1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
------------------------------------------------------------------------------
--- This library implements some operations to generate search trees
--- for various data types.
---
--- The library also provides combinators to support the easy definition
--- of search tree generators for user-defined data types.
--- If a data type is defined by
---
---     data T a1 ... an = ... | C t1 ... tn | ....
---
--- then one can define a search tree generator for this type by
---
---     genT gena1 ... genan =
---       ... ||| genCons<n> C gen_t1 ... gen_t1 ||| ...
---
--- where `gen_ti` denotes the search tree generator for type `ti`.
--- For instance, a search tree generator for the type
---
---     data Tree a = Leaf a
---                 | Node [Tree a]
---
--- can be defined by
---
---     genTree gena =  genCons1 Leaf gena
---                 ||| genCons1 Node (genList (genTree gena))
---
--- @author  Michael Hanus
--- @version February 2017
--- @category algorithm
------------------------------------------------------------------------------

module SearchTreeGenerators
  ( genBool, genNat, genInt, genFloat, genChar, genList
  , genMaybe, genEither, genUnit, genPair, genTriple, genTuple4, genTuple5
  , genOrdering
  , genCons0, genCons1, genCons2, genCons3, genCons4, genCons5
  , (|||)
  ) where

import Float
import SearchTree
import SearchTreeTraversal

infixr 1 |||

--- Replace in a given search tree each value node by a new search tree
--- according to the function provided as the second argument.
valsTo :: SearchTree a -> (a -> SearchTree b) -> SearchTree b
valsTo (Value a)  f = f a
valsTo (Fail i)   _ = Fail i
valsTo (Or t1 t2) f = Or (valsTo t1 f) (valsTo t2 f)

--- Constructs an alternative of two search trees.
(|||) :: SearchTree a -> SearchTree a -> SearchTree a
x ||| y = Or x y

--- Constructs a generator for a nullary constructor.
genCons0 :: a -> SearchTree a
genCons0 = Value

--- Constructs a generator for a unary constructor where the generator
--- for the argument type is provided.
genCons1 :: (a -> b) -> SearchTree a -> SearchTree b
genCons1 c gena = valsTo gena (Value . c)

--- Constructs a generator for a binary constructor where the generators
--- for the argument types are provided.
genCons2 :: (a1 -> a2 -> b) -> SearchTree a1 -> SearchTree a2 -> SearchTree b
genCons2 c gena1 gena2 =
  valsTo gena1 (\a1 ->
  valsTo gena2 (\a2 -> Value (c a1 a2)))

--- Constructs a generator for a ternary constructor where the generators
--- for the argument types are provided.
genCons3 :: (a1 -> a2 -> a3 -> b) -> SearchTree a1 -> SearchTree a2
         -> SearchTree a3 -> SearchTree b
genCons3 c gena1 gena2 gena3 =
  valsTo gena1 (\a1 ->
  valsTo gena2 (\a2 ->
  valsTo gena3 (\a3 -> Value (c a1 a2 a3))))

--- Constructs a generator for a constructor of arity 4 where the generators
--- for the argument types are provided.
genCons4 :: (a1 -> a2 -> a3 -> a4 -> b) -> SearchTree a1 -> SearchTree a2
         -> SearchTree a3 -> SearchTree a4 -> SearchTree b
genCons4 c gena1 gena2 gena3 gena4 =
  valsTo gena1 (\a1 ->
  valsTo gena2 (\a2 ->
  valsTo gena3 (\a3 ->
  valsTo gena4 (\a4 -> Value (c a1 a2 a3 a4)))))

--- Constructs a generator for a constructor of arity 5 where the generators
--- for the argument types are provided.
genCons5 :: (a1 -> a2 -> a3 -> a4 -> a5 -> b) -> SearchTree a1 -> SearchTree a2
         -> SearchTree a3 -> SearchTree a4 -> SearchTree a5 -> SearchTree b
genCons5 c gena1 gena2 gena3 gena4 gena5 =
  valsTo gena1 (\a1 ->
  valsTo gena2 (\a2 ->
  valsTo gena3 (\a3 ->
  valsTo gena4 (\a4 ->
  valsTo gena5 (\a5 -> Value (c a1 a2 a3 a4 a5))))))

