59 lines
2.3 KiB
Lua
59 lines
2.3 KiB
Lua
local env = environment()
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local N = Const("N")
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local p = Const("p")
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local q = Const("q")
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local a = Const("a")
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local b = Const("b")
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local f = Const("f")
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local H1 = Const("H1")
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local H2 = Const("H2")
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local And = Const("and")
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local and_intro = Const("and_intro")
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local A = Local("A", Prop)
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local B = Local("B", Prop)
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local C = Local("C", Prop)
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env = add_decl(env, mk_constant_assumption("N", Type))
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env = add_decl(env, mk_constant_assumption("p", mk_arrow(N, N, Prop)))
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env = add_decl(env, mk_constant_assumption("q", mk_arrow(N, Prop)))
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env = add_decl(env, mk_constant_assumption("f", mk_arrow(N, N)))
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env = add_decl(env, mk_constant_assumption("a", N))
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env = add_decl(env, mk_constant_assumption("b", N))
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env = add_decl(env, mk_constant_assumption("and", mk_arrow(Prop, Prop, Prop)))
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env = add_decl(env, mk_constant_assumption("and_intro", Pi(A, B, mk_arrow(A, B, And(A, B)))))
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env = add_decl(env, mk_constant_assumption("foo_intro", Pi(A, B, C, mk_arrow(B, B))))
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env = add_decl(env, mk_constant_assumption("foo_intro2", Pi(A, B, C, mk_arrow(B, B))))
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env = add_decl(env, mk_axiom("Ax1", q(a)))
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env = add_decl(env, mk_axiom("Ax2", q(a)))
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env = add_decl(env, mk_axiom("Ax3", q(b)))
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local Ax1 = Const("Ax1")
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local Ax2 = Const("Ax2")
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local Ax3 = Const("Ax3")
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local foo_intro = Const("foo_intro")
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local foo_intro2 = Const("foo_intro2")
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local ng = name_generator("foo")
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local tc = type_checker(env, ng)
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local m1 = mk_metavar("m1", Prop)
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print("before is_def_eq")
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local tc = type_checker(env, ng)
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r, cs = tc:is_def_eq(foo_intro(m1, q(a), q(a), Ax1), foo_intro(q(a), q(a), q(a), Ax2))
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assert(r)
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cs = cs:linearize()
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assert(#cs == 1)
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assert(cs[1]:lhs() == m1)
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assert(cs[1]:rhs() == q(a))
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local tc = type_checker(env, ng)
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print(tostring(foo_intro) .. " : " .. tostring(tc:check(foo_intro)))
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print(tostring(foo_intro2) .. " : " .. tostring(tc:check(foo_intro2)))
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assert(tc:is_def_eq(foo_intro, foo_intro2))
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print("before is_def_eq2")
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local r, cs = tc:is_def_eq(foo_intro(m1, q(a), q(b), Ax1), foo_intro2(q(a), q(a), q(a), Ax2))
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assert(r)
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cs = cs:linearize()
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assert(#cs == 0)
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local tc = type_checker(env, ng)
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print("before failure")
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assert(not pcall(function() print(tc:check(and_intro(m1, q(a), Ax1, Ax3))) end))
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print("before success")
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local t, cs = tc:check(and_intro(m1, q(a), Ax1, Ax2))
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cs = cs:linearize()
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assert(#cs == 1)
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