diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -140,7 +140,7 @@
 The above example also takes less than a second to run in a modern laptop.
 The selection of functions in the list of ingredients was minimized
 to what was absolutely needed here.
-With a larger collection as ingredients YMMV.
+With a larger collection of ingredients YMMV.
 
 
 Synthesizing from specifications (for advanced users)
diff --git a/TODO.md b/TODO.md
--- a/TODO.md
+++ b/TODO.md
@@ -3,17 +3,10 @@
 
 A non-exhaustive list of things TO DO for Conjure.
 
-* Make so that derived Listable instances `reset`
-  constructors that are not recursive.
-  This change will need to be done in LeanCheck itself.
-
 * Allow timeout setting?
 
 * Find most efficient of a given size (see below).
 
-* Better error reporting when `Listable` is out-of-scope when using `deriveConjurable`.
-  This needs to be implemented on LeanCheck itself.
-
 * forbid recursion into negatives (see below)
 
 * Add way to consider functions that don't increase size of arguments in recursive calls
@@ -49,7 +42,7 @@
 2. use this on `showDefn` somehow
 3. use this on `toDynamicWithDefn` somehow
 
-Alternative: include the guard as part of the pattern "internally".  As if we
+Alternative: include the guard as part of the pattern internally.  As if we
 had a n+k pattern.  Like so:
 
 	tri 1  =  1
diff --git a/bench/gps.txt b/bench/gps.txt
--- a/bench/gps.txt
+++ b/bench/gps.txt
@@ -33,7 +33,7 @@
 gps3 :: Int -> Int -> Int -> [Int]
 -- testing 2 combinations of argument values
 -- pruning with 11/33 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 64 candidates of size 4
@@ -41,7 +41,7 @@
 -- 1248 candidates of size 6
 -- 0 candidates of size 7
 -- 13680 candidates of size 8
--- tested 3238 candidates
+-- tested 3239 candidates
 gps3 x y z  =  enumFromThenTo x (x + z) (y - 1)
 
 gps3_alt :: Int -> Int -> Int -> [Int]
@@ -62,11 +62,14 @@
 -- 13311 candidates of size 13
 -- tested 20359 candidates
 gps3_alt  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- [], (:), (+), (<), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 gps4 :: [Char] -> [Char] -> [Char] -> Bool
 -- testing 9 combinations of argument values
 -- pruning with 11/15 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 0 candidates of size 4
@@ -75,9 +78,9 @@
 -- 0 candidates of size 7
 -- 0 candidates of size 8
 -- 51 candidates of size 9
--- 0 candidates of size 10
--- 15 candidates of size 11
--- tested 60 candidates
+-- 353 candidates of size 10
+-- 118 candidates of size 11
+-- tested 414 candidates
 gps4 cs ds es  =  length cs < length ds && length ds < length es
 
 gps5 :: [Char] -> [Char]
@@ -97,6 +100,9 @@
 -- 5 candidates of size 12
 -- tested 26 candidates
 gps5  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- "", (:), '!', (==), isLetter, and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 gps6direct :: Int -> Int
 -- testing 9 combinations of argument values
@@ -109,6 +115,9 @@
 -- 0 candidates of size 6
 -- tested 188 candidates
 gps6direct  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 1, 2, 3, (+), (*), div, even, and if-expressions
+-- consider increasing target/maxSize or refining the ingredients
 
 gps6step :: Int -> Int
 -- testing 9 combinations of argument values
@@ -134,11 +143,14 @@
 -- 0 candidates of size 6
 -- tested 188 candidates
 nextCollatz  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 1, 2, 3, (+), (*), div, even, and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 gps7 :: [Char] -> ([Char],Int)
 -- testing 4 combinations of argument values
 -- pruning with 5/10 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 1 candidates of size 4
@@ -149,23 +161,26 @@
 -- 88 candidates of size 9
 -- 201 candidates of size 10
 -- 442 candidates of size 11
--- tested 553 candidates
+-- tested 554 candidates
 gps7 cs  =  (init (unlines (words cs)),length (filter (not . isSpace) cs))
 
 gps8 :: [Char] -> [Char] -> [(Int,Char,Char)]
 -- testing 3 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 0 candidates of size 4
--- tested 0 candidates
+-- tested 1 candidates
 gps8  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 gps9 :: Int -> [Int]
 -- testing 3 combinations of argument values
 -- pruning with 13/14 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 4 candidates of size 3
 -- 4 candidates of size 4
@@ -175,41 +190,41 @@
 -- 69 candidates of size 8
 -- 114 candidates of size 9
 -- 212 candidates of size 10
--- tested 278 candidates
+-- tested 279 candidates
 gps9 x  =  filter even (filter (x >) (map sq [1..x]))
 
 wallisNext :: Ratio Integer -> Ratio Integer
 -- testing 6 combinations of argument values
 -- pruning with 37/64 rules
 -- 1 candidates of size 1
--- 0 candidates of size 2
+-- 1 candidates of size 2
 -- 3 candidates of size 3
 -- 15 candidates of size 4
 -- 4 candidates of size 5
 -- 86 candidates of size 6
 -- 5 candidates of size 7
 -- 513 candidates of size 8
--- tested 368 candidates
+-- tested 369 candidates
 wallisNext (x % y)  =  (y + 1) % (x + 1)
 
 wallisNext :: Ratio Integer -> Ratio Integer
 -- testing 6 combinations of argument values
 -- pruning with 15/26 rules
 -- 1 candidates of size 1
--- 0 candidates of size 2
+-- 1 candidates of size 2
 -- 4 candidates of size 3
 -- 16 candidates of size 4
 -- 3 candidates of size 5
 -- 71 candidates of size 6
 -- 5 candidates of size 7
 -- 393 candidates of size 8
--- tested 295 candidates
+-- tested 296 candidates
 wallisNext (x % y)  =  (y + 1) % (x + 1)
 
 gps10 :: Int -> Ratio Integer
 -- testing 6 combinations of argument values
 -- pruning with 3/4 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 3 candidates of size 3
 -- 3 candidates of size 4
@@ -217,17 +232,17 @@
 -- 5 candidates of size 6
 -- 8 candidates of size 7
 -- 13 candidates of size 8
--- tested 33 candidates
+-- tested 34 candidates
 gps10 x  =  product (take x (iterate wallisNext (2 % 3)))
 
 gps11 :: [[Char]] -> [Int]
 -- testing 4 combinations of argument values
 -- pruning with 1/1 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 1 candidates of size 3
--- 1 candidates of size 4
--- tested 2 candidates
+-- 2 candidates of size 4
+-- tested 3 candidates
 gps11 css  =  reverse (map length css)
 
 gps11 :: [[Char]] -> [Int]
@@ -279,22 +294,22 @@
 odd :: Int -> Bool
 -- testing 6 combinations of argument values
 -- pruning with 12/13 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 3 candidates of size 3
 -- 0 candidates of size 4
 -- 35 candidates of size 5
--- tested 15 candidates
+-- tested 16 candidates
 odd x  =  0 /= x `mod` 2
 
 gps14 :: [Int] -> Int
 -- testing 3 combinations of argument values
 -- pruning with 1/1 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 1 candidates of size 2
 -- 0 candidates of size 3
 -- 1 candidates of size 4
--- tested 2 candidates
+-- tested 3 candidates
 gps14 xs  =  length (filter odd xs)
 
 gps14 :: [Int] -> Int
@@ -314,22 +329,22 @@
 gps15 :: [Int] -> [Int] -> Bool
 -- testing 5 combinations of argument values
 -- pruning with 3/7 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 1 candidates of size 3
 -- 4 candidates of size 4
--- tested 3 candidates
+-- tested 4 candidates
 gps15 xs ys  =  xs == reverse ys
 
 gps16 :: [Char] -> [Char] -> Bool
 -- testing 6 combinations of argument values
 -- pruning with 3/3 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 2 candidates of size 3
 -- 6 candidates of size 4
 -- 2 candidates of size 5
--- tested 9 candidates
+-- tested 10 candidates
 gps16 cs ds  =  sort cs `isSubsequenceOf` sort ds
 
 gps17 :: Int -> Int
@@ -382,6 +397,9 @@
 -- 0 candidates of size 2
 -- tested 1 candidates
 gps19  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 isVowel :: Char -> Bool
 -- testing 12 combinations of argument values
@@ -442,11 +460,11 @@
 gps20c :: [Char] -> [Char]
 -- pruning with 1/1 rules
 -- 1 candidates of size 1
--- 1 candidates of size 2
--- 2 candidates of size 3
--- 3 candidates of size 4
--- 5 candidates of size 5
--- tested 12 candidates
+-- 2 candidates of size 2
+-- 3 candidates of size 3
+-- 6 candidates of size 4
+-- 10 candidates of size 5
+-- tested 17 candidates
 gps20c cs  =  unwords (map pig1 (words cs))
 
 gps21 :: [Int] -> [Int]
@@ -489,6 +507,9 @@
 -- 0 candidates of size 13
 -- tested 1 candidates
 scrabble1  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 1, 'd', 'g', 'b', 'c', 'm', 'p', 'f', 'h', 'v', 'w', 'y', 'k', 'j', 'x', 'q', and 'z'
+-- consider increasing target/maxSize or refining the ingredients
 
