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annotate sandbox/modus-ponens.agda @ 77:a2e6f61d5f2b default tip

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Add modus-ponens
author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Thu, 09 Feb 2017 06:32:03 +0000
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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1 module modus-ponens where
a2e6f61d5f2b Add modus-ponens
atton <atton@cr.ie.u-ryukyu.ac.jp>
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2
a2e6f61d5f2b Add modus-ponens
atton <atton@cr.ie.u-ryukyu.ac.jp>
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3 data _×_ (A B : Set) : Set where
a2e6f61d5f2b Add modus-ponens
atton <atton@cr.ie.u-ryukyu.ac.jp>
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4 <_,_> : A -> B -> A × B
a2e6f61d5f2b Add modus-ponens
atton <atton@cr.ie.u-ryukyu.ac.jp>
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5
a2e6f61d5f2b Add modus-ponens
atton <atton@cr.ie.u-ryukyu.ac.jp>
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6 fst : {A B : Set} -> A × B -> A
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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7 fst < a , _ > = a
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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8
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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9 snd : {A B : Set} -> A × B -> B
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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10 snd < _ , b > = b
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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11
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atton <atton@cr.ie.u-ryukyu.ac.jp>
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12 f : {A B C : Set} -> (A -> B) × (B -> C) -> (A -> C)
a2e6f61d5f2b Add modus-ponens
atton <atton@cr.ie.u-ryukyu.ac.jp>
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13 f = (\p x -> snd p ((fst p) x))