c3948cba24
This PR upstreams the definition of `Vector` from Batteries, along with the basic functions.
65 lines
2 KiB
Text
65 lines
2 KiB
Text
inductive Vector' (α : Type u) : Nat → Type u
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| nil : Vector' α 0
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| cons : α → Vector' α n → Vector' α (n+1)
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infix:67 " :: " => Vector'.cons
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inductive Ty where
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| int
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| bool
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| fn (a r : Ty)
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abbrev Ty.interp : Ty → Type
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| int => Int
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| bool => Bool
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| fn a r => a.interp → r.interp
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inductive HasType : Fin n → Vector' Ty n → Ty → Type where
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| stop : HasType 0 (ty :: ctx) ty
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| pop : HasType k ctx ty → HasType k.succ (u :: ctx) ty
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inductive Expr : Vector' Ty n → Ty → Type where
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| var : HasType i ctx ty → Expr ctx ty
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| val : Int → Expr ctx Ty.int
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| lam : Expr (a :: ctx) ty → Expr ctx (Ty.fn a ty)
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| app : Expr ctx (Ty.fn a ty) → Expr ctx a → Expr ctx ty
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| op : (a.interp → b.interp → c.interp) → Expr ctx a → Expr ctx b → Expr ctx c
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| ife : Expr ctx Ty.bool → Expr ctx a → Expr ctx a → Expr ctx a
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| delay : (Unit → Expr ctx a) → Expr ctx a
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inductive Env : Vector' Ty n → Type where
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| nil : Env Vector'.nil
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| cons : Ty.interp a → Env ctx → Env (a :: ctx)
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infix:67 " :: " => Env.cons
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def lookup : HasType i ctx ty → Env ctx → ty.interp
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| .stop, x :: xs => x
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| .pop k, x :: xs => lookup k xs
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def interp (env : Env ctx) : Expr ctx ty → ty.interp := fun e =>
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match e with
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| .var i => lookup i env
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| .val x => x
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| .lam b => fun x => interp (x :: env) b
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| .app f a => interp env f (interp env a)
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| .op o x y => o (interp env x) (interp env y)
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| .ife c t e => if interp env c then interp env t else interp env e
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| .delay a => interp env (a ())
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open Expr
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/- Examples -/
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def add : Expr ctx (Ty.fn Ty.int (Ty.fn Ty.int Ty.int)) :=
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lam (lam (op (.+.) (var .stop) (var (.pop .stop))))
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#guard interp Env.nil add 10 20 == 30
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def fact : Expr ctx (Ty.fn Ty.int Ty.int) :=
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lam (ife (op (.==.) (var .stop) (val 0))
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(val 1)
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(op (.*.) (delay fun _ => app fact (op (.-.) (var .stop) (val 1))) (var .stop)))
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decreasing_by sorry
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#guard interp Env.nil fact 10 == 3628800
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