 gps22 :: [Char] -> Int
 -- pruning with 5/9 rules
@@ -537,6 +558,9 @@
 -- 15042 candidates of size 10
 -- tested 20277 candidates
 gps25  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 10, [], (:), guarded equations, abs, (<), rem, and quot
+-- consider increasing target/maxSize or refining the ingredients
 
 gps26 :: Int -> Int -> Int -> Int -> Int -> Char
 -- testing 5 combinations of argument values
@@ -554,6 +578,9 @@
 -- 40000 candidates of size 11
 -- tested 40405 candidates
 gps26  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 'A', 'B', 'C', 'D', 'F', guarded equations, and (>=)
+-- consider increasing target/maxSize or refining the ingredients
 
 gps27_median :: Int -> Int -> Int -> Int
 -- testing 6 combinations of argument values
@@ -576,6 +603,9 @@
 -- 11664 candidates of size 16
 -- tested 20451 candidates
 gps27_median  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- (<=), (&&), (||), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 gps27b_median :: Int -> Int -> Int -> Int
 -- testing 6 combinations of argument values
diff --git a/bench/lowtests.txt b/bench/lowtests.txt
--- a/bench/lowtests.txt
+++ b/bench/lowtests.txt
@@ -13,26 +13,29 @@
 invalid:
 xs `isSubsequenceOf` sort xs == True
 -}
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 2 candidates of size 3
 -- 4 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
 -- 3 candidates of size 7
--- 2 candidates of size 8
--- 0 candidates of size 9
+-- 5 candidates of size 8
+-- 2 candidates of size 9
 -- 4 candidates of size 10
--- 8 candidates of size 11
--- 4 candidates of size 12
--- 0 candidates of size 13
+-- 12 candidates of size 11
+-- 12 candidates of size 12
+-- 4 candidates of size 13
 -- 0 candidates of size 14
 -- 0 candidates of size 15
 -- 0 candidates of size 16
 -- 0 candidates of size 17
 -- 0 candidates of size 18
--- tested 27 candidates
+-- tested 49 candidates
 subset  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- sort and isSubsequenceOf
+-- consider increasing target/maxSize or refining the ingredients
 
 subset :: [Int] -> [Int] -> Bool
 -- testing 44 combinations of argument values
@@ -44,12 +47,12 @@
 sort xs `isSubsequenceOf` xs == xs `isSubsequenceOf` sort xs
 
 -}
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 2 candidates of size 3
 -- 6 candidates of size 4
 -- 2 candidates of size 5
--- tested 9 candidates
+-- tested 10 candidates
 subset xs ys  =  sort xs `isSubsequenceOf` sort ys
 
 replicates :: [Char] -> Int -> [Char]
@@ -67,20 +70,23 @@
 -- 1 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
--- 1 candidates of size 7
+-- 2 candidates of size 7
 -- 0 candidates of size 8
 -- 0 candidates of size 9
--- 1 candidates of size 10
+-- 2 candidates of size 10
 -- 0 candidates of size 11
 -- 0 candidates of size 12
--- 1 candidates of size 13
+-- 2 candidates of size 13
 -- 0 candidates of size 14
 -- 0 candidates of size 15
--- 1 candidates of size 16
+-- 2 candidates of size 16
 -- 0 candidates of size 17
 -- 0 candidates of size 18
--- tested 6 candidates
+-- tested 10 candidates
 replicates  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- replicate, transpose, and concat
+-- consider increasing target/maxSize or refining the ingredients
 
 replicates :: [Char] -> Int -> [Char]
 -- testing 360 combinations of argument values
diff --git a/bench/psb2.txt b/bench/psb2.txt
--- a/bench/psb2.txt
+++ b/bench/psb2.txt
@@ -1,7 +1,7 @@
 gps1 :: [Int] -> Maybe Int
 -- testing 4 combinations of argument values
 -- pruning with 11/21 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 1 candidates of size 4
@@ -10,14 +10,14 @@
 -- 1 candidates of size 7
 -- 0 candidates of size 8
 -- 1 candidates of size 9
--- 2 candidates of size 10
--- tested 4 candidates
+-- 3 candidates of size 10
+-- tested 5 candidates
 gps1 xs  =  findIndex (0 >) (map (foldr (+) 0) (tail (inits xs)))
 
 gps1 :: [Int] -> Maybe Int
 -- testing 4 combinations of argument values
 -- pruning with 11/21 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 1 candidates of size 4
@@ -25,7 +25,7 @@
 -- 0 candidates of size 6
 -- 1 candidates of size 7
 -- 4 candidates of size 8
--- tested 4 candidates
+-- tested 5 candidates
 gps1 xs  =  findIndex (0 >) (map sum (tail (inits xs)))
 
 gps1 :: Int -> [Int] -> Int
@@ -37,6 +37,9 @@
 -- 5 candidates of size 4
 -- tested 12 candidates
 gps1  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 1, (+), (<), guarded equations, and undefined
+-- consider increasing target/maxSize or refining the ingredients
 
 gps2 :: Double -> Double -> Int -> Double
 -- testing 5 combinations of argument values
@@ -49,6 +52,9 @@
 -- 0 candidates of size 6
 -- tested 270 candidates
 gps2  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 1, (*), (/), (+), and (-)
+-- consider increasing target/maxSize or refining the ingredients
 
 gps3 :: [Char] -> Int
 gps3  =  error "could not reify specification, suggestion: conjureFromSpec"
@@ -63,13 +69,19 @@
 -- 119 candidates of size 6
 -- tested 203 candidates
 gps4  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- '-', "", (:), (==), head, tail, if-expressions, if-expressions, and toUpper
+-- consider increasing target/maxSize or refining the ingredients
 
 gps5 :: Int -> [Int]
 -- testing 6 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
--- tested 0 candidates
+-- 1 candidates of size 1
+-- tested 1 candidates
 gps5  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 tell :: [Int] -> Int -> [Int]
 -- pruning with 0/0 rules
@@ -116,25 +128,34 @@
 gps6 :: [Int] -> Int
 -- testing 360 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
--- tested 0 candidates
+-- tested 1 candidates
 gps6  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 gps7 :: Integer -> Integer -> Ratio Integer
 -- testing 6 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
--- tested 0 candidates
+-- 1 candidates of size 1
+-- tested 1 candidates
 gps7  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 gps8 :: Int -> [Int] -> (Int,Int)
 -- testing 3 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
--- tested 0 candidates
+-- tested 1 candidates
 gps8  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 gps9 :: Int -> [Char]
 -- testing 7 combinations of argument values
@@ -152,6 +173,9 @@
 -- 2976 candidates of size 11
 -- tested 3487 candidates
 gps9  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- "Fizz", "Buzz", "FizzBuzz", 0, 3, 5, False, True, divBy, (&&), show, and if-expressions
+-- consider increasing target/maxSize or refining the ingredients
 
 gps10 :: [Int] -> Int
 -- testing 7 combinations of argument values
@@ -185,12 +209,12 @@
 gps12 :: [Char] -> [Char] -> [Int]
 -- testing 5 combinations of argument values
 -- pruning with 1/2 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 0 candidates of size 4
 -- 4 candidates of size 5
--- tested 3 candidates
+-- tested 4 candidates
 gps12 cs ds  =  findIndices (ds `isPrefixOf`) (tails cs)
 
 gps13_leaders :: [Int] -> [Int]
@@ -252,6 +276,9 @@
 -- 4 candidates of size 6
 -- tested 8 candidates
 gps17_pds  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, guarded equations, not, null, (==), head, (+), and (&&)
+-- consider increasing target/maxSize or refining the ingredients
 
 gps17_pds :: [Int] -> Int
 -- testing 9 combinations of argument values
@@ -264,6 +291,9 @@
 -- 8 candidates of size 6
 -- tested 14 candidates
 gps17_pds  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, guarded equations, (==), and (+)
+-- consider increasing target/maxSize or refining the ingredients
 
 gps18_price :: [Double] -> [Double] -> Double
 -- testing 4 combinations of argument values
@@ -276,6 +306,9 @@
 -- 176 candidates of size 6
 -- tested 213 candidates
 gps18_price  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0.0, 1.0, (+), (*), and (-)
+-- consider increasing target/maxSize or refining the ingredients
 
 gps19_snowday :: Int -> Double -> Double -> Double -> Double
 -- testing 7 combinations of argument values
@@ -288,6 +321,9 @@
 -- 0 candidates of size 6
 -- tested 333 candidates
 gps19_snowday  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 1, max, (+), and (-)
+-- consider increasing target/maxSize or refining the ingredients
 
