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  • Indexed Core public By instantiating an indexed setoid one gets an ordinary setoid at i s s I Set i Setoid I s s I B Setoid S at i record Carrier S Carrier i S isEquivalence record refl S refl sym S sym trans S trans where module S Setoid S Simple properties of indexed binary relations Generalised implication infixr 4 a b A Set a B A Set

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Relation.Binary.Indexed.html (2015-10-11)
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  • A a A recursor builder constructs an instance of a recursion structure for a given input RecursorBuilder a A Set a RecStruct A Set RecursorBuilder Rec P Rec P P Universal Rec P A recursor can be used to actually compute prove something useful Recursor a A Set a RecStruct A Set Recursor Rec P Rec P P Universal P And recursors can be constructed from recursor builders build a

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Induction.html (2015-10-11)
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  • P x P The empty set Pred A zero λ The property of being empty Empty Pred A Set Empty P x x P Empty Empty Empty x The universe i e the subset containing all elements in A U Pred A zero U λ The property of being universal Universal Pred A Set Universal P x x P U Universal Universal U U Universal λ Set complement Pred A Pred A P λ x x P Universal Universal Universal λ x x x U Empty Empty U U Empty λ x x U x U P Q means that P is a subset of Q is a variant of infix 4 Pred A Pred A Set P Q x x P x Q Pred A Pred A Set P Q x x P x Q Pred A Pred A Set Q P P Q Pred A Pred A Set Q P P Q P Pred A P P U P Pred A P U U P Set union infixl 6 Pred A Pred A Pred A P Q λ x x P x Q Set intersection infixl 7 Pred A Pred A Pred A P Q λ x x

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Relation.Unary.html (2015-10-11)
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