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  • Data String s tail parenBase ShowS ShowS parenBase doc doc record PrEnv Set where constructor mk field level withLevel PrEnv withLevel x record level x top PrEnv top withLevel 2 ap PrEnv ap withLevel 1 atm PrEnv atm withLevel 0 open PrEnv emptyPrEnv PrEnv emptyPrEnv record level 2 paren PrEnv PrEnv PrEnv ShowS ShowS paren f Δ if level f Δ level Δ then id else parenBase prTm PrEnv Pr

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.Raw.Printer.html (2015-10-11)
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  • Abs Abs SynAbs Neutral Set Neutral pure Neutral1 Set Set Neutral1 liftA Neutral2 Set Set Set Neutral2 liftA2 infixr 0 infixr 1 infixr 2 Set E E α β α β E E β to E E E E E E to f f refl Coe Set Coe E α β α β E α E β coerce E E Coe E E coerce pf f f trans pf Neutral2 Neutral2 List List Neutral1 List Maybe Maybe Neutral1 Maybe 1 1 Neutral Set Empty Set Empty E E ø module FreeVars where Fv Set Fv E E List Name Combinators we do not have fvμ fv fv E E Fv E Fv E Fv E E fv fv fv x y fv x fv y fv E E Fv E Fv E Fv E E fv fv fv fv fv fvNeutral A Fv Neutral A fvNeutral fvName Fv Name fvName fvList E Fv E Fv List E fvList fvList fvE x xs fvE x fvList fvE xs fvMaybe E Fv E Fv Maybe E fvMaybe fvE maybe fvE abstract only here for debugging purposes fvDummy A B Set A List B fvDummy const fvMap E E E E Fv E

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.NominalTypes.html (2015-10-11)
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  • t u fv t fv u fv inj t fv t fv inj t fv t fv roll t fv t fv V x x fv bind b t rm b fv t module Rec r Universe where data Universe where tt σ τ σ τ σ τ inj σ τ σ σ τ inj σ τ τ σ τ roll r Rec V Name Name bind τ Abs τ Abs τ open Rec using tt inj inj V bind roll renaming to El forget r s El r s Any forget tt tt forget t u forget t forget u forget inj t inj forget t forget inj t inj forget t forget roll t roll forget t forget V x V x forget bind x t bind x forget t Universe u Rec u u fv r s El r s List Name fv FvAny fv forget fv tt fv t u fv t fv u fv inj t fv t fv inj t fv t fv roll t fv t fv V x x fv bind b t rm b fv t module TraverseEl r Universe E E app Applicative E Env trKit TrKit Env E Name where open Applicative E app open TrKit trKit tr s α β Env α β El r s α E El r s β tr Δ tt pure tt tr Δ t u pure tr Δ t tr Δ u tr Δ inj t pure inj tr Δ t tr Δ inj t pure inj tr Δ t tr Δ roll t pure roll tr Δ t tr Δ bind b t pure bind tr extEnv b Δ t tr Δ V x pure V trName Δ x module Generic r TraverseAFGNameGen r r λ η η TraverseEl tr r

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.NominalTypes.Generic.html (2015-10-11)
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  • τ like in NominalTypes but uses r instead of Name in the return type of V open Rec using tt inj inj V bind roll renaming to El Universe u Rec u u fv r s El r s List Name fv tt fv t u fv t fv u fv inj t fv t fv inj t fv t fv roll t fv t fv V x x fv bind b t rm b fv t module TraverseEl r E E app Applicative E Env trKit TrKit Env E El r r where open Applicative E app open TrKit trKit tr s α β Env α β El r s α E El r s β tr Δ tt pure tt tr Δ t u pure tr Δ t tr Δ u tr Δ inj t pure inj tr Δ t tr Δ inj t pure inj tr Δ t tr Δ roll t pure roll tr Δ t tr Δ bind b t pure bind tr extEnv b Δ t tr Δ V x trName Δ x tr α β Env α β r α E r β tr tr module Generic r where F r G r traverseAFGG TraverseA F G G traverseAFGG TraverseEl tr r traverseFGG Traverse F G G traverseFGG traverseAFGG id app traverseAFGName TraverseA F G Name traverseAFGName E app trKit TraverseEl tr r E app mapKit id V trKit where open Applicative E app open TraverseAFGNameGen traverseAFGName public open SubstGen F G V coerce traverseFGG public module Example where record TmA F Set where constructor mk field var Name F app F F F lam Abs F F F F F t u app t u α b F b α F α b t lam b t base functor TmF TmF F

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.NominalTypes.Generic.Subst.html (2015-10-11)
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  • inj σ τ τ σ τ roll r Rec V Name Name bind τ Abs τ Abs τ bind τ Abs τ Abs τ open Rec using tt inj inj V roll bind bind renaming to El Universe u Rec u u fv r s El r s List Name fv tt fv t u fv t fv u fv inj t fv t fv inj t fv t fv roll t fv t fv V x x fv bind b t rm b fv t fv bind t rm fv t module ToDeBruijn where Env EnvType Env α β Name α Name β extEnv α β Env α β Env α 1 β 1 extEnv protect 1 extEnv α β b Env α β Env b α β 1 extEnv b Γ exportWith 0 suc Γ tr r s α β Env α β El r s α El r s β tr Δ tt tt tr Δ t u tr Δ t tr Δ u tr Δ inj t inj tr Δ t tr Δ inj t inj tr Δ t tr Δ roll t roll tr Δ t tr Δ bind b t bind tr extEnv b Δ t tr Δ bind t bind tr extEnv Δ t tr Δ V x V Δ x module Example where record TmA F Set where constructor mk field var Name F app F F F lam Abs F F lam Abs F F F F F t u app t u α b F b α F α b t lam b t α F α 1 F α lam TmU Universe TmU Name Rec Rec Abs Rec Tm Tm TmU tmA TmA Tm tmA mk inj V app lam lam where app Tm Tm Tm app t u