 gps20 :: [Char] -> Bool
 gps20  =  error "could not reify specification, suggestion: conjureFromSpec"
@@ -296,14 +332,14 @@
 -- pruning with 6/6 rules
 -- reasoning produced 1 incorrect properties, please re-run with more tests for faster results
 -- 1 candidates of size 1
--- 1 candidates of size 2
--- 0 candidates of size 3
--- 0 candidates of size 4
+-- 2 candidates of size 2
+-- 1 candidates of size 3
+-- 1 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
 -- 0 candidates of size 7
 -- 4 candidates of size 8
--- tested 6 candidates
+-- tested 9 candidates
 spin cs
   | length cs >= 5  =  reverse cs
   | otherwise  =  cs
@@ -312,11 +348,11 @@
 -- pruning with 16/16 rules
 -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results
 -- 1 candidates of size 1
--- 2 candidates of size 2
--- 2 candidates of size 3
--- 3 candidates of size 4
--- 5 candidates of size 5
--- tested 12 candidates
+-- 3 candidates of size 2
+-- 4 candidates of size 3
+-- 7 candidates of size 4
+-- 10 candidates of size 5
+-- tested 19 candidates
 gps21_spinwords cs  =  unwords (map spin (words cs))
 
 gps22 :: Int -> [Char]
@@ -342,16 +378,19 @@
 -- 3 candidates of size 1
 -- 12 candidates of size 2
 -- 33 candidates of size 3
--- 36 candidates of size 4
--- 127 candidates of size 5
--- 507 candidates of size 6
--- 839 candidates of size 7
--- 784 candidates of size 8
--- 600 candidates of size 9
--- 2722 candidates of size 10
--- 5292 candidates of size 11
--- tested 10955 candidates
+-- 42 candidates of size 4
+-- 140 candidates of size 5
+-- 523 candidates of size 6
+-- 897 candidates of size 7
+-- 1127 candidates of size 8
+-- 1144 candidates of size 9
+-- 2959 candidates of size 10
+-- 6272 candidates of size 11
+-- tested 13152 candidates
 gps23  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- nothing
+-- consider increasing target/maxSize or refining the ingredients
 
 gps24 :: [Char] -> Twitter
 -- pruning with 4/8 rules
@@ -385,4 +424,7 @@
 -- 438 candidates of size 6
 -- tested 532 candidates
 gps25  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0.0, 2.0, (+), (-), (**), zipWith, map, and sqrt
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/bench/runtime/lapmatrud/bench/gps.runtime b/bench/runtime/lapmatrud/bench/gps.runtime
--- a/bench/runtime/lapmatrud/bench/gps.runtime
+++ b/bench/runtime/lapmatrud/bench/gps.runtime
@@ -1,1 +1,1 @@
-14.2
+19.0
diff --git a/bench/runtime/lapmatrud/bench/gps2.runtime b/bench/runtime/lapmatrud/bench/gps2.runtime
deleted file mode 100644
--- a/bench/runtime/lapmatrud/bench/gps2.runtime
+++ /dev/null
@@ -1,1 +0,0 @@
-11.7
diff --git a/bench/runtime/lapmatrud/bench/i12.runtime b/bench/runtime/lapmatrud/bench/i12.runtime
new file mode 100644
--- /dev/null
+++ b/bench/runtime/lapmatrud/bench/i12.runtime
@@ -0,0 +1,1 @@
+1.7
diff --git a/bench/runtime/lapmatrud/bench/i30.runtime b/bench/runtime/lapmatrud/bench/i30.runtime
new file mode 100644
--- /dev/null
+++ b/bench/runtime/lapmatrud/bench/i30.runtime
@@ -0,0 +1,1 @@
+0.0
diff --git a/bench/runtime/lapmatrud/bench/ill-hit.runtime b/bench/runtime/lapmatrud/bench/ill-hit.runtime
--- a/bench/runtime/lapmatrud/bench/ill-hit.runtime
+++ b/bench/runtime/lapmatrud/bench/ill-hit.runtime
@@ -1,1 +1,1 @@
-0.5
+0.6
diff --git a/bench/runtime/lapmatrud/bench/lowtests.runtime b/bench/runtime/lapmatrud/bench/lowtests.runtime
--- a/bench/runtime/lapmatrud/bench/lowtests.runtime
+++ b/bench/runtime/lapmatrud/bench/lowtests.runtime
@@ -1,1 +1,1 @@
-0.2
+0.4
diff --git a/bench/runtime/lapmatrud/bench/p12.runtime b/bench/runtime/lapmatrud/bench/p12.runtime
deleted file mode 100644
--- a/bench/runtime/lapmatrud/bench/p12.runtime
+++ /dev/null
@@ -1,1 +0,0 @@
-1.6
diff --git a/bench/runtime/lapmatrud/bench/p30.runtime b/bench/runtime/lapmatrud/bench/p30.runtime
deleted file mode 100644
--- a/bench/runtime/lapmatrud/bench/p30.runtime
+++ /dev/null
@@ -1,1 +0,0 @@
-0.0
diff --git a/bench/runtime/lapmatrud/bench/psb2.runtime b/bench/runtime/lapmatrud/bench/psb2.runtime
new file mode 100644
--- /dev/null
+++ b/bench/runtime/lapmatrud/bench/psb2.runtime
@@ -0,0 +1,1 @@
+12.3
diff --git a/bench/runtime/lapmatrud/bench/terpret.runtime b/bench/runtime/lapmatrud/bench/terpret.runtime
--- a/bench/runtime/lapmatrud/bench/terpret.runtime
+++ b/bench/runtime/lapmatrud/bench/terpret.runtime
@@ -1,1 +1,1 @@
-10.2
+10.4
diff --git a/bench/runtime/lapmatrud/bench/unique.runtime b/bench/runtime/lapmatrud/bench/unique.runtime
--- a/bench/runtime/lapmatrud/bench/unique.runtime
+++ b/bench/runtime/lapmatrud/bench/unique.runtime
@@ -1,1 +1,1 @@
-2.4
+2.5
diff --git a/bench/runtime/lapmatrud/eg/arith.runtime b/bench/runtime/lapmatrud/eg/arith.runtime
--- a/bench/runtime/lapmatrud/eg/arith.runtime
+++ b/bench/runtime/lapmatrud/eg/arith.runtime
@@ -1,1 +1,1 @@
-1.0
+0.9
diff --git a/bench/runtime/lapmatrud/eg/bst.runtime b/bench/runtime/lapmatrud/eg/bst.runtime
--- a/bench/runtime/lapmatrud/eg/bst.runtime
+++ b/bench/runtime/lapmatrud/eg/bst.runtime
@@ -1,1 +1,1 @@
-4.1
+4.6
diff --git a/bench/runtime/lapmatrud/eg/conditionals.runtime b/bench/runtime/lapmatrud/eg/conditionals.runtime
--- a/bench/runtime/lapmatrud/eg/conditionals.runtime
+++ b/bench/runtime/lapmatrud/eg/conditionals.runtime
@@ -1,1 +1,1 @@
-8.7
+8.6
diff --git a/bench/runtime/lapmatrud/eg/count.runtime b/bench/runtime/lapmatrud/eg/count.runtime
--- a/bench/runtime/lapmatrud/eg/count.runtime
+++ b/bench/runtime/lapmatrud/eg/count.runtime
@@ -1,1 +1,1 @@
-0.5
+0.6
diff --git a/bench/runtime/lapmatrud/eg/fib01.runtime b/bench/runtime/lapmatrud/eg/fib01.runtime
--- a/bench/runtime/lapmatrud/eg/fib01.runtime
+++ b/bench/runtime/lapmatrud/eg/fib01.runtime
@@ -1,1 +1,1 @@
-0.5
+0.6
diff --git a/bench/runtime/lapmatrud/eg/ints.runtime b/bench/runtime/lapmatrud/eg/ints.runtime
--- a/bench/runtime/lapmatrud/eg/ints.runtime
+++ b/bench/runtime/lapmatrud/eg/ints.runtime
@@ -1,1 +1,1 @@
-0.9
+1.0
diff --git a/bench/runtime/lapmatrud/eg/pow.runtime b/bench/runtime/lapmatrud/eg/pow.runtime
--- a/bench/runtime/lapmatrud/eg/pow.runtime
+++ b/bench/runtime/lapmatrud/eg/pow.runtime
@@ -1,1 +1,1 @@
-1.6
+2.4
diff --git a/bench/runtime/lapmatrud/eg/subset.runtime b/bench/runtime/lapmatrud/eg/subset.runtime
--- a/bench/runtime/lapmatrud/eg/subset.runtime
+++ b/bench/runtime/lapmatrud/eg/subset.runtime
@@ -1,1 +1,1 @@
-0.5
+0.6
diff --git a/bench/runtime/lapmatrud/eg/tri.runtime b/bench/runtime/lapmatrud/eg/tri.runtime
--- a/bench/runtime/lapmatrud/eg/tri.runtime
+++ b/bench/runtime/lapmatrud/eg/tri.runtime
@@ -1,1 +1,1 @@
-0.2
+0.3
diff --git a/bench/runtime/lapmatrud/versions b/bench/runtime/lapmatrud/versions
--- a/bench/runtime/lapmatrud/versions
+++ b/bench/runtime/lapmatrud/versions
@@ -1,4 +1,4 @@
 GHC 9.4.8
-leancheck-1.0.2
+leancheck-1.0.4
 express-1.0.18
 speculate-0.4.20
diff --git a/bench/self.txt b/bench/self.txt
--- a/bench/self.txt
+++ b/bench/self.txt
@@ -33,4 +33,7 @@
 -- 10 candidates of size 3
 -- tested 13 candidates
 d  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 1, (+), and (*)
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/bench/terpret.txt b/bench/terpret.txt
--- a/bench/terpret.txt
+++ b/bench/terpret.txt
@@ -52,7 +52,7 @@
 -- pruning with 37/47 rules
 -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results
 -- 1 candidates of size 1
--- 0 candidates of size 2
+-- 1 candidates of size 2
 -- 0 candidates of size 3
 -- 12 candidates of size 4
 -- 125 candidates of size 5
@@ -62,7 +62,7 @@
 -- 3087 candidates of size 9
 -- 9281 candidates of size 10
 -- 180325 candidates of size 11
--- tested 40096 candidates
+-- tested 40097 candidates
 cshift (p,q,r)
   | p  =  (p,r,q)
   | otherwise  =  (p,q,r)
@@ -71,15 +71,15 @@
 -- testing 4 combinations of argument values
 -- pruning with 37/47 rules
 -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 125 candidates of size 4
 -- 225 candidates of size 5
 -- 585 candidates of size 6
 -- 1242 candidates of size 7
--- 3088 candidates of size 8
--- tested 5265 candidates
+-- 3090 candidates of size 8
+-- tested 5266 candidates
 cshift False p q  =  (False,p,q)
 cshift True p q  =  (True,q,p)
 
