From mboxrd@z Thu Jan 1 00:00:00 1970 X-Received: by 10.129.58.9 with SMTP id h9mr9727059ywa.221.1520501124082; Thu, 08 Mar 2018 01:25:24 -0800 (PST) X-BeenThere: homotopytypetheory@googlegroups.com Received: by 2002:a25:ad1b:: with SMTP id y27-v6ls322278ybi.9.gmail; Thu, 08 Mar 2018 01:25:23 -0800 (PST) X-Received: by 2002:a25:850e:: with SMTP id w14-v6mr12129310ybk.9.1520501123380; Thu, 08 Mar 2018 01:25:23 -0800 (PST) ARC-Seal: i=1; a=rsa-sha256; t=1520501123; cv=none; d=google.com; s=arc-20160816; b=zsXxP6ZFCPT2rr5zqinSOTK9W4cfFG6ml4OSfn+4+GR9pt73yyJXyTL0eem8PY6i9M nxtjFuEIGwfTSiQSZSlqWPwlc+jBxFmtLGLNqks2ezrBbU+IJmcURuWuElVpQXMXHwL/ Dk0KM7iZ5M805LBTNJq3twFWlTiHLtc03OhUeK5wBkXAmjAG41mlqv5vPq58V1tVrADj Ra7rUl/pfAEllY1jvDMx+7LVoObam+QQKmGmutmkJZc+D5Zlm12SCOcJDHMoDeXbiRaD 5uSlbXWvQS3Ugk7UxIrsHoMmd8cBmFFwjr9tXDzjF+Qbx+fQFVWW6Jm6688JTkrIFTCU NgAQ== ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20160816; h=content-transfer-encoding:to:subject:message-id:date:from :references:in-reply-to:mime-version:dkim-signature :arc-authentication-results; bh=IIw4dm+XvJNUW3TYdYTUusZXWofDFu+HMnOlOOoRhA4=; b=OCxqir/5vQLCEYqvEvz1hsfHeLP3Mmi0TGhz3Jrifxp0HJW0BD27uLgIyYgfzPPuF2 PXm7XlIRbatqmDyJtKPIVmqzrj84PRyznh3mvM35gywZCWxjdV4ptBVyUYm1JOm5TbUA 6EQ6aH6h7YCg+rWtrN5mM9PuR0iKfyEqfW7gRhfBhXn/bIs1c/fseCkdm0dv58YGCwm5 /wIu9dfF2uYQFsHC/WVN/DXrDM7hoo+YK5Lgg/wIMoGajGzmSwgyqEQDRt12qwTxOWJF tUUNXfjp8VmO6VBK8zIZhulQ/N4U4srTow5kyN7Fmwgi1sR+joQ+TN4NkRjpW8fbhSQt HVjw== ARC-Authentication-Results: i=1; gmr-mx.google.com; dkim=pass head...@andrej-com.20150623.gappssmtp.com header.s=20150623 header.b=SbHWSW7B; spf=neutral (google.com: 2607:f8b0:4001:c0b::236 is neither permitted nor denied by best guess record for domain of andrej...@andrej.com) smtp.mailfrom=andrej...@andrej.com Return-Path: Received: from mail-it0-x236.google.com (mail-it0-x236.google.com. [2607:f8b0:4001:c0b::236]) by gmr-mx.google.com with ESMTPS id s5-v6si1119793ybk.4.2018.03.08.01.25.23 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Thu, 08 Mar 2018 01:25:23 -0800 (PST) Received-SPF: neutral (google.com: 2607:f8b0:4001:c0b::236 is neither permitted nor denied by best guess record for domain of andrej...@andrej.com) client-ip=2607:f8b0:4001:c0b::236; Authentication-Results: gmr-mx.google.com; dkim=pass head...@andrej-com.20150623.gappssmtp.com header.s=20150623 header.b=SbHWSW7B; spf=neutral (google.com: 2607:f8b0:4001:c0b::236 is neither permitted nor denied by best guess record for domain of andrej...@andrej.com) smtp.mailfrom=andrej...@andrej.com Received: by mail-it0-x236.google.com with SMTP id k79so7117723ita.2 for ; Thu, 08 Mar 2018 01:25:23 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=andrej-com.20150623.gappssmtp.com; s=20150623; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-transfer-encoding; bh=IIw4dm+XvJNUW3TYdYTUusZXWofDFu+HMnOlOOoRhA4=; b=SbHWSW7BQW7SbnXjFFCB25Gt1VcfCrTZEzDDSiEbY5edihFnNCM30pO9VYzM7OTpRW zj9sD61K9c+8tqZBdGeBVDaplZdoI06fuyCdsN2fWTZ0xFeVGeDW+9291E/j1BP8oFGf ZZcs99W6SSXj5gCaPNr//MlryEL/5IZUFjmikddT2+AqMukwRBaHsT/mTFal413pAFqa UFPk4dzKTwJSHcsxRl6TYjmDvUOr1TgkkuqLUmnAkavilSR/YkHW467CWZRKZ7GoznoJ mHaWmwvrska8rjX6ZVKzlsKSVrHNFiodVIJHD3eV2itjXMQONQ1Z+lKVRQHJvOLSL54M RnQA== X-Gm-Message-State: AElRT7GScvOntt6ORoWVIu2Cy3lKUF+zT58wtLiyftsF0uT9VXFFNMNb UGA0LutZM8lFwfqvwDsC1jEBTo6iS/IdrZT0RvkK6Q== X-Received: by 10.36.94.65 with SMTP id h62mr27989642itb.144.1520501122673; Thu, 08 Mar 2018 01:25:22 -0800 (PST) MIME-Version: 1.0 Received: by 10.192.171.138 with HTTP; Thu, 8 Mar 2018 01:25:22 -0800 (PST) X-Originating-IP: [2001:1470:fff0:830:bc42:b944:e3d3:1767] In-Reply-To: References: <7f3c276a-2d81-4235-8f2a-c4d82ea4f827@googlegroups.com> From: Andrej Bauer Date: Thu, 8 Mar 2018 10:25:22 +0100 Message-ID: Subject: Re: [HoTT] Re: Univalence from scratch To: Homotopy Type Theory Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Martin-L=C3=B6f's paper "25 years of constructive type theory" might be an appropriate reference. It's an updated version of earlier work, and somewhere near the beginning he says explicitly that terms are always constructed with their types. With kind regards, Andrej