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comparison agda/patterns.rb @ 61:18a0520445df

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Add patterns generator
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 24 Nov 2014 11:28:55 +0900
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children f9c9207c40b7
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60:73bb981cb1c6 61:18a0520445df
1 #!/usr/bin/env ruby
2
3 require 'pry'
4
5 # Agda {{{
6
7 Agda = %q(
8 open import list
9 open import basic
10
11 open import Level
12 open import Relation.Binary.PropositionalEquality
13 open ≡-Reasoning
14
15 module hoge where
16
17
18 data Delta {l : Level} (A : Set l) : (Set (suc l)) where
19 mono : A -> Delta A
20 delta : A -> Delta A -> Delta A
21
22 deltaAppend : {l : Level} {A : Set l} -> Delta A -> Delta A -> Delta A
23 deltaAppend (mono x) d = delta x d
24 deltaAppend (delta x d) ds = delta x (deltaAppend d ds)
25
26 headDelta : {l : Level} {A : Set l} -> Delta A -> Delta A
27 headDelta (mono x) = mono x
28 headDelta (delta x _) = mono x
29
30 tailDelta : {l : Level} {A : Set l} -> Delta A -> Delta A
31 tailDelta (mono x) = mono x
32 tailDelta (delta _ d) = d
33
34
35 -- Functor
36 fmap : {l ll : Level} {A : Set l} {B : Set ll} -> (A -> B) -> (Delta A) -> (Delta B)
37 fmap f (mono x) = mono (f x)
38 fmap f (delta x d) = delta (f x) (fmap f d)
39
40
41
42 -- Monad (Category)
43 eta : {l : Level} {A : Set l} -> A -> Delta A
44 eta x = mono x
45
46 bind : {l ll : Level} {A : Set l} {B : Set ll} -> (Delta A) -> (A -> Delta B) -> Delta B
47 bind (mono x) f = f x
48 bind (delta x d) f = deltaAppend (headDelta (f x)) (bind d (tailDelta ∙ f))
49
50 -- can not apply id. because different Level
51 mu : {l : Level} {A : Set l} -> Delta (Delta A) -> Delta A
52 mu d = bind d id
53
54
55 returnS : {l : Level} {A : Set l} -> A -> Delta A
56 returnS x = mono x
57
58 returnSS : {l : Level} {A : Set l} -> A -> A -> Delta A
59 returnSS x y = deltaAppend (returnS x) (returnS y)
60
61
62 -- Monad (Haskell)
63 return : {l : Level} {A : Set l} -> A -> Delta A
64 return = eta
65
66 _>>=_ : {l ll : Level} {A : Set l} {B : Set ll} ->
67 (x : Delta A) -> (f : A -> (Delta B)) -> (Delta B)
68 (mono x) >>= f = f x
69 (delta x d) >>= f = deltaAppend (headDelta (f x)) (d >>= (tailDelta ∙ f))
70
71
72
73 -- proofs
74
75
76 -- Functor-laws
77
78 -- Functor-law-1 : T(id) = id'
79 functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (fmap id) d ≡ id d
80 functor-law-1 (mono x) = refl
81 functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d)
82
83 -- Functor-law-2 : T(f . g) = T(f) . T(g)
84 functor-law-2 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} ->
85 (f : B -> C) -> (g : A -> B) -> (d : Delta A) ->
86 (fmap (f ∙ g)) d ≡ ((fmap f) ∙ (fmap g)) d
87 functor-law-2 f g (mono x) = refl
88 functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d)
89
90
91
92 -- Monad-laws (Category)
93 {-
94 monad-law-1-sub : {l : Level} {A : Set l} -> (x : Delta (Delta A)) (d : Delta (Delta (Delta A)))
95 -> deltaAppend (headDelta (bind x id)) (bind (fmap mu d) (tailDelta ∙ id)) ≡ bind (deltaAppend (headDelta x) (bind d (tailDelta ∙ id))) id
96 monad-law-1-sub (mono x) (mono (mono (mono x₁))) = refl
97 monad-law-1-sub (mono x) (mono (mono (delta x₁ d))) = refl
98 monad-law-1-sub (mono x) (mono (delta d d1)) = begin
99 deltaAppend (headDelta (bind (mono x) id)) (bind (fmap mu (mono (delta d d1))) (tailDelta ∙ id))
100 ≡⟨ refl ⟩
101 deltaAppend (headDelta (bind (mono x) id)) (bind ((mono (mu (delta d d1)))) (tailDelta ∙ id))
102 ≡⟨ refl ⟩
103 deltaAppend (headDelta (bind (mono x) id)) (bind (mono (bind (delta d d1) id)) (tailDelta ∙ id))
104 ≡⟨ refl ⟩
105 deltaAppend (headDelta (mu (mono x))) (((tailDelta ∙ id) (mu (delta d d1))))
106 ≡⟨ refl ⟩
107 deltaAppend (headDelta (mu (mono x))) (((tailDelta ∙ id) (bind (delta d d1) id)))
108 ≡⟨ {!!} ⟩
109 deltaAppend (headDelta (mu (mono x))) (((tailDelta ∙ id) (bind (delta d d1) id)))
110 -- bind (delta (mu (mono x)) (mono (mu (delta d d1)))) id
111 ≡⟨ {!!} ⟩
112 bind (deltaAppend (headDelta (mono x)) (bind (mono (delta d d1)) (tailDelta ∙ id))) id
113 ∎
114 monad-law-1-sub (delta x x₁) (mono d) = {!!}
115 monad-law-1-sub x (delta d d1) = begin
116 deltaAppend (headDelta (bind x id)) (bind (fmap mu (delta d d1)) (tailDelta ∙ id))
117 ≡⟨ {!!} ⟩
118 bind (deltaAppend (headDelta x) (bind (delta d d1) (tailDelta ∙ id))) id
119 ∎
120
121 -}
122 -- monad-law-1 : join . fmap join = join . join
123 monad-law-1 : {l : Level} {A : Set l} -> (d : Delta (Delta (Delta A))) -> ((mu ∙ (fmap mu)) d) ≡ ((mu ∙ mu) d)
124 )
125
126 # }}}
127
128 Rules = {
129 'T3' => ['(mono T2)', '(delta T2 T3)'],
130 'T2' => ['(mono T1)', '(delta T1 T2)'],
131 'T1' => ['(mono _)', '(delta _ T1)']
132 }
133
134 def generate_patterns source_patterns, operations
135 patterns = source_patterns.clone
136 operations.each do |op|
137 patterns = Rules[op].flat_map do |r|
138 patterns.flat_map{|p| p.gsub(op, r)}
139 end
140 end
141 patterns.uniq
142 end
143
144 def pattern_formatter non_format_patterns
145 formatted_patterns = non_format_patterns.clone
146
147 Rules.keys.each do |k|
148 formatted_patterns.map!{|p| p.gsub(k, '_')}
149 end
150
151 formatted_patterns
152 end
153
154 def generate_function function_name, patterns, body
155 patterns.map do |p|
156 "#{function_name} #{p} = #{body}"
157 end
158 end
159
160 def generate_agda function_body
161 Agda + function_body.join("\n")
162 end
163
164
165
166 patterns = ['(mono _)', '(delta T2 T3)']
167 operations = ['T3'].cycle(3).to_a + ['T2'].cycle(6).to_a + ['T1'].cycle(12).to_a
168
169
170 patterns = generate_patterns(patterns, operations)
171
172 puts patterns.size
173 function_body = generate_function('monad-law-1', pattern_formatter(patterns), 'refl')
174 agda = generate_agda(function_body)
175 File.open('hoge.agda', 'w').write(agda)