387 lines
11 KiB
Idris
387 lines
11 KiB
Idris
module Quox.Syntax.Term.Base
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import public Quox.Thin
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import public Quox.Syntax.Var
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import public Quox.Syntax.Shift
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import public Quox.Syntax.Subst
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import public Quox.Syntax.Qty
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import public Quox.Syntax.Dim
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import public Quox.Syntax.Term.TyConKind
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import public Quox.Name
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import public Quox.Loc
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import public Quox.Context
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import Quox.Pretty
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import public Data.DPair
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import Data.List
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import Data.Maybe
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import Data.Nat
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import public Data.So
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import Data.String
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import Derive.Prelude
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%default total
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%language ElabReflection
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%hide TT.Name
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public export
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TermLike : Type
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TermLike = Nat -> Nat -> Type
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public export
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TSubstLike : Type
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TSubstLike = Nat -> Nat -> Nat -> Type
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public export
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Universe : Type
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Universe = Nat
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public export
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TagVal : Type
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TagVal = String
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||| type-checkable terms, which consists of types and constructor forms.
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|||
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||| first argument `d` is dimension scope size; second `n` is term scope size
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public export
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data Term : (d, n : Nat) -> Type
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%name Term s, t, r
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||| inferrable terms, which consists of elimination forms like application and
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||| `case` (as well as other terms with an annotation)
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|||
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||| first argument `d` is dimension scope size; second `n` is term scope size
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public export
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data Elim : (d, n : Nat) -> Type
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%name Elim e, f
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public export
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ScopeTermN : Nat -> TermLike
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ScopeTermN s d n = ScopedN s (\n => Term d n) n
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public export
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DScopeTermN : Nat -> TermLike
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DScopeTermN s d n = ScopedN s (\d => Term d n) d
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public export
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ScopeTerm : TermLike
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ScopeTerm = ScopeTermN 1
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public export
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DScopeTerm : TermLike
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DScopeTerm = DScopeTermN 1
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public export
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TermT : TermLike
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TermT = Thinned2 (\d, n => Term d n)
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public export
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ElimT : TermLike
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ElimT = Thinned2 (\d, n => Elim d n)
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public export
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DimArg : TermLike
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DimArg d n = Dim d
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data Term where
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||| type of types
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TYPE : (l : Universe) -> (loc : Loc) -> Term 0 0
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||| function type
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Pi : Qty -> Subterms [Term, ScopeTerm] d n -> Loc -> Term d n
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||| function value
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Lam : ScopeTerm d n -> Loc -> Term d n
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||| pair type
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Sig : Subterms [Term, ScopeTerm] d n -> Loc -> Term d n
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||| pair value
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Pair : Subterms [Term, Term] d n -> Loc -> Term d n
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||| enum type
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Enum : List TagVal -> Loc -> Term 0 0
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||| enum value
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Tag : TagVal -> Loc -> Term 0 0
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||| equality type
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Eq : Subterms [DScopeTerm, Term, Term] d n -> Loc -> Term d n
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||| equality value
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DLam : DScopeTerm d n -> Loc -> Term d n
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||| natural numbers (temporary until 𝐖 gets added)
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Nat : Loc -> Term 0 0
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Zero : Loc -> Term 0 0
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Succ : Term d n -> Loc -> Term 0 0
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||| package a value with a quantity
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||| e.g. a value of [ω. A], when unpacked, can be used ω times,
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||| even if the box itself is linear
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BOX : Qty -> Term d n -> Loc -> Term d n
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Box : Term d n -> Loc -> Term d n
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E : Elim d n -> Term d n
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||| term closure/suspended substitution
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CloT : WithSubst2 Term Elim d n -> Term d n
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||| dimension closure/suspended substitution
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DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
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public export
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data Elim where
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||| free variable, possibly with a displacement (see @crude, or @mugen for a
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||| more abstract and formalised take)
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|||
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||| e.g. if f : ★₀ → ★₁, then f¹ : ★₁ → ★₂
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F : Name -> Universe -> Loc -> Elim 0 0
