.. _language-semantics:

Language semantics
------------------

.. class:: nodoc

> module Codec.Pesto.Graph (
> 	  toGraph
> 	, walkRoot
> 	, outgoingEdges
> 	, outgoingNodes
> 	, incomingEdges
> 	, incomingNodes
> 	, firstNodeId
> 	, resolveReferences
> 	, test
> 	, extract
> 	, extractIngredients
> 	, mergeQuantity
> 	, NodeId
> 	, Node
> 	, Nodes
> 	, Edge
> 	, Edges
> 	) where
> import Data.Char (toLower)
> import Data.List (sort, nub, sortOn)
> import Test.HUnit hiding (test, Node)
> import Data.Ratio ((%), Ratio)
>
> import Codec.Pesto.Parse hiding (test)

The parser’s output, a stream of instructions, may contain multiple recipes. A
recipe must start with the directive “pesto” and may end with
“buonappetito”, which allows embedding recipes into other (plain-text)
documents. This function extracts all recipes from the stream and removes
both directives.

> startDirective = Directive "pesto"
> endDirective = Directive "buonappetito"

> extract [] = []
> extract (s:stream) | s == startDirective = between:extract next
> 	where
> 		isEnd x | x `elem` [startDirective, endDirective] = True
> 		isEnd _ = False
> 		(between, next) = break isEnd stream
> extract (_:xs) = extract xs

Start and end directives are removed from the extracted instructions.  The
directive “buonappetito” is optional at the end of a stream.

> testExtract = [
> 	  extract [startDirective, endDirective] ~?= [[]]
> 	, extract [startDirective, Action "foobar", endDirective] ~?= [[Action "foobar"]]
> 	, extract [startDirective] ~?= [[]]
> 	, extract [startDirective, Directive "foobar"] ~?= [[Directive "foobar"]]

Instructions surrounding the start and end directive are removed.

> 	, extract [Unknown "Something", startDirective] ~?= [[]]
> 	, extract [Unknown "Something", Action "pour", startDirective] ~?= [[]]
> 	, extract [startDirective, endDirective, Annotation "something"] ~?= [[]]

The stream may contain multiple recipes. The start directive also ends the
previous recipe and starts a new one.

> 	, extract [
> 		  startDirective
> 		, Action "pour"
> 		, endDirective
> 		, Action "foobar"
> 		, startDirective
> 		, Annotation "something"]
> 		~?= [[Action "pour"], [Annotation "something"]]
> 	, extract [
> 		  startDirective
> 		, Action "heat"
> 		, startDirective
> 		, Annotation "something"]
> 		~?= [[Action "heat"], [Annotation "something"]]
> 	, extract [
> 		  startDirective
> 		, Annotation "foobar"
> 		, startDirective
> 		, endDirective]
> 		~?= [[Annotation "foobar"], []]
> 	]

Each recipe’s stream of instructions drives a stack-based machine that transforms
it into a directed graph. Think of the stack as your kitchen’s workspace that
is used to prepare the food’s components. You can add new ingredients, perform
actions on them, put them aside, and add them again.

This function processes a list of nodes, that is, instructions uniquely identified
by an integer, and returns the edges of the directed graph as a list of tuples.

> toGraph :: Nodes Instruction -> Edges
> toGraph nodes = third $ foldl f (Nothing, [[]], []) nodes
> 	where

Ingredients are simply added to the current workspace. They should, for example,
appear on the shopping list.

> 		f ctx (i, Ingredient _) = addToStack ctx i

The same happens for tools. However, they are not part of the final product
but are used in the process of making it.  Thus, they do not appear on the
shopping list. `Time is considered a tool <#time-is-a-tool>`_.

> 		f ctx (i, Tool _) = addToStack ctx i

Actions take all ingredients and tools currently on the workspace, perform some
action with them, and put the product back onto the workspace.

> 		f (_, stack:sx, edges) (i, Action _) = (Just i, [i]:stack:sx, edgesTo i stack ++ edges)
> 		f (_, [], _) (_, Action _) = undefined -- never reached

Results add a label to the current workspace’s contents and move them out of
the way. It should be a meaningful name, not just A and B.
Consecutive results add different labels to the same workspace. That’s useful
when an action yields multiple results at once that are processed in different
ways.

> 		f ctx (i, Result _) = consumeStack ctx i

Alternatives, too, add a label to the current workspace’s content, but they pick
one of the things on the workspace and throw everything else away. This allows
adding optional or equivalent ingredients to a recipe (i.e., margarine or butter).

> 		f ctx (i, Alternative _) = consumeStack ctx i

References are similar to ingredients. They are used to add items from a
workspace labeled with ``Result`` or ``Alternative``. More on that `in the next section
<#references>`_.

> 		f ctx (i, Reference _) = addToStack ctx i

Annotations add a description to any of the previous instructions. They can be
used to provide more information about ingredients (so “hot water” becomes
``+water (hot)``, tools (``&oven (200 °C)``), or actions (``[cook]
(until brown)``).

