -> let eliminator = fun truth_value -> if truth_value = false - then unit_dpm false - else bind_dpm entity1_dpm (fun e1 -> bind_dpm entity2_dpm (fun e2 -> unit_dpm (f e1 e2))) - in fun one_dpm -> unit_set (bind_dpm one_dpm eliminator);; + then dpm_unit false + else dpm_bind entity1_dpm (fun e1 -> dpm_bind entity2_dpm (fun e2 -> dpm_unit (f e1 e2))) + in fun one_dpm -> set_unit (dpm_bind one_dpm eliminator);; let new_peg_and_assign (var_to_bind : char) (d : entity) : bool -> bool dpm = fun truth_value -> @@ -116,7 +118,7 @@ (* from hint 5 *) let exists var : clause = let extend one_dpm (d : entity) = - bind_dpm one_dpm (new_peg_and_assign var d) + dpm_bind one_dpm (new_peg_and_assign var d) in fun one_dpm -> List.map (fun d -> extend one_dpm d) domain (* include negate_op, and_op, or_op, and if_op as above *) @@ -124,7 +126,7 @@ * More: (* some handy utilities *) - let (>>=) = bind_set;; + let (>>=) = set_bind;; let getx = get 'x';; let gety = get 'y';; let initial_set = [fun (r,h) -> (true,r,h)];;