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  • N Neu α S α data Neu α Set where V Name α Neu α Neu α S α Neu α mutual importN α β α β Neu α Neu β importN w V a V import w a importN w t u importN w t importV w u importV α β α β S α S β importV w f λ w v f trans w w v importV w N n N importN w n module NBE envPack ImportableEnvPack where open ImportableEnvPack envPack impEnv α β γ α β Env S α α γ Env S β β γ impEnv w importEnv w mapEnv importV w app α S α S α S α app f v f refl v app N n v N n v eval α β Env S α α β T β S α eval Γ a t λ w v eval impEnv w Γ a v t eval Γ V x N V id lookupEnv Γ x eval Γ t u eval Γ t app eval Γ u mutual reify α Fresh α S α T α reify g N n reifyn g n reify g f weakOf g reify nextOf g

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/NotSoFresh.Examples.NBE.html (2015-10-11)
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  • Set where V x Name α T α abs Abs T α T α t u T α T α open M SynAbs renaming T to Term open M FunAbs renaming T to Sem importSem α β α β Sem α Sem β importSem w V a V import w a importSem w t u importSem w t importSem w u importSem w f λ w v f trans w w v module NBE envPack ImportableEnvPack where open ImportableEnvPack envPack impEnv α β γ α β Env Sem α α γ Env Sem β β γ impEnv w importEnv w mapEnv importSem w app α Sem α Sem α Sem α app f v f refl v app n v n v eval α β Env Sem α α β Term β Sem α eval Γ a t λ w v eval impEnv w Γ a v t eval Γ V x V id lookupEnv Γ x eval Γ t u eval Γ t app eval Γ u reify α Fresh α Sem α Term α reify g V a V a reify g n v reify g n reify g v reify g f weakOf g reify nextOf g

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/NotSoFresh.Examples.NBE-short.html (2015-10-11)
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  • Γ Env S α α β abs SynAbs T β S α N Neu α S α data Neu α Set where V x Name α Neu α t Neu α u S α Neu α mutual importN α β α β Neu α Neu β importN w V a V import w a importN w t u importN w t importV w u importV α β α β S α S β importV w a t importEnv w mapEnv importV w a t importV w N n N importN w n mutual app α S α S α S α app Δ γ a t v eval Δ a v t app N n v N n v eval α β Env S α α β T β S α eval Γ a t Γ a t eval Γ V x N V id lookupEnv Γ x eval Γ t u eval Γ t app eval Γ u mutual reify α Fresh α S α T α reify g β Δ δ b t weakOf g reify nextOf g eval Δ b N V a t where open FreshPack a nameOf g w Of g Δ importEnv w mapEnv

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/NotSoFresh.Examples.NBE-closure.html (2015-10-11)
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  • TrustMe where open import Relation Binary PropositionalEquality private primitive primTrustMe a A Set a x y A x y trustMe x x y y evaluates to refl if x and y are definitionally equal For an example of the use

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Relation.Binary.PropositionalEquality.TrustMe.html (2015-10-11)
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  • open import Data Product Unary and binary operations open import Algebra FunctionProperties Core public Properties of operations Associative Op A Set Associative x y z x y z x y z Commutative Op A Set Commutative x y x y y x LeftIdentity A Op A Set LeftIdentity e x e x x RightIdentity A Op A Set RightIdentity e x x e x Identity A Op A Set Identity e LeftIdentity e RightIdentity e LeftZero A Op A Set LeftZero z x z x z RightZero A Op A Set RightZero z x x z z Zero A Op A Set Zero z LeftZero z RightZero z LeftInverse A Op A Op A Set LeftInverse e x x x e RightInverse A Op A Op A Set RightInverse e x x x e Inverse A Op A Op A Set Inverse e LeftInverse e RightInverse e DistributesOver Op A Op A Set DistributesOver x y z x y z x y x z DistributesOver Op A Op A Set DistributesOver x y z y z x y x z x DistributesOver Op A Op A Set DistributesOver DistributesOver DistributesOver IdempotentOn Op A A Set IdempotentOn x x x x

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Algebra.FunctionProperties.html (2015-10-11)
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  • Relation Binary PropositionalEquality module Relation Binary PropositionalEquality Core where open import Level open import Relation Binary Core open import Relation Binary Consequences Core Some properties sym a A Set a Symmetric A A sym refl refl trans a A Set a Transitive A A trans refl eq eq subst a p A Set a Substitutive A A p subst P refl p p resp a A Set a Rel A

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Relation.Binary.PropositionalEquality.Core.html (2015-10-11)
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  • t module InterchangeFromAssocCommCong isEquivalence IsEquivalence Op A assoc Associative comm Commutative cong x y z x y x z y z where open IsEquivalence isEquivalence open Equivalence Reasoning isEquivalence cong x y z y z x y x z cong x y z y z x y comm y x cong x y z z x comm x z interchange Interchange interchange x y z t x y z t

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Algebra.FunctionProperties.NP.html (2015-10-11)
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  • A C Set Trans P Q R i j k x P i j xs Q j k R i k substitutive to reflexive a A Set a Rel A Rel A Substitutive Reflexive substitutive to reflexive subst refl x subst x refl substitutive a A Set a Rel A Substitutive a PropEq substitutive subst substitutive to reflexive PropEq subst PropEq refl record Equality a A Set a Rel A Set suc a where field isEquivalence IsEquivalence subst Substitutive a open IsEquivalence isEquivalence public to reflexive Reflexive to reflexive substitutive to reflexive subst to propositional PropEq to propositional substitutive subst Equational reasoning combinators module Trans Reasoning a A Set a Rel A trans Transitive where infix 2 finally infixr 2 x y z A x y y z x z x y y z trans x y y z When there is no reflexivty available this combinator can be used to end the reasoning finally x y A x y x y finally x y x y syntax finally x y x y x x y y module Equivalence Reasoning a A Set a Rel A E IsEquivalence where open IsEquivalence E open Trans Reasoning trans public hiding finally infix

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