> 		f ctx@(Nothing, _, _) (_, Annotation _) = ctx
> 		f (Just prev, s, edges) (i, Annotation _) = (Just prev, s, (i, prev):edges)

Unused directives or unknown instructions are danging nodes with no connection to
other nodes.

> 		f ctx (_, Directive _) = ctx
> 		f ctx (_, Unknown _) = ctx

These are helper functions:

> 		addToStack (_, stack:sx, edges) i = (Just i, (i:stack):sx, edges)
> 		addToStack (_, [], _) _ = undefined -- never reached
> 		consumeStack (_, s, edges) i =
> 			let
> 				stack = dropWhile null s
> 				(top:sx) = if null stack then [[]] else stack
> 			in (Just i, []:top:sx, edgesTo i top ++ edges)
> 		edgesTo i = map (\x -> (x, i))

Here are a few examples of how this stack-machine works. Each edge is a tuple of
two integer numbers. These are the nodes it connects, starting with zero.
``Ingredient``, ``Tool``, and ``Reference`` itself do not create any edges:

> testGraph = [
> 	  cmpGraph "+ketchup &spoon *foobar" []

But ``Action``, ``Alternative`` and ``Result`` do in combination with them:

> 	, cmpGraph "+foobar [barbaz]" [(0, 1)]
> 	, cmpGraph "+foobar |barbaz" [(0, 1)]
> 	, cmpGraph "+foobar >barbaz" [(0, 1)]
> 	, cmpGraph "+foobar +B >barbaz" [(0, 2), (1, 2)]
> 	, cmpGraph "+foobar >barbaz +foobar >barbaz" [(0, 1), (2, 3)]
> 	, cmpGraph "+foobar [barbaz] +foobar >barbaz" [(0, 1), (1, 3), (2, 3)]
> 	, cmpGraph "&foobar [barbaz] [C] >D" [(0, 1), (1, 2), (2, 3)]

If the stack is empty, i.e. it was cleared by a ``Result`` or ``Alternative``
instruction, consecutive results or alternatives operate on the *previous*,
non-empty stack.

> 	, cmpGraph "+foobar >barbaz >C" [(0, 1), (0, 2)]
> 	, cmpGraph "+foobar >barbaz >C >D" [(0, 1), (0, 2), (0, 3)]
> 	, cmpGraph "+foobar |barbaz |C" [(0, 1), (0, 2)]
> 	, cmpGraph "+foobar >barbaz |C" [(0, 1), (0, 2)]

Unless that stack too is empty. Then they do nothing:

> 	, cmpGraph ">foobar >foobar" []
> 	, cmpGraph "|foobar |foobar" []
> 	, cmpGraph "(foobar) (foobar)" []
> 	, cmpGraph "[foobar]" []

The ``Annotation`` instruction always creates an edge to the most-recently processed
node that was not an annotation. Thus two consecutive annotations create edges
to the same node.

> 	, cmpGraph "+foobar (barbaz)" [(1, 0)]
> 	, cmpGraph "+foobar (barbaz) (C)" [(1, 0), (2, 0)]
> 	, cmpGraph "+foobar (barbaz) >barbaz" [(1, 0), (0, 2)]
> 	, cmpGraph "+foobar >barbaz (C)" [(0, 1), (2, 1)]
> 	, cmpGraph "+foobar |barbaz (C)" [(0, 1), (2, 1)]
> 	, cmpGraph "*foobar (C)" [(1, 0)]

Unknown directives or instructions are never connected to other nodes.

> 	, cmpGraph "%invalid" []
> 	, cmpGraph "invalid" []
> 	]

.. _references:

References
++++++++++

Results and alternatives can be referenced with the ``Reference`` instruction.
Resolving these references does not happen while building the graph but
afterward. This allows referencing a result or alternative before its
definition with regard to their processing order.

Resolving references is fairly simple: For every reference’s object name, a
case-insensitive lookup is performed in a table containing all results and
alternatives. If it succeeds, an edge from every result and alternative returned
to the reference in question is created.

> resolveReferences :: Nodes Instruction -> Edges
> resolveReferences nodes = foldl f [] nodes
> 	where
> 		f edges (i, ref@(Reference _)) = map (\x -> (x, i)) (findTargets nodes ref) ++ edges
> 		f edges _ = edges

> findTargets :: Nodes Instruction -> Instruction -> [NodeId]
> findTargets nodes (Reference (Quantity _ _ a)) = map fst $ filter (isTarget a) nodes
> 	where
> 		lc = map toLower
> 		isTarget dest (_, Result (Quantity _ _ x)) = lc x == lc dest
> 		isTarget dest (_, Alternative (Quantity _ _ x)) = lc x == lc dest
> 		isTarget _ _ = False
> findTargets _ _ = []

References are position-independent and can be used before or after the
result instruction they are referencing.

> testRef = [
> 	  cmpGraphRef ">foobar *foobar" [(0, 1)]
> 	, cmpGraphRef ">foobar |foobar *foobar" [(0, 2), (1, 2)]
> 	, cmpGraphRef "+A >foobar +B >barbaz *foobar *barbaz" [(1, 4), (3, 5)]
> 	, cmpGraphRef "*foobar >foobar" [(1, 0)]

Nonexistent references do not create an edge.

