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  • t u tr Δ t tr extEnv b Δ u module TraversePreTm E E app Applicative E Env trKit TrKit Env E PreTm where open Applicative E app open TraversePreTm E app trKit const pure V public open TraverseAGen V TraversePreTm tr public renaming rename to renamePreTm rename to renamePreTm export to export PreTm close to closePreTm coerce to coercePreTm coerceø to coerceøPreTm renameCoerce to renameCoercePreTm renameA to renamePreTmA open SubstGen V coercePreTm TraversePreTm tr id app public renaming subst to substPreTm openSynAbs to openSubstTm module PreTm Tm where α PreTm α Tm α V x V x V a a t u t u b t b t Let t b u Let b t u showTm Tm String showTm LC showTmø PreTm Tm module Tm PreTm where α Tm α PreTm α V x V x t u t u b t b t Let b t u Let t b u a V a parseTm String Tm parseTm map Tm PreTm LC parseTmø parseTm s s ok LC TmøOk s Tm parseTm s s ok Tm PreTm LC parseTmø s s ok module FreeVarsPreTm where fa α PreTm α List Atom fa V fa V x x fa fct arg fa fct fa arg fa t fa t fa Let t u fa t fa u closeTm Atom Tm AbsTm closeTm a t 0 tr renameEnv 1 refl t where β trAtm α β SubstEnv Name β α β Atom PreTm β trAtm Δ a if a a then V coerce SubstEnv pf Δ 0 else V a kit mapKit id V renameKit β tr TraversePreTm tr id app kit trAtm STARTING FROM HERE THIS IS THE EXACT SAME CODE AS WITH NomPa Examples LN openTm Atom AbsTm Tm openTm openSubstTm V mapAbsTm Atom Tm Tm AbsTm AbsTm mapAbsTm s f closeTm s f openTm s app Tm List Tm Tm app foldl Atom Tm Tm x t closeTm x t let Atom Tm Tm Tm let x t u Let t closeTm x u id Tm id x V x where x 0 false Tm false x x V x where x 0 true Tm true x y V x where x 0 y 1 ap Tm ap x y V x V y where x 0 y 1 Ω Tm Ω let δ x V x V x V δ V δ where δ 0 x 1 module Size where size Tm size V 1 size fct arg 1 size fct size arg size abs 1 size openTm 0 abs size Let t abs 1 size t size openTm 0 abs size V x Nameø elim x fuel extended to pass the termination checker size fuel Tm size suc n V 1 size suc n fct arg 1 size n fct size n arg size suc n abs 1 size n openTm 0 abs size suc n Let t abs 1 size n t size n openTm 0 abs size suc n V x Nameø

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.LocallyNamed.html (2015-10-11)
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  • M Tm B Tm A M Tm B traverseATm M app M go where open Applicative app M mapMTm A B A M Tm B Maybe A M Tm Maybe B mapMTm mapA compA app M app Tm mutual go A B A M Tm B Tm Maybe A M Tm Maybe B go f t go mapMTm f t go A B A M Tm B Tm A M Tm B go f V x f x go f t u pure go f t go f u go f t pure go f t go f Let t u pure Let go f t go f u go f κ pure κ mapATm M Set Set A B Applicative M A M B Tm A M Tm B mapATm app M f traverseATm app M V f where open Applicative app M Tm Name Tm mapTm id id mapTm f g mapTm f mapTm g isos in the iso section advocate for multiple representations A B Tm A Tm B open import Data Nat NP mapTm A B Maybe A Maybe B Tm A Tm B mapTm A B f go 0 where go Tm Maybe A Tm Maybe B go V x V f x go t u go t go u go t go suc t go Let t u Let go t go suc u go κ κ map A B A B Maybe A Maybe B map zero id map suc n map map n analog to subtract just A A Maybe A just zero id just suc n just just n shift A k Maybe A Maybe Maybe k A shift k map just k shiftTm A k Tm A Tm Maybe k A shiftTm mapTm shift analog to subtract Notice that this