@@ -88,7 +88,7 @@
 fadder :: Bool -> Bool -> Bool -> (Bool,Bool)
 -- testing 8 combinations of argument values
 -- pruning with 72/90 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 25 candidates of size 3
 -- 60 candidates of size 4
@@ -96,7 +96,7 @@
 -- 348 candidates of size 6
 -- 999 candidates of size 7
 -- 7009 candidates of size 8
--- tested 8567 candidates
+-- tested 8568 candidates
 fadder False False False  =  (False,False)
 fadder False False True  =  (False,True)
 fadder False True False  =  (False,True)
@@ -112,24 +112,27 @@
 -- testing 5 combinations of argument values
 -- pruning with 70/88 rules
 -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results
--- 0 candidates of size 1
--- 0 candidates of size 2
--- 0 candidates of size 3
+-- 1 candidates of size 1
+-- 2 candidates of size 2
+-- 1 candidates of size 3
 -- 8 candidates of size 4
 -- 128 candidates of size 5
 -- 408 candidates of size 6
--- tested 544 candidates
+-- tested 548 candidates
 adder2  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- False, True, not, (&&), (||), [], (:), guarded equations, (,,), (==), (^^), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 TerpreT benchmark #7: access
 
 access :: [A] -> Int -> A
 -- testing 5 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 1 candidates of size 3
--- tested 1 candidates
+-- tested 2 candidates
 xs `access` x  =  xs !! x
 
 access :: [A] -> Int -> A
@@ -143,7 +146,6 @@
 -- 0 candidates of size 6
 -- 3 candidates of size 7
 -- tested 5 candidates
-[] `access` x  =  undefined
 (x:xs) `access` 0  =  x
 (x:xs) `access` y  =  xs `access` (y - 1)
 
diff --git a/bench/weird.hs b/bench/weird.hs
--- a/bench/weird.hs
+++ b/bench/weird.hs
@@ -10,7 +10,19 @@
 -- we do not use partial definitions here.
 -- We use fully defined functions to conjure themselves.
 import Conjure
+import Test.LeanCheck.Error (errorToNothing)
+import Data.Maybe (isNothing)
 
+-- | An undefined function.
+bottom :: Int
+bottom  =  undefined
+
+-- | A specification for the above undefined function.
+bottomSpec :: Int -> [Property]
+bottomSpec bottom  =  [property $ isError bottom]
+  where
+  isError  =  isNothing . errorToNothing  -- TODO: add to LeanCheck.Error?
+
 -- | xor for integers
 --
 -- returns the sum but only when one of the arguments is 0
@@ -29,7 +41,15 @@
 
 main :: IO ()
 main  =  do
-  -- TODO: Conjure should find isq, but doesn't due to overpruning
+  -- We try to ask Conjure to generate undefined
+  -- Conjure complains about not being able to reify specification.
+  -- Fair enough: there's no way to distinguish an undefined function
+  -- from an empty specification.
+  conjure "bottom" bottom []
+
+  -- With a spec, Conjure finds the "implementation"
+  conjureFromSpec "bottom" bottomSpec []
+
   conjure "isq" isq ingredients
 
   conjure "^^^" (^^^)   ingredients
diff --git a/bench/weird.txt b/bench/weird.txt
--- a/bench/weird.txt
+++ b/bench/weird.txt
@@ -1,3 +1,12 @@
+bottom :: Int
+bottom  =  error "could not reify specification, suggestion: conjureFromSpec"
+
+bottom :: Int
+-- pruning with 0/0 rules
+-- 1 candidates of size 1
+-- tested 1 candidates
+bottom  =  undefined
+
 isq :: Bool -> Int -> Int
 -- testing 360 combinations of argument values
 -- pruning with 56/91 rules
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -2,6 +2,15 @@
 ============================
 
 
+v0.7.8 (August 2025)
+--------------------
+
+* automatically use `undefined` as RHS when no suitable symbols are found;
+* longer message upon search exhausted;
+* fix `Conjurable` derivation when `Listable` is not in scope;
+* improve a few examples and internal tests.
+
+
 v0.7.6 (August 2025)
 --------------------
 
diff --git a/code-conjure.cabal b/code-conjure.cabal
--- a/code-conjure.cabal
+++ b/code-conjure.cabal
@@ -3,7 +3,7 @@
 -- Copyright (C) 2021-2025 Rudy Matela
 -- Distributed under the 3-Clause BSD licence (see the file LICENSE).
 name:                code-conjure
-version:             0.7.6
+version:             0.7.8
 synopsis:            synthesize Haskell functions out of partial definitions
 description:
   Conjure is a tool that synthesizes Haskell functions out of partial definitions.
@@ -68,7 +68,7 @@
 source-repository this
   type:            git
   location:        https://github.com/rudymatela/conjure
-  tag:             v0.7.6
+  tag:             v0.7.8
 
 library
   exposed-modules: Conjure
diff --git a/eg/bst.hs b/eg/bst.hs
--- a/eg/bst.hs
+++ b/eg/bst.hs
@@ -6,14 +6,19 @@
 
 import Conjure
 import Test.LeanCheck
+import Data.Function (on)
 import Data.Express hiding (height,size)
 
 data Tree  =  Leaf
            |  Node Tree Int Tree
-  deriving (Eq, Ord, Show, Read)
+  deriving (Show, Read)
 
-deriveExpress ''Tree
+instance Eq Tree where
+  (==)  =  (==) `on` inorder
 
+instance Ord Tree where
+  compare  =  compare `on` inorder
+
 unit :: Int -> Tree
 unit x  =  Node Leaf x Leaf
 
@@ -78,6 +83,13 @@
   EQ -> Node l y r                -- 16
   GT -> Node l y (insert x r)     -- 22
 
+insertAlt :: Int -> Tree -> Tree
+insertAlt x Leaf          =  unit x  -- 2
+insertAlt x (Node l y r)
+  | x < y  =  Node (insert x l) y r  -- 12
+  | y < x  =  Node l y (insert x r)  -- 22
+  | otherwise  =  Node l y r         -- 25
+
 before :: Int -> Tree -> Tree
 before _ Leaf  =  Leaf
 before y (Node l x r)  =  case y `compare` x of
@@ -97,9 +109,13 @@
 union t (Node l x r)  =  Node (union (before x t) l) x (union (beyond x t) r)
 
 
+deriveExpress ''Tree
+
+
 instance Listable Tree where
   tiers  =  cons0 Leaf
-        \/  cons3 Node `suchThat` ordered
+         \/ cons3 Node `suchThat` (\(Node l x r) -> (nil l || rightmost l < x)
+                                                 && (nil r || x < leftmost r))
 
 instance Name Tree where
   name _  =  "t1"
@@ -124,8 +140,7 @@
 main = do
   conjure "mem" mem
     [ con False
-    , fun "||" (||)
-    , fun "==" ((==) :: Int -> Int -> Bool)
+    , con True
     , fun "<" ((<) :: Int -> Int -> Bool)
     , guard
     ]
@@ -137,10 +152,18 @@
     , ordcase (undefined :: Bool)
     ]
 
+  -- out of reach performance-wise as well (reaching 19 but needs size 25)
+  conjure "insert" insert
+    [ fun "Node" Node
+    , fun "unit" unit
+    , guard
+    , fun "<" ((<) :: Int -> Int -> Bool)
+    , maxSize 12
+    ]
+
   -- simply out of reach performance-wise (reaching 16 but need size 22)
   conjure "insert" insert
-    [ con Leaf
-    , fun "Node" Node
+    [ fun "Node" Node
     , fun "unit" unit
     , fun "`compare`" (compare :: Int -> Int -> Ordering)
     , ordcase (undefined :: Tree)
@@ -189,6 +212,12 @@
     , ordcase (undefined :: Tree)
     , maxSize 12
     , maxEquationSize 7
+    ]
+
+  conjure "insert" insert
+    [ fun "Node" Node
+    , fun "before" before
+    , fun "beyond" beyond
     ]
 
