Extended Example. List Forwarding In this section we present a final example that illustrates all the features of the OCaml implementation of λCoS, including dependent contracts. We also take advantage of OCaml’s support for parametric polymorphism and recursive types, which we have omitted in the formal model of λCoS for the sake of simplicity. The following function 1 let forwarder_body x = 2 let rec aux y = 3 function
Extended Example. In this section we will present a small but realistic example on a breast can- cer dataset. The dataset contains nodes about x-ray properties and is intended for diagnostic purposes. The focus in this paper concentrates on explaining an MPE, therefore we will not discuss the medical background or how the BN was created. For further information to the data set, see [1]. However, it is notable that this network contains 16 nodes, which means that MPEs are quite hard to comprehend. To compute an exemplary MPE, we choose the scenario that no imag- ing has been done yet, and select a number of observations that can be done in clinical practice, in particular, we take the observations that Age(35–49), SkinRetract(Yes), NippleDischarge(No) and Location(UpInQuad). Given this evidence, the MPE solution that we find is: AD(No), BC(No), BreastDensity(medium), FibrTissue-Dev (Yes), LymphNodes(no), Margin(Ill- defined ), Mass(No), MC(No), Metastasis-(no), Shape(Other), Size(1 cm), Spic- ulation(Yes). The explanation with our method is: “The observed evidence age 35–49 and no nipple discharge is best explained by no architectural distortions. Given age 35–49, no nipple discharge and no architectural distortions, no metas- tasis is very likely. With the description of the previous sentence no lymph nodes will most probable be highly likely. Since no lymph nodes is highly likely and age 35–49 and no nipple discharge is given, no microcalcifications is very likely. Given age 35–49, no nipple discharge, no architectural distortions, no metasta- sis, no lymph nodes and no microcalcifications, breast cancer is very unlikely. With the description of the previous sentence size smaller than 1 cm will most probable be highly likely. In the pre-established combination other shape is highly likely. With the prior explanation no mass will most probable be highly likely. Given skin retract and UpInQuad location, fibrous tissue development is likely. Since fibrous tissue development is likely and skin retract and UpInQuad loca- tion is given, ill-defined margin is likely. With the description of the previous sentence spiculation is highly likely. Given no architectural distortions, no nip- ple discharge, size smaller than 1 cm, other shape and medium breast density is plausible”. We believe that this is a reasonable explanation that could be understandable for physician, although clearly not trivial. The explanation shows, which other nodes are important for the explanation of a node, ...
Extended Example. List Forwarding In this section we present a final example that illustrates all the features of the OCaml implementation of λCoS, including dependent contracts. We also take advantage of OCaml’s support for parametric polymorphism and recursive types, which we have omitted in the formal model of λCoS for the sake of simplicity. The following function 1 let forwarder_body x = 2 let rec aux y = 3 function 4 | [] → close (right y) 5 | v :: l → aux (send v (left y)) l in 6 let l, x = receive x in (* receive the elements to be forwarded *) 7 let y, x = receive x in (* receive the destination endpoint *) 8 close x; aux y l models the body of a forwarding service that delivers a list of elements to a given recipient, one element at a time. The service interacts with the client using the endpoint x, from which it receives a list l of elements (line 6) and another endpoint y on which the elements of the list should be forwarded (line 7). The main loop of the service (lines 2–5) iterates over the list: when the list is empty (line 4), the service selects the “right” branch of the protocol and closes the endpoint; when the list contains at least one element v, the service selects the “left” branch of the protocol, it sends v on y, and then iterates over the tail of the list (line 5). OCaml infers for forwarder_body the signature val forwarder_body : ?(α list).?(rec A.(!α .A) ⊕ end).end mt → unit where rec A.(!α .A) ⊕ end stands for the equi-recursive session type T that satisfies the equation T = (!α .T ) ⊕ end.1 As the type suggests, forwarder_body performs an arbitrary number of outputs on the delegated endpoint y, and by parametricity we also deduce that the elements being sent in these outputs must come from the list l. However, we do not know whether the number of forwarded elements actually matches the length of the list. The service can advertise this guarantee by means of the following contract: 1 let forwarder_c = 3 if n > 0 then (* more list elements *)
