initial draft of plan options

spec/Section 5 -- Execution.md

@@ -10,3 +10,109 @@ request.
 The supergraph is a GraphQL IDL document that contains metadata for the query
 planner that describes the relationship between type system members and the type
 system members on subgraphs.
+
+## PlanOptions Algorithm
+
+The PlanOptions algorithm computes which source schemas (options) can resolve a specific path in the
+composite schema. The algorithm examines each step of the path to determine which source schemas can
+fulfill the requested fields.
+
+### Formal Specification
+
+me 
+
+Query.me.profile.age
+[
+  (Query, me),
+  (User, profile),
+  (Profile, age)
+]
+
+Mutation.createUser.query.me 
+[
+  (Mutation, createUser),
+  (CreateUserPayload, query),
+  (Query, me)
+]
+// Technically the first item doesnt have to check all source schemas twice (inintializ eoptions as [])
+//
+
+
+
+PlanOptions(path):
+- Let {pathElements} be the list of tuples ({type}, {field}) in the provided {path}.
+
+- Let ({initialType}, {initialField}) be the first element in {pathElements}.
+
+- Let {sourceSchemas} be an empty set.
+- For each {sourceSchema} in all source schemas:
+  - If {sourceSchema} does not define {initialType}.{initialField}
+    - Continue to the next {sourceSchema}.
+  - Add {sourceSchema} to {sourceSchemas}.
+
+PlanOptionsInternal(path, sourceSchemas):
+- For each {pathElement} in {pathElements} starting from the second element:
+  - Initialize a new empty set {nextSchemas}.
+  - Set {currentType} and {currentField} to the respective elements of the current {pathElement}.
+  - For each {currentSchema} in {sourceSchemas}:
+    - For each {candidateSchema} in all source schemas:
+      - If {candidateSchema} does not define {currentType}.{currentField}
+        - Continue to the next {candidateSchema}.
+
+      - If {candidateSchema} not equals {currentSchema}: 
+        - If {IsReachable(currentSchema, candidateSchema, currentType)} returns false:
+            - Continue to the next {candidateSchema}.
+
+      - If {currentField} on {currentType} in {candidateSchema} defines a requirement:
+        - If {ResolveRequirement(currentSchema, candidateSchema, currentType, currentField)} returns false:
+            - Continue to the next {candidateSchema}.
+
+      - Add {candidateSchema} to {nextSchemas}.
+
+  - If {nextSchemas} is empty:
+    - Return an empty set.
+
+  - Set {sourceSchemas} equal to {nextSchemas} to proceed to the next element in the path.
+
+- return {sourceSchemas}.
+
+IsReachable(sourceSchema, targetSchema, type):
+- If {targetSchema} does not define {type}
+  - return false
+- If {sourceSchema} equals {targetSchema}
+  - Assert: TODO This should be a precondition
+- Let {lookups} be the set of all lookup fields in {targetSchema} that return {type}
+- For each {lookup} in {lookups}:
+  - Let {keyFields} be the set of fields that form the key for {lookup} in {targetSchema}
+  - For each {keyField} in {keyFields}:
+    - If {ResolveRequirement(sourceSchema, targetSchema, type, keyField)} returns false
+      - // Continue to the next {lookup}
+  - return true
+- return false
+
+ResolveRequirement(currentSchema, candidateSchema, type, field):
+- Let {requirements} be the parsed selection map from requirements on {field}
+- Let {otherSchemas} be the set of all source schemas excluding {candidateSchema} and {currentSchema}
+- For each {requiredField} in {requirements}:
+  - Let {fieldPath} be the path to {requiredField} starting from {type}
+  - Let {canResolve} be false
+  - If {currentSchema} defines {type} and {fieldPath}
+    - If {PlanOptionsInternal(fieldPath, [currentSchema])} returns an non empty set
+      - Set {canResolve} to true
+  - For each {otherSchema} in {otherSchemas}:
+    - If {otherSchema} defines {type} and {fieldPath}
+      - // IsReachable
+        - If {PlanOptionsInternal(fieldPath, [currentSchema])} returns an non empty set
+          - Set {canResolve} to true
+          - Break
+  - If {canResolve} is false
+    - return false
+- return true
+
+Notes:
+{ user { profile { name id }} }
+user.profile.name
+user.profile.id
+user.profile.id -> UserSerivce
+profile.name -> ProfileService through a Lookup on user
+