   -- reachable in 55s, candidate #173109 at size 13.
diff --git a/eg/bst.txt b/eg/bst.txt
--- a/eg/bst.txt
+++ b/eg/bst.txt
@@ -1,21 +1,28 @@
 mem :: Int -> Tree -> Bool
 -- testing 360 combinations of argument values
--- pruning with 20/30 rules
--- 1 candidates of size 1
+-- pruning with 9/17 rules
+-- 2 candidates of size 1
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 0 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
--- 0 candidates of size 7
--- 24 candidates of size 8
--- 48 candidates of size 9
+-- 4 candidates of size 7
+-- 0 candidates of size 8
+-- 80 candidates of size 9
 -- 0 candidates of size 10
--- 180 candidates of size 11
--- 80 candidates of size 12
--- tested 274 candidates
+-- 144 candidates of size 11
+-- 48 candidates of size 12
+-- 0 candidates of size 13
+-- 1136 candidates of size 14
+-- 0 candidates of size 15
+-- 5056 candidates of size 16
+-- tested 2632 candidates
 mem x Leaf  =  False
-mem x (Node t1 y t2)  =  mem x t1 || (x == y || mem x t2)
+mem x (Node t1 y t2)
+  | x < y  =  mem x t1
+  | y < x  =  mem x t2
+  | otherwise  =  True
 
 mem :: Int -> Tree -> Bool
 -- testing 360 combinations of argument values
@@ -41,22 +48,46 @@
 
 insert :: Int -> Tree -> Tree
 -- testing 360 combinations of argument values
--- pruning with 2/3 rules
--- 2 candidates of size 1
--- 0 candidates of size 2
+-- pruning with 4/4 rules
+-- 1 candidates of size 1
+-- 1 candidates of size 2
 -- 0 candidates of size 3
--- 4 candidates of size 4
--- 0 candidates of size 5
--- 0 candidates of size 6
--- 26 candidates of size 7
--- 0 candidates of size 8
--- 0 candidates of size 9
--- 176 candidates of size 10
--- 0 candidates of size 11
--- 32 candidates of size 12
--- tested 240 candidates
+-- 1 candidates of size 4
+-- 6 candidates of size 5
+-- 1 candidates of size 6
+-- 2 candidates of size 7
+-- 22 candidates of size 8
+-- 22 candidates of size 9
+-- 39 candidates of size 10
+-- 148 candidates of size 11
+-- 310 candidates of size 12
+-- tested 553 candidates
 insert  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Node, unit, guarded equations, and (<)
+-- consider increasing target/maxSize or refining the ingredients
 
+insert :: Int -> Tree -> Tree
+-- testing 360 combinations of argument values
+-- pruning with 1/2 rules
+-- 1 candidates of size 1
+-- 1 candidates of size 2
+-- 0 candidates of size 3
+-- 1 candidates of size 4
+-- 6 candidates of size 5
+-- 1 candidates of size 6
+-- 2 candidates of size 7
+-- 25 candidates of size 8
+-- 25 candidates of size 9
+-- 42 candidates of size 10
+-- 198 candidates of size 11
+-- 380 candidates of size 12
+-- tested 682 candidates
+insert  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Node, unit, compare, and case
+-- consider increasing target/maxSize or refining the ingredients
+
 before :: Int -> Tree -> Tree
 -- pruning with 5/6 rules
 -- 2 candidates of size 1
@@ -72,6 +103,9 @@
 -- 3543 candidates of size 11
 -- tested 5343 candidates
 before  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Leaf, Node, (==), (<), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 beyond :: Int -> Tree -> Tree
 -- pruning with 5/6 rules
@@ -88,41 +122,64 @@
 -- 3543 candidates of size 11
 -- tested 5343 candidates
 beyond  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Leaf, Node, (==), (<=), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 before :: Int -> Tree -> Tree
--- pruning with 2/4 rules
+-- pruning with 3/5 rules
 -- 2 candidates of size 1
 -- 2 candidates of size 2
 -- 0 candidates of size 3
 -- 4 candidates of size 4
 -- 21 candidates of size 5
 -- 0 candidates of size 6
--- 68 candidates of size 7
--- 287 candidates of size 8
+-- 60 candidates of size 7
+-- 176 candidates of size 8
 -- 32 candidates of size 9
--- 1216 candidates of size 10
--- 5103 candidates of size 11
--- 1472 candidates of size 12
--- tested 8207 candidates
+-- 716 candidates of size 10
+-- 2373 candidates of size 11
+-- 896 candidates of size 12
+-- tested 4282 candidates
 before  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Leaf, Node, compare, and case
+-- consider increasing target/maxSize or refining the ingredients
 
 beyond :: Int -> Tree -> Tree
--- pruning with 2/4 rules
+-- pruning with 3/5 rules
 -- 2 candidates of size 1
 -- 2 candidates of size 2
 -- 0 candidates of size 3
 -- 4 candidates of size 4
 -- 21 candidates of size 5
 -- 0 candidates of size 6
--- 68 candidates of size 7
--- 287 candidates of size 8
+-- 60 candidates of size 7
+-- 176 candidates of size 8
 -- 32 candidates of size 9
--- 1216 candidates of size 10
--- 5103 candidates of size 11
--- 1472 candidates of size 12
--- tested 8207 candidates
+-- 716 candidates of size 10
+-- 2373 candidates of size 11
+-- 896 candidates of size 12
+-- tested 4282 candidates
 beyond  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Leaf, Node, compare, and case
+-- consider increasing target/maxSize or refining the ingredients
 
+insert :: Int -> Tree -> Tree
+-- testing 360 combinations of argument values
+-- pruning with 3/6 rules
+-- 1 candidates of size 1
+-- 0 candidates of size 2
+-- 2 candidates of size 3
+-- 1 candidates of size 4
+-- 1 candidates of size 5
+-- 6 candidates of size 6
+-- 2 candidates of size 7
+-- 15 candidates of size 8
+-- tested 25 candidates
+insert x t1  =  Node (before x t1) x (beyond x t1)
+
 union :: Tree -> Tree -> Tree
 -- testing 360 combinations of argument values
 -- pruning with 6/8 rules
@@ -135,7 +192,10 @@
 -- 152 candidates of size 7
 -- 82 candidates of size 8
 -- 2438 candidates of size 9
--- 3970 candidates of size 10
--- tested 6735 candidates
+-- 4322 candidates of size 10
+-- tested 7087 candidates
 union  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Leaf, Node, before, and beyond
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/eg/count.txt b/eg/count.txt
--- a/eg/count.txt
+++ b/eg/count.txt
@@ -1,12 +1,12 @@
 count :: A -> [A] -> Int
 -- testing 13 combinations of argument values
 -- pruning with 1/2 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 1 candidates of size 2
 -- 0 candidates of size 3
 -- 0 candidates of size 4
 -- 1 candidates of size 5
--- tested 2 candidates
+-- tested 3 candidates
 count x xs  =  length (filter (x ==) xs)
 
 count :: A -> [A] -> Int
diff --git a/eg/digits.txt b/eg/digits.txt
--- a/eg/digits.txt
+++ b/eg/digits.txt
@@ -61,4 +61,7 @@
 -- 12715 candidates of size 7
 -- tested 13449 candidates
 digitCount  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 10, (+), div, mod, (==), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/eg/dupos.txt b/eg/dupos.txt
--- a/eg/dupos.txt
+++ b/eg/dupos.txt
@@ -67,4 +67,7 @@
 -- 1363 candidates of size 13
 -- tested 1858 candidates
 positionsFrom  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- [], 1, (+), (:), (==), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/eg/either.txt b/eg/either.txt
--- a/eg/either.txt
+++ b/eg/either.txt
@@ -36,11 +36,11 @@
 
 either :: (A -> A) -> (A -> A) -> Either A A -> A
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 1 candidates of size 2
 -- 4 candidates of size 3
 -- 12 candidates of size 4
--- tested 11 candidates
+-- tested 12 candidates
 either f g (Left x)  =  f x
 either f g (Right x)  =  g x
 
