Add ADT calculator entity, sum and product type capabilities (#663)

Add `ADT calculator` entity (recipe: `calculator` + `I/O cable` + `typewriter`) which conveys capabilities to work with sum and product types (`inl`, `inr`, `case`; pairs, `fst`, `snd`).

Closes #563 .

data/entities.yaml

@@ -722,12 +722,12 @@
   capabilities: [drill]
   properties: [portable]
 
-- name: printer
+- name: typewriter
   display:
     attr: device
     char: 'Д'
   description:
-  - A printer is used to inscribe symbols on paper, thus reifying pure, platonic
+  - A typewriter is used to inscribe symbols on paper, thus reifying pure, platonic
     information into a physical form.
   properties: [portable]
 
@@ -908,6 +908,40 @@
   properties: [portable]
   capabilities: [arith]
 
+- name: ADT calculator
+  display:
+    attr: device
+    char: '±'
+  description:
+  - |
+    A calculator with Advanced Display Technology (an attached
+    typewriter that can print out the results).  For some reason, in
+    addition to the usual arithmetic on numbers, an ADT calculator can
+    also do arithmetic on types!  After all, the helpful typewritten manual
+    explains, a type is just a collection of values, and a finite collection
+    of values is just a fancy number.  For example, the type `bool` is
+    just a fancy version of the number 2, where the two things happen to be
+    labelled `false` and `true`.
+  - |
+    The product of two types is a type of pairs, since, for example,
+    if `t` is a type with three elements, then there are 2 * 3 = 6
+    different pairs containing a `bool` and a `t`, that is, 6 elements
+    of type `bool * t`.  For working with products of types, the ADT
+    calculator enables pair syntax `(a, b)` as well as the projection
+    functions `fst : a * b -> a` and `snd : a * b -> b`.
+  - |
+    The sum of two types is a type with two options; for example, a
+    value of type `bool + t` is either a `bool` value or a `t` value,
+    and there are 2 + 3 = 5 such values.  For working with sums of
+    types, the ADT calculator provides the injection functions `inl :
+    a -> a + b` and `inr : b -> a + b`, as well as the case analysis
+    function `case : (a + b) -> (a -> c) -> (b -> c) -> c`.  For
+    example, `case (inl 3) (\x. 2*x) (\y. 3*y) == 6`, and `case (inr
+    3) (\x. 2*x) (\y. 3*y) == 9`.
+
+  properties: [portable]
+  capabilities: [arith, sum, prod]
+
 - name: compass
   display:
     attr: device

data/recipes.yaml

@@ -89,7 +89,7 @@
   - [1, board]
   - [8, wooden gear]
   out:
-  - [1, printer]
+  - [1, typewriter]
 
 #########################################
 ##                BITS                 ##
@@ -651,6 +651,13 @@
   out:
   - [1, calculator]
 
+- in:
+  - [1, calculator]
+  - [1, typewriter]
+  - [1, I/O cable]
+  out:
+  - [1, ADT calculator]
+
 - in:
   - [1, glass]
   - [1, silver]

data/scenarios/Testing/508-capability-subset.yaml

@@ -33,6 +33,7 @@ robots:
       - [1, Tardis]
       - [1, logger]
       - [1, solar panel]
+      - [1, ADT calculator]
 known: [water]
 world:
   default: [ice, water]

src/Swarm/Language/Capability.hs

@@ -116,6 +116,10 @@ data Capability
     CTime
   | -- | Capability to execute `try`.
     CTry
+  | -- | Capability for working with sum types.
+    CSum
+  | -- | Capability for working with product types.
+    CProd
   | -- | God-like capabilities.  For e.g. commands intended only for
     --   checking challenge mode win conditions, and not for use by
     --   players.
@@ -218,6 +222,15 @@ constCaps = \case
   -- ----------------------------------------------------------------
   -- exceptions
   Try -> Just CTry
+  -- ----------------------------------------------------------------
+  -- type-level arithmetic
+  Inl -> Just CSum
+  Inr -> Just CSum
+  Case -> Just CSum
+  Fst -> Just CProd
+  Snd -> Just CProd
+  -- XXX pair syntax should require CProd too
+
   -- ----------------------------------------------------------------
   -- Some additional straightforward ones, which however currently
   -- cannot be used in classic mode since there is no craftable item
@@ -230,9 +243,4 @@ constCaps = \case
   -- Some more constants which *ought* to have their own capability but
   -- currently don't. TODO: #26
   View -> Nothing -- XXX this should also require something.
-  Inl -> Nothing -- XXX should require cap for sums
-  Inr -> Nothing
-  Case -> Nothing
-  Fst -> Nothing -- XXX should require cap for pairs
-  Snd -> Nothing
   Knows -> Nothing

src/Swarm/Language/Requirement.hs

@@ -235,7 +235,7 @@ requirements' = go
     -- the RHS.
     TBind mx t1 t2 -> go ctx t1 <> go (maybe id Ctx.delete mx ctx) t2
     -- Everything else is straightforward.
-    TPair t1 t2 -> go ctx t1 <> go ctx t2
+    TPair t1 t2 -> insert (ReqCap CProd) $ go ctx t1 <> go ctx t2
     TDelay _ t -> go ctx t
     -- This case should never happen if the term has been
     -- typechecked; Def commands are only allowed at the top level,