------------------------------------------------------------------------------
-- Generators for specific types:

--- Generates a search tree for positive natural numbers:
genNat :: SearchTree Int
genNat = Or (Value 1)
            (Or (valsTo genNat (\n -> Value (2*n)))
                (valsTo genNat (\n -> Value (2*n+1))))

--- Generates a search tree for integer values.
genInt :: SearchTree Int
genInt = Or genNat
            (Or (Value 0)
                (valsTo genNat (Value . (0 -))))

--- Generates a search tree for Float values.
genFloat :: SearchTree Float
genFloat = Or genPosFloat
              (Or (Value 0.0)
                  (valsTo genPosFloat (Value . (0.0 -.))))

--- Generates a search tree for positive Float values.
genPosFloat :: SearchTree Float
genPosFloat = valsTo (genPair genNat genNat) ii2f
 where
  -- Combine two naturals to a float value:
  ii2f (x,y) = Value (i2f x +. nat2float 0.1 y)
  -- Transform an natural to float<1, e.g., nat2float 0.1 135 = 0.531
  nat2float m i =
    if i == 0 then 0.0
              else nat2float (m/.10) (i `div` 10) +. m *. i2f (i `mod` 10)

--- Generates a search tree for Boolean values.
genBool :: SearchTree Bool
genBool = Or (Value False) (Value True)

--- Generates a search tree for character values.
--- In order to obtain readable values, we only generate letters and digits.
genChar :: SearchTree Char
genChar = foldr1 Or (map Value chars)
 where
   chars = map chr ([65..90] ++ [97..122] ++ [48..57])
-- or use this for generating all characters:
-- genChar = valsTo genNat (Value . chr . (+1))

--- Generates a search tree for list values where the search tree for
--- the elements is given as a parameter.
genList :: SearchTree a -> SearchTree [a]
genList genx =
  Or (Value [])
     (genCons2 (:) genx (genList genx))

--- Generates a search tree for `Maybe` values where the search tree for
--- the possible element is given as a parameter.
genMaybe :: SearchTree a -> SearchTree (Maybe a)
genMaybe genx = Value Nothing ||| genCons1 Just genx

--- Generates a search tree for `Either` values where the search tree for
--- the possible elements is given as a parameter.
genEither :: SearchTree a -> SearchTree b -> SearchTree (Either a b)
genEither genx geny = genCons1 Left  genx ||| genCons1 Right geny

--- Generates a search tree for the unit values.
genUnit :: SearchTree ()
genUnit = Value ()

--- Generates a search tree for pair of values where the search tree generators
--- for the components types are given as parameters.
genPair :: SearchTree a -> SearchTree b -> SearchTree (a,b)
genPair = genCons2 (\x y -> (x,y))

--- Generates a search tree for triple of values where the search tree
--- generators for the components types are given as parameters.
genTriple :: SearchTree a -> SearchTree b -> SearchTree c
          -> SearchTree (a,b,c)
genTriple = genCons3 (\x y z -> (x,y,z))

--- Generates a search tree for quadruple of values where the search tree
--- generators for the components types are given as parameters.
genTuple4 :: SearchTree a -> SearchTree b -> SearchTree c -> SearchTree d
          -> SearchTree (a,b,c,d)
genTuple4 = genCons4 (\x y z1 z2 -> (x,y,z1,z2))

--- Generates a search tree for 5-tuple of values where the search tree
--- generators for the components types are given as parameters.
genTuple5 :: SearchTree a -> SearchTree b -> SearchTree c -> SearchTree d
          -> SearchTree e -> SearchTree (a,b,c,d,e)
genTuple5 = genCons5 (\x y z1 z2 z3 -> (x,y,z1,z2,z3))

--- Generates a search tree for the `Ordering` values.
genOrdering :: SearchTree Ordering
genOrdering = Or (Value LT) (Or (Value EQ) (Value GT))