63357484d9
* Examples of Coq code, and what one wishes one could do. * Examples of similar model in Cur, and what is currently required.
36 lines
999 B
Racket
36 lines
999 B
Racket
#lang cur
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(require
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cur/stdlib/sugar
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cur/stdlib/nat
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cur/stdlib/prop)
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;; TODO: Axioms
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;; TODO: implicits
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;; No way to define axioms in Cur, yet, although it is a simple change.
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;; No implicits in Cur, yet
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(define (plus_0_n (f_equal : (-> (A : Type) (a1 : A) (a2 : A) (B : Type) (f : (-> A B))
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(== A a1 a2)
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(== B (f a1) (f a2)))) (n : Nat))
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(match n
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;; TODO: This should work
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#:return (== Nat n (plus z n))
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[z (refl Nat z)]
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[(s (n : Nat))
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(f_equal Nat n (plus z n) Nat s (recur n))]))
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(:: plus_n_0
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(forall
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(f_equal : (-> (A : Type) (a1 : A) (a2 : A) (B : Type) (f : (-> A B))
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(== A a1 a2) (== B (f a1) (f a2))))
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(n : Nat)
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(== Nat n (plus z n))))
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#;(define (plus_n_Sm (n : Nat) (m : Nat))
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(elim Nat Type
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(lambda (n : Nat) (== Nat (plus n m) (plus m n)))
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(plus_n_0 m)
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(lambda (y : Nat) (ih : ))
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(elim == Type)))
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#;(:: plus_n_Sm (forall (n : Nat) (m : Nat) (== (s (plus n m)) (plus n (s m)))))
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