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annotate agda/patterns.rb @ 69:295e8ed39c0c

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