@@ -51,4 +51,7 @@
 -- 0 candidates of size 2
 -- tested 1 candidates
 lefts  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- Left, Right, False, True, [], and (:)
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/eg/fib01.txt b/eg/fib01.txt
--- a/eg/fib01.txt
+++ b/eg/fib01.txt
@@ -8,6 +8,9 @@
 -- 27 candidates of size 5
 -- tested 52 candidates
 fib01  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, dec, and (+)
+-- consider increasing target/maxSize or refining the ingredients
 
 fib01 :: Int -> Int -> Int -> Int
 -- testing 8 combinations of argument values
@@ -15,4 +18,7 @@
 -- 4 candidates of size 1
 -- tested 4 candidates
 fib01  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, (+), dec, (<=), and if-expressions
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/eg/ints.txt b/eg/ints.txt
--- a/eg/ints.txt
+++ b/eg/ints.txt
@@ -1,20 +1,20 @@
 second :: [Int] -> Int
 -- testing 360 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 1 candidates of size 2
--- 1 candidates of size 3
--- tested 2 candidates
+-- 2 candidates of size 3
+-- tested 3 candidates
 second xs  =  head (tail xs)
 
 third :: [Int] -> Int
 -- testing 360 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 1 candidates of size 2
 -- 1 candidates of size 3
--- 1 candidates of size 4
--- tested 3 candidates
+-- 2 candidates of size 4
+-- tested 4 candidates
 third xs  =  head (tail (tail xs))
 
 sum :: [Int] -> Int
diff --git a/eg/list.hs b/eg/list.hs
--- a/eg/list.hs
+++ b/eg/list.hs
@@ -83,13 +83,11 @@
     , fun ":" ((:) :: Int -> [Int] -> [Int])
     , fun "null" (null :: [Int] -> Bool)
     , guard
-    , fun "undefined" (undefined :: Int)
     ]
 
   conjure "last" last'
     [ con ([] :: [Int])
     , fun ":" ((:) :: Int -> [Int] -> [Int])
-    , fun "undefined" (undefined :: Int)
     , maxPatternDepth 2
     ]
 
@@ -99,7 +97,7 @@
     , fun "," ((,) :: Int -> Int -> (Int,Int))
     ]
 
-  conjure "\\/" (\/)
+  conjure "\\/" (Main.\/)
     [ con ([] :: [Int])
     , fun ":" ((:) :: Int -> [Int] -> [Int])
     ]
diff --git a/eg/list.txt b/eg/list.txt
--- a/eg/list.txt
+++ b/eg/list.txt
@@ -56,9 +56,8 @@
 -- 0 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
--- 4 candidates of size 7
+-- 2 candidates of size 7
 -- tested 2 candidates
-last []  =  undefined
 last (x:xs)
   | null xs  =  x
   | otherwise  =  last xs
@@ -70,10 +69,9 @@
 -- 0 candidates of size 2
 -- 0 candidates of size 3
 -- 1 candidates of size 4
--- 2 candidates of size 5
--- 2 candidates of size 6
--- tested 6 candidates
-last []  =  undefined
+-- 0 candidates of size 5
+-- 1 candidates of size 6
+-- tested 3 candidates
 last [x]  =  x
 last (x:y:xs)  =  last (y:xs)
 
diff --git a/eg/oddeven.txt b/eg/oddeven.txt
--- a/eg/oddeven.txt
+++ b/eg/oddeven.txt
@@ -31,22 +31,22 @@
 odd :: Int -> Bool
 -- testing 6 combinations of argument values
 -- pruning with 36/55 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 3 candidates of size 3
 -- 0 candidates of size 4
 -- 44 candidates of size 5
--- tested 30 candidates
+-- tested 31 candidates
 odd x  =  1 == x `mod` 2
 
 even :: Int -> Bool
 -- testing 6 combinations of argument values
 -- pruning with 36/55 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 3 candidates of size 3
 -- 0 candidates of size 4
 -- 44 candidates of size 5
--- tested 20 candidates
+-- tested 21 candidates
 even x  =  0 == x `mod` 2
 
diff --git a/eg/peano.hs b/eg/peano.hs
--- a/eg/peano.hs
+++ b/eg/peano.hs
@@ -7,7 +7,6 @@
 -- Distributed under the 3-Clause BSD licence (see the file LICENSE).
 {-# LANGUAGE TemplateHaskell #-}
 import Conjure
-import Test.LeanCheck
 
 data Peano  =  Z | S Peano
   deriving (Show, Eq)
diff --git a/eg/pow.hs b/eg/pow.hs
--- a/eg/pow.hs
+++ b/eg/pow.hs
@@ -23,15 +23,19 @@
     ]
 
   -- pow b 0  =  1
-  -- pow b e  =  pow b (halve e) * pow b (halve e) * if odd e then b else 1
-  --             2   3  4     5  6 7   8  9    10 11 12 13 14     15     16
-  -- out of reach performance wise, OOM at size 9
+  -- pow b e
+  --   | odd e  =  b * pow b (e - 1)             -- 11
+  --   | otherwise  =  square (pow b (halve e))  -- 16
   conjure "pow" pow
     [ con (0::Int)
     , con (1::Int)
---  , fun "sq" ((\x -> x*x) :: Int -> Int) -- cheat! OOM still
+    , fun "square" ((\x -> x*x) :: Int -> Int) -- cheat
     , fun "*" ((*) :: Int -> Int -> Int)
-    , fun "halve" ((`div` 2) :: Int -> Int)
-    , iif (undefined :: Int)
-    , maxSize 6 -- OOM at size 9
+    , fun "-" ((-) :: Int -> Int -> Int)
+    , fun "halve" ((`div` 2) :: Int -> Int) -- cheat
+    , fun "odd" (odd :: Int -> Bool)
+    , guard
+    , maxSize 6 -- remove to find the first version...
+    -- simply out of reach:
+    -- , maxSize 16, carryOn
     ]
diff --git a/eg/pow.txt b/eg/pow.txt
--- a/eg/pow.txt
+++ b/eg/pow.txt
@@ -15,13 +15,16 @@
 
 pow :: Int -> Int -> Int
 -- testing 5 combinations of argument values
--- pruning with 15/19 rules
+-- pruning with 49/71 rules
 -- 4 candidates of size 1
--- 2 candidates of size 2
--- 5 candidates of size 3
--- 9 candidates of size 4
--- 31 candidates of size 5
--- 178 candidates of size 6
--- tested 229 candidates
+-- 4 candidates of size 2
+-- 17 candidates of size 3
+-- 60 candidates of size 4
+-- 294 candidates of size 5
+-- 1386 candidates of size 6
+-- tested 1765 candidates
 pow  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- 0, 1, square, (*), (-), halve, odd, and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
diff --git a/eg/sort.txt b/eg/sort.txt
--- a/eg/sort.txt
+++ b/eg/sort.txt
@@ -67,6 +67,9 @@
 -- 3728 candidates of size 16
 -- tested 5768 candidates
 merge  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- [], (:), (<=), and guarded equations
+-- consider increasing target/maxSize or refining the ingredients
 
 qsort :: [Int] -> [Int]
 -- testing 9 combinations of argument values
diff --git a/eg/spec.txt b/eg/spec.txt
--- a/eg/spec.txt
+++ b/eg/spec.txt
@@ -29,11 +29,11 @@
 -- pruning with 3/3 rules
 -- 2 candidates of size 1
 -- 4 candidates of size 2
--- 11 candidates of size 3
--- 31 candidates of size 4
--- 94 candidates of size 5
--- 225 candidates of size 6
--- tested 286 candidates
+-- 13 candidates of size 3
+-- 35 candidates of size 4
+-- 113 candidates of size 5
+-- 288 candidates of size 6
+-- tested 347 candidates
 [] ++ xs  =  xs
 (x:xs) ++ ys  =  x:(xs ++ ys)
 
diff --git a/eg/subset.txt b/eg/subset.txt
--- a/eg/subset.txt
+++ b/eg/subset.txt
@@ -16,11 +16,11 @@
 subset :: [Int] -> [Int] -> Bool
 -- testing 44 combinations of argument values
 -- pruning with 3/3 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 2 candidates of size 3
 -- 6 candidates of size 4
 -- 2 candidates of size 5
--- tested 9 candidates
+-- tested 10 candidates
 subset xs ys  =  sort xs `isSubsequenceOf` sort ys
 
diff --git a/eg/these.hs b/eg/these.hs
--- a/eg/these.hs
+++ b/eg/these.hs
@@ -2,7 +2,6 @@
 {-# LANGUAGE TemplateHaskell #-}
 
 import Conjure
-import Test.LeanCheck
 
 
 -- This was inspired by the These datatype from the cathis package.
diff --git a/eg/these.txt b/eg/these.txt
--- a/eg/these.txt
+++ b/eg/these.txt
@@ -1,7 +1,7 @@
 fromThese :: A -> B -> These A B -> (A,B)
 -- testing 4 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 1 candidates of size 3
 -- 0 candidates of size 4
@@ -11,7 +11,7 @@
 -- 0 candidates of size 8
 -- 0 candidates of size 9
 -- 1 candidates of size 10
--- tested 2 candidates
+-- tested 3 candidates
 fromThese x y Neither  =  (x,y)
 fromThese x y (This z)  =  (z,y)
 fromThese x y (That z)  =  (x,z)
diff --git a/eg/tree.hs b/eg/tree.hs
--- a/eg/tree.hs
+++ b/eg/tree.hs
@@ -97,15 +97,13 @@
 main :: IO ()
 main = do
   conjure "leftmost" leftmost
-    [ fun "undefined" (undefined :: Int)
-    , iif (undefined :: Int)
-    , fun "nil" nil
+    [ fun "nil" nil
+    , guard
     ]
 
   conjure "rightmost" rightmost
-    [ fun "undefined" (undefined :: Int)
-    , iif (undefined :: Int)
-    , fun "nil" nil
+    [ fun "nil" nil
+    , guard
     ]
 