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||| bound variable
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B : Loc -> Elim 0 1
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||| term application
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App : Subterms [Elim, Term] d n -> Loc -> Elim d n
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||| pair match
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||| - the subterms are, in order: [head, return type, body]
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||| - the quantity is that of the head, and since pairs only have one
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||| constructor, can be 0
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CasePair : Qty -> Subterms [Elim, ScopeTerm, ScopeTermN 2] d n ->
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Loc -> Elim d n
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||| enum match
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CaseEnum : Qty -> (arms : List TagVal) ->
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Subterms (Elim :: ScopeTerm :: (Term <$ arms)) d n ->
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Loc -> Elim d n
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||| nat match
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CaseNat : Qty -> Qty ->
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Subterms [Elim, ScopeTerm, Term, ScopeTermN 2] d n ->
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Loc -> Elim d n
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||| box match
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CaseBox : Qty -> Subterms [Elim, ScopeTerm, ScopeTerm] d n -> Loc -> Elim d n
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||| dim application
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DApp : Subterms [Elim, DimArg] d n -> Loc -> Elim d n
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||| type-annotated term
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Ann : Subterms [Term, Term] d n -> Loc -> Elim d n
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||| coerce a value along a type equality, or show its coherence
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||| [@xtt; §2.1.1]
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Coe : Subterms [DScopeTerm, DimArg, DimArg, Term] d n ->
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Loc -> Elim d n
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||| "generalised composition" [@xtt; §2.1.2]
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Comp : Subterms [Term, DimArg, DimArg, Term,
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DimArg, DScopeTerm, DScopeTerm] d n ->
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Loc -> Elim d n
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||| match on types. needed for b.s. of coercions [@xtt; §2.2]
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TypeCase : Subterms [Elim, Term, -- head, type
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Term, -- ★
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ScopeTermN 2, -- pi
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ScopeTermN 2, -- sig
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Term, -- enum
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ScopeTermN 5, -- eq
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Term, -- nat
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ScopeTerm -- box
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] d n -> Loc -> Elim d n
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||| term closure/suspended substitution
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CloE : WithSubst2 Elim Elim d n -> Elim d n
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||| dimension closure/suspended substitution
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DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
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-- this kills the idris ☹
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-- export %hint
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-- EqTerm : Eq (Term d n)
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-- export %hint
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-- EqElim : Eq (Elim d n)
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-- EqTerm = deriveEq
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-- EqElim = deriveEq
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-- mutual
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-- export %hint
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-- ShowTerm : Show (Term d n)
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-- ShowTerm = assert_total {a = Show (Term d n)} deriveShow
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-- export %hint
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-- ShowElim : Show (Elim d n)
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-- ShowElim = assert_total {a = Show (Elim d n)} deriveShow
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-- ||| scope which ignores all its binders
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-- public export %inline
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-- SN : {s : Nat} -> f n -> Scoped s f n
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-- SN = S (replicate s $ BN Unused noLoc) . N
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-- ||| scope which uses its binders
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-- public export %inline
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-- SY : BContext s -> f (s + n) -> Scoped s f n
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-- SY ns = S ns . Y
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-- public export %inline
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-- name : Scoped 1 f n -> BindName
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-- name (S [< x] _) = x
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-- public export %inline
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-- (.name) : Scoped 1 f n -> BindName
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-- s.name = name s
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-- ||| more convenient Pi
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-- public export %inline
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-- PiY : (qty : Qty) -> (x : BindName) ->
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-- (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
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-- PiY {qty, x, arg, res, loc} = Pi {qty, arg, res = SY [< x] res, loc}
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-- ||| more convenient Lam
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-- public export %inline
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-- LamY : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
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-- LamY {x, body, loc} = Lam {body = SY [< x] body, loc}
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-- public export %inline
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-- LamN : (body : Term d n) -> (loc : Loc) -> Term d n
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-- LamN {body, loc} = Lam {body = SN body, loc}
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-- ||| non dependent function type
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-- public export %inline
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-- Arr : (qty : Qty) -> (arg, res : Term d n) -> (loc : Loc) -> Term d n
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-- Arr {qty, arg, res, loc} = Pi {qty, arg, res = SN res, loc}
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-- ||| more convenient Sig
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-- public export %inline
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-- SigY : (x : BindName) -> (fst : Term d n) ->
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-- (snd : Term d (S n)) -> (loc : Loc) -> Term d n
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-- SigY {x, fst, snd, loc} = Sig {fst, snd = SY [< x] snd, loc}
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-- ||| non dependent pair type
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-- public export %inline
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-- And : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
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-- And {fst, snd, loc} = Sig {fst, snd = SN snd, loc}
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-- ||| more convenient Eq
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-- public export %inline
