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fixed issues in parser, added η-equality for functions

master
Rachel Lambda Samuelsson 2022-07-23 06:01:17 +02:00
parent a7d9ac4c0b
commit 48e9a474ff
4 changed files with 156 additions and 48 deletions
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2
README.md
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@ -22,8 +22,6 @@ A dependently typed system
# TODO
* Parser
* Fun types
* Id

33
src/Core/Convert.idr
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@ -23,38 +23,28 @@ convert u1 u2 = do
logS ("with value representations '" ++ show u1' ++ "' and '" ++ show u2' ++ "'.")
assert_total $ -- :(
case (u1', u2') of
(VGen k1, VGen k2) => pure (k1 == k2)
(VType, VType) => pure True
(VTop, VTop) => pure True
(VStar, VStar) => pure True
(VBot, VBot) => pure True
(VNat, VNat) => pure True
(VNatTr n, VNatTr m) => pure (n == m)
(VApp f1 x1, VApp f2 x2) => (&&) <$> convert f1 f2 <*> delay <$> convert x1 x2
(VGen k1, VGen k2) => pure (k1 == k2)
(VPair a1 b1, VPair a2 b2) => (&&) <$> convert a1 a2 <*> delay <$> convert b1 b2
(VClos env1 (TLam sc1), VClos env2 (TLam sc2)) => do
v <- VGen <$> fresh
convert (VClos (v :: env1) sc1) (VClos (v :: env2) sc2)
(VClos env1 (TPi a1 b1), VClos env2 (TPi a2 b2)) => do
v <- VGen <$> fresh
s1 <- case headM env1 of
Nothing => pure ""
Just x => pure (show x)
s2 <- case headM env2 of
Nothing => pure ""
Just x => pure (show x)
guardS (s1 ++ " | " ++ s2) =<< convert (VClos env1 a1) (VClos env2 a2)
guardS (show a1 ++ " | " ++ show a2) =<< convert (VClos env1 a1) (VClos env2 a2)
convert (VClos (v :: env1) b1) (VClos (v :: env2) b2)
(VNatTr n, VNatTr m) => pure (n == m)
(VPair a1 b1, VPair a2 b2) => (&&) <$> convert a1 a2 <*> delay <$> convert b1 b2
(VClos env1 (TTopInd c1 st1), VClos env2 (TTopInd c2 st2)) => do
termGuard env1 env2 c1 c2
termConv env1 env2 st1 st2
@ -75,7 +65,16 @@ convert u1 u2 = do
termGuard env1 env2 b1 b2
termGuard env1 env2 c1 c2
termConv env1 env2 f1 f2
-- η rules
-- fresh cannot appear in vsc, so this is fine
(vsc, VClos env (TLam (TApp sc (TVar 0)))) => do
v <- VGen <$> fresh
convert vsc (VClos (v :: env) sc)
(VClos env (TLam (TApp sc (TVar 0))), vsc) => do
v <- VGen <$> fresh
convert vsc (VClos (v :: env) sc)
_ => pure False
where
termConv : Ctx n -> Ctx m -> Term n -> Term m -> PI Bool

80
src/Parser/Parse.idr
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@ -138,35 +138,44 @@ ignored (MkBounded (Tok PTIgnore _) _ _) = True
ignored _ = False
identifier : Lexer
identifier = some (alphaNum <|> symbol)
identifier = some (alphaNum <|> oneOf "-_")
keywords : List (String, PiTokenKind)
keywords = [
("in", PTIn),
("let", PTLet),
("Type", PTType),
("⊤-ind", PTTopInd),
("⊥-ind", PTBotInd),
("ℕ-ind", PTNatInd),
("Σ-ind", PTSigInd),
("λ", PTLambda),
(".", PTDot),
("→", PTArrow),
("Π", PTPi),
("Σ", PTSigma),
(",", PTComma),
("(", PTLParen),
(")", PTRParen),
(":", PTColon),
("≔", PTDefEq),
("⊤", PTTop),
("⊥", PTBot),
("ℕ", PTNat),
("★", PTStar)
("suc", PTSuc),
("Type", PTType)
]
tokenmap : List (Lexer, PiTokenKind)
tokenmap = [
(exact "⊤-ind", PTTopInd),
(exact "⊥-ind", PTBotInd),
(exact "ℕ-ind", PTNatInd),
(exact "Σ-ind", PTSigInd),
(is 'λ', PTLambda),
(is '.', PTDot),
(is '→', PTArrow),
(is 'Π', PTPi),
(is '∏', PTPi),
(is 'Σ', PTSigma),
(is '∑', PTSigma),
(is ',', PTComma),
(is '(', PTLParen),
(is ')', PTRParen),
(is ':', PTColon),
(is '≔', PTDefEq),
(is '⊤', PTTop),
(is '⊥', PTBot),
(is 'ℕ', PTNat),
(is '★', PTStar),
(is '0', PTZero)
]
piTokenMap : TokenMap PiToken
piTokenMap = (spaces, Tok PTIgnore) ::
toTokenMap tokenmap ++
[(identifier, \s =>
case lookup s keywords of
(Just kind) => Tok kind s
@ -184,7 +193,13 @@ lexPi str =
{- de bruijn indecies, and a Nat to keep track of context size -}
mutual
expr : (n : Nat) -> Vect n String -> Grammar state PiToken True (Term n)
expr n env = ttopind n env
expr n env = tpi n env
<|> tsigma n env
<|> tarr n env
<|> expr1 n env
expr1 : (n : Nat) -> Vect n String -> Grammar state PiToken True (Term n)
expr1 n env = ttopind n env
<|> tbotind n env
<|> tsuc n env
<|> tnatind n env
@ -200,11 +215,9 @@ mutual
<|> tbot
<|> tnat
<|> tzero
<|> tsigma n env
<|> tpair n env
<|> tlet n env
<|> tlam n env
<|> tpi n env
<|> tvar n env
<|> paren n env
@ -264,17 +277,17 @@ mutual
match PTLParen
arg <- match PTIdentifier
match PTColon
a <- term n env
a <- expr n env
match PTRParen
b <- term (S n) (arg :: env)
b <- expr (S n) (arg :: env)
pure (TSigma a (TLam b))
tpair : (n : Nat) -> Vect n String -> Grammar state PiToken True (Term n)
tpair n env = do
match PTLParen
commit
x <- expr n env
match PTComma
commit
y <- expr n env
match PTRParen
pure (TPair x y)
@ -308,7 +321,7 @@ mutual
commit
arg <- match PTIdentifier
match PTDot
e <- term (S n) (arg :: env)
e <- expr (S n) (arg :: env)
pure (TLam e)
tpi : (n : Nat) -> Vect n String -> Grammar state PiToken True (Term n)
@ -318,11 +331,19 @@ mutual
match PTLParen
arg <- match PTIdentifier
match PTColon
a <- term n env
a <- expr n env
match PTRParen
b <- term (S n) (arg :: env)
b <- expr (S n) (arg :: env)
pure (TPi a b)
tarr : (n : Nat) -> Vect n String -> Grammar state PiToken True (Term n)
tarr n env = do
l <- expr1 n env
match PTArrow
commit
r <- expr (S n) ("" :: env)
pure (TPi l r)
tapp : (n : Nat) -> Vect n String -> Term n -> Grammar state PiToken True (Term n)
tapp n env e1 = do
e2 <- term n env
@ -339,6 +360,7 @@ mutual
paren : (n : Nat) -> Vect n String -> Grammar state PiToken True (Term n)
paren n env = do
match PTLParen
commit
e <- expr n env
match PTRParen
pure e