   conjure "size" size
diff --git a/eg/tree.txt b/eg/tree.txt
--- a/eg/tree.txt
+++ b/eg/tree.txt
@@ -7,12 +7,11 @@
 -- 0 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
--- 16 candidates of size 7
+-- 8 candidates of size 7
 -- tested 2 candidates
-leftmost Leaf  =  undefined
-leftmost (Node t1 x t2)  =  if nil t1
-                            then x
-                            else leftmost t1
+leftmost (Node t1 x t2)
+  | nil t1  =  x
+  | otherwise  =  leftmost t1
 
 rightmost :: Tree -> Int
 -- testing 360 combinations of argument values
@@ -23,12 +22,11 @@
 -- 0 candidates of size 4
 -- 0 candidates of size 5
 -- 0 candidates of size 6
--- 16 candidates of size 7
--- tested 11 candidates
-rightmost Leaf  =  undefined
-rightmost (Node t1 x t2)  =  if nil t2
-                             then x
-                             else rightmost t2
+-- 8 candidates of size 7
+-- tested 7 candidates
+rightmost (Node t1 x t2)
+  | nil t2  =  x
+  | otherwise  =  rightmost t2
 
 size :: Tree -> Int
 -- testing 360 combinations of argument values
@@ -96,14 +94,17 @@
 -- 712 candidates of size 12
 -- tested 1127 candidates
 ordered  =  undefined  -- search exhausted
+-- could not find implementation using only
+-- True, False, (&&), (||), (<), rightmost, leftmost, and nil
+-- consider increasing target/maxSize or refining the ingredients
 
 ordered :: Tree -> Bool
 -- testing 360 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 0 candidates of size 2
 -- 1 candidates of size 3
--- tested 1 candidates
+-- tested 2 candidates
 ordered t1  =  strictlyOrdered (inorder t1)
 
 preorder :: Tree -> [Int]
diff --git a/eg/tuple.txt b/eg/tuple.txt
--- a/eg/tuple.txt
+++ b/eg/tuple.txt
@@ -1,27 +1,27 @@
 fst :: (A,A) -> A
 -- testing 4 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 2 candidates of size 2
--- tested 1 candidates
+-- tested 2 candidates
 fst (x,y)  =  x
 
 snd :: (A,A) -> A
 -- testing 4 combinations of argument values
 -- pruning with 0/0 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 2 candidates of size 2
--- tested 2 candidates
+-- tested 3 candidates
 snd (x,y)  =  y
 
 swap :: (A,A) -> (A,A)
 -- testing 4 combinations of argument values
 -- pruning with 10/10 rules
 -- 1 candidates of size 1
--- 0 candidates of size 2
+-- 1 candidates of size 2
 -- 0 candidates of size 3
 -- 4 candidates of size 4
--- tested 4 candidates
+-- tested 5 candidates
 swap (x,y)  =  (y,x)
 
 curry :: ((A,A) -> A) -> A -> A -> A
@@ -35,11 +35,11 @@
 
 uncurry :: (A -> A -> A) -> (A,A) -> A
 -- pruning with 10/10 rules
--- 0 candidates of size 1
+-- 1 candidates of size 1
 -- 4 candidates of size 2
 -- 0 candidates of size 3
 -- 4 candidates of size 4
--- tested 6 candidates
+-- tested 7 candidates
 uncurry f (x,y)  =  f x y
 
 pairwise :: [A] -> [(A,A)]
diff --git a/src/Conjure.hs b/src/Conjure.hs
--- a/src/Conjure.hs
+++ b/src/Conjure.hs
@@ -120,11 +120,27 @@
   , reifyEquality
   , reifyTiers
   , conjureType
-  , Name (..)
-  , Express (..)
   , deriveConjurable
   , deriveConjurableIfNeeded
   , deriveConjurableCascading
+  , Name (..)
+  , Express (..)
+  , Listable (..)
+  , cons0
+  , cons1
+  , cons2
+  , cons3
+  , cons4
+  , cons5
+  , cons6
+  , (\/)
+  , reset
+  , cons7
+  , cons8
+  , cons9
+  , cons10
+  , cons11
+  , cons12
 
 -- * Pure interfaces
   , Results (..)
diff --git a/src/Conjure/Conjurable.hs b/src/Conjure/Conjurable.hs
--- a/src/Conjure/Conjurable.hs
+++ b/src/Conjure/Conjurable.hs
@@ -41,6 +41,22 @@
   , cevl
   , Name (..)
   , Express (..)
+  , Listable (..)
+  , cons0
+  , cons1
+  , cons2
+  , cons3
+  , cons4
+  , cons5
+  , cons6
+  , (\/)
+  , reset
+  , cons7
+  , cons8
+  , cons9
+  , cons10
+  , cons11
+  , cons12
   , conjureArgumentPats
   , conjureMostGeneralCanonicalVariation
   , conjureCasesFor
@@ -149,6 +165,10 @@
   conjureSubTypes :: a -> Reification
   conjureSubTypes _  =  id
 
+  -- | Returns an undefined value of the return value type.
+  conjureUndefined :: a -> Expr
+  conjureUndefined x  =  value "undefined" (undefined `asTypeOf` x)
+
   -- | Returns an if-function encoded as an 'Expr'.
   conjureIf :: a -> Expr
   conjureIf   =  ifFor
@@ -619,6 +639,7 @@
   conjureArgumentHoles f  =  hole (argTy f) : conjureArgumentHoles (f undefined)
   conjureResultHole f  =  conjureResultHole (f undefined)
   conjureSubTypes f  =  conjureType (argTy f) . conjureType (resTy f)
+  conjureUndefined f  =  conjureUndefined (f undefined)
   conjureIf f  =  conjureIf (f undefined)
   conjureArgumentCases f  =  conjureCases (argTy f) : conjureArgumentCases (f undefined)
   conjureExpress f e
diff --git a/src/Conjure/Defn.hs b/src/Conjure/Defn.hs
--- a/src/Conjure/Defn.hs
+++ b/src/Conjure/Defn.hs
@@ -70,7 +70,7 @@
 -- > sum []  =  0
 -- > sum (x:xs)  =  x + sum xs
 showDefn :: Defn -> String
-showDefn  =  unlines . map show1
+showDefn  =  unlines . map show1 . removeUndefinedBindings
   where
   show1 (lhs,rhs)  =
     case rhs of
@@ -356,3 +356,15 @@
     | otherwise     =  d
   reduce (lhs :$ _, rhs :$ _)  =  (lhs, rhs)
   reduce _  =  error "Conjure.Defn.etaReduce: the impossible happened, this is a bug"
+
+
+removeUndefinedBindings :: Defn -> Defn
+removeUndefinedBindings defn  =
+  case u defn of
+  []  ->  defn
+  bs  ->  bs
+  where
+  u []  =  []
+  u ((lhs,Value "undefined" _):bs)
+    | nor [lhs `isInstanceOf` l | (l,_) <- bs]  =  removeUndefinedBindings bs
+  u (b:bs)  =  b:removeUndefinedBindings bs
diff --git a/src/Conjure/Engine.hs b/src/Conjure/Engine.hs
--- a/src/Conjure/Engine.hs
+++ b/src/Conjure/Engine.hs
@@ -159,7 +159,7 @@
 --
 --   This works like the functions 'conjure' and 'conjureFromSpec' combined.
 conjure0 :: Conjurable f => String -> f -> (f -> [Property]) -> [Ingredient] -> IO ()
-conjure0 nm f p es  =  do
+conjure0 nm f p ingredients  =  do
   -- the code section below became quite ugly with time and patches.
   -- it is still maintainable and readable as it is, but perhaps
   -- needs to be cleaned up and simplified
@@ -201,8 +201,14 @@
   where
   showEq eq  =  showExpr (fst eq) ++ " == " ++ showExpr (snd eq)
   pr :: Integer -> Int -> Int -> [([Defn], [Defn])] -> IO ()
-  pr t0 n t []  =  do putWithTimeSince t0 $ "tested " ++ show t ++ " candidates"
-                      putStrLn $ nm ++ "  =  undefined  -- search exhausted\n"
+  pr t0 n t []  =  do
+    putWithTimeSince t0 $ "tested " ++ show t ++ " candidates"
+    putStrLn $ nm ++ "  =  undefined  -- search exhausted"
+    when (not carryOn) $
+      putStrLn $ "-- could not find implementation using only\n-- "
+              ++ command [showSymbol e | (e,_) <- actual ingredients]
+              ++ "\n-- consider increasing target/maxSize or refining the ingredients"
+    putStrLn ""
   pr t0 n t ((is,cs):rs)  =  do
     let nc  =  length cs
     putWithTimeSince t0 $ show nc ++ " candidates of size " ++ show n
@@ -221,21 +227,25 @@
       putStrLn $ showDefn $ etaReduce $ normalizeDefn thy i
       when carryOn $ pr1 t' is (drop 1 cs'')
   rs  =  zip iss css
-  results  =  conjpure0 nm f p es
+  results  =  conjpure0 nm f p ingredients
   iss  =  implementationss results
   css  =  candidatess results
   ts   =  bindings results
   thy  =  theory results
   nRules  =  length (rules thy)
   nREs  =  length (equations thy) + nRules
+  showSymbol e
+    | isGuardSymbol e  =  "guarded equations"
+    | isIfSymbol e  =  "if-expressions"
+    | otherwise  =  showExpr e
   -- we could avoid the following as most are called once
   -- but is nice to have a summary of which settings are used
-  carryOn              =  carryOnI es
-  showTests            =  showTestsI es
-  showTheory           =  showTheoryI es
-  showPatterns         =  showPatternsI es
-  showCandidates       =  showCandidatesI es
-  showDeconstructions  =  showDeconstructionsI es
+  carryOn              =  carryOnI ingredients
+  showTests            =  showTestsI ingredients
+  showTheory           =  showTheoryI ingredients
+  showPatterns         =  showPatternsI ingredients
+  showCandidates       =  showCandidatesI ingredients
+  showDeconstructions  =  showDeconstructionsI ingredients
 