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.LC.Maybe.html (2015-10-11)
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  • A hmap f g g f called runH in Staged Haskell runHV Repr A HV Repr A Repr A runHV m m record Lib Set where constructor mk field HA Repr Set Set S A Set Set LamM Set LamM M Repr Set Set A B H funM Functor M sSym SimpleSym Repr LamPure Repr S HV HA Repr S A H Repr A M HV HA Repr S A H Repr B M HV H Repr A B field lam LamM href Repr S A H HV HA Repr S A H Repr A var H M Repr A M app Applicative M HV H Repr A M HV H Repr A weaken H H A Set M Repr Set Set M app Functor M M HV H Repr A M HV H H Repr A module M2 Cst Set Env Set 1 Env Env Binder Set Ty Set Env Binder Ty Env Binder Env Set 1 Env Ty Env Env Env Set Ty Ty Ty ε Env ε Γ ε Γ Γ b τ b Γ Γ Γ b τ cong Γ Γ τ Γ Γ Γ 1 τ Γ 1 τ trans Transitive 1 Env Env 1 1 Γ τ Γ 1 Γ 1 τ Env Ty Set where record Sym Set where infixl 6 field Γ σ τ t Γ σ τ u Γ σ Γ τ Γ σ τ f b b Γ Γ b σ σ Γ b σ τ Γ σ τ Γ σ τ f Γ 1 σ σ Γ 1 σ τ Γ σ τ Let α t Tm α u Tm α 1 Tm α 1 Tm α α t b Tm b α Tm b α Tm α Let α t Tm α u b Tm b α Tm

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.LC.SymanticsTy.html (2015-10-11)
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  • Function open import Data Empty open import NomPa Record open import NomPa Implem using nomPa import NomPa Examples LC open NomPa Examples LC nomPa λ open NomPa nomPa ap Tm ø ap showTmø parseTm λx λy x y uncurry showTmø

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.LC.Tests.html (2015-10-11)
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  • Tm Cst α transform bindTm cst var untag constants and free variables coerceTmø closed terms inhabit any world f operates on a locally closed term substTm cst inj tag the free variables as constants bindTm cst inj tag the original constants Less general module M less nice Tm Set World Set cst α Cst Cst Tm Cst α var α Cst Name α Tm Cst α substTm α β Cst

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.LocallyClosed.html (2015-10-11)
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  • t u pure tr Δ t tr Δ u tr Δ b τ t pure tr Δ τ tr extEnv b Δ t tr Δ Π b σ τ pure Π tr Δ σ tr extEnv b Δ τ tr Δ κ pure κ open TraverseAGen V TraverseTm tr public renaming rename to renameTm rename to renameTm export to exportTm close to closeTm coerce to coerceTm coerceø to coerceTmø renameCoerce to renameCoerceTm renameA to renameTmA open SubstGen V coerceTm TraverseTm tr id app public renaming subst to substTm substø to substø Tm substC to substCTm substCø to substCøTm substC to substC Tm substCø to substCø Tm openSynAbs to openSubstTm not used data Tel α World Set where ε Tel α α β b τ Ty α Γ Tel b α β Tel α β data Cx α World Set where ε Cx α α β b Γ Cx α β b b β τ Ty β Cx α b β module Lookup where open Applicative L zero applicative lookup ω α x Name α Γ Cx ω α Maybe Ty α lookup x ε nothing lookup x Γ b τ coerceTm b exportWith just τ λ x lookup x Γ x open Lookup public impTmWith b α b α Tm α Tm b α impTmWith coerceTm module Member where data ω α x Name α τ Ty α Γ Cx ω α Set where here β b x Name b β τ Ty b β b b β τ Γ x b x name b τ τ τ impTmWith b τ x τ Γ b τ there β b x Name b β τ Ty b β b b β x τ σ Γ expOk export x just x τ τ τ impTmWith b τ x τ Γ x τ

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.PTS.html (2015-10-11)
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  • where R R open NomPa nomPa open NomPa Derived nomPa open PTS nomPa Sort open Typing κ R α b Ty b α Ty α b τ Π b τ Λ α b Tm b α Tm α Λ b t b t there b ω α b b α x τ σ Γ Cx ω α x τ Γ x τ Γ coerce b x impTmWith b τ Γ b σ there x there export coerce success refl x V b α Tm b α V b V name b V k x α Tm k x α V k x V name k x V V 0 V V 1 V V 2 V V 3 V V 4 V V 5 V V 6 V V 7 V V 8 module IdentityExample where A 0 A ø 0 x 1 x 1 x ø 1 idT Tm ø idT Λ A x V A V x idτ Ty ø idτ A x V A V A idτ ε A x V A V A idτ Π x V here V there here idτ ε idτ idτ Π A idτ idT idτ ε idT idτ idT idτ A

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Examples.PTS.F.html (2015-10-11)
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  • Name α Reg α Let b s Reg α t Reg b α Reg α 0 1 Reg α s t Reg α Reg α μ b f Reg b α Reg α data Tel α World Set where ε

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