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.NominalTypes.Generic.Combined.html (2015-10-11)
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  • using SynAbs open NomPa Traverse nomPa open Data Indexed Sort World using Set pure liftA liftA2 List Maybe Set Set Name Sort Name κ Γ Name Γ κ Sort World Sort World Sort World Γ κ α κ if κ κ then α else Γ κ Sort κ F Γ b F Γ κ b Γ κ Neutral Set Neutral pure Neutral1 Set Set Neutral1 liftA Neutral2 Set Set Set Neutral2 liftA2 infixr 0 infixr 0 infixr 1 infixr 2 Neutral2 Neutral2 List List Neutral1 List Maybe Maybe Neutral1 Maybe Set 1 1 Neutral Some nominal algebras Untyped λ calculus v Λ var v Λ λ v Λ Λ app Λ Λ Λ First order logic v ι Φ var v ι 0 ι 1 ι ι ι ι ι ι Φ Φ Φ Φ v Φ Φ Second order logic v v ι Φ var v ι var v ι 0 ι S ι ι ι ι Φ Φ Φ Φ v Φ Φ Λ v Φ Φ π calculus v ι 0 ι ι ι ι τ ι ι v v ι ι ν v ι ι in v v ι ι out v v ι ι module

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.NominalTypes.MultiSorts.html (2015-10-11)
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  • to Applicative import NomPa Encodings NominalTypes MultiSorts as NomSig module NomPa Encodings NominalTypes MultiSorts Test where module Client nomPa NomPa where A Nominal Signature Extended from example 2 2 in Nominal Unification sort of atoms vtm vty sort of data Tm Ty function symbols var vty Ty arr Ty Ty Ty all vty Ty Ty vr vtm Tm app Tm Tm Tm fn Ty vtm Tm Tm App Tm Ty Tm Fn vty Tm Tm data Sort Set where vtm vty Sort x y Sort Bool vtm vtm true vty vty true vtm vty false vty vtm false open NomSig nomPa Sort E data Ty E where var Name vty Ty arr Ty Ty Ty all vty Ty Ty data Tm E where vr Name vtm Tm app Tm Tm Tm fn Ty vtm Tm Tm App Tm Ty Tm Fn vty Tm Tm open NomPa Derived nomPa fvtmTm Tm List Name vtm fvtmTm vr x x fvtmTm app t u fvtmTm t fvtmTm u fvtmTm fn b t rm b fvtmTm t fvtmTm App t τ fvtmTm t fvtmTm Fn b t fvtmTm t no b to remove fvtyTy Ty List Name vty fvtyTy var x x fvtyTy arr

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.NominalTypes.MultiSorts.Test.html (2015-10-11)
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  • P List P open import Data List open import Data Maybe module FreeVars where open NomTypes FreeVars public record Fv α β Op World World Set where constructor mk field fvO List Name α fvI List Name β rmP γ List Name Op γ List Name γ Fv Set Fv P P Fv fv P Fv P Fv P fv fv mk p with fv p mk fvO fvI rmP fvO rmP fvI abstract only here for debugging purposes fv dummy A Set α β Op A Fv α β Op fv dummy mk const fv Map P Q Q P Fv P Fv Q fv Map f fvP fvP f fvBinder Fv Binder fvBinder binder b mk rm b fvBinder Fv Binder fvBinder binder mk rm α β Op Op Fv α β Op Fv α β Op Fv α β Op Op mk fvO fvI rmP mk fvO fvI rmP mk fvO fvO fvI fvI rmP rmP fv P P Fv P Fv P Fv P P fv fv fv p p fv p fv p fv P P Fv P Fv P Fv P P fv fv fv fv fv fvInner E Fv E Fv Inner E fvInner fvE inner x mk fvE x id fvOuter E Fv E Fv Outer E fvOuter fvE outer x mk fvE x id fvNeutral A Fv Neutral A fvNeutral neutral mk id fv1 Fv 1 fv1 fvNeutral fvList P Fv P Fv List P fvList fvP k fvNeutral k fvList fvP x xs fvP x fvList fvP xs module LC Example where data Tm where var Name Tm app Tm Tm Tm lam Binder Inner Tm Tm let Binder Outer Tm Inner Tm Tm module Ctors where Tm Tm Tm t u app t u α b Tm b α Tm α b t lam mk binder b inner t Let α b Tm α Tm b α Tm α Let b t u let mk binder b outer t inner u module Terms where open Ctors idTm Tm ø idTm 0 var 0 apTm Tm ø apTm 0 1 var 0 var 1 module LC Example2 where TmF TmF Tm var Name app Tm Tm lam Binder Inner Tm let Binder Outer Tm Inner Tm postulate μ roll F F μ F μ F unroll F μ F F μ F Tm μ TmF data Tm where roll TmF Tm Tm unrollTm Tm TmF Tm unrollTm roll x x module Ctors where var Name Tm var roll inj app Tm Tm Tm app t u roll inj inj t u lam α b Tm b α Tm α lam b t roll inj inj inj mk binder b inner t module Terms where open Ctors idTm Tm ø idTm lam 0 var 0 apTm Tm ø apTm lam 0 lam 1 app var 0 var 1 module ML Example where Tag mutual data Tm where var Name Tm app Tm Tm Tm lam Binder Inner Tm Tm ctor Neutral

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Encodings.AlphaCaml.html (2015-10-11)
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