> 	, cmpGraphRef ">foobar *barbaz" []

References can use amounts and units.

> 	, cmpGraphRef ">foobar *1 _ foobar *2 _ foobar" [(0, 1), (0, 2)]

There are a few cases that do not make sense here (like loops or multiple
results with the same name). They are permitted at this stage, but rejected
`later <#reject-loops>`_.

> 	, cmpGraphRef "*foobar |foobar >foobar" [(1, 0), (2, 0)]
> 	, cmpGraphRef "|foobar *foobar >foobar *foobar" [(0, 1), (0, 3), (2, 1), (2, 3)]
> 	]

Quantities
++++++++++

.. Does not really fit here. Move?

Lists of quantities, for instance for a shopping basket, can be extracted and merged.

> extractIngredients :: [Node Instruction] -> [Quantity]
> extractIngredients nodes = foldl f [] nodes
> 	where
> 		f xs (_, Ingredient q) = q:xs
> 		f xs _ = xs

> mergeQuantity :: [Quantity] -> [Quantity]
> mergeQuantity ingredients = reverse $ foldl foldQty [] sortedIngredients
> 	where
> 		sortedIngredients = sortOn sortKey ingredients
> 		sortKey (Quantity _ b c) = (c, b)
> 		foldQty ((Quantity (Exact (AmountRatio prevAmount)) prevUnit prevObject):xs)
> 				(Quantity (Exact (AmountRatio qamount)) qunit qobject)
> 				| prevObject == qobject && prevUnit == qunit
> 				= (Quantity (Exact (AmountRatio (prevAmount + qamount))) qunit qobject):xs
> 		foldQty ((Quantity (Exact (AmountStr "")) prevUnit prevObject):xs)
> 				(Quantity (Exact (AmountStr "")) qunit qobject)
> 				| prevObject == qobject && prevUnit == qunit
> 				= (Quantity (Exact (AmountStr "")) qunit qobject):xs
> 		foldQty xs x = x:xs

> testQuantity :: [Test]
> testQuantity = [

Quantities are merged when their objects and units match.

> 	  cmpMerge [
> 			  exactRatioQuantity (1%1) "kg" "apples"
> 			, exactRatioQuantity (2%1) "kg" "apples"
> 			, exactRatioQuantity (1%2) "" "bananas"
> 			, exactRatioQuantity (3%4) "" "bananas"
> 			, exactRatioQuantity (5%1) "" "peas"
> 			, exactRatioQuantity (200%1) "g" "peas"
> 			]
> 			[
> 			  exactRatioQuantity (3%1) "kg" "apples"
> 			, exactRatioQuantity (5%4) "" "bananas"
> 			, exactRatioQuantity (5%1) "" "peas"
> 			, exactRatioQuantity (200%1) "g" "peas"
> 			]

Objects without any quantity can also be merged.

> 	, cmpMerge [
> 			  strQuantity "apples"
> 			, strQuantity "apples"
> 			]
> 			[ strQuantity "apples" ]

The merged quantities are sorted.

> 	, cmpMerge [
> 			  strQuantity "b"
> 			, strQuantity "c"
> 			, strQuantity "a"
> 			]
> 			[
> 			  strQuantity "a"
> 			, strQuantity "b"
> 			, strQuantity "c"
> 			]
> 	]

Appendix
++++++++

> runGraphWith f doc expect = sort edges ~?= sort expect
> 	where
> 		(Right op) = (head . extract . snd . unzip) <$> parse ("%pesto " ++ doc)
> 		nodes = zip [firstNodeId..] op
> 		edges = f nodes
> cmpGraph = runGraphWith toGraph
> cmpGraphRef = runGraphWith resolveReferences

> type NodeId = Int
> type Node a = (NodeId, a)
> type Nodes a = [Node a]
> type Edge = (NodeId, NodeId)
> type Edges = [Edge]
> firstNodeId = 0 :: NodeId

Find graph’s root node(s), that is a node without outgoing edges:

> walkRoot nodes edges = let out = nub $ map fst edges
> 	in filter (\(x, _) -> notElem x out) nodes

Get all nodes with edges pointing towards nodeid

> incomingEdges edges nodeid = filter ((==) nodeid . snd) edges
> incomingNodes nodes edges nodeid = map ((!!) nodes . fst) $ incomingEdges edges nodeid

> outgoingEdges edges nodeid = filter ((==) nodeid . fst) edges
> outgoingNodes nodes edges nodeid = map ((!!) nodes . snd) $ outgoingEdges edges nodeid

> test = [
> 	  "graph" ~: testGraph
> 	, "ref" ~: testRef
> 	, "extract" ~: testExtract
> 	, "quantity" ~: testQuantity
> 	]

> cmpMerge value expected = (mergeQuantity value) ~?= expected
> strQuantity = Quantity (Exact (AmountStr "")) ""
> exactRatioQuantity :: Ratio Integer -> Unit -> Object -> Quantity
> exactRatioQuantity qamount qunit qobject =
> 	Quantity (Exact (AmountRatio qamount)) qunit qobject


> third (_, _, x) = x