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-- EqY : (i : BindName) -> (ty : Term (S d) n) ->
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-- (l, r : Term d n) -> (loc : Loc) -> Term d n
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-- EqY {i, ty, l, r, loc} = Eq {ty = SY [< i] ty, l, r, loc}
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-- ||| more convenient DLam
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-- public export %inline
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-- DLamY : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
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-- DLamY {i, body, loc} = DLam {body = SY [< i] body, loc}
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-- public export %inline
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-- DLamN : (body : Term d n) -> (loc : Loc) -> Term d n
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-- DLamN {body, loc} = DLam {body = SN body, loc}
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-- ||| non dependent equality type
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-- public export %inline
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-- Eq0 : (ty, l, r : Term d n) -> (loc : Loc) -> Term d n
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-- Eq0 {ty, l, r, loc} = Eq {ty = SN ty, l, r, loc}
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||| same as `F` but as a term
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public export %inline
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FT : Name -> Universe -> Loc -> Term 0 0
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FT x u loc = E $ F x u loc
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||| abbreviation for a bound variable like `BV 4` instead of
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||| `B (VS (VS (VS (VS VZ))))`
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public export %inline
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BV : (i : Fin n) -> (loc : Loc) -> ElimT d n
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BV i loc = Th2 zero (one' i) $ B loc
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||| same as `BV` but as a term
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public export %inline
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BVT : (i : Fin n) -> (loc : Loc) -> TermT d n
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BVT i loc = Th2 zero (one' i) $ E $ B loc
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public export
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makeNat : Nat -> Loc -> Term 0 0
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makeNat 0 loc = Zero loc
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makeNat (S k) loc = Succ (makeNat k loc) loc
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export
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Located (Elim d n) where
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(F _ _ loc).loc = loc
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(B loc).loc = loc
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(App _ loc).loc = loc
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(CasePair _ _ loc).loc = loc
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(CaseEnum _ _ _ loc).loc = loc
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(CaseNat _ _ _ loc).loc = loc
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(CaseBox _ _ loc).loc = loc
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(DApp _ loc).loc = loc
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(Ann _ loc).loc = loc
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(Coe _ loc).loc = loc
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(Comp _ loc).loc = loc
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(TypeCase _ loc).loc = loc
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(CloE (Sub2 e _)).loc = e.loc
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(DCloE (Sub e _)).loc = e.loc
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export
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Located (Term d n) where
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(TYPE _ loc).loc = loc
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(Pi _ _ loc).loc = loc
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(Lam _ loc).loc = loc
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(Sig _ loc).loc = loc
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(Pair _ loc).loc = loc
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(Enum _ loc).loc = loc
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(Tag _ loc).loc = loc
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(Eq _ loc).loc = loc
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(DLam _ loc).loc = loc
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(Nat loc).loc = loc
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(Zero loc).loc = loc
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(Succ _ loc).loc = loc
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(BOX _ _ loc).loc = loc
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(Box _ loc).loc = loc
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(E e).loc = e.loc
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(CloT (Sub2 t _)).loc = t.loc
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(DCloT (Sub t _)).loc = t.loc
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export
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Relocatable (Elim d n) where
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setLoc loc (F x u _) = F x u loc
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setLoc loc (B _) = B loc
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setLoc loc (App ts _) = App ts loc
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setLoc loc (CasePair qty ts _) = CasePair qty ts loc
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setLoc loc (CaseEnum qty arms ts _) = CaseEnum qty arms ts loc
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setLoc loc (CaseNat qty qtyIH ts _) = CaseNat qty qtyIH ts loc
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setLoc loc (CaseBox qty ts _) = CaseBox qty ts loc
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setLoc loc (DApp ts _) = DApp ts loc
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setLoc loc (Ann ts _) = Ann ts loc
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setLoc loc (Coe ts _) = Coe ts loc
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setLoc loc (Comp ts _) = Comp ts loc
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setLoc loc (TypeCase ts _) = TypeCase ts loc
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setLoc loc (CloE (Sub2 term subst)) = CloE $ Sub2 (setLoc loc term) subst
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setLoc loc (DCloE (Sub term subst)) = DCloE $ Sub (setLoc loc term) subst
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export
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Relocatable (Term d n) where
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setLoc loc (TYPE l _) = TYPE l loc
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setLoc loc (Pi qty ts _) = Pi qty ts loc
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setLoc loc (Lam body _) = Lam body loc
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setLoc loc (Sig ts _) = Sig ts loc
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setLoc loc (Pair ts _) = Pair ts loc
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setLoc loc (Enum cases _) = Enum cases loc
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setLoc loc (Tag tag _) = Tag tag loc
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setLoc loc (Eq ts _) = Eq ts loc
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setLoc loc (DLam body _) = DLam body loc
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setLoc loc (Nat _) = Nat loc
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setLoc loc (Zero _) = Zero loc
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setLoc loc (Succ p _) = Succ p loc
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setLoc loc (BOX qty ty _) = BOX qty ty loc
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setLoc loc (Box val _) = Box val loc
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setLoc loc (E e) = E $ setLoc loc e
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setLoc loc (CloT (Sub2 term subst)) = CloT $ Sub2 (setLoc loc term) subst
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setLoc loc (DCloT (Sub term subst)) = DCloT $ Sub (setLoc loc term) subst
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