89
src/Parser/Tests.idr 100644
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@ -0,0 +1,89 @@
module Parser.Tests
import Core.Term
import Core.Check
import Core.Convert
import Core.Misc
import Core.Normalize
import Core.Value
import Control.Monad.RWS
import Control.Monad.Identity
import Control.Monad.Either
import Data.Fin
import Parser.Parse
%default total
convCheck : Term 0 -> Term 0 -> Either String (Bool, List String)
convCheck a b = resolve action
where
action : PI Bool
action = do
x <- eval ctx0 a
y <- eval ctx0 b
convert x y
{- λA. λx. x : ∏ (A : Type) → A → A -}
test_id : Either String (Bool, List String)
test_id = do
ty <- parse0 "Π ( A : Type ) A → A"
tr <- parse0 "λA.λx.x"
typecheck tr ty
{- λA. λB. λf. λx. f x : ∏ (A : Type) ∏ (B : A → Type) ∏ (f : ∏ (x : A) B x) ∏ (x : A) B x -}
test_app : Either String (Bool, List String)
test_app = do
ty <- parse0 "Π (A : Type) Π (B : A → Type) Π (f : Π (x : A) B x) Π (x : A) B x"
tr <- parse0 "λA. λB. λf. λx. f x"
typecheck tr ty
{- λf. f ≃ λf. λx. f x -}
eta_test : Either String (Bool, List String)
eta_test = do
a <- parse0 "λf. f"
b <- parse0 "λf. λx. f x"
convCheck a b
additionty_test : Either String (Bool, List String)
additionty_test = do
ty <- parse0 "ℕ → ℕ → ℕ"
typecheck ty TType
addition_test : Either String (Bool, List String)
addition_test = do
ty <- parse0 "ℕ → ℕ → ℕ"
tr <- parse0 "ℕ-ind (λ_. ℕ → ℕ) (λx.x) (λn.λnp.λm. suc (np m))"
typecheck tr ty
-- no, not that kind
unit_test : Either String (Bool, List String)
unit_test = do
ty <- parse0 "⊤"
tr <- parse0 "★"
typecheck tr ty
absurd_test : Either String (Bool, List String)
absurd_test = do
ty <- parse0 "Π(A : Type) ⊥ → A"
tr <- parse0 "λA. ⊥-ind (λ_. A)"
typecheck tr ty
pr1_test : Either String (Bool, List String)
pr1_test = do
tr <- parse0 $ "let pr1 : Π (A : Type) Π (B : A → Type) (Σ (a : A) B a) → A"
++ "≔ λA.λB. Σ-ind A B (λ_. A) (λa.λBa. a)"
++ "in ★"
typecheck tr TTop
pr1_pr2_test : Either String (Bool, List String)
pr1_pr2_test = do
tr <- parse0 $ "let pr1 : Π (A : Type) Π (B : A → Type) (Σ (a : A) B a) → A"
++ "≔ λA.λB. Σ-ind A B (λ_. A) (λa.λBa. a)"
++ "in let pr2 : Π (A : Type) Π (B : A → Type) Π (s : Σ (a : A) B a) B (pr1 A B s)"
++ "≔ λA.λB. Σ-ind A B (λs. B (pr1 A B s)) (λa.λBa. Ba)"
++ "in ★"
typecheck tr TTop