mirror of
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109 lines
2.8 KiB
Plaintext
109 lines
2.8 KiB
Plaintext
|%
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+$ word
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$% [%lam p=$-(word word)]
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[%pi p=word q=$-(word word)]
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[%appl p=word q=word]
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[%ann p=word q=word]
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[%free p=@]
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[%star ~]
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[%box ~]
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==
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+$ unfurl
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|= [lvl=@ f=$-(word word)]
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(f %free lvl)
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::+$ unfurl2
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:: |= [lvl=@ f=$-(word word) g=$-(word word
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:: (f %free lvl)
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::let unfurl lvl f = f (FreeVar lvl)
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::let unfurl2 lvl (f, g) = (unfurl lvl f, unfurl lvl g)
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::let rec print lvl =
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:: let plunge f = print (lvl + 1) (unfurl lvl f) in
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:: function
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:: | Lam f -> "(λ" ^ plunge f ^ ")"
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:: | Pi (a, f) -> "(Π" ^ print lvl a ^ "." ^ plunge f ^ ")"
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:: | Appl (m, n) -> "(" ^ print lvl m ^ " " ^ print lvl n ^ ")"
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:: | Ann (m, a) -> "(" ^ print lvl m ^ " : " ^ print lvl a ^ ")"
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:: | FreeVar x -> string_of_int x
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:: | Star -> "*"
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:: | Box -> "☐"
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++ eval
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|= wor=word
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^- word
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?- -.wor !!
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%lam [%lam |=(w=word (eval (p.wor w)))]
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%pi [%pi (eval p.wor) |=(w=word (eval (q.wor w)))]
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%ann (eval p.wor)
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?(%free %star %box) wor
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%appl
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=/ [m=word n=word] [(eval p.wor) (eval q.wor)]
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?. ?=(%lam -.m)
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[%appl m n]
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(p.m q)
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==
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++ equate
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|= [lvl=@ f=word g=word]
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=* eq $
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|^ ^- ?
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?+ [-.f -.g] %.n
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[%lam %lam] ?>(?=(%lam -.g) (plunge p.f p.g))
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[%pi %pi] ?>(?=(%pi -.g) &(eq(p.f p.g) eq(q.f q.g)))
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[%appl %appl] ?>(?=(%appl -.g) &(eq(p.f p.g) eq(q.f q.g)))
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[%ann %ann] ?>(?=(%ann -.g) &(eq(p.f p.g) eq(q.f q.g)))
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[%free %free] ?>(?=(%free -.g) =(p.f p.g))
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[%star %star] %.y
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[%box %box] %.y
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==
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++ plunge
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|= [f=word q=word] eq(lvl +(lvl), f (unfurl lvl f), g (unfurl lvl g))
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--
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++ type
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|_ [lvl=@ud ctx=(list word)]
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++ infer
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|= w=word
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^- word
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?- -.w
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%pi
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=+ sort
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run(lvl +(lvl), [(eval p.w) ctx] (unfurl lvl f))
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::
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%appl
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=/ m (run p.w)
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?. ?=(%pi -.m)
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~| "want a pi type got {<m>}" !!
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=+ (check lvl ctx p.w p.m)
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(p.m q.w)
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::
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%ann
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=+ (sort lvl ctx q.w)
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==
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++ check
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|= [p=word q=word]
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==
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let rec infer_ty lvl ctx = function
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| Ann (m, a) ->
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let _s = infer_sort lvl ctx a in
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check_ty lvl ctx (m, eval a)
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| FreeVar x -> List.nth ctx (lvl - x - 1)
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| Star -> Box
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| Box -> panic lvl Box "Has no type"
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| t -> panic lvl t "Not inferrable"
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and infer_sort lvl ctx a =
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match infer_ty lvl ctx a with
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| (Star | Box) as s -> s
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| ty -> panic lvl a "Want a sort, got %s" (print lvl ty)
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and check_ty lvl ctx = function
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| Lam f, Pi (a, g) ->
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let _ = check_ty (lvl + 1) (a :: ctx) (unfurl2 lvl (f, g)) in
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Pi (a, g)
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| Lam f, ty -> panic lvl (Lam f) "Want a Pi type, got %s" (print lvl ty)
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| t, ty ->
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let got_ty = infer_ty lvl ctx t in
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if equate lvl (ty, got_ty) then ty
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else panic lvl t "Want type %s, got %s" (print lvl ty) (print lvl got_ty)
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--
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