 
 -- | Results to the 'conjpure' family of functions.
@@ -267,7 +277,7 @@
 -- 'conjpure', 'conjpureFromSpec', 'conjure' and 'conjureFromSpec'
 -- all refer to this.
 conjpure0 :: Conjurable f => String -> f -> (f -> [Property]) -> [Ingredient] -> Results
-conjpure0 nm f p es  =  Results
+conjpure0 nm f p is  =  Results
   { implementationss  =  implementationsT
   , candidatess  =  candidatesT
   , bindings  =  tests
@@ -284,17 +294,17 @@
                $  (if target > 0 then targetiers target else id)
                $  (if maxSize > 0 then take maxSize else id)
                $  candidatesTT
-  (candidatesTT, thy, patternss, deconstructions)  =  candidateDefns nm f es
+  (candidatesTT, thy, patternss, deconstructions)  =  candidateDefns nm f is
 
   test dfn  =  all (errorToFalse . deval (conjureExpress f) maxRecursions dfn False)
             $  [funToVar lhs -==- rhs | (lhs, rhs) <- tests]
   tests  =  conjureTestDefn maxTests maxSearchTests nm f
   (-==-)  =  conjureMkEquation f
-  maxTests  =  maxTestsI es
-  (target, maxSize)  =  targetAndMaxSizeI es
-  maxRecursions  =  maxRecursionsI es
-  maxSearchTests  =  maxSearchTestsI es
-  uniqueCandidates  =  uniqueCandidatesI es
+  maxTests  =  maxTestsI is
+  (target, maxSize)  =  targetAndMaxSizeI is
+  maxRecursions  =  maxRecursionsI is
+  maxSearchTests  =  maxSearchTestsI is
+  uniqueCandidates  =  uniqueCandidatesI is
 
 
 -- | Return apparently unique candidate definitions.
@@ -396,8 +406,8 @@
        | otherwise           =                        conjurePats maxPatternDepth es nm f
   partialDefns  =  concatMapT partialDefnsFromPats pats
   -- replaces the any guard symbol with a guard of the correct type
-  ps  =  actual is  -- extract actual ingredients/primitives from the list
-  es  =  [if isGuardSymbol e then conjureGuard f else e | (e,_) <- ps]
+  ais  =  actual is
+  es  =  [if isGuardSymbol e then conjureGuard f else e | (e,_) <- ais]
 
   eh  =  conjureResultHole f
   efxs  =  conjureVarApplication nm f
@@ -423,10 +433,10 @@
     keepConstant | maxConstantSize > 0  =  \e -> isFun e || isConst e || not (isGround e) || size e <= maxConstantSize
                  | otherwise            =  const True
 
-  isRedundant | adHocRedundancy  =  \e -> isRedundantDefn e || isRedundantModuloRewriting (normalize thy) e
+  isRedundant | assortedPruning  =  \e -> isRedundantDefn e || isRedundantModuloRewriting (normalize thy) e
               | otherwise        =  const False
 
-  hasRedundant | adHocRedundancy  =  hasRedundantRecursion
+  hasRedundant | assortedPruning  =  hasRedundantRecursion
                | otherwise        =  const False
 
   isNumeric  =  conjureIsNumeric f
@@ -458,6 +468,7 @@
       | copyBindings && isGroundPat f pat  =  [[(pat, toValPat f pat)]]
       | otherwise  =  mapT (pat,)
                    .  filterT keepB
+                   .  insemptier (conjureUndefined f)
                    .  appsWith pat
                    .  drop 1 -- this excludes the function name itself
                    $  vars pat ++ [eh | any (uncurry should) (zip aess aes)]
@@ -549,8 +560,8 @@
 
   thy  =  doubleCheck (===)
        .  theoryFromAtoms (===) maxEquationSize . (:[]) . nub
-       $  cjHoles (fun nm f:ps) ++ [val False, val True] ++ es
-  (===)  =  cjAreEqual (fun nm f:ps) maxTests
+       $  cjHoles (fun nm f:ais) ++ [val False, val True] ++ es
+  (===)  =  cjAreEqual (fun nm f:ais) maxTests
   isUnbreakable  =  conjureIsUnbreakable f
 
   maxTests               =  maxTestsI is
@@ -563,7 +574,7 @@
   requireDescent         =  requireDescentI is
   maxEarlyTests          =  maxEarlyTestsI is
   copyBindings           =  copyBindingsI is
-  adHocRedundancy        =  assortedPruningI is -- TODO: rename
+  assortedPruning        =  assortedPruningI is -- TODO: rename
   atomicNumbers          =  atomicNumbersI is
   rewriting              =  rewriteI is
 
@@ -720,3 +731,9 @@
 catconMapT f  =  foldr (\+:/) [] . map (foldr (\/) []) . mapT f
   where
   xss \+:/ yss  =  ([]:yss) \/ xss
+
+-- | If the first tier is empty,
+--   populate it with the given value.
+insemptier :: a -> [[a]] -> [[a]]
+insemptier x ([]:xss)  =  [x]:xss
+insemptier _ xss  =  xss
diff --git a/src/Conjure/Expr.hs b/src/Conjure/Expr.hs
--- a/src/Conjure/Expr.hs
+++ b/src/Conjure/Expr.hs
@@ -39,6 +39,7 @@
   , isGuardSymbol
   , isGuard
   , hasGuard
+  , isIfSymbol
   , mapInnerFirstOuterLast
   , mappArgs
   , mappFun
@@ -599,6 +600,10 @@
 isGuardSymbol :: Expr -> Bool
 isGuardSymbol (Value "|" _)  =  True
 isGuardSymbol _  =  False
+
+isIfSymbol :: Expr -> Bool
+isIfSymbol (Value "if" _)  =  True
+isIfSymbol _  =  False
 
 -- | Is the expression a guard application?
 isGuard :: Expr -> Bool
diff --git a/src/Conjure/Ingredient.hs b/src/Conjure/Ingredient.hs
--- a/src/Conjure/Ingredient.hs
+++ b/src/Conjure/Ingredient.hs
@@ -165,8 +165,12 @@
 -- >   | otherwise  =  last xs
 guard :: Ingredient
 guard  =  (guardFor (undefined :: Bool), conjureType (undefined :: Bool))
--- internally we always return a guard of the Bool return type,
--- this is replaced by Conjure when enumerating candidates
+-- Internally we always return a guard of the Bool return type,
+-- this is replaced by Conjure when enumerating candidates.
+-- The choice of Bool here is not incidental:
+-- when reifying types based on this,
+-- only Bool type information would be included.
+-- With other types as the element type, we would have a spurious inclusion.
 
 
 -- | Provides a case condition bound to the given return type.
diff --git a/src/Conjure/Utils.hs b/src/Conjure/Utils.hs
--- a/src/Conjure/Utils.hs
+++ b/src/Conjure/Utils.hs
@@ -40,6 +40,7 @@
   , classifyBy -- from LeanCheck.Stats
   , classifyOn -- from LeanCheck.Stats
   , none
+  , nor
   , updateAt
   , first
   , second
@@ -47,6 +48,7 @@
   , (+++)
   , isSubsetOf
   , prods
+  , command
   )
 where
 
@@ -176,6 +178,9 @@
 none :: (a -> Bool) -> [a] -> Bool
 none p  =  not . any p
 
+nor :: [Bool] -> Bool
+nor  =  not . or
+
 -- | Updates the value in a list at a given position.
 --
 -- > > updateAt 2 (*10) [1,2,3,4]
@@ -224,3 +229,18 @@
 prods :: [[a]] -> [[a]]
 prods []  =  [[]]
 prods (xs:xss)  =  [y:ys | y <- xs, ys <- prods xss]
+
+-- | Separate a list of strings using comma-and-and.
+--
+-- This function includes the Oxford comma.
+--
+-- > > command ["this", "that"]
+-- > "this and that"
+--
+-- > > command ["this", "that", "these"]
+-- > "this, that, and these"
+command :: [String] -> String
+command []  =  "nothing"
+command [x]  =  x
+command [x,y]  =  x ++ " and " ++ y
+command xs  =  intercalate ", " (init xs) ++ ", and " ++ (last xs)