From c2dfffffb7586662c67e44a2d255a1a97ab0398b Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Thu, 2 Apr 2020 17:57:48 +0200
Subject: Brand-spanking new version using Spartan infrastructure

---
 tests/Test.thy | 110 ---------------------------------------------------------
 1 file changed, 110 deletions(-)
 delete mode 100644 tests/Test.thy

(limited to 'tests')

diff --git a/tests/Test.thy b/tests/Test.thy
deleted file mode 100644
index 6f9f996..0000000
--- a/tests/Test.thy
+++ /dev/null
@@ -1,110 +0,0 @@
-(*
-Title:  tests/Test.thy
-Author: Joshua Chen
-Date:   2018
-
-This is an old test suite from early implementations.
-It is not always guaranteed to be up to date or to reflect most recent versions of the theory.
-*)
-
-theory Test
-imports "../HoTT"
-
-begin
-
-
-text \<open>
-A bunch of theorems and other statements for sanity-checking, as well as things that should be automatically simplified.
-
-Things that *should* be automated:
-\<^item> Checking that @{term A} is a well-formed type, when writing things like @{prop "x: A"} and @{prop "A: U i"}.
-\<^item> Checking that the argument to a (dependent/non-dependent) function matches the type? Also the arguments to a pair?
-\<close>
-
-declare[[unify_trace_simp, unify_trace_types, simp_trace, simp_trace_depth_limit=5]]
-\<comment> \<open>Turn on trace for unification and the Simplifier, for debugging.\<close>
-
-
-section \<open>\<Prod>-type\<close>
-
-subsection \<open>Typing functions\<close>
-
-text \<open>Declaring @{thm Prod_intro} with the @{attribute intro} attribute enables @{method rule} to prove the following.\<close>
-
-proposition assumes "A : U(i)" shows "\<^bold>\<lambda>x. x: A \<rightarrow> A"
-by (routine add: assms)
-
-proposition
-  assumes "A : U(i)" and "A \<equiv> B"
-  shows "\<^bold>\<lambda>x. x : B \<rightarrow> A"
-proof -
-  have "A \<rightarrow> A \<equiv> B \<rightarrow> A" using assms by simp
-  moreover have "\<^bold>\<lambda>x. x : A \<rightarrow> A" by (routine add: assms)
-  ultimately show "\<^bold>\<lambda>x. x : B \<rightarrow> A" by simp
-qed
-
-proposition
-  assumes "A : U(i)" and "B : U(i)"
-  shows "\<^bold>\<lambda>x y. x : A \<rightarrow> B \<rightarrow> A"
-by (routine add: assms)
-
-subsection \<open>Function application\<close>
-
-proposition assumes "a : A" shows "(\<^bold>\<lambda>x. x)`a \<equiv> a"
-by (derive lems: assms)
-
-lemma
-  assumes "a : A" and "\<And>x. x: A \<Longrightarrow> B(x): U(i)"
-  shows "(\<^bold>\<lambda>x y. y)`a \<equiv> \<^bold>\<lambda>y. y"
-by (derive lems: assms)
-
-lemma "\<lbrakk>A: U(i); B: U(i); a : A; b : B\<rbrakk> \<Longrightarrow> (\<^bold>\<lambda>x y. y)`a`b \<equiv> b"
-by derive
-
-lemma "\<lbrakk>A: U(i); a : A\<rbrakk> \<Longrightarrow> (\<^bold>\<lambda>x y. f x y)`a \<equiv> \<^bold>\<lambda>y. f a y"
-proof derive
-oops  \<comment> \<open>Missing some premises.\<close>
-
-lemma "\<lbrakk>a : A; b : B(a); c : C(a)(b)\<rbrakk> \<Longrightarrow> (\<^bold>\<lambda>x. \<^bold>\<lambda>y. \<^bold>\<lambda>z. f x y z)`a`b`c \<equiv> f a b c"
-proof derive
-oops
-
-
-subsection \<open>Currying functions\<close>
-
-proposition curried_function_formation:
-  assumes "A : U(i)" and "B: A \<longrightarrow> U(i)" and "\<And>x. C(x): B(x) \<longrightarrow> U(i)"
-  shows "\<Prod>x:A. \<Prod>y:B(x). C x y : U(i)"
-by (routine add: assms)
-
-proposition higher_order_currying_formation:
-  assumes
-    "A: U(i)" and "B: A \<longrightarrow> U(i)" and
-    "\<And>x y. y: B(x) \<Longrightarrow> C(x)(y): U(i)" and
-    "\<And>x y z. z : C(x)(y) \<Longrightarrow> D(x)(y)(z): U(i)"
-  shows "\<Prod>x:A. \<Prod>y:B(x). \<Prod>z:C(x)(y). D(x)(y)(z): U(i)"
-by (routine add: assms)
-
-lemma curried_type_judgment:
-  assumes "A: U(i)" and "B: A \<longrightarrow> U(i)" and "\<And>x y. \<lbrakk>x : A; y : B(x)\<rbrakk> \<Longrightarrow> f x y : C x y"
-  shows "\<^bold>\<lambda>x y. f x y : \<Prod>x:A. \<Prod>y:B(x). C x y"
-by (routine add: assms)
-
-
-text \<open>
-Polymorphic identity function is now trivial due to lambda expression polymorphism.
-It was more involved in previous monomorphic incarnations.
-\<close>
-
-lemma "x: A \<Longrightarrow> id`x \<equiv> x"
-by derive
-  
-
-section \<open>Natural numbers\<close>
-
-text \<open>Automatic proof methods recognize natural numbers.\<close>
-
-proposition "succ(succ(succ 0)): \<nat>" by routine
-
-
-end
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