Add yielding to help proof search

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

src/Bergamot/Rules.elm

@@ -63,6 +63,9 @@ pure a env ps = Search.pure (a, ps)
 fail : Prover a
 fail env ps = Search.fail
 
+yield : Prover a -> Prover a
+yield p env ps = Search.yield (p env ps)
+
 getEnv : Prover RuleEnv
 getEnv env ps = Search.pure (env, ps)
 
@@ -110,7 +113,7 @@ provePremises = mapM proveTerm
 proveTerm : Term UnificationVar -> Prover ProofTree
 proveTerm t =
     getEnv
-    |> andThen (\env -> List.foldl (\r -> interleave (rule t r)) fail env.rules)
+    |> andThen (\env -> List.foldl (\r -> interleave (yield (rule t r))) fail env.rules)
 
 prove : Term Metavariable -> Prover ProofTree
 prove mt =

src/Bergamot/Search.elm

@@ -1,8 +1,9 @@
-module Bergamot.Search exposing (Search, map, apply, andThen, pure, fail, interleave, one)
+module Bergamot.Search exposing (Search, map, apply, andThen, pure, fail, yield, interleave, one)
 
 type SearchStep a
     = Empty
     | Found a (Search a)
+    | Yield (Search a)
 
 type alias Search a = () -> SearchStep a
 
@@ -11,18 +12,21 @@ map f s () =
     case s () of
         Empty -> Empty
         Found a sp -> Found (f a) (map f sp)
+        Yield sp -> Yield (map f sp)
 
 apply : Search a -> Search (a -> b) -> Search b
 apply sa sf () =
     case sf () of
         Empty -> Empty
         Found f sfp -> interleave (map f sa) (apply sa sfp) ()
+        Yield sfp -> Yield (apply sa sfp)
 
 andThen : (a -> Search b) -> Search a -> Search b
 andThen f sa () =
     case sa () of
         Empty -> Empty
         Found a sap -> interleave (f a) (andThen f sap) ()
+        Yield sap -> Yield (andThen f sap)
 
 pure : a -> Search a
 pure a () = Found a (\() -> Empty)
@@ -30,14 +34,26 @@ pure a () = Found a (\() -> Empty)
 fail : Search a
 fail () = Empty
 
+yield : Search a -> Search a
+yield s () = Yield s
+
 interleave : Search a -> Search a -> Search a
 interleave s1 s2 () =
     case s1 () of
         Empty -> s2 ()
         Found a s1p -> Found a (interleave s2 s1p)
+        Yield s1p -> Yield (interleave s2 s1p)
 
 one : Search a -> Maybe (a, Search a)
 one s =
-    case s () of
-        Empty -> Nothing
-        Found a sp -> Just (a, sp)
+    let
+        go n sp =
+            if n > 0
+            then
+                case sp () of
+                    Empty -> Nothing
+                    Found a spp -> Just (a, spp)
+                    Yield spp -> go (n - 1) spp
+            else Nothing
+    in
+        go 10000 s